Research ArticleResearch on Cutting Force of Turn-Milling Based onThin-Walled Blade

Lida Zhu1 Baoguang Liu1 Xiaobang Wang12 and Zhiwei Xu1

1School of Mechanical Engineering and Automation Northeastern University Shenyang 110819 China2School of Mechanical Engineering and Automation Dalian University of Technology Dalian 116024 China

Correspondence should be addressed to Lida Zhu zld1999gmailcom

Received 18 February 2016 Revised 7 April 2016 Accepted 10 April 2016

Academic Editor Massimiliano Barletta

Copyright copy 2016 Lida Zhu et alThis is an open access article distributed under the Creative CommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Turn-milling is regarded as the milling of a curved surface while rotating the workpiece around its center point which combineseffectively the advantages of both turning andmilling wherein it allows for goodmetal removal with the difficult-to-cut thin-walledworkpieces in aviationThe objective of the present work is to study cutting force by turn-milling in cutting condition Aiming at thedeformation properties of thin-walled blade the predicted models of rigid cutting force and flexible cutting force with ball cutterare provided respectively in turn-milling process The deformation values of blade and cutter are calculated respectively basedon the engaged trajectory by using the iterative algorithm The rigid and flexible cutting forces are compared and the influencedegrees of cutting parameters on cutting forces are analyzed These conclusions provide theoretical foundation and reference forturn-milling mechanism research

1 Introduction

As a newly emerging cutting technology turn-milling makesuse of the advantages of turning and milling in which bothworkpiece and cutting tool are given rotary motion simulta-neously The machining accuracy and processing efficiencyare obtained by the advancedmachiningmethod So it enjoysthe advantages of turning andmilling and excels atmachiningrevolving workpieces like crankshafts or camshafts Actuallyits strengths are far more than this Owing to the intermittentcuts and simultaneous rotations of tools and workpiecesit keeps low thermal stresses lowers cutting forces andhas good removal rates With the rapid development ofprocessing technology the new machining techniques arewell used to demand the requirements of product complexityand production of high-efficiency [1ndash3]

There are many researches on machining mechanismby turn-milling Skoric et al [4] have given an analysis ofthe suitability of turn-milling process For the purpose ofa comparative estimation of the process a set of functionsand methods are proposed and defined The theoreticaland real chip geometry is presented respectively in centricposition and eccentric position Pogacnik and Kopac in

[5] have described a complex kinematics process of thistechnology and the geometry of the tool and its positionIn their study practical data have formed a contrast of theroughness between the centric and eccentric turn-millingunder different cutting parameters Meanwhile by theirexperimental work it has been shown that there is a stronginfluence of vibration on turn-milling process Finally theyhave emphasized that turn-milling can lead to a better surfaceroughness and is much more suitable for cutting machiningthan turning Choudhury and Bajpai in [6] and Choudhuryand Mangrulkar in [7] have demonstrated by experimentsthat the surface roughness by orthogonal turn-milling riseswith increase of cutter speed and lowers with increase ofaxial feed rate This has also indicated that the roughness oforthogonal turn-milling is about ten times lower than that ofturningMoreover the chips and surface quality of the formerone are smaller and better than those of the latter one Byexperiment techniques some other experiments have beenconducted to study the surface finish in which mild-steelworkpiece and high-speed steel cutting tools are employedBesides Calleja et al in [8] have focused on the study of theoptimalmachining strategy for blades turn-milling Differentstrategies and tilt angles have been tested The proposed

Hindawi Publishing CorporationAdvances in Materials Science and EngineeringVolume 2016 Article ID 2638261 11 pageshttpdxdoiorg10115520162638261

2 Advances in Materials Science and Engineering

theoretical concepts have been applied in order to obtainthe best turn-milling parameters for blades Sava et al in[9 10] have found a cutting parameter optimization approachwhen machining cylindrical parts This approach can lead tominimum surface roughness by using genetic algorithm inthe tangential turn-milling process during which the valueof surface roughness can be easily controlled according tocutting parameters

Biermann et al [11] have proposed an FE model of theworkpiece coupled with a geometric milling simulation forcomputing regenerative workpiece vibrations during the five-axis milling process Lazoglu et al [12] have predicted accu-rately the machining forces in high performance cutting offree form surfaces in aerospace automotive biomedical anddiemold industries and generalized approach for predictionof cutting forces in five-axis machining of parts with complexfree form surfaces Budak et al [13ndash17] have proposed that thevariable pitch cutters can be used to calculate cutting forcein milling of these extremely flexible components And thenthey have studied the notion that the workpiece dynamicsaffect milling force in machining of flexible parts and pre-sented a methodology for prediction of in-process workpiecedynamics based on a structural dynamic modification byusing the FE model of the workpiece

Herranz et al in [18] have proposed a working methodol-ogy for efficient process planning based on the previous anal-ysis of those static and dynamic phenomena that may happenduring high-speed cutting This methodology includes (1)several steps in order to minimize the bending and vibrationeffects (2) optimal monitoring methods to detect processinstability and (3) description of the best way for the tuningof cutting conditions and chip load by means of simulationat different machining stages In this paper engine blade iscomplex thin-walled curved parts and plays an importantpart in the aerospace industry Youngrsquos modulus of titaniumis smaller which is prone to distortion in the cutting processIf the cutting force is too large it will cause large bladedeformation and easily lead to poor quality so machiningerror achieves processing requirements difficultly

Olvera et al in [19] have provided stiffness values for thistype of machines clamping a common workpiece To obtainthis information an experimental methodology to measurestatic stiffness along kinematic chain of the turning centeris proposed Lamikiz et al in [20] have presented assemblyerrors that are introduced as additional geometric parametersin the element transformation matrices resulting in the realtransformation matrix for a real and therefore imperfectfive-axis milling machine This matrix defines the real posi-tion of the tool in the absolute reference systemThepredictedmodels of rigid and flexible cutting force with ball cutter areproposed respectively in turn-milling process in this paperThe deformation values of blade and cutter are calculatedrespectively by using the iterative algorithm The accurateprediction of milling force will provide some theoreticalfoundations and references for choosing reasonable tools Sothe cutting force prediction can provide critical guidance forthe cutting parameters optimization

This paper is divided into four main sections The firstentitled The Principle of Turn-Milling Blades will introduce

Axial feed (fa)

Radial feed (fr)Rotation of blade(nb)

Rotation of cutter(nt)

Figure 1 Turn-milling blade principle diagram

the basic motions in turn-milling process The secondsection Rigid Cutting Force Model and Main Parameterswill consider the influence of ball-end cutter and cuttingparameters on cutting force The third part Flexible Cut-ting Force Model will consider the influence of flexibilitydeformation on cutting force by the iterative algorithm andidentification of cutting force coefficients The next partSimulation Analysis of Ball-End Cutting Force will comparerigid and flexible cutting forces and analyze the influencedegree of main cutting parameters on the cutting forcesFinally some conclusions from this study are given

2 The Principle of Turn-Milling Blades

Turn-milling involves four basic motions including rotationof cutter rotation of workpiece axial feed and radial feedof cutter as shown in Figure 1 Milling blade is not simplythe turning and milling processing methods into a singlemachine for processing blade but the use of turn-millingmotion to accomplish complex surfacemachining bladesThemain cutting motion is the rotary motion of ball milling thespeeds of ball milling rotation and blades rotation togetherdetermine the cutting speed The rotational speed of ballcutter plays a dominated role in the whole cutting process sothe rotation speed of the blade is even ignored in high-speedand super-speed process

The complex surface of the blade is engaged by using thecomposite turn-milling motion It can be seen that duringeach cutting period several cutting inserts are in contactwith the workpiece at the same time so intermittent cuttingand enough quenching time for each cutting edge can begained So machining heat transfers more to chips resultingin low workpiece temperature little thermal deformationhigh surface finish and small tool wear Meanwhile goodchip removal rate and automatic chip disposal can alsobe achieved because of the short chips produced in turn-milling

3 Rigid Cutting Force Model andMain Parameters

In turn-milling cutting forces depend on the instantaneousuncut chip thickness Hence accurate calculation of chipthickness is quite critical for turn-milling cutting forcepredictions The uncut chip thickness can be quite compli-cated since the tool can rotate as well as translate withina tool path segment The geometry model of ball-end mill

Advances in Materials Science and Engineering 3

P

n

X

Y

R(z)

Y

Discrete point

Cutting edge

X

ndFt

dFr

dFa120595

R0

120579120601

120573

OOc

Xc

Yc

Z Zc

Figure 2 Geometry model of the ball-end mill

and cutting forces in differential direction are shown inFigure 2 The three coordinates are established in the modelincluding machine coordinate (119883119884 119885) the tool coordinate(119883119888 119884119888 119885119888) and the blade coordinate (119883

119887 119884119887 119885119887) Assume 119875

is the random point on the cutting edge and 119862 is the centerof the ball-end mill tip For a differential chip load in theengagement domain the differential cutting forces in radialaxial and tangential direction are written as follows [10]

119889119865119903= 119870119903119888sdot (119905119888sdot 119889119911) + 119870

119903119890sdot 119889119911

119889119865119886= 119870119886119888(119905119888sdot 119889119911) + 119870

119886119890sdot 119889119911

119889119865119905= 119870119886119888sdot (119905119888sdot 119889119911) + 119870

119905119890sdot 119889119911

(1)

The effects of the lead and tilt angles on the cut geometryhave to be considered in curve machining Consider twofluted ball-end mills where one of the cutting flutes is alignedwith the 119883-axis The angle between the 119884-axis and thereference cutting flute is represented as the reference rotationangle The rotation angle is the angle between the cross-feeddirection and the cutting flutes [12]

In order to obtain the transformation from the coor-dinate frame to feed coordinate cutting forces in rotatingdynamometer coordinate frame are calculated from thefollowing transformations

[[

[

119889119865119909

119889119865119910

119889119865119911

]]

]

=

[[[

[

minus sin (120595) times sin (120601) minus cos (120595) times sin (120601) minus cos (120601)minus sin (120595) times cos (120601) minus cos (120595) times cos (120601) sin (120601)

cos (120595) minus sin (120595) 0

]]]

]

[[

[

cos (120573 + 120579) minus sin ((120573 + 120579)) 0

sin (120573 + 120579) cos (120573 + 120579) 0

0 0 1

]]

]

[[

[

119889119865119903

119889119865119886

119889119865119905

]]

]

(2)

4 Flexible Cutting Force Model

Flexible cutting forcemethod considers not only the feedbackeffect of tool-workpiece deformation on engagement zonebut also the impact of various modifications and couplingeffects due to the change in stiffness of the workpiecematerialremoval which is used in thin-walled components Theblade is regarded as a workpiece of which the thickness isequivalent to the size of the deformed thin-walled parts

41 Iterative Correction of Actual Cutting Depth It is impor-tant that the direction to the contact between tool and part isvariable with feed of tool and position of blade so the cuttingforces are variable in different directions Since the elasticdeformation of tool and workpiece in the interaction forcethe displacements occur in the opposite directions and theactual cutting capacity (such as the radial depth of cut) is notequal to the nominal value of the design Surface error 119890

119905119887at

any point of the surface generated can be expressed as follows

119890119905119887= 120575119905+ 120575119887 (3)

In a transient of milling the actual chip thickness ofcutter node (119894 119895) is smaller than the calculated nominal valueWithin next cycles the additional amount left by cutter node(119894 119895) will be cut by cutter node (119894 + 1 119895) and so forth Afterthe cutter period of rotation the instantaneous undeformedchip thickness converges to the results calculated based onnotional amount of a single tooth feed So the actual radialdepth of cut can be given as follows

119886(119896+1)

119890(119894 119895) = 119886

119890minus [120575(119896)

119905(119894 119895) + 120575

(119896)

119887(119894 119895)] (4)

42 Deformation Calculation of Tool The horizontal direc-tion component is a major factor of the cutter deflectionand the cutter clamping deflection Although vertical forceis also acting on the cutter the axial deflection of toolingsystem is usually ignored resulting from the stiffness in the

4 Advances in Materials Science and Engineering

Ls

Lf

L

2Kc 2Kc

(a) Ball-end millingbending system

120575s

120575f

120601s

(b) Simplified intoa ladder cylindricalcantilever beam

Figure 3 Bending model of ball-end milling

axial direction which is relatively high Consequently thedeflection in the cutting system can be expressed as [21]

120575119905= 120575119908+ 120575119888 (5)

As a cantilever beam tool the tool bending deflection 120575119908

can be expressed as follows

120575119908

=119865

6119864119868(119911119865minus 119911)3

minus (119871 minus 119911)3

+ 3 (119871 minus 119911)2

(119871 minus 119911119865)

(6)

where 119865 is the cutting force 119868 is the area moment of inertiaof the cutter 119864 is Youngrsquos modulus 119871 is the overhand 119911

119865is

the 119911-directional position of the applied force and 119911 is theposition of the deflection

As shown in Figure 3 the clamping deflection at shankclamping 120575

119888can be expressed as follows [22]

120575119888= 120575119904+ 120575119891+ 120601119904(119871119891minus 119911)

=119865

6119864119868minus (119871 minus 119871

119891)3

+ 3 (119871 minus 119871119891)2

(119871 minus 119911119865)

+119865

6119864119868119891

(119911119865minus 119911)3

minus (119871 minus 119911)3

+ 3 (119871 minus 119911)2

(119871 minus 119911119865)

+119865

2119864119868minus (119871 minus 119871

119891)2

+ 2 (119871 minus 119871119891) (119871 minus 119911

119865)

sdot (119871119891minus 119911)

(7)

where 120575119904is deflection of the shank 120575

119891is deflection of the flute

120601119904is deflection angle of the shank 119871

119891is length of the flute

and 119868119891is the moment of inertia relative to shaped mandrel of

cutter edge sectionTo calculate the clamping deflection an experiment needs

to be done to get the stiffness at clamping

120575119888=119865

119870119888

(8)

2Kc

2Kc

120572

120572

120575

120575998400

Figure 4 Actual deformation in processing of ball-end milling

Then the ball-end milling horizontal offset can be given asfollows

120575119905=119865119862

6119864119868minus (119871 minus 119871

119891)3

+ 3 (119871 minus 119871119891)2

(119871 minus 119911119865)

+119865119862

6119864119868119891

(119911119865minus 119911)3

minus (119871 minus 119911)3

+ 3 (119871 minus 119911)2

(119871 minus 119911119865)

+119865119862

2119864119868minus (119871 minus 119871

119891)2

+ 2 (119871 minus 119871119891) (119871 minus 119911

119865)

sdot (119871119891minus 119911) +

119865119862

119870119888

(9)

where 119865119862= 119865119909sin120601 + 119865

119910cos120601 and 119911

119865is given as follows

119911119865= 119903 minus 119903 sin(120587

2minus 120572 minus

1

2arccos

119877 minus 119886119901

119877) (10)

The surface form error is usually defined as a distancebetween the nominal surface and the machined one inthe direction of the surface normal From the calculatedhorizontal deflection due to the lead and tilt angles inFigure 4 the surface form error normal to the surface can becalculated as

119890 = 120575 sdot |sin120572| (11)

43 Deformation Calculation of Blade In the process ofmilling blades the force on the vertical direction of blade sur-face will be produced which produces bending deformationof blades while making the tool bend Since the blades arethin-walled workpiece its thickness has a great influence onthe deformation

The slope angle of each point is equal to rotation angleof the rotating coordinate system required in the next step asshown in Figure 5 As a result 119886

119887(rotation angle of system

11988311198741198841) and 119886

119904(rotation angle of system 119883

21198741198842) can be

expressed as follows

120572119887= arctan 119896

119887

= arctan (1198861+ 21198862119909 + 3119886

31199092

+ 411988641199093

+ 511988651199094

)

120572119904= arctan 119896

119904

= arctan (1198871+ 21198872119909 + 3119887

31199092

+ 411988741199093

+ 511988751199094

)

(12)

Advances in Materials Science and Engineering 5

Horizontalline

Tangent line

Blade shape

Y1Y2

Y3

O

a1a1

a2

a2

X3

X2

X1

F1

F2

h1

h2

Figure 5 Instantaneous thickness in blade machining

The equations of blade basin and back of blade areexpressed respectively as follows

119909119887

= 119909 cos 119886119887

+ (1198860+ 1198861119909 + 11988621199092

+ 11988631199093

+ 11988641199094

+ 11988651199095

) sin 119886119901

119910119887

= (1198860+ 1198861119909 + 11988621199092

+ 11988631199093

+ 11988641199094

+ 11988651199095

) cos 119886119901

minus 119909 sin 119886119901

(13)

119909119904

= 119909 cos 119886119904

+ (1198870+ 1198871119909 + 11988721199092

+ 11988731199093

+ 11988741199094

+ 11988751199095

) sin 119886119904

119910119904

= (1198870+ 1198871119909 + 11988721199092

+ 11988731199093

+ 11988741199094

+ 11988751199095

) cos 119886119904

minus 119909 sin 119886119904

(14)

For any cutting points the value of instantaneous thick-ness is calculated as follows

ℎ119887= 119910119887

1003816100381610038161003816119909119887minus 119910119904

1003816100381610038161003816119909119904

ℎ119904= 119910119887

1003816100381610038161003816119909119904minus 119910119904

1003816100381610038161003816119909119904

(15)

The instantaneous blade thickness curve can be obtainedas shown in Figure 6 Based on the formula the instantaneousstiffness on the point of cutter can be obtained

119896 =119864ℎ3

12 (1 minus ]2) (16)

The instantaneous stiffness is obtained based on (16) Itcan be seen from Figure 7 that stiffness of the cutting pointat the ends of the airfoil is relatively small while the localstiffness of the thicker intermediate is larger Using the curvedthin plate reciprocal theory solution of the problem can beobtained

minus10 0 10 20 30 40 50 60 700

10

20

30

40

50

60

Edge path (mm)

Thic

knes

s (m

m)

Back of bladeBasin of blade

Figure 6 Instantaneous blade thickness curve

Back of bladeBasin of blade

0 10 20 30 40 50 600

1

2

3

4

5

6

7

8

Edge path (mm)

Bend

ing

stiffn

ess (

mm

2kg

s2)

times109

Figure 7 Instantaneous stiffness on the point of cutter

44 Identification of Cutting Force Coefficients

441 Cutting Coefficients Model In order to calculate thecutting forces the edge-specific coefficients and the shear-specific coefficients need to be obtained beforehand whichare determined by materials and geometry of tool andworkpiece In the research proposed by Cao et al thesecoefficients are obtained from the experiments using theplanar surfaces [23] The coefficients can be calculated by

119870119905119888=

2120587

1198731198601

sdot

1198623119865119909119888minus (1198622minus 1198621) 119865119910119888

1198622

3+ (1198622minus 1198621)2

119870119903119888=

2120587

119873 (1198602

2+ 1198602

3)

6 Advances in Materials Science and Engineering

sdot [

1198602(1198622minus 1198621) 119865119909119888+ 1198623119865119910119888

1198622

3+ (1198622minus 1198621)2

minus1198603119865119911119888

1198625

]

119870119886119888=

2120587

119873 (1198602

2+ 1198602

3)

sdot [

1198603(1198622minus 1198621) 119865119909119888+ 1198623119865119910119888

1198622

3+ (1198622minus 1198621)2

+1198602119865119911119888

1198625

]

119870119905119890=minus2120587

1198731198611

sdot

1198624119865119909119890+ 1198625119865119910119890

1198622

4+ 1198622

5

119870119903119890=

2120587

119873 (1198612

2+ 1198612

3)

sdot [

1198612(1198625119865119909119890minus 1198624119865119910119890)

1198622

4+ 1198625

2+1198613119865119911119890

21198621

]

119870119903119890=

2120587

119873 (1198612

2+ 1198612

3)

sdot [

1198613(1198625119865119909119890minus 1198624119865119910119890)

1198622

4+ 1198622

5

minus1198612119865119911119890

21198621

]

(17)

where 119860119894 119861119894 and 119862

119894(119894 = 1 2 3 4 5) are the parameters

associated with start and exit radial immersion angles 120593stand 120593ex and with two boundaries of the position angles 120579minand 120579max 119865119902119888 and 119865119902119890 (119902 = 119883 119884 119885) are the average cuttingforce components for different inclination angles and couldbe obtained from following cutting tests

The relationship among them is shown as the followingthe details of the numerical procedure of computing param-eters are available in [23]

Where 119889119904(120579) = |119889119901(119883119862 119884119862 119885119862)119879

| =

radic(1198831015840

119862)2

+ (1198841015840

119862)2

+ (1198851015840

119862)2

119889120579 is the length of each differentialelement of the cutting edge (119883

119862 119884119862 119885119862) is the arbitrary

point on the cutting edge Consider

1198601= int

120579max

120579min

119877 sin 120579 119889120579

1198602= int

120579max

120579min

119877 sin 1205792119889120579

1198603= int

120579max

120579min

119877 sin 120579 cos 120579 119889120579

1198611= int

120579max

120579min

119889119904 (120579)

1198612= int

120579max

120579min

sin 120579 119889119904 (120579)

1198613= int

120579max

120579min

cos 120579 119889119904 (120579)

Table 1 Main parameters of machining center

Control system FANUC-OI (MC)control system

Maximum spindle speed 6000 rminStroke (119883119884119885) 850mm500mm630mmSpindle maximum torque 70909 (continuous30min) NMMaximum fast feed speed 119883 and 119884 24mmin 119885 15mminMaximum working load 500 kgPower 1175 KW

Workpiece Tool

Feed direction Engagement part

Figure 8 TH5650 vertical machining center

1198621=1

21205931003816100381610038161003816

120593ex120593st

1198622=1

4sin 21205931003816100381610038161003816

120593ex120593st

1198623=1

4cos 21205931003816100381610038161003816

120593ex120593st

1198624= sin1205931003816100381610038161003816

120593ex120593st

1198625= cos1205931003816100381610038161003816

120593ex120593st

(18)

442 Cutting Force Coefficient Identification Test Experi-mental cutting force coefficient identification was conductedusing the TH5650 vertical machining center (Figure 8) Thematerial used for the machining tests was Ti-6Al-4V (TC4)alloy A three-component Kistler dynamometer type Kistler9257B (Figure 9) has beenmounted on themachine table andthe coordinates system has been set to level with the forcesensor surfaces The tool has been chosen to ensure stabledepth of cut in milling a two-flute cutter with 10mm diam-eter has been selected and mounted with 20mm overhangon an HSK32ER20 tool-holder The main parameters of themachine are as in Table 1

In this experiment the cutting tool is a hard alloymaterial of the ball-end mill the milling cutter helix angleis 30 degrees whose diameter is 10mm Selection of millingparameters is as follows spindle speed 300 rmin each toothfeed (002 004 006)mmz and axial cutting deep (1 23)mm

Advances in Materials Science and Engineering 7

Table 2 Milling test data

Test ID Spindle speed119899 (rmin)

Feed pertooth

119888 (mm119911)

Axial cuttingdepth119886119901(mm)

119883 axialperiodic force

119865119909(N)

119884 axialperiodic force

119865119910(N)

119885 axialperiodic force

119865119911(N)

1 300 002 1 minus5032 9223 10732 300 004 1 minus7258 10572 20453 300 006 1 minus9683 12034 53124 300 002 2 minus4436 19876 129565 300 004 2 minus3288 23766 88926 300 006 2 minus1225 30654 42787 300 002 3 minus197 38725 2378 300 004 3 2278 44944 minus3946

9 300 006 3 1657 58689 minus7683

Table 3 Cutting force coefficient

Cutting forceparameter

Numerical(Mpa)

Cutting forceparameter

Numerical(Nm)

119870119905119888

15998 119870119905119890

207119870119903119888

5201 119870119903119890

428119870119886119888

6482 119870119886119890

79

Dynamometer

Figure 9 Kistler 9257B dynamometer

A series of experimental data was obtained as shown inTable 2

From the experimental data in (17) by analyzing therelationship of cutting force the cutting coefficient is shownin Table 3

5 Simulation Analysis ofBall-End Cutting Force

51 Prediction and Simulation of Milling Force The influenceof cutting parameter and geometer parameter of tool oncutting forces is analyzed by turn-milling process The ballmilling cutting force is simulated based on the model ofmilling force by using MATLAB program in the differentcutting parameters The titanium alloy is used as workpiecematerial The diameter of cutter is 10mm The depth of cutis 05mm The different cutting force simulation results areshown in Figures 10ndash15 as follows

0 50 100 150 200 250 300 350 400minus400

minus300

minus200

minus100

0

100

200

300

400

500

600

F (N

)

Cutter rotation angle (∘)

FxiFyi

FziF

(Small symbol ae = 12R big symbol ae = 16R)

Figure 10 Effect of cutting width 119886119890on cutting force

511 The Influence of Cutting Width and Tilt Angle on CuttingForce Similarly when the cutting depth is reduced cuttingforces in three directions119883119884 and119885 are all decreased wherethe magnitudes of decreases are relatively large and the totalcutting force becomes smaller from Figure 10 But when thecutting depth is reduced cutting-in angle is constant whilecutting-out angle becomes smaller As can be seen fromFigure 11 cutting force decreases with increasing of dip Sothe tilt angle can be increased to reduce the cutting forceduring processing

512 The Influence of Tooth Number and Cutting Depth onCutting Force It can be noticed from Figure 12 the change ofmilling cutter blade has no effect on the cutting force but itaffects the numbers of milling force cycle in a rotary cuttercycle The numbers of milling force cycle are equal to thenumber of milling cutter blade and entrance angle and exitangle go backwards with the increasing number of cuttingedge

8 Advances in Materials Science and Engineering

0 50 100 150 200 250 300 350 400minus300

minus200

minus100

0

100

200

300

400

500(Small symbol l = 25∘ big symbol l = 15∘)

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

Figure 11 Effect of tilt angle on cutting force

0 50 100 150 200 250 300 350 400minus100

minus50

0

50

100

150

200

250

300

350

400

450

N = 2N = 3

Cutter rotation angle (∘)

F (N

)

Figure 12 Effect of tooth number on cutting force

When the cutting depth is reduced cutting forces in threedirections119883 119884 and 119885 are all decreased and the total cuttingforce becomes smaller from Figure 13 But when the cuttingdepth decreases entrance angle and exit angle are constant

513 The Influence of Cutter Diameter on Cutting ForceWhen focusing on the effect of cutter diameter on cuttingforce the larger the cutter diameter is the larger the cuttingforce becomes no matter whether it is a given value or not inFigure 14 With the change of cutter diameter entrance angleremains unchanged while exit angle changes

514 The Influence of Cutter Diameter and Feed on CuttingForce It can be noticed from Figure 15 that cutting forceand cutting-in angle are not affected by different helix angleBut the cutting-out angle will be bigger when the helix angleincreases The last parameter is the rational speed Feed has

0 50 100 150 200 250 300 350 4000

100

200

300

400

500

600

Cutter rotation angle (∘)

ap = 08mm

ap = 10mm

ap = 12mm

F (N

)

Figure 13 Effect of cutting depth on cutting force

a great impact on the maximum cutting force as shown inFigure 16 And slight increase can cause large changes ofthe total cutting force so that the amount of feed should beselected with season during processing

52 Comparison of Rigid and Flexible Cutting Force Inorder to illustrate the contribution of flexible cutting forcecomparison of flexible cutting forces and rigid cutting forceswas simulated based on the same cutting conditions inFigure 15

It can be seen from Figure 17 that flexible cutting force issmaller than rigid cutting force in differential direction butthe value is more by 19N in the 119883 direction Consequentlyit is necessary that the flexible model of cutting force isanalyzed For the validation of the model another simulation(in Figure 18) is conducted in the same cutting condition[24] as follows 119886

119899= 0 spindle speed = 269 rmin 119877

0=

9526mm 1198940= 30 st = 00508mm and 119886

119901= 635mm

The predicted cutting forces are compared and matched wellwith the experiment [24] Therefore it provides a theoreticalfoundation and reference for the turn-milling mechanismresearch

6 Conclusions

In this paper the cutting force of blade by turn-milling wasstudied in cutting parameters A rigid model and a flexiblemodel of cutting force with ball-end cutter are establishedrespectively based on the analysis of space geometry of theball-end mill and blades Some suggestions are providedto choose cutting parameters to reduce cutting forces andreach high productivity This study will provide a theoreticalfoundation and reference for the turn-milling mechanismresearch Based on this work the following conclusions canbe drawn

(i) The influences of cutting parameters and geometryshape of cutter on the cutting forces are analyzedby turn-milling The deformation values of blade

Advances in Materials Science and Engineering 9

0 50 100 150 200 250 300 350 400minus300

minus200

minus100

0

100

200

300

400

500

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

(a) 119886119890is a multiple of the diameter

0 50 100 150 200 250 300 350 400minus400

minus300

minus200

minus100

0

100

200

300

400

500

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

(b) 119886119890is constant

Figure 14 Effect of cutter diameter on cutting force (big symbol119863 = 8mm small symbol119863 = 5mm)

0 50 100 150 200 250 300 350 400minus300

minus200

minus100

0

100

200

300

400

500

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

(Big symbol 120573 = small symbol 120573 = 18∘)38∘

Figure 15 Effect of helix angle on cutting force

and cutter on the engaged trajectory are calculatedrespectively by using the iterative algorithm

(ii) In milling blades case cutting force is sensitive to theamount of feed but the influence of helix angle is thesmallestThe amount of deformation of the blade willnot be the same in a different thickness position ofthe bladeThe thinner the thickness is the greater thebending deformation becomes And cutting force isalso affected by the deformation

(iii) In milling titanium blades case flexible cutting forceis smaller than rigid cutting force in each direction

0 50 100 150 200 250 300 350 4000

50

100

150

200

250

300

350

400

450

500

Cutter rotation angle (∘)

= 01mms

= 02mms

= 03mms

F (N

)

Figure 16 Effect of feed on cutting force

but it is less 20N Since stiffness of titanium alloy isrelatively large the deformation of titanium alloy issmall and deformation of the tool is of the order ofminus5 times

Nomenclature

119899119905 Rotation speed of cutter (rmin)

119899119887 Rotation speed of blade (rmin)

119886119901 Depth of cut (mm)

119891119911 Feed per tooth (mmz)

119905119888 Uncut chip thickness (mm)

] Poisson ratio of blade120575119905 Deflection value of tool

120575119887 Deflection value of blade

10 Advances in Materials Science and Engineering

0 50 100 150 200 250 300 350 400minus400

minus300

minus200

minus100

0

100

200

300

400

Flexible Rigid

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

Figure 17 Comparisons of cutting forces in flexible and rigidmodel

0 50 100 150 200minus1000

minus800

minus600

minus400

minus200

0

200

400

600

800

1000

Cutti

ng fo

rce (

N)

FxFyFz

Rotation angle (∘)

Figure 18 Simulated cutting forces in end milling

120575119908 Cutter bending deflection

120575119888 Clamping deflection

119870119903119888 119870119886119888 and119870

119905119888 Radial axial and tangential cutting forcecoefficients

119870119903119890119870119886119890 and119870

119905119890 Edge force coefficients

120595 Immersion angle of cutting point120601 Cutting element position angle120573 Angle between the 119884-axis and the

reference cutting flute120579 Angle between the cross-feed direction

and the cutting flute119870119888 Measured clamping stiffness of cutter

119903 Radius (mm)

119911 The number of teeth on the cutter119891119886 Axial feed (mmr)

119891119903 Radial feed (mmr)

119864 Elastic modulus of bladeℎ Thickness of blade119890119905119887 Surface error

119886119890 Radial depth of cut

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (NSFC) (51105072 and 51475087) sup-ported by the Fundamental Research Funds for the CentralUniversities (N150304005)

References

[1] U Karaguzel M Bakkal and E Budak ldquoProcess modeling ofturn-milling using analytical approachrdquo Procedia CIRP vol 4pp 131ndash139 2012

[2] U Karaguzel E Uysal E Budak and M Bakkal ldquoAnalyticalmodeling of turn-milling process geometry kinematics andmechanicsrdquo International Journal of Machine Tools amp Manufac-ture vol 91 pp 24ndash33 2015

[3] S Ekinovic E Begovic and A Silajdzija ldquoComparison ofmachined surface quality obtained by high-speed machiningand conventional turningrdquo Machining Science and Technologyvol 11 no 4 pp 531ndash551 2007

[4] S Skoric TUdiljak andDCiglar ldquoStudy of the suitability of themachining of rotating surfacesrdquoTransactions of Famena vol 32no 2 pp 69ndash83 2008

[5] M Pogacnik and J Kopac ldquoDynamic stabilization of the turn-milling process by parameter optimizationrdquo Proceedings of theInstitution of Mechanical Engineers Part B vol 214 no 2 pp127ndash135 2000

[6] S K Choudhury and J B Bajpai ldquoInvestigation in orthogonalturn-milling towards better surface finishrdquo Journal of MaterialsProcessing Technology vol 170 no 3 pp 487ndash493 2005

[7] S K Choudhury and K S Mangrulkar ldquoInvestigation oforthogonal turn-milling for the machining of rotationallysymmetrical work piecesrdquo Journal of Materials Processing Tech-nology vol 99 no 1 pp 120ndash128 2000

[8] A Calleja A Fernandez A Rodriguez L N de Lacalle andA Lamikiz ldquoTurn-milling of blades in turning centres andmultitasking machines controlling tool tilt anglerdquo Proceedingsof the Institution of Mechanical Engineers Part B Journal ofEngineering Manufacture vol 229 no 8 pp 1324ndash1336 2015

[9] C M Lee S W Kim Y H Lee and D W Lee ldquoThe optimalcutter orientation in ball end milling of cantilever-shaped thinplaterdquo Journal of Materials Processing Technology vol 153ndash154pp 900ndash906 2004

[10] M Fontaine A Moufki A Devillez and D Dudzinski ldquoMod-elling of cutting forces in ball-end milling with tool-surfaceinclination Part I predictive force model and experimentalvalidationrdquo Journal of Materials Processing Technology vol 189no 1ndash3 pp 73ndash84 2007

Advances in Materials Science and Engineering 11

[11] D Biermann P Kersting and T Surmann ldquoA general approachto simulating workpiece vibrations during five-axis milling ofturbine bladesrdquo CIRP AnnalsmdashManufacturing Technology vol59 no 1 pp 125ndash128 2010

[12] I Lazoglu Y Boz and H Erdim ldquoFive-axis milling mechanicsfor complex free form surfacesrdquo CIRP Annals-ManufacturingTechnology vol 60 no 1 pp 117ndash120 2011

[13] E Budak E Ozturk and L T Tunc ldquoModeling and simulationof 5-axismilling processesrdquoCIRPAnnalsmdashManufacturing Tech-nology vol 58 no 1 pp 347ndash350 2009

[14] E Budak ldquoImproving 5-axis milling operations using processmodelsrdquoMM Science Journal pp 358ndash365 2012

[15] E Ozturk and E Budak ldquoDynamics and stability of five-axis ball-end millingrdquo Journal of Manufacturing Science andEngineering vol 132 no 2 2010

[16] E Ozturk L T Tunc and E Budak ldquoInvestigation of leadand tilt angle effects in 5-axis ball-end milling processesrdquoInternational Journal of Machine Tools amp Manufacture vol 49no 14 pp 1053ndash1062 2009

[17] E Budak A Comak and E Ozturk ldquoStability and highperformance machining conditions in simultaneous millingrdquoCIRP AnnalsmdashManufacturing Technology vol 62 no 1 pp403ndash406 2013

[18] S Herranz F J Campa L N L De Lacalle et al ldquoThemilling of airframe components with low rigidity a generalapproach to avoid static and dynamic problemsrdquo Proceedingsof the Institution of Mechanical Engineers Part B Journal ofEngineering Manufacture vol 219 no 11 pp 789ndash801 2005

[19] D Olvera L N L de Lacalle F I Compean A Fz-ValdivielsoA Lamikiz and F J Campa ldquoAnalysis of the tool tip radialstiffness of turn-milling centersrdquo The International Journal ofAdvancedManufacturing Technology vol 60 no 9 pp 883ndash8912012

[20] A Lamikiz L N Lopez de Lacalle O Ocerin D Dıez and EMaidagan ldquoThe Denavit and Hartenberg approach applied toevaluate the consequences in the tool tip position of geometricalerrors in five-axis milling centresrdquo The International Journal ofAdvanced Manufacturing Technology vol 37 no 1 pp 122ndash1392008

[21] G M Kim B H Kim and C N Chu ldquoEstimation ofcutter deflection and form error in ball-end milling processesrdquoInternational Journal ofMachine Tools andManufacture vol 43no 9 pp 917ndash924 2003

[22] E B Kivanc and E Budak ldquoStructural modeling of end millsfor form error and stability analysisrdquo International Journal ofMachine ToolsampManufacture vol 44 no 11 pp 1151ndash1161 2004

[23] Q Cao J Zhao S Han and X Chen ldquoForce coefficientsidentification considering inclination angle for ball-end finishmillingrdquo Precision Engineering vol 36 no 2 pp 252ndash260 2012

[24] P Lee and Y Altintas ldquoPrediction of ball-end milling forcesfrom orthogonal cutting datardquo International Journal of MachineTools and Manufacture vol 36 no 9 pp 1059ndash1072 1996

Submit your manuscripts athttpwwwhindawicom

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Biomaterials

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TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

2 Advances in Materials Science and Engineering

theoretical concepts have been applied in order to obtainthe best turn-milling parameters for blades Sava et al in[9 10] have found a cutting parameter optimization approachwhen machining cylindrical parts This approach can lead tominimum surface roughness by using genetic algorithm inthe tangential turn-milling process during which the valueof surface roughness can be easily controlled according tocutting parameters

Biermann et al [11] have proposed an FE model of theworkpiece coupled with a geometric milling simulation forcomputing regenerative workpiece vibrations during the five-axis milling process Lazoglu et al [12] have predicted accu-rately the machining forces in high performance cutting offree form surfaces in aerospace automotive biomedical anddiemold industries and generalized approach for predictionof cutting forces in five-axis machining of parts with complexfree form surfaces Budak et al [13ndash17] have proposed that thevariable pitch cutters can be used to calculate cutting forcein milling of these extremely flexible components And thenthey have studied the notion that the workpiece dynamicsaffect milling force in machining of flexible parts and pre-sented a methodology for prediction of in-process workpiecedynamics based on a structural dynamic modification byusing the FE model of the workpiece

Herranz et al in [18] have proposed a working methodol-ogy for efficient process planning based on the previous anal-ysis of those static and dynamic phenomena that may happenduring high-speed cutting This methodology includes (1)several steps in order to minimize the bending and vibrationeffects (2) optimal monitoring methods to detect processinstability and (3) description of the best way for the tuningof cutting conditions and chip load by means of simulationat different machining stages In this paper engine blade iscomplex thin-walled curved parts and plays an importantpart in the aerospace industry Youngrsquos modulus of titaniumis smaller which is prone to distortion in the cutting processIf the cutting force is too large it will cause large bladedeformation and easily lead to poor quality so machiningerror achieves processing requirements difficultly

Olvera et al in [19] have provided stiffness values for thistype of machines clamping a common workpiece To obtainthis information an experimental methodology to measurestatic stiffness along kinematic chain of the turning centeris proposed Lamikiz et al in [20] have presented assemblyerrors that are introduced as additional geometric parametersin the element transformation matrices resulting in the realtransformation matrix for a real and therefore imperfectfive-axis milling machine This matrix defines the real posi-tion of the tool in the absolute reference systemThepredictedmodels of rigid and flexible cutting force with ball cutter areproposed respectively in turn-milling process in this paperThe deformation values of blade and cutter are calculatedrespectively by using the iterative algorithm The accurateprediction of milling force will provide some theoreticalfoundations and references for choosing reasonable tools Sothe cutting force prediction can provide critical guidance forthe cutting parameters optimization

This paper is divided into four main sections The firstentitled The Principle of Turn-Milling Blades will introduce

Axial feed (fa)

Radial feed (fr)Rotation of blade(nb)

Rotation of cutter(nt)

Figure 1 Turn-milling blade principle diagram

the basic motions in turn-milling process The secondsection Rigid Cutting Force Model and Main Parameterswill consider the influence of ball-end cutter and cuttingparameters on cutting force The third part Flexible Cut-ting Force Model will consider the influence of flexibilitydeformation on cutting force by the iterative algorithm andidentification of cutting force coefficients The next partSimulation Analysis of Ball-End Cutting Force will comparerigid and flexible cutting forces and analyze the influencedegree of main cutting parameters on the cutting forcesFinally some conclusions from this study are given

2 The Principle of Turn-Milling Blades

Turn-milling involves four basic motions including rotationof cutter rotation of workpiece axial feed and radial feedof cutter as shown in Figure 1 Milling blade is not simplythe turning and milling processing methods into a singlemachine for processing blade but the use of turn-millingmotion to accomplish complex surfacemachining bladesThemain cutting motion is the rotary motion of ball milling thespeeds of ball milling rotation and blades rotation togetherdetermine the cutting speed The rotational speed of ballcutter plays a dominated role in the whole cutting process sothe rotation speed of the blade is even ignored in high-speedand super-speed process

The complex surface of the blade is engaged by using thecomposite turn-milling motion It can be seen that duringeach cutting period several cutting inserts are in contactwith the workpiece at the same time so intermittent cuttingand enough quenching time for each cutting edge can begained So machining heat transfers more to chips resultingin low workpiece temperature little thermal deformationhigh surface finish and small tool wear Meanwhile goodchip removal rate and automatic chip disposal can alsobe achieved because of the short chips produced in turn-milling

3 Rigid Cutting Force Model andMain Parameters

In turn-milling cutting forces depend on the instantaneousuncut chip thickness Hence accurate calculation of chipthickness is quite critical for turn-milling cutting forcepredictions The uncut chip thickness can be quite compli-cated since the tool can rotate as well as translate withina tool path segment The geometry model of ball-end mill

Advances in Materials Science and Engineering 3

P

n

X

Y

R(z)

Y

Discrete point

Cutting edge

X

ndFt

dFr

dFa120595

R0

120579120601

120573

OOc

Xc

Yc

Z Zc

Figure 2 Geometry model of the ball-end mill

and cutting forces in differential direction are shown inFigure 2 The three coordinates are established in the modelincluding machine coordinate (119883119884 119885) the tool coordinate(119883119888 119884119888 119885119888) and the blade coordinate (119883

119887 119884119887 119885119887) Assume 119875

is the random point on the cutting edge and 119862 is the centerof the ball-end mill tip For a differential chip load in theengagement domain the differential cutting forces in radialaxial and tangential direction are written as follows [10]

119889119865119903= 119870119903119888sdot (119905119888sdot 119889119911) + 119870

119903119890sdot 119889119911

119889119865119886= 119870119886119888(119905119888sdot 119889119911) + 119870

119886119890sdot 119889119911

119889119865119905= 119870119886119888sdot (119905119888sdot 119889119911) + 119870

119905119890sdot 119889119911

(1)

The effects of the lead and tilt angles on the cut geometryhave to be considered in curve machining Consider twofluted ball-end mills where one of the cutting flutes is alignedwith the 119883-axis The angle between the 119884-axis and thereference cutting flute is represented as the reference rotationangle The rotation angle is the angle between the cross-feeddirection and the cutting flutes [12]

In order to obtain the transformation from the coor-dinate frame to feed coordinate cutting forces in rotatingdynamometer coordinate frame are calculated from thefollowing transformations

[[

[

119889119865119909

119889119865119910

119889119865119911

]]

]

=

[[[

[

minus sin (120595) times sin (120601) minus cos (120595) times sin (120601) minus cos (120601)minus sin (120595) times cos (120601) minus cos (120595) times cos (120601) sin (120601)

cos (120595) minus sin (120595) 0

]]]

]

[[

[

cos (120573 + 120579) minus sin ((120573 + 120579)) 0

sin (120573 + 120579) cos (120573 + 120579) 0

0 0 1

]]

]

[[

[

119889119865119903

119889119865119886

119889119865119905

]]

]

(2)

4 Flexible Cutting Force Model

Flexible cutting forcemethod considers not only the feedbackeffect of tool-workpiece deformation on engagement zonebut also the impact of various modifications and couplingeffects due to the change in stiffness of the workpiecematerialremoval which is used in thin-walled components Theblade is regarded as a workpiece of which the thickness isequivalent to the size of the deformed thin-walled parts

41 Iterative Correction of Actual Cutting Depth It is impor-tant that the direction to the contact between tool and part isvariable with feed of tool and position of blade so the cuttingforces are variable in different directions Since the elasticdeformation of tool and workpiece in the interaction forcethe displacements occur in the opposite directions and theactual cutting capacity (such as the radial depth of cut) is notequal to the nominal value of the design Surface error 119890

119905119887at

any point of the surface generated can be expressed as follows

119890119905119887= 120575119905+ 120575119887 (3)

In a transient of milling the actual chip thickness ofcutter node (119894 119895) is smaller than the calculated nominal valueWithin next cycles the additional amount left by cutter node(119894 119895) will be cut by cutter node (119894 + 1 119895) and so forth Afterthe cutter period of rotation the instantaneous undeformedchip thickness converges to the results calculated based onnotional amount of a single tooth feed So the actual radialdepth of cut can be given as follows

119886(119896+1)

119890(119894 119895) = 119886

119890minus [120575(119896)

119905(119894 119895) + 120575

(119896)

119887(119894 119895)] (4)

42 Deformation Calculation of Tool The horizontal direc-tion component is a major factor of the cutter deflectionand the cutter clamping deflection Although vertical forceis also acting on the cutter the axial deflection of toolingsystem is usually ignored resulting from the stiffness in the

4 Advances in Materials Science and Engineering

Ls

Lf

L

2Kc 2Kc

(a) Ball-end millingbending system

120575s

120575f

120601s

(b) Simplified intoa ladder cylindricalcantilever beam

Figure 3 Bending model of ball-end milling

axial direction which is relatively high Consequently thedeflection in the cutting system can be expressed as [21]

120575119905= 120575119908+ 120575119888 (5)

As a cantilever beam tool the tool bending deflection 120575119908

can be expressed as follows

120575119908

=119865

6119864119868(119911119865minus 119911)3

minus (119871 minus 119911)3

+ 3 (119871 minus 119911)2

(119871 minus 119911119865)

(6)

where 119865 is the cutting force 119868 is the area moment of inertiaof the cutter 119864 is Youngrsquos modulus 119871 is the overhand 119911

119865is

the 119911-directional position of the applied force and 119911 is theposition of the deflection

As shown in Figure 3 the clamping deflection at shankclamping 120575

119888can be expressed as follows [22]

120575119888= 120575119904+ 120575119891+ 120601119904(119871119891minus 119911)

=119865

6119864119868minus (119871 minus 119871

119891)3

+ 3 (119871 minus 119871119891)2

(119871 minus 119911119865)

+119865

6119864119868119891

(119911119865minus 119911)3

minus (119871 minus 119911)3

+ 3 (119871 minus 119911)2

(119871 minus 119911119865)

+119865

2119864119868minus (119871 minus 119871

119891)2

+ 2 (119871 minus 119871119891) (119871 minus 119911

119865)

sdot (119871119891minus 119911)

(7)

where 120575119904is deflection of the shank 120575

119891is deflection of the flute

120601119904is deflection angle of the shank 119871

119891is length of the flute

and 119868119891is the moment of inertia relative to shaped mandrel of

cutter edge sectionTo calculate the clamping deflection an experiment needs

to be done to get the stiffness at clamping

120575119888=119865

119870119888

(8)

2Kc

2Kc

120572

120572

120575

120575998400

Figure 4 Actual deformation in processing of ball-end milling

Then the ball-end milling horizontal offset can be given asfollows

120575119905=119865119862

6119864119868minus (119871 minus 119871

119891)3

+ 3 (119871 minus 119871119891)2

(119871 minus 119911119865)

+119865119862

6119864119868119891

(119911119865minus 119911)3

minus (119871 minus 119911)3

+ 3 (119871 minus 119911)2

(119871 minus 119911119865)

+119865119862

2119864119868minus (119871 minus 119871

119891)2

+ 2 (119871 minus 119871119891) (119871 minus 119911

119865)

sdot (119871119891minus 119911) +

119865119862

119870119888

(9)

where 119865119862= 119865119909sin120601 + 119865

119910cos120601 and 119911

119865is given as follows

119911119865= 119903 minus 119903 sin(120587

2minus 120572 minus

1

2arccos

119877 minus 119886119901

119877) (10)

The surface form error is usually defined as a distancebetween the nominal surface and the machined one inthe direction of the surface normal From the calculatedhorizontal deflection due to the lead and tilt angles inFigure 4 the surface form error normal to the surface can becalculated as

119890 = 120575 sdot |sin120572| (11)

43 Deformation Calculation of Blade In the process ofmilling blades the force on the vertical direction of blade sur-face will be produced which produces bending deformationof blades while making the tool bend Since the blades arethin-walled workpiece its thickness has a great influence onthe deformation

The slope angle of each point is equal to rotation angleof the rotating coordinate system required in the next step asshown in Figure 5 As a result 119886

119887(rotation angle of system

11988311198741198841) and 119886

119904(rotation angle of system 119883

21198741198842) can be

expressed as follows

120572119887= arctan 119896

119887

= arctan (1198861+ 21198862119909 + 3119886

31199092

+ 411988641199093

+ 511988651199094

)

120572119904= arctan 119896

119904

= arctan (1198871+ 21198872119909 + 3119887

31199092

+ 411988741199093

+ 511988751199094

)

(12)

Advances in Materials Science and Engineering 5

Horizontalline

Tangent line

Blade shape

Y1Y2

Y3

O

a1a1

a2

a2

X3

X2

X1

F1

F2

h1

h2

Figure 5 Instantaneous thickness in blade machining

The equations of blade basin and back of blade areexpressed respectively as follows

119909119887

= 119909 cos 119886119887

+ (1198860+ 1198861119909 + 11988621199092

+ 11988631199093

+ 11988641199094

+ 11988651199095

) sin 119886119901

119910119887

= (1198860+ 1198861119909 + 11988621199092

+ 11988631199093

+ 11988641199094

+ 11988651199095

) cos 119886119901

minus 119909 sin 119886119901

(13)

119909119904

= 119909 cos 119886119904

+ (1198870+ 1198871119909 + 11988721199092

+ 11988731199093

+ 11988741199094

+ 11988751199095

) sin 119886119904

119910119904

= (1198870+ 1198871119909 + 11988721199092

+ 11988731199093

+ 11988741199094

+ 11988751199095

) cos 119886119904

minus 119909 sin 119886119904

(14)

For any cutting points the value of instantaneous thick-ness is calculated as follows

ℎ119887= 119910119887

1003816100381610038161003816119909119887minus 119910119904

1003816100381610038161003816119909119904

ℎ119904= 119910119887

1003816100381610038161003816119909119904minus 119910119904

1003816100381610038161003816119909119904

(15)

The instantaneous blade thickness curve can be obtainedas shown in Figure 6 Based on the formula the instantaneousstiffness on the point of cutter can be obtained

119896 =119864ℎ3

12 (1 minus ]2) (16)

The instantaneous stiffness is obtained based on (16) Itcan be seen from Figure 7 that stiffness of the cutting pointat the ends of the airfoil is relatively small while the localstiffness of the thicker intermediate is larger Using the curvedthin plate reciprocal theory solution of the problem can beobtained

minus10 0 10 20 30 40 50 60 700

10

20

30

40

50

60

Edge path (mm)

Thic

knes

s (m

m)

Back of bladeBasin of blade

Figure 6 Instantaneous blade thickness curve

Back of bladeBasin of blade

0 10 20 30 40 50 600

1

2

3

4

5

6

7

8

Edge path (mm)

Bend

ing

stiffn

ess (

mm

2kg

s2)

times109

Figure 7 Instantaneous stiffness on the point of cutter

44 Identification of Cutting Force Coefficients

441 Cutting Coefficients Model In order to calculate thecutting forces the edge-specific coefficients and the shear-specific coefficients need to be obtained beforehand whichare determined by materials and geometry of tool andworkpiece In the research proposed by Cao et al thesecoefficients are obtained from the experiments using theplanar surfaces [23] The coefficients can be calculated by

119870119905119888=

2120587

1198731198601

sdot

1198623119865119909119888minus (1198622minus 1198621) 119865119910119888

1198622

3+ (1198622minus 1198621)2

119870119903119888=

2120587

119873 (1198602

2+ 1198602

3)

6 Advances in Materials Science and Engineering

sdot [

1198602(1198622minus 1198621) 119865119909119888+ 1198623119865119910119888

1198622

3+ (1198622minus 1198621)2

minus1198603119865119911119888

1198625

]

119870119886119888=

2120587

119873 (1198602

2+ 1198602

3)

sdot [

1198603(1198622minus 1198621) 119865119909119888+ 1198623119865119910119888

1198622

3+ (1198622minus 1198621)2

+1198602119865119911119888

1198625

]

119870119905119890=minus2120587

1198731198611

sdot

1198624119865119909119890+ 1198625119865119910119890

1198622

4+ 1198622

5

119870119903119890=

2120587

119873 (1198612

2+ 1198612

3)

sdot [

1198612(1198625119865119909119890minus 1198624119865119910119890)

1198622

4+ 1198625

2+1198613119865119911119890

21198621

]

119870119903119890=

2120587

119873 (1198612

2+ 1198612

3)

sdot [

1198613(1198625119865119909119890minus 1198624119865119910119890)

1198622

4+ 1198622

5

minus1198612119865119911119890

21198621

]

(17)

where 119860119894 119861119894 and 119862

119894(119894 = 1 2 3 4 5) are the parameters

associated with start and exit radial immersion angles 120593stand 120593ex and with two boundaries of the position angles 120579minand 120579max 119865119902119888 and 119865119902119890 (119902 = 119883 119884 119885) are the average cuttingforce components for different inclination angles and couldbe obtained from following cutting tests

The relationship among them is shown as the followingthe details of the numerical procedure of computing param-eters are available in [23]

Where 119889119904(120579) = |119889119901(119883119862 119884119862 119885119862)119879

| =

radic(1198831015840

119862)2

+ (1198841015840

119862)2

+ (1198851015840

119862)2

119889120579 is the length of each differentialelement of the cutting edge (119883

119862 119884119862 119885119862) is the arbitrary

point on the cutting edge Consider

1198601= int

120579max

120579min

119877 sin 120579 119889120579

1198602= int

120579max

120579min

119877 sin 1205792119889120579

1198603= int

120579max

120579min

119877 sin 120579 cos 120579 119889120579

1198611= int

120579max

120579min

119889119904 (120579)

1198612= int

120579max

120579min

sin 120579 119889119904 (120579)

1198613= int

120579max

120579min

cos 120579 119889119904 (120579)

Table 1 Main parameters of machining center

Control system FANUC-OI (MC)control system

Maximum spindle speed 6000 rminStroke (119883119884119885) 850mm500mm630mmSpindle maximum torque 70909 (continuous30min) NMMaximum fast feed speed 119883 and 119884 24mmin 119885 15mminMaximum working load 500 kgPower 1175 KW

Workpiece Tool

Feed direction Engagement part

Figure 8 TH5650 vertical machining center

1198621=1

21205931003816100381610038161003816

120593ex120593st

1198622=1

4sin 21205931003816100381610038161003816

120593ex120593st

1198623=1

4cos 21205931003816100381610038161003816

120593ex120593st

1198624= sin1205931003816100381610038161003816

120593ex120593st

1198625= cos1205931003816100381610038161003816

120593ex120593st

(18)

442 Cutting Force Coefficient Identification Test Experi-mental cutting force coefficient identification was conductedusing the TH5650 vertical machining center (Figure 8) Thematerial used for the machining tests was Ti-6Al-4V (TC4)alloy A three-component Kistler dynamometer type Kistler9257B (Figure 9) has beenmounted on themachine table andthe coordinates system has been set to level with the forcesensor surfaces The tool has been chosen to ensure stabledepth of cut in milling a two-flute cutter with 10mm diam-eter has been selected and mounted with 20mm overhangon an HSK32ER20 tool-holder The main parameters of themachine are as in Table 1

In this experiment the cutting tool is a hard alloymaterial of the ball-end mill the milling cutter helix angleis 30 degrees whose diameter is 10mm Selection of millingparameters is as follows spindle speed 300 rmin each toothfeed (002 004 006)mmz and axial cutting deep (1 23)mm

Advances in Materials Science and Engineering 7

Table 2 Milling test data

Test ID Spindle speed119899 (rmin)

Feed pertooth

119888 (mm119911)

Axial cuttingdepth119886119901(mm)

119883 axialperiodic force

119865119909(N)

119884 axialperiodic force

119865119910(N)

119885 axialperiodic force

119865119911(N)

1 300 002 1 minus5032 9223 10732 300 004 1 minus7258 10572 20453 300 006 1 minus9683 12034 53124 300 002 2 minus4436 19876 129565 300 004 2 minus3288 23766 88926 300 006 2 minus1225 30654 42787 300 002 3 minus197 38725 2378 300 004 3 2278 44944 minus3946

9 300 006 3 1657 58689 minus7683

Table 3 Cutting force coefficient

Cutting forceparameter

Numerical(Mpa)

Cutting forceparameter

Numerical(Nm)

119870119905119888

15998 119870119905119890

207119870119903119888

5201 119870119903119890

428119870119886119888

6482 119870119886119890

79

Dynamometer

Figure 9 Kistler 9257B dynamometer

A series of experimental data was obtained as shown inTable 2

From the experimental data in (17) by analyzing therelationship of cutting force the cutting coefficient is shownin Table 3

5 Simulation Analysis ofBall-End Cutting Force

51 Prediction and Simulation of Milling Force The influenceof cutting parameter and geometer parameter of tool oncutting forces is analyzed by turn-milling process The ballmilling cutting force is simulated based on the model ofmilling force by using MATLAB program in the differentcutting parameters The titanium alloy is used as workpiecematerial The diameter of cutter is 10mm The depth of cutis 05mm The different cutting force simulation results areshown in Figures 10ndash15 as follows

0 50 100 150 200 250 300 350 400minus400

minus300

minus200

minus100

0

100

200

300

400

500

600

F (N

)

Cutter rotation angle (∘)

FxiFyi

FziF

(Small symbol ae = 12R big symbol ae = 16R)

Figure 10 Effect of cutting width 119886119890on cutting force

511 The Influence of Cutting Width and Tilt Angle on CuttingForce Similarly when the cutting depth is reduced cuttingforces in three directions119883119884 and119885 are all decreased wherethe magnitudes of decreases are relatively large and the totalcutting force becomes smaller from Figure 10 But when thecutting depth is reduced cutting-in angle is constant whilecutting-out angle becomes smaller As can be seen fromFigure 11 cutting force decreases with increasing of dip Sothe tilt angle can be increased to reduce the cutting forceduring processing

512 The Influence of Tooth Number and Cutting Depth onCutting Force It can be noticed from Figure 12 the change ofmilling cutter blade has no effect on the cutting force but itaffects the numbers of milling force cycle in a rotary cuttercycle The numbers of milling force cycle are equal to thenumber of milling cutter blade and entrance angle and exitangle go backwards with the increasing number of cuttingedge

8 Advances in Materials Science and Engineering

0 50 100 150 200 250 300 350 400minus300

minus200

minus100

0

100

200

300

400

500(Small symbol l = 25∘ big symbol l = 15∘)

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

Figure 11 Effect of tilt angle on cutting force

0 50 100 150 200 250 300 350 400minus100

minus50

0

50

100

150

200

250

300

350

400

450

N = 2N = 3

Cutter rotation angle (∘)

F (N

)

Figure 12 Effect of tooth number on cutting force

When the cutting depth is reduced cutting forces in threedirections119883 119884 and 119885 are all decreased and the total cuttingforce becomes smaller from Figure 13 But when the cuttingdepth decreases entrance angle and exit angle are constant

513 The Influence of Cutter Diameter on Cutting ForceWhen focusing on the effect of cutter diameter on cuttingforce the larger the cutter diameter is the larger the cuttingforce becomes no matter whether it is a given value or not inFigure 14 With the change of cutter diameter entrance angleremains unchanged while exit angle changes

514 The Influence of Cutter Diameter and Feed on CuttingForce It can be noticed from Figure 15 that cutting forceand cutting-in angle are not affected by different helix angleBut the cutting-out angle will be bigger when the helix angleincreases The last parameter is the rational speed Feed has

0 50 100 150 200 250 300 350 4000

100

200

300

400

500

600

Cutter rotation angle (∘)

ap = 08mm

ap = 10mm

ap = 12mm

F (N

)

Figure 13 Effect of cutting depth on cutting force

a great impact on the maximum cutting force as shown inFigure 16 And slight increase can cause large changes ofthe total cutting force so that the amount of feed should beselected with season during processing

52 Comparison of Rigid and Flexible Cutting Force Inorder to illustrate the contribution of flexible cutting forcecomparison of flexible cutting forces and rigid cutting forceswas simulated based on the same cutting conditions inFigure 15

It can be seen from Figure 17 that flexible cutting force issmaller than rigid cutting force in differential direction butthe value is more by 19N in the 119883 direction Consequentlyit is necessary that the flexible model of cutting force isanalyzed For the validation of the model another simulation(in Figure 18) is conducted in the same cutting condition[24] as follows 119886

119899= 0 spindle speed = 269 rmin 119877

0=

9526mm 1198940= 30 st = 00508mm and 119886

119901= 635mm

The predicted cutting forces are compared and matched wellwith the experiment [24] Therefore it provides a theoreticalfoundation and reference for the turn-milling mechanismresearch

6 Conclusions

In this paper the cutting force of blade by turn-milling wasstudied in cutting parameters A rigid model and a flexiblemodel of cutting force with ball-end cutter are establishedrespectively based on the analysis of space geometry of theball-end mill and blades Some suggestions are providedto choose cutting parameters to reduce cutting forces andreach high productivity This study will provide a theoreticalfoundation and reference for the turn-milling mechanismresearch Based on this work the following conclusions canbe drawn

(i) The influences of cutting parameters and geometryshape of cutter on the cutting forces are analyzedby turn-milling The deformation values of blade

Advances in Materials Science and Engineering 9

0 50 100 150 200 250 300 350 400minus300

minus200

minus100

0

100

200

300

400

500

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

(a) 119886119890is a multiple of the diameter

0 50 100 150 200 250 300 350 400minus400

minus300

minus200

minus100

0

100

200

300

400

500

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

(b) 119886119890is constant

Figure 14 Effect of cutter diameter on cutting force (big symbol119863 = 8mm small symbol119863 = 5mm)

0 50 100 150 200 250 300 350 400minus300

minus200

minus100

0

100

200

300

400

500

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

(Big symbol 120573 = small symbol 120573 = 18∘)38∘

Figure 15 Effect of helix angle on cutting force

and cutter on the engaged trajectory are calculatedrespectively by using the iterative algorithm

(ii) In milling blades case cutting force is sensitive to theamount of feed but the influence of helix angle is thesmallestThe amount of deformation of the blade willnot be the same in a different thickness position ofthe bladeThe thinner the thickness is the greater thebending deformation becomes And cutting force isalso affected by the deformation

(iii) In milling titanium blades case flexible cutting forceis smaller than rigid cutting force in each direction

0 50 100 150 200 250 300 350 4000

50

100

150

200

250

300

350

400

450

500

Cutter rotation angle (∘)

= 01mms

= 02mms

= 03mms

F (N

)

Figure 16 Effect of feed on cutting force

but it is less 20N Since stiffness of titanium alloy isrelatively large the deformation of titanium alloy issmall and deformation of the tool is of the order ofminus5 times

Nomenclature

119899119905 Rotation speed of cutter (rmin)

119899119887 Rotation speed of blade (rmin)

119886119901 Depth of cut (mm)

119891119911 Feed per tooth (mmz)

119905119888 Uncut chip thickness (mm)

] Poisson ratio of blade120575119905 Deflection value of tool

120575119887 Deflection value of blade

10 Advances in Materials Science and Engineering

0 50 100 150 200 250 300 350 400minus400

minus300

minus200

minus100

0

100

200

300

400

Flexible Rigid

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

Figure 17 Comparisons of cutting forces in flexible and rigidmodel

0 50 100 150 200minus1000

minus800

minus600

minus400

minus200

0

200

400

600

800

1000

Cutti

ng fo

rce (

N)

FxFyFz

Rotation angle (∘)

Figure 18 Simulated cutting forces in end milling

120575119908 Cutter bending deflection

120575119888 Clamping deflection

119870119903119888 119870119886119888 and119870

119905119888 Radial axial and tangential cutting forcecoefficients

119870119903119890119870119886119890 and119870

119905119890 Edge force coefficients

120595 Immersion angle of cutting point120601 Cutting element position angle120573 Angle between the 119884-axis and the

reference cutting flute120579 Angle between the cross-feed direction

and the cutting flute119870119888 Measured clamping stiffness of cutter

119903 Radius (mm)

119911 The number of teeth on the cutter119891119886 Axial feed (mmr)

119891119903 Radial feed (mmr)

119864 Elastic modulus of bladeℎ Thickness of blade119890119905119887 Surface error

119886119890 Radial depth of cut

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (NSFC) (51105072 and 51475087) sup-ported by the Fundamental Research Funds for the CentralUniversities (N150304005)

References

[1] U Karaguzel M Bakkal and E Budak ldquoProcess modeling ofturn-milling using analytical approachrdquo Procedia CIRP vol 4pp 131ndash139 2012

[2] U Karaguzel E Uysal E Budak and M Bakkal ldquoAnalyticalmodeling of turn-milling process geometry kinematics andmechanicsrdquo International Journal of Machine Tools amp Manufac-ture vol 91 pp 24ndash33 2015

[3] S Ekinovic E Begovic and A Silajdzija ldquoComparison ofmachined surface quality obtained by high-speed machiningand conventional turningrdquo Machining Science and Technologyvol 11 no 4 pp 531ndash551 2007

[4] S Skoric TUdiljak andDCiglar ldquoStudy of the suitability of themachining of rotating surfacesrdquoTransactions of Famena vol 32no 2 pp 69ndash83 2008

[5] M Pogacnik and J Kopac ldquoDynamic stabilization of the turn-milling process by parameter optimizationrdquo Proceedings of theInstitution of Mechanical Engineers Part B vol 214 no 2 pp127ndash135 2000

[6] S K Choudhury and J B Bajpai ldquoInvestigation in orthogonalturn-milling towards better surface finishrdquo Journal of MaterialsProcessing Technology vol 170 no 3 pp 487ndash493 2005

[7] S K Choudhury and K S Mangrulkar ldquoInvestigation oforthogonal turn-milling for the machining of rotationallysymmetrical work piecesrdquo Journal of Materials Processing Tech-nology vol 99 no 1 pp 120ndash128 2000

[8] A Calleja A Fernandez A Rodriguez L N de Lacalle andA Lamikiz ldquoTurn-milling of blades in turning centres andmultitasking machines controlling tool tilt anglerdquo Proceedingsof the Institution of Mechanical Engineers Part B Journal ofEngineering Manufacture vol 229 no 8 pp 1324ndash1336 2015

[9] C M Lee S W Kim Y H Lee and D W Lee ldquoThe optimalcutter orientation in ball end milling of cantilever-shaped thinplaterdquo Journal of Materials Processing Technology vol 153ndash154pp 900ndash906 2004

[10] M Fontaine A Moufki A Devillez and D Dudzinski ldquoMod-elling of cutting forces in ball-end milling with tool-surfaceinclination Part I predictive force model and experimentalvalidationrdquo Journal of Materials Processing Technology vol 189no 1ndash3 pp 73ndash84 2007

Advances in Materials Science and Engineering 11

[11] D Biermann P Kersting and T Surmann ldquoA general approachto simulating workpiece vibrations during five-axis milling ofturbine bladesrdquo CIRP AnnalsmdashManufacturing Technology vol59 no 1 pp 125ndash128 2010

[12] I Lazoglu Y Boz and H Erdim ldquoFive-axis milling mechanicsfor complex free form surfacesrdquo CIRP Annals-ManufacturingTechnology vol 60 no 1 pp 117ndash120 2011

[13] E Budak E Ozturk and L T Tunc ldquoModeling and simulationof 5-axismilling processesrdquoCIRPAnnalsmdashManufacturing Tech-nology vol 58 no 1 pp 347ndash350 2009

[14] E Budak ldquoImproving 5-axis milling operations using processmodelsrdquoMM Science Journal pp 358ndash365 2012

[15] E Ozturk and E Budak ldquoDynamics and stability of five-axis ball-end millingrdquo Journal of Manufacturing Science andEngineering vol 132 no 2 2010

[16] E Ozturk L T Tunc and E Budak ldquoInvestigation of leadand tilt angle effects in 5-axis ball-end milling processesrdquoInternational Journal of Machine Tools amp Manufacture vol 49no 14 pp 1053ndash1062 2009

[17] E Budak A Comak and E Ozturk ldquoStability and highperformance machining conditions in simultaneous millingrdquoCIRP AnnalsmdashManufacturing Technology vol 62 no 1 pp403ndash406 2013

[18] S Herranz F J Campa L N L De Lacalle et al ldquoThemilling of airframe components with low rigidity a generalapproach to avoid static and dynamic problemsrdquo Proceedingsof the Institution of Mechanical Engineers Part B Journal ofEngineering Manufacture vol 219 no 11 pp 789ndash801 2005

[19] D Olvera L N L de Lacalle F I Compean A Fz-ValdivielsoA Lamikiz and F J Campa ldquoAnalysis of the tool tip radialstiffness of turn-milling centersrdquo The International Journal ofAdvancedManufacturing Technology vol 60 no 9 pp 883ndash8912012

[20] A Lamikiz L N Lopez de Lacalle O Ocerin D Dıez and EMaidagan ldquoThe Denavit and Hartenberg approach applied toevaluate the consequences in the tool tip position of geometricalerrors in five-axis milling centresrdquo The International Journal ofAdvanced Manufacturing Technology vol 37 no 1 pp 122ndash1392008

[21] G M Kim B H Kim and C N Chu ldquoEstimation ofcutter deflection and form error in ball-end milling processesrdquoInternational Journal ofMachine Tools andManufacture vol 43no 9 pp 917ndash924 2003

[22] E B Kivanc and E Budak ldquoStructural modeling of end millsfor form error and stability analysisrdquo International Journal ofMachine ToolsampManufacture vol 44 no 11 pp 1151ndash1161 2004

[23] Q Cao J Zhao S Han and X Chen ldquoForce coefficientsidentification considering inclination angle for ball-end finishmillingrdquo Precision Engineering vol 36 no 2 pp 252ndash260 2012

[24] P Lee and Y Altintas ldquoPrediction of ball-end milling forcesfrom orthogonal cutting datardquo International Journal of MachineTools and Manufacture vol 36 no 9 pp 1059ndash1072 1996

Submit your manuscripts athttpwwwhindawicom

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BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Advances in Materials Science and Engineering 3

P

n

X

Y

R(z)

Y

Discrete point

Cutting edge

X

ndFt

dFr

dFa120595

R0

120579120601

120573

OOc

Xc

Yc

Z Zc

Figure 2 Geometry model of the ball-end mill

and cutting forces in differential direction are shown inFigure 2 The three coordinates are established in the modelincluding machine coordinate (119883119884 119885) the tool coordinate(119883119888 119884119888 119885119888) and the blade coordinate (119883

119887 119884119887 119885119887) Assume 119875

is the random point on the cutting edge and 119862 is the centerof the ball-end mill tip For a differential chip load in theengagement domain the differential cutting forces in radialaxial and tangential direction are written as follows [10]

119889119865119903= 119870119903119888sdot (119905119888sdot 119889119911) + 119870

119903119890sdot 119889119911

119889119865119886= 119870119886119888(119905119888sdot 119889119911) + 119870

119886119890sdot 119889119911

119889119865119905= 119870119886119888sdot (119905119888sdot 119889119911) + 119870

119905119890sdot 119889119911

(1)

The effects of the lead and tilt angles on the cut geometryhave to be considered in curve machining Consider twofluted ball-end mills where one of the cutting flutes is alignedwith the 119883-axis The angle between the 119884-axis and thereference cutting flute is represented as the reference rotationangle The rotation angle is the angle between the cross-feeddirection and the cutting flutes [12]

In order to obtain the transformation from the coor-dinate frame to feed coordinate cutting forces in rotatingdynamometer coordinate frame are calculated from thefollowing transformations

[[

[

119889119865119909

119889119865119910

119889119865119911

]]

]

=

[[[

[

minus sin (120595) times sin (120601) minus cos (120595) times sin (120601) minus cos (120601)minus sin (120595) times cos (120601) minus cos (120595) times cos (120601) sin (120601)

cos (120595) minus sin (120595) 0

]]]

]

[[

[

cos (120573 + 120579) minus sin ((120573 + 120579)) 0

sin (120573 + 120579) cos (120573 + 120579) 0

0 0 1

]]

]

[[

[

119889119865119903

119889119865119886

119889119865119905

]]

]

(2)

4 Flexible Cutting Force Model

Flexible cutting forcemethod considers not only the feedbackeffect of tool-workpiece deformation on engagement zonebut also the impact of various modifications and couplingeffects due to the change in stiffness of the workpiecematerialremoval which is used in thin-walled components Theblade is regarded as a workpiece of which the thickness isequivalent to the size of the deformed thin-walled parts

41 Iterative Correction of Actual Cutting Depth It is impor-tant that the direction to the contact between tool and part isvariable with feed of tool and position of blade so the cuttingforces are variable in different directions Since the elasticdeformation of tool and workpiece in the interaction forcethe displacements occur in the opposite directions and theactual cutting capacity (such as the radial depth of cut) is notequal to the nominal value of the design Surface error 119890

119905119887at

any point of the surface generated can be expressed as follows

119890119905119887= 120575119905+ 120575119887 (3)

In a transient of milling the actual chip thickness ofcutter node (119894 119895) is smaller than the calculated nominal valueWithin next cycles the additional amount left by cutter node(119894 119895) will be cut by cutter node (119894 + 1 119895) and so forth Afterthe cutter period of rotation the instantaneous undeformedchip thickness converges to the results calculated based onnotional amount of a single tooth feed So the actual radialdepth of cut can be given as follows

119886(119896+1)

119890(119894 119895) = 119886

119890minus [120575(119896)

119905(119894 119895) + 120575

(119896)

119887(119894 119895)] (4)

42 Deformation Calculation of Tool The horizontal direc-tion component is a major factor of the cutter deflectionand the cutter clamping deflection Although vertical forceis also acting on the cutter the axial deflection of toolingsystem is usually ignored resulting from the stiffness in the

4 Advances in Materials Science and Engineering

Ls

Lf

L

2Kc 2Kc

(a) Ball-end millingbending system

120575s

120575f

120601s

(b) Simplified intoa ladder cylindricalcantilever beam

Figure 3 Bending model of ball-end milling

axial direction which is relatively high Consequently thedeflection in the cutting system can be expressed as [21]

120575119905= 120575119908+ 120575119888 (5)

As a cantilever beam tool the tool bending deflection 120575119908

can be expressed as follows

120575119908

=119865

6119864119868(119911119865minus 119911)3

minus (119871 minus 119911)3

+ 3 (119871 minus 119911)2

(119871 minus 119911119865)

(6)

where 119865 is the cutting force 119868 is the area moment of inertiaof the cutter 119864 is Youngrsquos modulus 119871 is the overhand 119911

119865is

the 119911-directional position of the applied force and 119911 is theposition of the deflection

As shown in Figure 3 the clamping deflection at shankclamping 120575

119888can be expressed as follows [22]

120575119888= 120575119904+ 120575119891+ 120601119904(119871119891minus 119911)

=119865

6119864119868minus (119871 minus 119871

119891)3

+ 3 (119871 minus 119871119891)2

(119871 minus 119911119865)

+119865

6119864119868119891

(119911119865minus 119911)3

minus (119871 minus 119911)3

+ 3 (119871 minus 119911)2

(119871 minus 119911119865)

+119865

2119864119868minus (119871 minus 119871

119891)2

+ 2 (119871 minus 119871119891) (119871 minus 119911

119865)

sdot (119871119891minus 119911)

(7)

where 120575119904is deflection of the shank 120575

119891is deflection of the flute

120601119904is deflection angle of the shank 119871

119891is length of the flute

and 119868119891is the moment of inertia relative to shaped mandrel of

cutter edge sectionTo calculate the clamping deflection an experiment needs

to be done to get the stiffness at clamping

120575119888=119865

119870119888

(8)

2Kc

2Kc

120572

120572

120575

120575998400

Figure 4 Actual deformation in processing of ball-end milling

Then the ball-end milling horizontal offset can be given asfollows

120575119905=119865119862

6119864119868minus (119871 minus 119871

119891)3

+ 3 (119871 minus 119871119891)2

(119871 minus 119911119865)

+119865119862

6119864119868119891

(119911119865minus 119911)3

minus (119871 minus 119911)3

+ 3 (119871 minus 119911)2

(119871 minus 119911119865)

+119865119862

2119864119868minus (119871 minus 119871

119891)2

+ 2 (119871 minus 119871119891) (119871 minus 119911

119865)

sdot (119871119891minus 119911) +

119865119862

119870119888

(9)

where 119865119862= 119865119909sin120601 + 119865

119910cos120601 and 119911

119865is given as follows

119911119865= 119903 minus 119903 sin(120587

2minus 120572 minus

1

2arccos

119877 minus 119886119901

119877) (10)

The surface form error is usually defined as a distancebetween the nominal surface and the machined one inthe direction of the surface normal From the calculatedhorizontal deflection due to the lead and tilt angles inFigure 4 the surface form error normal to the surface can becalculated as

119890 = 120575 sdot |sin120572| (11)

43 Deformation Calculation of Blade In the process ofmilling blades the force on the vertical direction of blade sur-face will be produced which produces bending deformationof blades while making the tool bend Since the blades arethin-walled workpiece its thickness has a great influence onthe deformation

The slope angle of each point is equal to rotation angleof the rotating coordinate system required in the next step asshown in Figure 5 As a result 119886

119887(rotation angle of system

11988311198741198841) and 119886

119904(rotation angle of system 119883

21198741198842) can be

expressed as follows

120572119887= arctan 119896

119887

= arctan (1198861+ 21198862119909 + 3119886

31199092

+ 411988641199093

+ 511988651199094

)

120572119904= arctan 119896

119904

= arctan (1198871+ 21198872119909 + 3119887

31199092

+ 411988741199093

+ 511988751199094

)

(12)

Advances in Materials Science and Engineering 5

Horizontalline

Tangent line

Blade shape

Y1Y2

Y3

O

a1a1

a2

a2

X3

X2

X1

F1

F2

h1

h2

Figure 5 Instantaneous thickness in blade machining

The equations of blade basin and back of blade areexpressed respectively as follows

119909119887

= 119909 cos 119886119887

+ (1198860+ 1198861119909 + 11988621199092

+ 11988631199093

+ 11988641199094

+ 11988651199095

) sin 119886119901

119910119887

= (1198860+ 1198861119909 + 11988621199092

+ 11988631199093

+ 11988641199094

+ 11988651199095

) cos 119886119901

minus 119909 sin 119886119901

(13)

119909119904

= 119909 cos 119886119904

+ (1198870+ 1198871119909 + 11988721199092

+ 11988731199093

+ 11988741199094

+ 11988751199095

) sin 119886119904

119910119904

= (1198870+ 1198871119909 + 11988721199092

+ 11988731199093

+ 11988741199094

+ 11988751199095

) cos 119886119904

minus 119909 sin 119886119904

(14)

For any cutting points the value of instantaneous thick-ness is calculated as follows

ℎ119887= 119910119887

1003816100381610038161003816119909119887minus 119910119904

1003816100381610038161003816119909119904

ℎ119904= 119910119887

1003816100381610038161003816119909119904minus 119910119904

1003816100381610038161003816119909119904

(15)

The instantaneous blade thickness curve can be obtainedas shown in Figure 6 Based on the formula the instantaneousstiffness on the point of cutter can be obtained

119896 =119864ℎ3

12 (1 minus ]2) (16)

The instantaneous stiffness is obtained based on (16) Itcan be seen from Figure 7 that stiffness of the cutting pointat the ends of the airfoil is relatively small while the localstiffness of the thicker intermediate is larger Using the curvedthin plate reciprocal theory solution of the problem can beobtained

minus10 0 10 20 30 40 50 60 700

10

20

30

40

50

60

Edge path (mm)

Thic

knes

s (m

m)

Back of bladeBasin of blade

Figure 6 Instantaneous blade thickness curve

Back of bladeBasin of blade

0 10 20 30 40 50 600

1

2

3

4

5

6

7

8

Edge path (mm)

Bend

ing

stiffn

ess (

mm

2kg

s2)

times109

Figure 7 Instantaneous stiffness on the point of cutter

44 Identification of Cutting Force Coefficients

441 Cutting Coefficients Model In order to calculate thecutting forces the edge-specific coefficients and the shear-specific coefficients need to be obtained beforehand whichare determined by materials and geometry of tool andworkpiece In the research proposed by Cao et al thesecoefficients are obtained from the experiments using theplanar surfaces [23] The coefficients can be calculated by

119870119905119888=

2120587

1198731198601

sdot

1198623119865119909119888minus (1198622minus 1198621) 119865119910119888

1198622

3+ (1198622minus 1198621)2

119870119903119888=

2120587

119873 (1198602

2+ 1198602

3)

6 Advances in Materials Science and Engineering

sdot [

1198602(1198622minus 1198621) 119865119909119888+ 1198623119865119910119888

1198622

3+ (1198622minus 1198621)2

minus1198603119865119911119888

1198625

]

119870119886119888=

2120587

119873 (1198602

2+ 1198602

3)

sdot [

1198603(1198622minus 1198621) 119865119909119888+ 1198623119865119910119888

1198622

3+ (1198622minus 1198621)2

+1198602119865119911119888

1198625

]

119870119905119890=minus2120587

1198731198611

sdot

1198624119865119909119890+ 1198625119865119910119890

1198622

4+ 1198622

5

119870119903119890=

2120587

119873 (1198612

2+ 1198612

3)

sdot [

1198612(1198625119865119909119890minus 1198624119865119910119890)

1198622

4+ 1198625

2+1198613119865119911119890

21198621

]

119870119903119890=

2120587

119873 (1198612

2+ 1198612

3)

sdot [

1198613(1198625119865119909119890minus 1198624119865119910119890)

1198622

4+ 1198622

5

minus1198612119865119911119890

21198621

]

(17)

where 119860119894 119861119894 and 119862

119894(119894 = 1 2 3 4 5) are the parameters

associated with start and exit radial immersion angles 120593stand 120593ex and with two boundaries of the position angles 120579minand 120579max 119865119902119888 and 119865119902119890 (119902 = 119883 119884 119885) are the average cuttingforce components for different inclination angles and couldbe obtained from following cutting tests

The relationship among them is shown as the followingthe details of the numerical procedure of computing param-eters are available in [23]

Where 119889119904(120579) = |119889119901(119883119862 119884119862 119885119862)119879

| =

radic(1198831015840

119862)2

+ (1198841015840

119862)2

+ (1198851015840

119862)2

119889120579 is the length of each differentialelement of the cutting edge (119883

119862 119884119862 119885119862) is the arbitrary

point on the cutting edge Consider

1198601= int

120579max

120579min

119877 sin 120579 119889120579

1198602= int

120579max

120579min

119877 sin 1205792119889120579

1198603= int

120579max

120579min

119877 sin 120579 cos 120579 119889120579

1198611= int

120579max

120579min

119889119904 (120579)

1198612= int

120579max

120579min

sin 120579 119889119904 (120579)

1198613= int

120579max

120579min

cos 120579 119889119904 (120579)

Table 1 Main parameters of machining center

Control system FANUC-OI (MC)control system

Maximum spindle speed 6000 rminStroke (119883119884119885) 850mm500mm630mmSpindle maximum torque 70909 (continuous30min) NMMaximum fast feed speed 119883 and 119884 24mmin 119885 15mminMaximum working load 500 kgPower 1175 KW

Workpiece Tool

Feed direction Engagement part

Figure 8 TH5650 vertical machining center

1198621=1

21205931003816100381610038161003816

120593ex120593st

1198622=1

4sin 21205931003816100381610038161003816

120593ex120593st

1198623=1

4cos 21205931003816100381610038161003816

120593ex120593st

1198624= sin1205931003816100381610038161003816

120593ex120593st

1198625= cos1205931003816100381610038161003816

120593ex120593st

(18)

442 Cutting Force Coefficient Identification Test Experi-mental cutting force coefficient identification was conductedusing the TH5650 vertical machining center (Figure 8) Thematerial used for the machining tests was Ti-6Al-4V (TC4)alloy A three-component Kistler dynamometer type Kistler9257B (Figure 9) has beenmounted on themachine table andthe coordinates system has been set to level with the forcesensor surfaces The tool has been chosen to ensure stabledepth of cut in milling a two-flute cutter with 10mm diam-eter has been selected and mounted with 20mm overhangon an HSK32ER20 tool-holder The main parameters of themachine are as in Table 1

In this experiment the cutting tool is a hard alloymaterial of the ball-end mill the milling cutter helix angleis 30 degrees whose diameter is 10mm Selection of millingparameters is as follows spindle speed 300 rmin each toothfeed (002 004 006)mmz and axial cutting deep (1 23)mm

Advances in Materials Science and Engineering 7

Table 2 Milling test data

Test ID Spindle speed119899 (rmin)

Feed pertooth

119888 (mm119911)

Axial cuttingdepth119886119901(mm)

119883 axialperiodic force

119865119909(N)

119884 axialperiodic force

119865119910(N)

119885 axialperiodic force

119865119911(N)

1 300 002 1 minus5032 9223 10732 300 004 1 minus7258 10572 20453 300 006 1 minus9683 12034 53124 300 002 2 minus4436 19876 129565 300 004 2 minus3288 23766 88926 300 006 2 minus1225 30654 42787 300 002 3 minus197 38725 2378 300 004 3 2278 44944 minus3946

9 300 006 3 1657 58689 minus7683

Table 3 Cutting force coefficient

Cutting forceparameter

Numerical(Mpa)

Cutting forceparameter

Numerical(Nm)

119870119905119888

15998 119870119905119890

207119870119903119888

5201 119870119903119890

428119870119886119888

6482 119870119886119890

79

Dynamometer

Figure 9 Kistler 9257B dynamometer

A series of experimental data was obtained as shown inTable 2

From the experimental data in (17) by analyzing therelationship of cutting force the cutting coefficient is shownin Table 3

5 Simulation Analysis ofBall-End Cutting Force

51 Prediction and Simulation of Milling Force The influenceof cutting parameter and geometer parameter of tool oncutting forces is analyzed by turn-milling process The ballmilling cutting force is simulated based on the model ofmilling force by using MATLAB program in the differentcutting parameters The titanium alloy is used as workpiecematerial The diameter of cutter is 10mm The depth of cutis 05mm The different cutting force simulation results areshown in Figures 10ndash15 as follows

0 50 100 150 200 250 300 350 400minus400

minus300

minus200

minus100

0

100

200

300

400

500

600

F (N

)

Cutter rotation angle (∘)

FxiFyi

FziF

(Small symbol ae = 12R big symbol ae = 16R)

Figure 10 Effect of cutting width 119886119890on cutting force

511 The Influence of Cutting Width and Tilt Angle on CuttingForce Similarly when the cutting depth is reduced cuttingforces in three directions119883119884 and119885 are all decreased wherethe magnitudes of decreases are relatively large and the totalcutting force becomes smaller from Figure 10 But when thecutting depth is reduced cutting-in angle is constant whilecutting-out angle becomes smaller As can be seen fromFigure 11 cutting force decreases with increasing of dip Sothe tilt angle can be increased to reduce the cutting forceduring processing

512 The Influence of Tooth Number and Cutting Depth onCutting Force It can be noticed from Figure 12 the change ofmilling cutter blade has no effect on the cutting force but itaffects the numbers of milling force cycle in a rotary cuttercycle The numbers of milling force cycle are equal to thenumber of milling cutter blade and entrance angle and exitangle go backwards with the increasing number of cuttingedge

8 Advances in Materials Science and Engineering

0 50 100 150 200 250 300 350 400minus300

minus200

minus100

0

100

200

300

400

500(Small symbol l = 25∘ big symbol l = 15∘)

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

Figure 11 Effect of tilt angle on cutting force

0 50 100 150 200 250 300 350 400minus100

minus50

0

50

100

150

200

250

300

350

400

450

N = 2N = 3

Cutter rotation angle (∘)

F (N

)

Figure 12 Effect of tooth number on cutting force

When the cutting depth is reduced cutting forces in threedirections119883 119884 and 119885 are all decreased and the total cuttingforce becomes smaller from Figure 13 But when the cuttingdepth decreases entrance angle and exit angle are constant

513 The Influence of Cutter Diameter on Cutting ForceWhen focusing on the effect of cutter diameter on cuttingforce the larger the cutter diameter is the larger the cuttingforce becomes no matter whether it is a given value or not inFigure 14 With the change of cutter diameter entrance angleremains unchanged while exit angle changes

514 The Influence of Cutter Diameter and Feed on CuttingForce It can be noticed from Figure 15 that cutting forceand cutting-in angle are not affected by different helix angleBut the cutting-out angle will be bigger when the helix angleincreases The last parameter is the rational speed Feed has

0 50 100 150 200 250 300 350 4000

100

200

300

400

500

600

Cutter rotation angle (∘)

ap = 08mm

ap = 10mm

ap = 12mm

F (N

)

Figure 13 Effect of cutting depth on cutting force

a great impact on the maximum cutting force as shown inFigure 16 And slight increase can cause large changes ofthe total cutting force so that the amount of feed should beselected with season during processing

52 Comparison of Rigid and Flexible Cutting Force Inorder to illustrate the contribution of flexible cutting forcecomparison of flexible cutting forces and rigid cutting forceswas simulated based on the same cutting conditions inFigure 15

It can be seen from Figure 17 that flexible cutting force issmaller than rigid cutting force in differential direction butthe value is more by 19N in the 119883 direction Consequentlyit is necessary that the flexible model of cutting force isanalyzed For the validation of the model another simulation(in Figure 18) is conducted in the same cutting condition[24] as follows 119886

119899= 0 spindle speed = 269 rmin 119877

0=

9526mm 1198940= 30 st = 00508mm and 119886

119901= 635mm

The predicted cutting forces are compared and matched wellwith the experiment [24] Therefore it provides a theoreticalfoundation and reference for the turn-milling mechanismresearch

6 Conclusions

In this paper the cutting force of blade by turn-milling wasstudied in cutting parameters A rigid model and a flexiblemodel of cutting force with ball-end cutter are establishedrespectively based on the analysis of space geometry of theball-end mill and blades Some suggestions are providedto choose cutting parameters to reduce cutting forces andreach high productivity This study will provide a theoreticalfoundation and reference for the turn-milling mechanismresearch Based on this work the following conclusions canbe drawn

(i) The influences of cutting parameters and geometryshape of cutter on the cutting forces are analyzedby turn-milling The deformation values of blade

Advances in Materials Science and Engineering 9

0 50 100 150 200 250 300 350 400minus300

minus200

minus100

0

100

200

300

400

500

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

(a) 119886119890is a multiple of the diameter

0 50 100 150 200 250 300 350 400minus400

minus300

minus200

minus100

0

100

200

300

400

500

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

(b) 119886119890is constant

Figure 14 Effect of cutter diameter on cutting force (big symbol119863 = 8mm small symbol119863 = 5mm)

0 50 100 150 200 250 300 350 400minus300

minus200

minus100

0

100

200

300

400

500

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

(Big symbol 120573 = small symbol 120573 = 18∘)38∘

Figure 15 Effect of helix angle on cutting force

and cutter on the engaged trajectory are calculatedrespectively by using the iterative algorithm

(ii) In milling blades case cutting force is sensitive to theamount of feed but the influence of helix angle is thesmallestThe amount of deformation of the blade willnot be the same in a different thickness position ofthe bladeThe thinner the thickness is the greater thebending deformation becomes And cutting force isalso affected by the deformation

(iii) In milling titanium blades case flexible cutting forceis smaller than rigid cutting force in each direction

0 50 100 150 200 250 300 350 4000

50

100

150

200

250

300

350

400

450

500

Cutter rotation angle (∘)

= 01mms

= 02mms

= 03mms

F (N

)

Figure 16 Effect of feed on cutting force

but it is less 20N Since stiffness of titanium alloy isrelatively large the deformation of titanium alloy issmall and deformation of the tool is of the order ofminus5 times

Nomenclature

119899119905 Rotation speed of cutter (rmin)

119899119887 Rotation speed of blade (rmin)

119886119901 Depth of cut (mm)

119891119911 Feed per tooth (mmz)

119905119888 Uncut chip thickness (mm)

] Poisson ratio of blade120575119905 Deflection value of tool

120575119887 Deflection value of blade

10 Advances in Materials Science and Engineering

0 50 100 150 200 250 300 350 400minus400

minus300

minus200

minus100

0

100

200

300

400

Flexible Rigid

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

Figure 17 Comparisons of cutting forces in flexible and rigidmodel

0 50 100 150 200minus1000

minus800

minus600

minus400

minus200

0

200

400

600

800

1000

Cutti

ng fo

rce (

N)

FxFyFz

Rotation angle (∘)

Figure 18 Simulated cutting forces in end milling

120575119908 Cutter bending deflection

120575119888 Clamping deflection

119870119903119888 119870119886119888 and119870

119905119888 Radial axial and tangential cutting forcecoefficients

119870119903119890119870119886119890 and119870

119905119890 Edge force coefficients

120595 Immersion angle of cutting point120601 Cutting element position angle120573 Angle between the 119884-axis and the

reference cutting flute120579 Angle between the cross-feed direction

and the cutting flute119870119888 Measured clamping stiffness of cutter

119903 Radius (mm)

119911 The number of teeth on the cutter119891119886 Axial feed (mmr)

119891119903 Radial feed (mmr)

119864 Elastic modulus of bladeℎ Thickness of blade119890119905119887 Surface error

119886119890 Radial depth of cut

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (NSFC) (51105072 and 51475087) sup-ported by the Fundamental Research Funds for the CentralUniversities (N150304005)

References

[1] U Karaguzel M Bakkal and E Budak ldquoProcess modeling ofturn-milling using analytical approachrdquo Procedia CIRP vol 4pp 131ndash139 2012

[2] U Karaguzel E Uysal E Budak and M Bakkal ldquoAnalyticalmodeling of turn-milling process geometry kinematics andmechanicsrdquo International Journal of Machine Tools amp Manufac-ture vol 91 pp 24ndash33 2015

[3] S Ekinovic E Begovic and A Silajdzija ldquoComparison ofmachined surface quality obtained by high-speed machiningand conventional turningrdquo Machining Science and Technologyvol 11 no 4 pp 531ndash551 2007

[4] S Skoric TUdiljak andDCiglar ldquoStudy of the suitability of themachining of rotating surfacesrdquoTransactions of Famena vol 32no 2 pp 69ndash83 2008

[5] M Pogacnik and J Kopac ldquoDynamic stabilization of the turn-milling process by parameter optimizationrdquo Proceedings of theInstitution of Mechanical Engineers Part B vol 214 no 2 pp127ndash135 2000

[6] S K Choudhury and J B Bajpai ldquoInvestigation in orthogonalturn-milling towards better surface finishrdquo Journal of MaterialsProcessing Technology vol 170 no 3 pp 487ndash493 2005

[7] S K Choudhury and K S Mangrulkar ldquoInvestigation oforthogonal turn-milling for the machining of rotationallysymmetrical work piecesrdquo Journal of Materials Processing Tech-nology vol 99 no 1 pp 120ndash128 2000

[8] A Calleja A Fernandez A Rodriguez L N de Lacalle andA Lamikiz ldquoTurn-milling of blades in turning centres andmultitasking machines controlling tool tilt anglerdquo Proceedingsof the Institution of Mechanical Engineers Part B Journal ofEngineering Manufacture vol 229 no 8 pp 1324ndash1336 2015

[9] C M Lee S W Kim Y H Lee and D W Lee ldquoThe optimalcutter orientation in ball end milling of cantilever-shaped thinplaterdquo Journal of Materials Processing Technology vol 153ndash154pp 900ndash906 2004

[10] M Fontaine A Moufki A Devillez and D Dudzinski ldquoMod-elling of cutting forces in ball-end milling with tool-surfaceinclination Part I predictive force model and experimentalvalidationrdquo Journal of Materials Processing Technology vol 189no 1ndash3 pp 73ndash84 2007

Advances in Materials Science and Engineering 11

[11] D Biermann P Kersting and T Surmann ldquoA general approachto simulating workpiece vibrations during five-axis milling ofturbine bladesrdquo CIRP AnnalsmdashManufacturing Technology vol59 no 1 pp 125ndash128 2010

[12] I Lazoglu Y Boz and H Erdim ldquoFive-axis milling mechanicsfor complex free form surfacesrdquo CIRP Annals-ManufacturingTechnology vol 60 no 1 pp 117ndash120 2011

[13] E Budak E Ozturk and L T Tunc ldquoModeling and simulationof 5-axismilling processesrdquoCIRPAnnalsmdashManufacturing Tech-nology vol 58 no 1 pp 347ndash350 2009

[14] E Budak ldquoImproving 5-axis milling operations using processmodelsrdquoMM Science Journal pp 358ndash365 2012

[15] E Ozturk and E Budak ldquoDynamics and stability of five-axis ball-end millingrdquo Journal of Manufacturing Science andEngineering vol 132 no 2 2010

[16] E Ozturk L T Tunc and E Budak ldquoInvestigation of leadand tilt angle effects in 5-axis ball-end milling processesrdquoInternational Journal of Machine Tools amp Manufacture vol 49no 14 pp 1053ndash1062 2009

[17] E Budak A Comak and E Ozturk ldquoStability and highperformance machining conditions in simultaneous millingrdquoCIRP AnnalsmdashManufacturing Technology vol 62 no 1 pp403ndash406 2013

[18] S Herranz F J Campa L N L De Lacalle et al ldquoThemilling of airframe components with low rigidity a generalapproach to avoid static and dynamic problemsrdquo Proceedingsof the Institution of Mechanical Engineers Part B Journal ofEngineering Manufacture vol 219 no 11 pp 789ndash801 2005

[19] D Olvera L N L de Lacalle F I Compean A Fz-ValdivielsoA Lamikiz and F J Campa ldquoAnalysis of the tool tip radialstiffness of turn-milling centersrdquo The International Journal ofAdvancedManufacturing Technology vol 60 no 9 pp 883ndash8912012

[20] A Lamikiz L N Lopez de Lacalle O Ocerin D Dıez and EMaidagan ldquoThe Denavit and Hartenberg approach applied toevaluate the consequences in the tool tip position of geometricalerrors in five-axis milling centresrdquo The International Journal ofAdvanced Manufacturing Technology vol 37 no 1 pp 122ndash1392008

[21] G M Kim B H Kim and C N Chu ldquoEstimation ofcutter deflection and form error in ball-end milling processesrdquoInternational Journal ofMachine Tools andManufacture vol 43no 9 pp 917ndash924 2003

[22] E B Kivanc and E Budak ldquoStructural modeling of end millsfor form error and stability analysisrdquo International Journal ofMachine ToolsampManufacture vol 44 no 11 pp 1151ndash1161 2004

[23] Q Cao J Zhao S Han and X Chen ldquoForce coefficientsidentification considering inclination angle for ball-end finishmillingrdquo Precision Engineering vol 36 no 2 pp 252ndash260 2012

[24] P Lee and Y Altintas ldquoPrediction of ball-end milling forcesfrom orthogonal cutting datardquo International Journal of MachineTools and Manufacture vol 36 no 9 pp 1059ndash1072 1996

Submit your manuscripts athttpwwwhindawicom

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MaterialsJournal of

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Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

4 Advances in Materials Science and Engineering

Ls

Lf

L

2Kc 2Kc

(a) Ball-end millingbending system

120575s

120575f

120601s

(b) Simplified intoa ladder cylindricalcantilever beam

Figure 3 Bending model of ball-end milling

axial direction which is relatively high Consequently thedeflection in the cutting system can be expressed as [21]

120575119905= 120575119908+ 120575119888 (5)

As a cantilever beam tool the tool bending deflection 120575119908

can be expressed as follows

120575119908

=119865

6119864119868(119911119865minus 119911)3

minus (119871 minus 119911)3

+ 3 (119871 minus 119911)2

(119871 minus 119911119865)

(6)

where 119865 is the cutting force 119868 is the area moment of inertiaof the cutter 119864 is Youngrsquos modulus 119871 is the overhand 119911

119865is

the 119911-directional position of the applied force and 119911 is theposition of the deflection

As shown in Figure 3 the clamping deflection at shankclamping 120575

119888can be expressed as follows [22]

120575119888= 120575119904+ 120575119891+ 120601119904(119871119891minus 119911)

=119865

6119864119868minus (119871 minus 119871

119891)3

+ 3 (119871 minus 119871119891)2

(119871 minus 119911119865)

+119865

6119864119868119891

(119911119865minus 119911)3

minus (119871 minus 119911)3

+ 3 (119871 minus 119911)2

(119871 minus 119911119865)

+119865

2119864119868minus (119871 minus 119871

119891)2

+ 2 (119871 minus 119871119891) (119871 minus 119911

119865)

sdot (119871119891minus 119911)

(7)

where 120575119904is deflection of the shank 120575

119891is deflection of the flute

120601119904is deflection angle of the shank 119871

119891is length of the flute

and 119868119891is the moment of inertia relative to shaped mandrel of

cutter edge sectionTo calculate the clamping deflection an experiment needs

to be done to get the stiffness at clamping

120575119888=119865

119870119888

(8)

2Kc

2Kc

120572

120572

120575

120575998400

Figure 4 Actual deformation in processing of ball-end milling

Then the ball-end milling horizontal offset can be given asfollows

120575119905=119865119862

6119864119868minus (119871 minus 119871

119891)3

+ 3 (119871 minus 119871119891)2

(119871 minus 119911119865)

+119865119862

6119864119868119891

(119911119865minus 119911)3

minus (119871 minus 119911)3

+ 3 (119871 minus 119911)2

(119871 minus 119911119865)

+119865119862

2119864119868minus (119871 minus 119871

119891)2

+ 2 (119871 minus 119871119891) (119871 minus 119911

119865)

sdot (119871119891minus 119911) +

119865119862

119870119888

(9)

where 119865119862= 119865119909sin120601 + 119865

119910cos120601 and 119911

119865is given as follows

119911119865= 119903 minus 119903 sin(120587

2minus 120572 minus

1

2arccos

119877 minus 119886119901

119877) (10)

The surface form error is usually defined as a distancebetween the nominal surface and the machined one inthe direction of the surface normal From the calculatedhorizontal deflection due to the lead and tilt angles inFigure 4 the surface form error normal to the surface can becalculated as

119890 = 120575 sdot |sin120572| (11)

43 Deformation Calculation of Blade In the process ofmilling blades the force on the vertical direction of blade sur-face will be produced which produces bending deformationof blades while making the tool bend Since the blades arethin-walled workpiece its thickness has a great influence onthe deformation

The slope angle of each point is equal to rotation angleof the rotating coordinate system required in the next step asshown in Figure 5 As a result 119886

119887(rotation angle of system

11988311198741198841) and 119886

119904(rotation angle of system 119883

21198741198842) can be

expressed as follows

120572119887= arctan 119896

119887

= arctan (1198861+ 21198862119909 + 3119886

31199092

+ 411988641199093

+ 511988651199094

)

120572119904= arctan 119896

119904

= arctan (1198871+ 21198872119909 + 3119887

31199092

+ 411988741199093

+ 511988751199094

)

(12)

Advances in Materials Science and Engineering 5

Horizontalline

Tangent line

Blade shape

Y1Y2

Y3

O

a1a1

a2

a2

X3

X2

X1

F1

F2

h1

h2

Figure 5 Instantaneous thickness in blade machining

The equations of blade basin and back of blade areexpressed respectively as follows

119909119887

= 119909 cos 119886119887

+ (1198860+ 1198861119909 + 11988621199092

+ 11988631199093

+ 11988641199094

+ 11988651199095

) sin 119886119901

119910119887

= (1198860+ 1198861119909 + 11988621199092

+ 11988631199093

+ 11988641199094

+ 11988651199095

) cos 119886119901

minus 119909 sin 119886119901

(13)

119909119904

= 119909 cos 119886119904

+ (1198870+ 1198871119909 + 11988721199092

+ 11988731199093

+ 11988741199094

+ 11988751199095

) sin 119886119904

119910119904

= (1198870+ 1198871119909 + 11988721199092

+ 11988731199093

+ 11988741199094

+ 11988751199095

) cos 119886119904

minus 119909 sin 119886119904

(14)

For any cutting points the value of instantaneous thick-ness is calculated as follows

ℎ119887= 119910119887

1003816100381610038161003816119909119887minus 119910119904

1003816100381610038161003816119909119904

ℎ119904= 119910119887

1003816100381610038161003816119909119904minus 119910119904

1003816100381610038161003816119909119904

(15)

The instantaneous blade thickness curve can be obtainedas shown in Figure 6 Based on the formula the instantaneousstiffness on the point of cutter can be obtained

119896 =119864ℎ3

12 (1 minus ]2) (16)

The instantaneous stiffness is obtained based on (16) Itcan be seen from Figure 7 that stiffness of the cutting pointat the ends of the airfoil is relatively small while the localstiffness of the thicker intermediate is larger Using the curvedthin plate reciprocal theory solution of the problem can beobtained

minus10 0 10 20 30 40 50 60 700

10

20

30

40

50

60

Edge path (mm)

Thic

knes

s (m

m)

Back of bladeBasin of blade

Figure 6 Instantaneous blade thickness curve

Back of bladeBasin of blade

0 10 20 30 40 50 600

1

2

3

4

5

6

7

8

Edge path (mm)

Bend

ing

stiffn

ess (

mm

2kg

s2)

times109

Figure 7 Instantaneous stiffness on the point of cutter

44 Identification of Cutting Force Coefficients

441 Cutting Coefficients Model In order to calculate thecutting forces the edge-specific coefficients and the shear-specific coefficients need to be obtained beforehand whichare determined by materials and geometry of tool andworkpiece In the research proposed by Cao et al thesecoefficients are obtained from the experiments using theplanar surfaces [23] The coefficients can be calculated by

119870119905119888=

2120587

1198731198601

sdot

1198623119865119909119888minus (1198622minus 1198621) 119865119910119888

1198622

3+ (1198622minus 1198621)2

119870119903119888=

2120587

119873 (1198602

2+ 1198602

3)

6 Advances in Materials Science and Engineering

sdot [

1198602(1198622minus 1198621) 119865119909119888+ 1198623119865119910119888

1198622

3+ (1198622minus 1198621)2

minus1198603119865119911119888

1198625

]

119870119886119888=

2120587

119873 (1198602

2+ 1198602

3)

sdot [

1198603(1198622minus 1198621) 119865119909119888+ 1198623119865119910119888

1198622

3+ (1198622minus 1198621)2

+1198602119865119911119888

1198625

]

119870119905119890=minus2120587

1198731198611

sdot

1198624119865119909119890+ 1198625119865119910119890

1198622

4+ 1198622

5

119870119903119890=

2120587

119873 (1198612

2+ 1198612

3)

sdot [

1198612(1198625119865119909119890minus 1198624119865119910119890)

1198622

4+ 1198625

2+1198613119865119911119890

21198621

]

119870119903119890=

2120587

119873 (1198612

2+ 1198612

3)

sdot [

1198613(1198625119865119909119890minus 1198624119865119910119890)

1198622

4+ 1198622

5

minus1198612119865119911119890

21198621

]

(17)

where 119860119894 119861119894 and 119862

119894(119894 = 1 2 3 4 5) are the parameters

associated with start and exit radial immersion angles 120593stand 120593ex and with two boundaries of the position angles 120579minand 120579max 119865119902119888 and 119865119902119890 (119902 = 119883 119884 119885) are the average cuttingforce components for different inclination angles and couldbe obtained from following cutting tests

The relationship among them is shown as the followingthe details of the numerical procedure of computing param-eters are available in [23]

Where 119889119904(120579) = |119889119901(119883119862 119884119862 119885119862)119879

| =

radic(1198831015840

119862)2

+ (1198841015840

119862)2

+ (1198851015840

119862)2

119889120579 is the length of each differentialelement of the cutting edge (119883

119862 119884119862 119885119862) is the arbitrary

point on the cutting edge Consider

1198601= int

120579max

120579min

119877 sin 120579 119889120579

1198602= int

120579max

120579min

119877 sin 1205792119889120579

1198603= int

120579max

120579min

119877 sin 120579 cos 120579 119889120579

1198611= int

120579max

120579min

119889119904 (120579)

1198612= int

120579max

120579min

sin 120579 119889119904 (120579)

1198613= int

120579max

120579min

cos 120579 119889119904 (120579)

Table 1 Main parameters of machining center

Control system FANUC-OI (MC)control system

Maximum spindle speed 6000 rminStroke (119883119884119885) 850mm500mm630mmSpindle maximum torque 70909 (continuous30min) NMMaximum fast feed speed 119883 and 119884 24mmin 119885 15mminMaximum working load 500 kgPower 1175 KW

Workpiece Tool

Feed direction Engagement part

Figure 8 TH5650 vertical machining center

1198621=1

21205931003816100381610038161003816

120593ex120593st

1198622=1

4sin 21205931003816100381610038161003816

120593ex120593st

1198623=1

4cos 21205931003816100381610038161003816

120593ex120593st

1198624= sin1205931003816100381610038161003816

120593ex120593st

1198625= cos1205931003816100381610038161003816

120593ex120593st

(18)

442 Cutting Force Coefficient Identification Test Experi-mental cutting force coefficient identification was conductedusing the TH5650 vertical machining center (Figure 8) Thematerial used for the machining tests was Ti-6Al-4V (TC4)alloy A three-component Kistler dynamometer type Kistler9257B (Figure 9) has beenmounted on themachine table andthe coordinates system has been set to level with the forcesensor surfaces The tool has been chosen to ensure stabledepth of cut in milling a two-flute cutter with 10mm diam-eter has been selected and mounted with 20mm overhangon an HSK32ER20 tool-holder The main parameters of themachine are as in Table 1

In this experiment the cutting tool is a hard alloymaterial of the ball-end mill the milling cutter helix angleis 30 degrees whose diameter is 10mm Selection of millingparameters is as follows spindle speed 300 rmin each toothfeed (002 004 006)mmz and axial cutting deep (1 23)mm

Advances in Materials Science and Engineering 7

Table 2 Milling test data

Test ID Spindle speed119899 (rmin)

Feed pertooth

119888 (mm119911)

Axial cuttingdepth119886119901(mm)

119883 axialperiodic force

119865119909(N)

119884 axialperiodic force

119865119910(N)

119885 axialperiodic force

119865119911(N)

1 300 002 1 minus5032 9223 10732 300 004 1 minus7258 10572 20453 300 006 1 minus9683 12034 53124 300 002 2 minus4436 19876 129565 300 004 2 minus3288 23766 88926 300 006 2 minus1225 30654 42787 300 002 3 minus197 38725 2378 300 004 3 2278 44944 minus3946

9 300 006 3 1657 58689 minus7683

Table 3 Cutting force coefficient

Cutting forceparameter

Numerical(Mpa)

Cutting forceparameter

Numerical(Nm)

119870119905119888

15998 119870119905119890

207119870119903119888

5201 119870119903119890

428119870119886119888

6482 119870119886119890

79

Dynamometer

Figure 9 Kistler 9257B dynamometer

A series of experimental data was obtained as shown inTable 2

From the experimental data in (17) by analyzing therelationship of cutting force the cutting coefficient is shownin Table 3

5 Simulation Analysis ofBall-End Cutting Force

51 Prediction and Simulation of Milling Force The influenceof cutting parameter and geometer parameter of tool oncutting forces is analyzed by turn-milling process The ballmilling cutting force is simulated based on the model ofmilling force by using MATLAB program in the differentcutting parameters The titanium alloy is used as workpiecematerial The diameter of cutter is 10mm The depth of cutis 05mm The different cutting force simulation results areshown in Figures 10ndash15 as follows

0 50 100 150 200 250 300 350 400minus400

minus300

minus200

minus100

0

100

200

300

400

500

600

F (N

)

Cutter rotation angle (∘)

FxiFyi

FziF

(Small symbol ae = 12R big symbol ae = 16R)

Figure 10 Effect of cutting width 119886119890on cutting force

511 The Influence of Cutting Width and Tilt Angle on CuttingForce Similarly when the cutting depth is reduced cuttingforces in three directions119883119884 and119885 are all decreased wherethe magnitudes of decreases are relatively large and the totalcutting force becomes smaller from Figure 10 But when thecutting depth is reduced cutting-in angle is constant whilecutting-out angle becomes smaller As can be seen fromFigure 11 cutting force decreases with increasing of dip Sothe tilt angle can be increased to reduce the cutting forceduring processing

512 The Influence of Tooth Number and Cutting Depth onCutting Force It can be noticed from Figure 12 the change ofmilling cutter blade has no effect on the cutting force but itaffects the numbers of milling force cycle in a rotary cuttercycle The numbers of milling force cycle are equal to thenumber of milling cutter blade and entrance angle and exitangle go backwards with the increasing number of cuttingedge

8 Advances in Materials Science and Engineering

0 50 100 150 200 250 300 350 400minus300

minus200

minus100

0

100

200

300

400

500(Small symbol l = 25∘ big symbol l = 15∘)

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

Figure 11 Effect of tilt angle on cutting force

0 50 100 150 200 250 300 350 400minus100

minus50

0

50

100

150

200

250

300

350

400

450

N = 2N = 3

Cutter rotation angle (∘)

F (N

)

Figure 12 Effect of tooth number on cutting force

When the cutting depth is reduced cutting forces in threedirections119883 119884 and 119885 are all decreased and the total cuttingforce becomes smaller from Figure 13 But when the cuttingdepth decreases entrance angle and exit angle are constant

513 The Influence of Cutter Diameter on Cutting ForceWhen focusing on the effect of cutter diameter on cuttingforce the larger the cutter diameter is the larger the cuttingforce becomes no matter whether it is a given value or not inFigure 14 With the change of cutter diameter entrance angleremains unchanged while exit angle changes

514 The Influence of Cutter Diameter and Feed on CuttingForce It can be noticed from Figure 15 that cutting forceand cutting-in angle are not affected by different helix angleBut the cutting-out angle will be bigger when the helix angleincreases The last parameter is the rational speed Feed has

0 50 100 150 200 250 300 350 4000

100

200

300

400

500

600

Cutter rotation angle (∘)

ap = 08mm

ap = 10mm

ap = 12mm

F (N

)

Figure 13 Effect of cutting depth on cutting force

a great impact on the maximum cutting force as shown inFigure 16 And slight increase can cause large changes ofthe total cutting force so that the amount of feed should beselected with season during processing

52 Comparison of Rigid and Flexible Cutting Force Inorder to illustrate the contribution of flexible cutting forcecomparison of flexible cutting forces and rigid cutting forceswas simulated based on the same cutting conditions inFigure 15

It can be seen from Figure 17 that flexible cutting force issmaller than rigid cutting force in differential direction butthe value is more by 19N in the 119883 direction Consequentlyit is necessary that the flexible model of cutting force isanalyzed For the validation of the model another simulation(in Figure 18) is conducted in the same cutting condition[24] as follows 119886

119899= 0 spindle speed = 269 rmin 119877

0=

9526mm 1198940= 30 st = 00508mm and 119886

119901= 635mm

The predicted cutting forces are compared and matched wellwith the experiment [24] Therefore it provides a theoreticalfoundation and reference for the turn-milling mechanismresearch

6 Conclusions

In this paper the cutting force of blade by turn-milling wasstudied in cutting parameters A rigid model and a flexiblemodel of cutting force with ball-end cutter are establishedrespectively based on the analysis of space geometry of theball-end mill and blades Some suggestions are providedto choose cutting parameters to reduce cutting forces andreach high productivity This study will provide a theoreticalfoundation and reference for the turn-milling mechanismresearch Based on this work the following conclusions canbe drawn

(i) The influences of cutting parameters and geometryshape of cutter on the cutting forces are analyzedby turn-milling The deformation values of blade

Advances in Materials Science and Engineering 9

0 50 100 150 200 250 300 350 400minus300

minus200

minus100

0

100

200

300

400

500

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

(a) 119886119890is a multiple of the diameter

0 50 100 150 200 250 300 350 400minus400

minus300

minus200

minus100

0

100

200

300

400

500

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

(b) 119886119890is constant

Figure 14 Effect of cutter diameter on cutting force (big symbol119863 = 8mm small symbol119863 = 5mm)

0 50 100 150 200 250 300 350 400minus300

minus200

minus100

0

100

200

300

400

500

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

(Big symbol 120573 = small symbol 120573 = 18∘)38∘

Figure 15 Effect of helix angle on cutting force

and cutter on the engaged trajectory are calculatedrespectively by using the iterative algorithm

(ii) In milling blades case cutting force is sensitive to theamount of feed but the influence of helix angle is thesmallestThe amount of deformation of the blade willnot be the same in a different thickness position ofthe bladeThe thinner the thickness is the greater thebending deformation becomes And cutting force isalso affected by the deformation

(iii) In milling titanium blades case flexible cutting forceis smaller than rigid cutting force in each direction

0 50 100 150 200 250 300 350 4000

50

100

150

200

250

300

350

400

450

500

Cutter rotation angle (∘)

= 01mms

= 02mms

= 03mms

F (N

)

Figure 16 Effect of feed on cutting force

but it is less 20N Since stiffness of titanium alloy isrelatively large the deformation of titanium alloy issmall and deformation of the tool is of the order ofminus5 times

Nomenclature

119899119905 Rotation speed of cutter (rmin)

119899119887 Rotation speed of blade (rmin)

119886119901 Depth of cut (mm)

119891119911 Feed per tooth (mmz)

119905119888 Uncut chip thickness (mm)

] Poisson ratio of blade120575119905 Deflection value of tool

120575119887 Deflection value of blade

10 Advances in Materials Science and Engineering

0 50 100 150 200 250 300 350 400minus400

minus300

minus200

minus100

0

100

200

300

400

Flexible Rigid

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

Figure 17 Comparisons of cutting forces in flexible and rigidmodel

0 50 100 150 200minus1000

minus800

minus600

minus400

minus200

0

200

400

600

800

1000

Cutti

ng fo

rce (

N)

FxFyFz

Rotation angle (∘)

Figure 18 Simulated cutting forces in end milling

120575119908 Cutter bending deflection

120575119888 Clamping deflection

119870119903119888 119870119886119888 and119870

119905119888 Radial axial and tangential cutting forcecoefficients

119870119903119890119870119886119890 and119870

119905119890 Edge force coefficients

120595 Immersion angle of cutting point120601 Cutting element position angle120573 Angle between the 119884-axis and the

reference cutting flute120579 Angle between the cross-feed direction

and the cutting flute119870119888 Measured clamping stiffness of cutter

119903 Radius (mm)

119911 The number of teeth on the cutter119891119886 Axial feed (mmr)

119891119903 Radial feed (mmr)

119864 Elastic modulus of bladeℎ Thickness of blade119890119905119887 Surface error

119886119890 Radial depth of cut

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (NSFC) (51105072 and 51475087) sup-ported by the Fundamental Research Funds for the CentralUniversities (N150304005)

References

[1] U Karaguzel M Bakkal and E Budak ldquoProcess modeling ofturn-milling using analytical approachrdquo Procedia CIRP vol 4pp 131ndash139 2012

[2] U Karaguzel E Uysal E Budak and M Bakkal ldquoAnalyticalmodeling of turn-milling process geometry kinematics andmechanicsrdquo International Journal of Machine Tools amp Manufac-ture vol 91 pp 24ndash33 2015

[3] S Ekinovic E Begovic and A Silajdzija ldquoComparison ofmachined surface quality obtained by high-speed machiningand conventional turningrdquo Machining Science and Technologyvol 11 no 4 pp 531ndash551 2007

[4] S Skoric TUdiljak andDCiglar ldquoStudy of the suitability of themachining of rotating surfacesrdquoTransactions of Famena vol 32no 2 pp 69ndash83 2008

[5] M Pogacnik and J Kopac ldquoDynamic stabilization of the turn-milling process by parameter optimizationrdquo Proceedings of theInstitution of Mechanical Engineers Part B vol 214 no 2 pp127ndash135 2000

[6] S K Choudhury and J B Bajpai ldquoInvestigation in orthogonalturn-milling towards better surface finishrdquo Journal of MaterialsProcessing Technology vol 170 no 3 pp 487ndash493 2005

[7] S K Choudhury and K S Mangrulkar ldquoInvestigation oforthogonal turn-milling for the machining of rotationallysymmetrical work piecesrdquo Journal of Materials Processing Tech-nology vol 99 no 1 pp 120ndash128 2000

[8] A Calleja A Fernandez A Rodriguez L N de Lacalle andA Lamikiz ldquoTurn-milling of blades in turning centres andmultitasking machines controlling tool tilt anglerdquo Proceedingsof the Institution of Mechanical Engineers Part B Journal ofEngineering Manufacture vol 229 no 8 pp 1324ndash1336 2015

[9] C M Lee S W Kim Y H Lee and D W Lee ldquoThe optimalcutter orientation in ball end milling of cantilever-shaped thinplaterdquo Journal of Materials Processing Technology vol 153ndash154pp 900ndash906 2004

[10] M Fontaine A Moufki A Devillez and D Dudzinski ldquoMod-elling of cutting forces in ball-end milling with tool-surfaceinclination Part I predictive force model and experimentalvalidationrdquo Journal of Materials Processing Technology vol 189no 1ndash3 pp 73ndash84 2007

Advances in Materials Science and Engineering 11

[11] D Biermann P Kersting and T Surmann ldquoA general approachto simulating workpiece vibrations during five-axis milling ofturbine bladesrdquo CIRP AnnalsmdashManufacturing Technology vol59 no 1 pp 125ndash128 2010

[12] I Lazoglu Y Boz and H Erdim ldquoFive-axis milling mechanicsfor complex free form surfacesrdquo CIRP Annals-ManufacturingTechnology vol 60 no 1 pp 117ndash120 2011

[13] E Budak E Ozturk and L T Tunc ldquoModeling and simulationof 5-axismilling processesrdquoCIRPAnnalsmdashManufacturing Tech-nology vol 58 no 1 pp 347ndash350 2009

[14] E Budak ldquoImproving 5-axis milling operations using processmodelsrdquoMM Science Journal pp 358ndash365 2012

[15] E Ozturk and E Budak ldquoDynamics and stability of five-axis ball-end millingrdquo Journal of Manufacturing Science andEngineering vol 132 no 2 2010

[16] E Ozturk L T Tunc and E Budak ldquoInvestigation of leadand tilt angle effects in 5-axis ball-end milling processesrdquoInternational Journal of Machine Tools amp Manufacture vol 49no 14 pp 1053ndash1062 2009

[17] E Budak A Comak and E Ozturk ldquoStability and highperformance machining conditions in simultaneous millingrdquoCIRP AnnalsmdashManufacturing Technology vol 62 no 1 pp403ndash406 2013

[18] S Herranz F J Campa L N L De Lacalle et al ldquoThemilling of airframe components with low rigidity a generalapproach to avoid static and dynamic problemsrdquo Proceedingsof the Institution of Mechanical Engineers Part B Journal ofEngineering Manufacture vol 219 no 11 pp 789ndash801 2005

[19] D Olvera L N L de Lacalle F I Compean A Fz-ValdivielsoA Lamikiz and F J Campa ldquoAnalysis of the tool tip radialstiffness of turn-milling centersrdquo The International Journal ofAdvancedManufacturing Technology vol 60 no 9 pp 883ndash8912012

[20] A Lamikiz L N Lopez de Lacalle O Ocerin D Dıez and EMaidagan ldquoThe Denavit and Hartenberg approach applied toevaluate the consequences in the tool tip position of geometricalerrors in five-axis milling centresrdquo The International Journal ofAdvanced Manufacturing Technology vol 37 no 1 pp 122ndash1392008

[21] G M Kim B H Kim and C N Chu ldquoEstimation ofcutter deflection and form error in ball-end milling processesrdquoInternational Journal ofMachine Tools andManufacture vol 43no 9 pp 917ndash924 2003

[22] E B Kivanc and E Budak ldquoStructural modeling of end millsfor form error and stability analysisrdquo International Journal ofMachine ToolsampManufacture vol 44 no 11 pp 1151ndash1161 2004

[23] Q Cao J Zhao S Han and X Chen ldquoForce coefficientsidentification considering inclination angle for ball-end finishmillingrdquo Precision Engineering vol 36 no 2 pp 252ndash260 2012

[24] P Lee and Y Altintas ldquoPrediction of ball-end milling forcesfrom orthogonal cutting datardquo International Journal of MachineTools and Manufacture vol 36 no 9 pp 1059ndash1072 1996

Submit your manuscripts athttpwwwhindawicom

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MaterialsJournal of

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Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Advances in Materials Science and Engineering 5

Horizontalline

Tangent line

Blade shape

Y1Y2

Y3

O

a1a1

a2

a2

X3

X2

X1

F1

F2

h1

h2

Figure 5 Instantaneous thickness in blade machining

The equations of blade basin and back of blade areexpressed respectively as follows

119909119887

= 119909 cos 119886119887

+ (1198860+ 1198861119909 + 11988621199092

+ 11988631199093

+ 11988641199094

+ 11988651199095

) sin 119886119901

119910119887

= (1198860+ 1198861119909 + 11988621199092

+ 11988631199093

+ 11988641199094

+ 11988651199095

) cos 119886119901

minus 119909 sin 119886119901

(13)

119909119904

= 119909 cos 119886119904

+ (1198870+ 1198871119909 + 11988721199092

+ 11988731199093

+ 11988741199094

+ 11988751199095

) sin 119886119904

119910119904

= (1198870+ 1198871119909 + 11988721199092

+ 11988731199093

+ 11988741199094

+ 11988751199095

) cos 119886119904

minus 119909 sin 119886119904

(14)

For any cutting points the value of instantaneous thick-ness is calculated as follows

ℎ119887= 119910119887

1003816100381610038161003816119909119887minus 119910119904

1003816100381610038161003816119909119904

ℎ119904= 119910119887

1003816100381610038161003816119909119904minus 119910119904

1003816100381610038161003816119909119904

(15)

The instantaneous blade thickness curve can be obtainedas shown in Figure 6 Based on the formula the instantaneousstiffness on the point of cutter can be obtained

119896 =119864ℎ3

12 (1 minus ]2) (16)

The instantaneous stiffness is obtained based on (16) Itcan be seen from Figure 7 that stiffness of the cutting pointat the ends of the airfoil is relatively small while the localstiffness of the thicker intermediate is larger Using the curvedthin plate reciprocal theory solution of the problem can beobtained

minus10 0 10 20 30 40 50 60 700

10

20

30

40

50

60

Edge path (mm)

Thic

knes

s (m

m)

Back of bladeBasin of blade

Figure 6 Instantaneous blade thickness curve

Back of bladeBasin of blade

0 10 20 30 40 50 600

1

2

3

4

5

6

7

8

Edge path (mm)

Bend

ing

stiffn

ess (

mm

2kg

s2)

times109

Figure 7 Instantaneous stiffness on the point of cutter

44 Identification of Cutting Force Coefficients

441 Cutting Coefficients Model In order to calculate thecutting forces the edge-specific coefficients and the shear-specific coefficients need to be obtained beforehand whichare determined by materials and geometry of tool andworkpiece In the research proposed by Cao et al thesecoefficients are obtained from the experiments using theplanar surfaces [23] The coefficients can be calculated by

119870119905119888=

2120587

1198731198601

sdot

1198623119865119909119888minus (1198622minus 1198621) 119865119910119888

1198622

3+ (1198622minus 1198621)2

119870119903119888=

2120587

119873 (1198602

2+ 1198602

3)

6 Advances in Materials Science and Engineering

sdot [

1198602(1198622minus 1198621) 119865119909119888+ 1198623119865119910119888

1198622

3+ (1198622minus 1198621)2

minus1198603119865119911119888

1198625

]

119870119886119888=

2120587

119873 (1198602

2+ 1198602

3)

sdot [

1198603(1198622minus 1198621) 119865119909119888+ 1198623119865119910119888

1198622

3+ (1198622minus 1198621)2

+1198602119865119911119888

1198625

]

119870119905119890=minus2120587

1198731198611

sdot

1198624119865119909119890+ 1198625119865119910119890

1198622

4+ 1198622

5

119870119903119890=

2120587

119873 (1198612

2+ 1198612

3)

sdot [

1198612(1198625119865119909119890minus 1198624119865119910119890)

1198622

4+ 1198625

2+1198613119865119911119890

21198621

]

119870119903119890=

2120587

119873 (1198612

2+ 1198612

3)

sdot [

1198613(1198625119865119909119890minus 1198624119865119910119890)

1198622

4+ 1198622

5

minus1198612119865119911119890

21198621

]

(17)

where 119860119894 119861119894 and 119862

119894(119894 = 1 2 3 4 5) are the parameters

associated with start and exit radial immersion angles 120593stand 120593ex and with two boundaries of the position angles 120579minand 120579max 119865119902119888 and 119865119902119890 (119902 = 119883 119884 119885) are the average cuttingforce components for different inclination angles and couldbe obtained from following cutting tests

The relationship among them is shown as the followingthe details of the numerical procedure of computing param-eters are available in [23]

Where 119889119904(120579) = |119889119901(119883119862 119884119862 119885119862)119879

| =

radic(1198831015840

119862)2

+ (1198841015840

119862)2

+ (1198851015840

119862)2

119889120579 is the length of each differentialelement of the cutting edge (119883

119862 119884119862 119885119862) is the arbitrary

point on the cutting edge Consider

1198601= int

120579max

120579min

119877 sin 120579 119889120579

1198602= int

120579max

120579min

119877 sin 1205792119889120579

1198603= int

120579max

120579min

119877 sin 120579 cos 120579 119889120579

1198611= int

120579max

120579min

119889119904 (120579)

1198612= int

120579max

120579min

sin 120579 119889119904 (120579)

1198613= int

120579max

120579min

cos 120579 119889119904 (120579)

Table 1 Main parameters of machining center

Control system FANUC-OI (MC)control system

Maximum spindle speed 6000 rminStroke (119883119884119885) 850mm500mm630mmSpindle maximum torque 70909 (continuous30min) NMMaximum fast feed speed 119883 and 119884 24mmin 119885 15mminMaximum working load 500 kgPower 1175 KW

Workpiece Tool

Feed direction Engagement part

Figure 8 TH5650 vertical machining center

1198621=1

21205931003816100381610038161003816

120593ex120593st

1198622=1

4sin 21205931003816100381610038161003816

120593ex120593st

1198623=1

4cos 21205931003816100381610038161003816

120593ex120593st

1198624= sin1205931003816100381610038161003816

120593ex120593st

1198625= cos1205931003816100381610038161003816

120593ex120593st

(18)

442 Cutting Force Coefficient Identification Test Experi-mental cutting force coefficient identification was conductedusing the TH5650 vertical machining center (Figure 8) Thematerial used for the machining tests was Ti-6Al-4V (TC4)alloy A three-component Kistler dynamometer type Kistler9257B (Figure 9) has beenmounted on themachine table andthe coordinates system has been set to level with the forcesensor surfaces The tool has been chosen to ensure stabledepth of cut in milling a two-flute cutter with 10mm diam-eter has been selected and mounted with 20mm overhangon an HSK32ER20 tool-holder The main parameters of themachine are as in Table 1

In this experiment the cutting tool is a hard alloymaterial of the ball-end mill the milling cutter helix angleis 30 degrees whose diameter is 10mm Selection of millingparameters is as follows spindle speed 300 rmin each toothfeed (002 004 006)mmz and axial cutting deep (1 23)mm

Advances in Materials Science and Engineering 7

Table 2 Milling test data

Test ID Spindle speed119899 (rmin)

Feed pertooth

119888 (mm119911)

Axial cuttingdepth119886119901(mm)

119883 axialperiodic force

119865119909(N)

119884 axialperiodic force

119865119910(N)

119885 axialperiodic force

119865119911(N)

1 300 002 1 minus5032 9223 10732 300 004 1 minus7258 10572 20453 300 006 1 minus9683 12034 53124 300 002 2 minus4436 19876 129565 300 004 2 minus3288 23766 88926 300 006 2 minus1225 30654 42787 300 002 3 minus197 38725 2378 300 004 3 2278 44944 minus3946

9 300 006 3 1657 58689 minus7683

Table 3 Cutting force coefficient

Cutting forceparameter

Numerical(Mpa)

Cutting forceparameter

Numerical(Nm)

119870119905119888

15998 119870119905119890

207119870119903119888

5201 119870119903119890

428119870119886119888

6482 119870119886119890

79

Dynamometer

Figure 9 Kistler 9257B dynamometer

A series of experimental data was obtained as shown inTable 2

From the experimental data in (17) by analyzing therelationship of cutting force the cutting coefficient is shownin Table 3

5 Simulation Analysis ofBall-End Cutting Force

51 Prediction and Simulation of Milling Force The influenceof cutting parameter and geometer parameter of tool oncutting forces is analyzed by turn-milling process The ballmilling cutting force is simulated based on the model ofmilling force by using MATLAB program in the differentcutting parameters The titanium alloy is used as workpiecematerial The diameter of cutter is 10mm The depth of cutis 05mm The different cutting force simulation results areshown in Figures 10ndash15 as follows

0 50 100 150 200 250 300 350 400minus400

minus300

minus200

minus100

0

100

200

300

400

500

600

F (N

)

Cutter rotation angle (∘)

FxiFyi

FziF

(Small symbol ae = 12R big symbol ae = 16R)

Figure 10 Effect of cutting width 119886119890on cutting force

511 The Influence of Cutting Width and Tilt Angle on CuttingForce Similarly when the cutting depth is reduced cuttingforces in three directions119883119884 and119885 are all decreased wherethe magnitudes of decreases are relatively large and the totalcutting force becomes smaller from Figure 10 But when thecutting depth is reduced cutting-in angle is constant whilecutting-out angle becomes smaller As can be seen fromFigure 11 cutting force decreases with increasing of dip Sothe tilt angle can be increased to reduce the cutting forceduring processing

512 The Influence of Tooth Number and Cutting Depth onCutting Force It can be noticed from Figure 12 the change ofmilling cutter blade has no effect on the cutting force but itaffects the numbers of milling force cycle in a rotary cuttercycle The numbers of milling force cycle are equal to thenumber of milling cutter blade and entrance angle and exitangle go backwards with the increasing number of cuttingedge

8 Advances in Materials Science and Engineering

0 50 100 150 200 250 300 350 400minus300

minus200

minus100

0

100

200

300

400

500(Small symbol l = 25∘ big symbol l = 15∘)

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

Figure 11 Effect of tilt angle on cutting force

0 50 100 150 200 250 300 350 400minus100

minus50

0

50

100

150

200

250

300

350

400

450

N = 2N = 3

Cutter rotation angle (∘)

F (N

)

Figure 12 Effect of tooth number on cutting force

When the cutting depth is reduced cutting forces in threedirections119883 119884 and 119885 are all decreased and the total cuttingforce becomes smaller from Figure 13 But when the cuttingdepth decreases entrance angle and exit angle are constant

513 The Influence of Cutter Diameter on Cutting ForceWhen focusing on the effect of cutter diameter on cuttingforce the larger the cutter diameter is the larger the cuttingforce becomes no matter whether it is a given value or not inFigure 14 With the change of cutter diameter entrance angleremains unchanged while exit angle changes

514 The Influence of Cutter Diameter and Feed on CuttingForce It can be noticed from Figure 15 that cutting forceand cutting-in angle are not affected by different helix angleBut the cutting-out angle will be bigger when the helix angleincreases The last parameter is the rational speed Feed has

0 50 100 150 200 250 300 350 4000

100

200

300

400

500

600

Cutter rotation angle (∘)

ap = 08mm

ap = 10mm

ap = 12mm

F (N

)

Figure 13 Effect of cutting depth on cutting force

a great impact on the maximum cutting force as shown inFigure 16 And slight increase can cause large changes ofthe total cutting force so that the amount of feed should beselected with season during processing

52 Comparison of Rigid and Flexible Cutting Force Inorder to illustrate the contribution of flexible cutting forcecomparison of flexible cutting forces and rigid cutting forceswas simulated based on the same cutting conditions inFigure 15

It can be seen from Figure 17 that flexible cutting force issmaller than rigid cutting force in differential direction butthe value is more by 19N in the 119883 direction Consequentlyit is necessary that the flexible model of cutting force isanalyzed For the validation of the model another simulation(in Figure 18) is conducted in the same cutting condition[24] as follows 119886

119899= 0 spindle speed = 269 rmin 119877

0=

9526mm 1198940= 30 st = 00508mm and 119886

119901= 635mm

The predicted cutting forces are compared and matched wellwith the experiment [24] Therefore it provides a theoreticalfoundation and reference for the turn-milling mechanismresearch

6 Conclusions

In this paper the cutting force of blade by turn-milling wasstudied in cutting parameters A rigid model and a flexiblemodel of cutting force with ball-end cutter are establishedrespectively based on the analysis of space geometry of theball-end mill and blades Some suggestions are providedto choose cutting parameters to reduce cutting forces andreach high productivity This study will provide a theoreticalfoundation and reference for the turn-milling mechanismresearch Based on this work the following conclusions canbe drawn

(i) The influences of cutting parameters and geometryshape of cutter on the cutting forces are analyzedby turn-milling The deformation values of blade

Advances in Materials Science and Engineering 9

0 50 100 150 200 250 300 350 400minus300

minus200

minus100

0

100

200

300

400

500

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

(a) 119886119890is a multiple of the diameter

0 50 100 150 200 250 300 350 400minus400

minus300

minus200

minus100

0

100

200

300

400

500

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

(b) 119886119890is constant

Figure 14 Effect of cutter diameter on cutting force (big symbol119863 = 8mm small symbol119863 = 5mm)

0 50 100 150 200 250 300 350 400minus300

minus200

minus100

0

100

200

300

400

500

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

(Big symbol 120573 = small symbol 120573 = 18∘)38∘

Figure 15 Effect of helix angle on cutting force

and cutter on the engaged trajectory are calculatedrespectively by using the iterative algorithm

(ii) In milling blades case cutting force is sensitive to theamount of feed but the influence of helix angle is thesmallestThe amount of deformation of the blade willnot be the same in a different thickness position ofthe bladeThe thinner the thickness is the greater thebending deformation becomes And cutting force isalso affected by the deformation

(iii) In milling titanium blades case flexible cutting forceis smaller than rigid cutting force in each direction

0 50 100 150 200 250 300 350 4000

50

100

150

200

250

300

350

400

450

500

Cutter rotation angle (∘)

= 01mms

= 02mms

= 03mms

F (N

)

Figure 16 Effect of feed on cutting force

but it is less 20N Since stiffness of titanium alloy isrelatively large the deformation of titanium alloy issmall and deformation of the tool is of the order ofminus5 times

Nomenclature

119899119905 Rotation speed of cutter (rmin)

119899119887 Rotation speed of blade (rmin)

119886119901 Depth of cut (mm)

119891119911 Feed per tooth (mmz)

119905119888 Uncut chip thickness (mm)

] Poisson ratio of blade120575119905 Deflection value of tool

120575119887 Deflection value of blade

10 Advances in Materials Science and Engineering

0 50 100 150 200 250 300 350 400minus400

minus300

minus200

minus100

0

100

200

300

400

Flexible Rigid

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

Figure 17 Comparisons of cutting forces in flexible and rigidmodel

0 50 100 150 200minus1000

minus800

minus600

minus400

minus200

0

200

400

600

800

1000

Cutti

ng fo

rce (

N)

FxFyFz

Rotation angle (∘)

Figure 18 Simulated cutting forces in end milling

120575119908 Cutter bending deflection

120575119888 Clamping deflection

119870119903119888 119870119886119888 and119870

119905119888 Radial axial and tangential cutting forcecoefficients

119870119903119890119870119886119890 and119870

119905119890 Edge force coefficients

120595 Immersion angle of cutting point120601 Cutting element position angle120573 Angle between the 119884-axis and the

reference cutting flute120579 Angle between the cross-feed direction

and the cutting flute119870119888 Measured clamping stiffness of cutter

119903 Radius (mm)

119911 The number of teeth on the cutter119891119886 Axial feed (mmr)

119891119903 Radial feed (mmr)

119864 Elastic modulus of bladeℎ Thickness of blade119890119905119887 Surface error

119886119890 Radial depth of cut

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (NSFC) (51105072 and 51475087) sup-ported by the Fundamental Research Funds for the CentralUniversities (N150304005)

References

[1] U Karaguzel M Bakkal and E Budak ldquoProcess modeling ofturn-milling using analytical approachrdquo Procedia CIRP vol 4pp 131ndash139 2012

[2] U Karaguzel E Uysal E Budak and M Bakkal ldquoAnalyticalmodeling of turn-milling process geometry kinematics andmechanicsrdquo International Journal of Machine Tools amp Manufac-ture vol 91 pp 24ndash33 2015

[3] S Ekinovic E Begovic and A Silajdzija ldquoComparison ofmachined surface quality obtained by high-speed machiningand conventional turningrdquo Machining Science and Technologyvol 11 no 4 pp 531ndash551 2007

[4] S Skoric TUdiljak andDCiglar ldquoStudy of the suitability of themachining of rotating surfacesrdquoTransactions of Famena vol 32no 2 pp 69ndash83 2008

[5] M Pogacnik and J Kopac ldquoDynamic stabilization of the turn-milling process by parameter optimizationrdquo Proceedings of theInstitution of Mechanical Engineers Part B vol 214 no 2 pp127ndash135 2000

[6] S K Choudhury and J B Bajpai ldquoInvestigation in orthogonalturn-milling towards better surface finishrdquo Journal of MaterialsProcessing Technology vol 170 no 3 pp 487ndash493 2005

[7] S K Choudhury and K S Mangrulkar ldquoInvestigation oforthogonal turn-milling for the machining of rotationallysymmetrical work piecesrdquo Journal of Materials Processing Tech-nology vol 99 no 1 pp 120ndash128 2000

[8] A Calleja A Fernandez A Rodriguez L N de Lacalle andA Lamikiz ldquoTurn-milling of blades in turning centres andmultitasking machines controlling tool tilt anglerdquo Proceedingsof the Institution of Mechanical Engineers Part B Journal ofEngineering Manufacture vol 229 no 8 pp 1324ndash1336 2015

[9] C M Lee S W Kim Y H Lee and D W Lee ldquoThe optimalcutter orientation in ball end milling of cantilever-shaped thinplaterdquo Journal of Materials Processing Technology vol 153ndash154pp 900ndash906 2004

[10] M Fontaine A Moufki A Devillez and D Dudzinski ldquoMod-elling of cutting forces in ball-end milling with tool-surfaceinclination Part I predictive force model and experimentalvalidationrdquo Journal of Materials Processing Technology vol 189no 1ndash3 pp 73ndash84 2007

Advances in Materials Science and Engineering 11

[11] D Biermann P Kersting and T Surmann ldquoA general approachto simulating workpiece vibrations during five-axis milling ofturbine bladesrdquo CIRP AnnalsmdashManufacturing Technology vol59 no 1 pp 125ndash128 2010

[12] I Lazoglu Y Boz and H Erdim ldquoFive-axis milling mechanicsfor complex free form surfacesrdquo CIRP Annals-ManufacturingTechnology vol 60 no 1 pp 117ndash120 2011

[13] E Budak E Ozturk and L T Tunc ldquoModeling and simulationof 5-axismilling processesrdquoCIRPAnnalsmdashManufacturing Tech-nology vol 58 no 1 pp 347ndash350 2009

[14] E Budak ldquoImproving 5-axis milling operations using processmodelsrdquoMM Science Journal pp 358ndash365 2012

[15] E Ozturk and E Budak ldquoDynamics and stability of five-axis ball-end millingrdquo Journal of Manufacturing Science andEngineering vol 132 no 2 2010

[16] E Ozturk L T Tunc and E Budak ldquoInvestigation of leadand tilt angle effects in 5-axis ball-end milling processesrdquoInternational Journal of Machine Tools amp Manufacture vol 49no 14 pp 1053ndash1062 2009

[17] E Budak A Comak and E Ozturk ldquoStability and highperformance machining conditions in simultaneous millingrdquoCIRP AnnalsmdashManufacturing Technology vol 62 no 1 pp403ndash406 2013

[18] S Herranz F J Campa L N L De Lacalle et al ldquoThemilling of airframe components with low rigidity a generalapproach to avoid static and dynamic problemsrdquo Proceedingsof the Institution of Mechanical Engineers Part B Journal ofEngineering Manufacture vol 219 no 11 pp 789ndash801 2005

[19] D Olvera L N L de Lacalle F I Compean A Fz-ValdivielsoA Lamikiz and F J Campa ldquoAnalysis of the tool tip radialstiffness of turn-milling centersrdquo The International Journal ofAdvancedManufacturing Technology vol 60 no 9 pp 883ndash8912012

[20] A Lamikiz L N Lopez de Lacalle O Ocerin D Dıez and EMaidagan ldquoThe Denavit and Hartenberg approach applied toevaluate the consequences in the tool tip position of geometricalerrors in five-axis milling centresrdquo The International Journal ofAdvanced Manufacturing Technology vol 37 no 1 pp 122ndash1392008

[21] G M Kim B H Kim and C N Chu ldquoEstimation ofcutter deflection and form error in ball-end milling processesrdquoInternational Journal ofMachine Tools andManufacture vol 43no 9 pp 917ndash924 2003

[22] E B Kivanc and E Budak ldquoStructural modeling of end millsfor form error and stability analysisrdquo International Journal ofMachine ToolsampManufacture vol 44 no 11 pp 1151ndash1161 2004

[23] Q Cao J Zhao S Han and X Chen ldquoForce coefficientsidentification considering inclination angle for ball-end finishmillingrdquo Precision Engineering vol 36 no 2 pp 252ndash260 2012

[24] P Lee and Y Altintas ldquoPrediction of ball-end milling forcesfrom orthogonal cutting datardquo International Journal of MachineTools and Manufacture vol 36 no 9 pp 1059ndash1072 1996

Submit your manuscripts athttpwwwhindawicom

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Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

6 Advances in Materials Science and Engineering

sdot [

1198602(1198622minus 1198621) 119865119909119888+ 1198623119865119910119888

1198622

3+ (1198622minus 1198621)2

minus1198603119865119911119888

1198625

]

119870119886119888=

2120587

119873 (1198602

2+ 1198602

3)

sdot [

1198603(1198622minus 1198621) 119865119909119888+ 1198623119865119910119888

1198622

3+ (1198622minus 1198621)2

+1198602119865119911119888

1198625

]

119870119905119890=minus2120587

1198731198611

sdot

1198624119865119909119890+ 1198625119865119910119890

1198622

4+ 1198622

5

119870119903119890=

2120587

119873 (1198612

2+ 1198612

3)

sdot [

1198612(1198625119865119909119890minus 1198624119865119910119890)

1198622

4+ 1198625

2+1198613119865119911119890

21198621

]

119870119903119890=

2120587

119873 (1198612

2+ 1198612

3)

sdot [

1198613(1198625119865119909119890minus 1198624119865119910119890)

1198622

4+ 1198622

5

minus1198612119865119911119890

21198621

]

(17)

where 119860119894 119861119894 and 119862

119894(119894 = 1 2 3 4 5) are the parameters

associated with start and exit radial immersion angles 120593stand 120593ex and with two boundaries of the position angles 120579minand 120579max 119865119902119888 and 119865119902119890 (119902 = 119883 119884 119885) are the average cuttingforce components for different inclination angles and couldbe obtained from following cutting tests

The relationship among them is shown as the followingthe details of the numerical procedure of computing param-eters are available in [23]

Where 119889119904(120579) = |119889119901(119883119862 119884119862 119885119862)119879

| =

radic(1198831015840

119862)2

+ (1198841015840

119862)2

+ (1198851015840

119862)2

119889120579 is the length of each differentialelement of the cutting edge (119883

119862 119884119862 119885119862) is the arbitrary

point on the cutting edge Consider

1198601= int

120579max

120579min

119877 sin 120579 119889120579

1198602= int

120579max

120579min

119877 sin 1205792119889120579

1198603= int

120579max

120579min

119877 sin 120579 cos 120579 119889120579

1198611= int

120579max

120579min

119889119904 (120579)

1198612= int

120579max

120579min

sin 120579 119889119904 (120579)

1198613= int

120579max

120579min

cos 120579 119889119904 (120579)

Table 1 Main parameters of machining center

Control system FANUC-OI (MC)control system

Maximum spindle speed 6000 rminStroke (119883119884119885) 850mm500mm630mmSpindle maximum torque 70909 (continuous30min) NMMaximum fast feed speed 119883 and 119884 24mmin 119885 15mminMaximum working load 500 kgPower 1175 KW

Workpiece Tool

Feed direction Engagement part

Figure 8 TH5650 vertical machining center

1198621=1

21205931003816100381610038161003816

120593ex120593st

1198622=1

4sin 21205931003816100381610038161003816

120593ex120593st

1198623=1

4cos 21205931003816100381610038161003816

120593ex120593st

1198624= sin1205931003816100381610038161003816

120593ex120593st

1198625= cos1205931003816100381610038161003816

120593ex120593st

(18)

442 Cutting Force Coefficient Identification Test Experi-mental cutting force coefficient identification was conductedusing the TH5650 vertical machining center (Figure 8) Thematerial used for the machining tests was Ti-6Al-4V (TC4)alloy A three-component Kistler dynamometer type Kistler9257B (Figure 9) has beenmounted on themachine table andthe coordinates system has been set to level with the forcesensor surfaces The tool has been chosen to ensure stabledepth of cut in milling a two-flute cutter with 10mm diam-eter has been selected and mounted with 20mm overhangon an HSK32ER20 tool-holder The main parameters of themachine are as in Table 1

In this experiment the cutting tool is a hard alloymaterial of the ball-end mill the milling cutter helix angleis 30 degrees whose diameter is 10mm Selection of millingparameters is as follows spindle speed 300 rmin each toothfeed (002 004 006)mmz and axial cutting deep (1 23)mm

Advances in Materials Science and Engineering 7

Table 2 Milling test data

Test ID Spindle speed119899 (rmin)

Feed pertooth

119888 (mm119911)

Axial cuttingdepth119886119901(mm)

119883 axialperiodic force

119865119909(N)

119884 axialperiodic force

119865119910(N)

119885 axialperiodic force

119865119911(N)

1 300 002 1 minus5032 9223 10732 300 004 1 minus7258 10572 20453 300 006 1 minus9683 12034 53124 300 002 2 minus4436 19876 129565 300 004 2 minus3288 23766 88926 300 006 2 minus1225 30654 42787 300 002 3 minus197 38725 2378 300 004 3 2278 44944 minus3946

9 300 006 3 1657 58689 minus7683

Table 3 Cutting force coefficient

Cutting forceparameter

Numerical(Mpa)

Cutting forceparameter

Numerical(Nm)

119870119905119888

15998 119870119905119890

207119870119903119888

5201 119870119903119890

428119870119886119888

6482 119870119886119890

79

Dynamometer

Figure 9 Kistler 9257B dynamometer

A series of experimental data was obtained as shown inTable 2

From the experimental data in (17) by analyzing therelationship of cutting force the cutting coefficient is shownin Table 3

5 Simulation Analysis ofBall-End Cutting Force

51 Prediction and Simulation of Milling Force The influenceof cutting parameter and geometer parameter of tool oncutting forces is analyzed by turn-milling process The ballmilling cutting force is simulated based on the model ofmilling force by using MATLAB program in the differentcutting parameters The titanium alloy is used as workpiecematerial The diameter of cutter is 10mm The depth of cutis 05mm The different cutting force simulation results areshown in Figures 10ndash15 as follows

0 50 100 150 200 250 300 350 400minus400

minus300

minus200

minus100

0

100

200

300

400

500

600

F (N

)

Cutter rotation angle (∘)

FxiFyi

FziF

(Small symbol ae = 12R big symbol ae = 16R)

Figure 10 Effect of cutting width 119886119890on cutting force

511 The Influence of Cutting Width and Tilt Angle on CuttingForce Similarly when the cutting depth is reduced cuttingforces in three directions119883119884 and119885 are all decreased wherethe magnitudes of decreases are relatively large and the totalcutting force becomes smaller from Figure 10 But when thecutting depth is reduced cutting-in angle is constant whilecutting-out angle becomes smaller As can be seen fromFigure 11 cutting force decreases with increasing of dip Sothe tilt angle can be increased to reduce the cutting forceduring processing

512 The Influence of Tooth Number and Cutting Depth onCutting Force It can be noticed from Figure 12 the change ofmilling cutter blade has no effect on the cutting force but itaffects the numbers of milling force cycle in a rotary cuttercycle The numbers of milling force cycle are equal to thenumber of milling cutter blade and entrance angle and exitangle go backwards with the increasing number of cuttingedge

8 Advances in Materials Science and Engineering

0 50 100 150 200 250 300 350 400minus300

minus200

minus100

0

100

200

300

400

500(Small symbol l = 25∘ big symbol l = 15∘)

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

Figure 11 Effect of tilt angle on cutting force

0 50 100 150 200 250 300 350 400minus100

minus50

0

50

100

150

200

250

300

350

400

450

N = 2N = 3

Cutter rotation angle (∘)

F (N

)

Figure 12 Effect of tooth number on cutting force

When the cutting depth is reduced cutting forces in threedirections119883 119884 and 119885 are all decreased and the total cuttingforce becomes smaller from Figure 13 But when the cuttingdepth decreases entrance angle and exit angle are constant

513 The Influence of Cutter Diameter on Cutting ForceWhen focusing on the effect of cutter diameter on cuttingforce the larger the cutter diameter is the larger the cuttingforce becomes no matter whether it is a given value or not inFigure 14 With the change of cutter diameter entrance angleremains unchanged while exit angle changes

514 The Influence of Cutter Diameter and Feed on CuttingForce It can be noticed from Figure 15 that cutting forceand cutting-in angle are not affected by different helix angleBut the cutting-out angle will be bigger when the helix angleincreases The last parameter is the rational speed Feed has

0 50 100 150 200 250 300 350 4000

100

200

300

400

500

600

Cutter rotation angle (∘)

ap = 08mm

ap = 10mm

ap = 12mm

F (N

)

Figure 13 Effect of cutting depth on cutting force

a great impact on the maximum cutting force as shown inFigure 16 And slight increase can cause large changes ofthe total cutting force so that the amount of feed should beselected with season during processing

52 Comparison of Rigid and Flexible Cutting Force Inorder to illustrate the contribution of flexible cutting forcecomparison of flexible cutting forces and rigid cutting forceswas simulated based on the same cutting conditions inFigure 15

It can be seen from Figure 17 that flexible cutting force issmaller than rigid cutting force in differential direction butthe value is more by 19N in the 119883 direction Consequentlyit is necessary that the flexible model of cutting force isanalyzed For the validation of the model another simulation(in Figure 18) is conducted in the same cutting condition[24] as follows 119886

119899= 0 spindle speed = 269 rmin 119877

0=

9526mm 1198940= 30 st = 00508mm and 119886

119901= 635mm

The predicted cutting forces are compared and matched wellwith the experiment [24] Therefore it provides a theoreticalfoundation and reference for the turn-milling mechanismresearch

6 Conclusions

In this paper the cutting force of blade by turn-milling wasstudied in cutting parameters A rigid model and a flexiblemodel of cutting force with ball-end cutter are establishedrespectively based on the analysis of space geometry of theball-end mill and blades Some suggestions are providedto choose cutting parameters to reduce cutting forces andreach high productivity This study will provide a theoreticalfoundation and reference for the turn-milling mechanismresearch Based on this work the following conclusions canbe drawn

(i) The influences of cutting parameters and geometryshape of cutter on the cutting forces are analyzedby turn-milling The deformation values of blade

Advances in Materials Science and Engineering 9

0 50 100 150 200 250 300 350 400minus300

minus200

minus100

0

100

200

300

400

500

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

(a) 119886119890is a multiple of the diameter

0 50 100 150 200 250 300 350 400minus400

minus300

minus200

minus100

0

100

200

300

400

500

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

(b) 119886119890is constant

Figure 14 Effect of cutter diameter on cutting force (big symbol119863 = 8mm small symbol119863 = 5mm)

0 50 100 150 200 250 300 350 400minus300

minus200

minus100

0

100

200

300

400

500

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

(Big symbol 120573 = small symbol 120573 = 18∘)38∘

Figure 15 Effect of helix angle on cutting force

and cutter on the engaged trajectory are calculatedrespectively by using the iterative algorithm

(ii) In milling blades case cutting force is sensitive to theamount of feed but the influence of helix angle is thesmallestThe amount of deformation of the blade willnot be the same in a different thickness position ofthe bladeThe thinner the thickness is the greater thebending deformation becomes And cutting force isalso affected by the deformation

(iii) In milling titanium blades case flexible cutting forceis smaller than rigid cutting force in each direction

0 50 100 150 200 250 300 350 4000

50

100

150

200

250

300

350

400

450

500

Cutter rotation angle (∘)

= 01mms

= 02mms

= 03mms

F (N

)

Figure 16 Effect of feed on cutting force

but it is less 20N Since stiffness of titanium alloy isrelatively large the deformation of titanium alloy issmall and deformation of the tool is of the order ofminus5 times

Nomenclature

119899119905 Rotation speed of cutter (rmin)

119899119887 Rotation speed of blade (rmin)

119886119901 Depth of cut (mm)

119891119911 Feed per tooth (mmz)

119905119888 Uncut chip thickness (mm)

] Poisson ratio of blade120575119905 Deflection value of tool

120575119887 Deflection value of blade

10 Advances in Materials Science and Engineering

0 50 100 150 200 250 300 350 400minus400

minus300

minus200

minus100

0

100

200

300

400

Flexible Rigid

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

Figure 17 Comparisons of cutting forces in flexible and rigidmodel

0 50 100 150 200minus1000

minus800

minus600

minus400

minus200

0

200

400

600

800

1000

Cutti

ng fo

rce (

N)

FxFyFz

Rotation angle (∘)

Figure 18 Simulated cutting forces in end milling

120575119908 Cutter bending deflection

120575119888 Clamping deflection

119870119903119888 119870119886119888 and119870

119905119888 Radial axial and tangential cutting forcecoefficients

119870119903119890119870119886119890 and119870

119905119890 Edge force coefficients

120595 Immersion angle of cutting point120601 Cutting element position angle120573 Angle between the 119884-axis and the

reference cutting flute120579 Angle between the cross-feed direction

and the cutting flute119870119888 Measured clamping stiffness of cutter

119903 Radius (mm)

119911 The number of teeth on the cutter119891119886 Axial feed (mmr)

119891119903 Radial feed (mmr)

119864 Elastic modulus of bladeℎ Thickness of blade119890119905119887 Surface error

119886119890 Radial depth of cut

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (NSFC) (51105072 and 51475087) sup-ported by the Fundamental Research Funds for the CentralUniversities (N150304005)

References

[1] U Karaguzel M Bakkal and E Budak ldquoProcess modeling ofturn-milling using analytical approachrdquo Procedia CIRP vol 4pp 131ndash139 2012

[2] U Karaguzel E Uysal E Budak and M Bakkal ldquoAnalyticalmodeling of turn-milling process geometry kinematics andmechanicsrdquo International Journal of Machine Tools amp Manufac-ture vol 91 pp 24ndash33 2015

[3] S Ekinovic E Begovic and A Silajdzija ldquoComparison ofmachined surface quality obtained by high-speed machiningand conventional turningrdquo Machining Science and Technologyvol 11 no 4 pp 531ndash551 2007

[4] S Skoric TUdiljak andDCiglar ldquoStudy of the suitability of themachining of rotating surfacesrdquoTransactions of Famena vol 32no 2 pp 69ndash83 2008

[5] M Pogacnik and J Kopac ldquoDynamic stabilization of the turn-milling process by parameter optimizationrdquo Proceedings of theInstitution of Mechanical Engineers Part B vol 214 no 2 pp127ndash135 2000

[6] S K Choudhury and J B Bajpai ldquoInvestigation in orthogonalturn-milling towards better surface finishrdquo Journal of MaterialsProcessing Technology vol 170 no 3 pp 487ndash493 2005

[7] S K Choudhury and K S Mangrulkar ldquoInvestigation oforthogonal turn-milling for the machining of rotationallysymmetrical work piecesrdquo Journal of Materials Processing Tech-nology vol 99 no 1 pp 120ndash128 2000

[8] A Calleja A Fernandez A Rodriguez L N de Lacalle andA Lamikiz ldquoTurn-milling of blades in turning centres andmultitasking machines controlling tool tilt anglerdquo Proceedingsof the Institution of Mechanical Engineers Part B Journal ofEngineering Manufacture vol 229 no 8 pp 1324ndash1336 2015

[9] C M Lee S W Kim Y H Lee and D W Lee ldquoThe optimalcutter orientation in ball end milling of cantilever-shaped thinplaterdquo Journal of Materials Processing Technology vol 153ndash154pp 900ndash906 2004

[10] M Fontaine A Moufki A Devillez and D Dudzinski ldquoMod-elling of cutting forces in ball-end milling with tool-surfaceinclination Part I predictive force model and experimentalvalidationrdquo Journal of Materials Processing Technology vol 189no 1ndash3 pp 73ndash84 2007

Advances in Materials Science and Engineering 11

[11] D Biermann P Kersting and T Surmann ldquoA general approachto simulating workpiece vibrations during five-axis milling ofturbine bladesrdquo CIRP AnnalsmdashManufacturing Technology vol59 no 1 pp 125ndash128 2010

[12] I Lazoglu Y Boz and H Erdim ldquoFive-axis milling mechanicsfor complex free form surfacesrdquo CIRP Annals-ManufacturingTechnology vol 60 no 1 pp 117ndash120 2011

[13] E Budak E Ozturk and L T Tunc ldquoModeling and simulationof 5-axismilling processesrdquoCIRPAnnalsmdashManufacturing Tech-nology vol 58 no 1 pp 347ndash350 2009

[14] E Budak ldquoImproving 5-axis milling operations using processmodelsrdquoMM Science Journal pp 358ndash365 2012

[15] E Ozturk and E Budak ldquoDynamics and stability of five-axis ball-end millingrdquo Journal of Manufacturing Science andEngineering vol 132 no 2 2010

[16] E Ozturk L T Tunc and E Budak ldquoInvestigation of leadand tilt angle effects in 5-axis ball-end milling processesrdquoInternational Journal of Machine Tools amp Manufacture vol 49no 14 pp 1053ndash1062 2009

[17] E Budak A Comak and E Ozturk ldquoStability and highperformance machining conditions in simultaneous millingrdquoCIRP AnnalsmdashManufacturing Technology vol 62 no 1 pp403ndash406 2013

[18] S Herranz F J Campa L N L De Lacalle et al ldquoThemilling of airframe components with low rigidity a generalapproach to avoid static and dynamic problemsrdquo Proceedingsof the Institution of Mechanical Engineers Part B Journal ofEngineering Manufacture vol 219 no 11 pp 789ndash801 2005

[19] D Olvera L N L de Lacalle F I Compean A Fz-ValdivielsoA Lamikiz and F J Campa ldquoAnalysis of the tool tip radialstiffness of turn-milling centersrdquo The International Journal ofAdvancedManufacturing Technology vol 60 no 9 pp 883ndash8912012

[20] A Lamikiz L N Lopez de Lacalle O Ocerin D Dıez and EMaidagan ldquoThe Denavit and Hartenberg approach applied toevaluate the consequences in the tool tip position of geometricalerrors in five-axis milling centresrdquo The International Journal ofAdvanced Manufacturing Technology vol 37 no 1 pp 122ndash1392008

[21] G M Kim B H Kim and C N Chu ldquoEstimation ofcutter deflection and form error in ball-end milling processesrdquoInternational Journal ofMachine Tools andManufacture vol 43no 9 pp 917ndash924 2003

[22] E B Kivanc and E Budak ldquoStructural modeling of end millsfor form error and stability analysisrdquo International Journal ofMachine ToolsampManufacture vol 44 no 11 pp 1151ndash1161 2004

[23] Q Cao J Zhao S Han and X Chen ldquoForce coefficientsidentification considering inclination angle for ball-end finishmillingrdquo Precision Engineering vol 36 no 2 pp 252ndash260 2012

[24] P Lee and Y Altintas ldquoPrediction of ball-end milling forcesfrom orthogonal cutting datardquo International Journal of MachineTools and Manufacture vol 36 no 9 pp 1059ndash1072 1996

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Advances in Materials Science and Engineering 7

Table 2 Milling test data

Test ID Spindle speed119899 (rmin)

Feed pertooth

119888 (mm119911)

Axial cuttingdepth119886119901(mm)

119883 axialperiodic force

119865119909(N)

119884 axialperiodic force

119865119910(N)

119885 axialperiodic force

119865119911(N)

1 300 002 1 minus5032 9223 10732 300 004 1 minus7258 10572 20453 300 006 1 minus9683 12034 53124 300 002 2 minus4436 19876 129565 300 004 2 minus3288 23766 88926 300 006 2 minus1225 30654 42787 300 002 3 minus197 38725 2378 300 004 3 2278 44944 minus3946

9 300 006 3 1657 58689 minus7683

Table 3 Cutting force coefficient

Cutting forceparameter

Numerical(Mpa)

Cutting forceparameter

Numerical(Nm)

119870119905119888

15998 119870119905119890

207119870119903119888

5201 119870119903119890

428119870119886119888

6482 119870119886119890

79

Dynamometer

Figure 9 Kistler 9257B dynamometer

A series of experimental data was obtained as shown inTable 2

From the experimental data in (17) by analyzing therelationship of cutting force the cutting coefficient is shownin Table 3

5 Simulation Analysis ofBall-End Cutting Force

51 Prediction and Simulation of Milling Force The influenceof cutting parameter and geometer parameter of tool oncutting forces is analyzed by turn-milling process The ballmilling cutting force is simulated based on the model ofmilling force by using MATLAB program in the differentcutting parameters The titanium alloy is used as workpiecematerial The diameter of cutter is 10mm The depth of cutis 05mm The different cutting force simulation results areshown in Figures 10ndash15 as follows

0 50 100 150 200 250 300 350 400minus400

minus300

minus200

minus100

0

100

200

300

400

500

600

F (N

)

Cutter rotation angle (∘)

FxiFyi

FziF

(Small symbol ae = 12R big symbol ae = 16R)

Figure 10 Effect of cutting width 119886119890on cutting force

511 The Influence of Cutting Width and Tilt Angle on CuttingForce Similarly when the cutting depth is reduced cuttingforces in three directions119883119884 and119885 are all decreased wherethe magnitudes of decreases are relatively large and the totalcutting force becomes smaller from Figure 10 But when thecutting depth is reduced cutting-in angle is constant whilecutting-out angle becomes smaller As can be seen fromFigure 11 cutting force decreases with increasing of dip Sothe tilt angle can be increased to reduce the cutting forceduring processing

512 The Influence of Tooth Number and Cutting Depth onCutting Force It can be noticed from Figure 12 the change ofmilling cutter blade has no effect on the cutting force but itaffects the numbers of milling force cycle in a rotary cuttercycle The numbers of milling force cycle are equal to thenumber of milling cutter blade and entrance angle and exitangle go backwards with the increasing number of cuttingedge

8 Advances in Materials Science and Engineering

0 50 100 150 200 250 300 350 400minus300

minus200

minus100

0

100

200

300

400

500(Small symbol l = 25∘ big symbol l = 15∘)

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

Figure 11 Effect of tilt angle on cutting force

0 50 100 150 200 250 300 350 400minus100

minus50

0

50

100

150

200

250

300

350

400

450

N = 2N = 3

Cutter rotation angle (∘)

F (N

)

Figure 12 Effect of tooth number on cutting force

When the cutting depth is reduced cutting forces in threedirections119883 119884 and 119885 are all decreased and the total cuttingforce becomes smaller from Figure 13 But when the cuttingdepth decreases entrance angle and exit angle are constant

513 The Influence of Cutter Diameter on Cutting ForceWhen focusing on the effect of cutter diameter on cuttingforce the larger the cutter diameter is the larger the cuttingforce becomes no matter whether it is a given value or not inFigure 14 With the change of cutter diameter entrance angleremains unchanged while exit angle changes

514 The Influence of Cutter Diameter and Feed on CuttingForce It can be noticed from Figure 15 that cutting forceand cutting-in angle are not affected by different helix angleBut the cutting-out angle will be bigger when the helix angleincreases The last parameter is the rational speed Feed has

0 50 100 150 200 250 300 350 4000

100

200

300

400

500

600

Cutter rotation angle (∘)

ap = 08mm

ap = 10mm

ap = 12mm

F (N

)

Figure 13 Effect of cutting depth on cutting force

a great impact on the maximum cutting force as shown inFigure 16 And slight increase can cause large changes ofthe total cutting force so that the amount of feed should beselected with season during processing

52 Comparison of Rigid and Flexible Cutting Force Inorder to illustrate the contribution of flexible cutting forcecomparison of flexible cutting forces and rigid cutting forceswas simulated based on the same cutting conditions inFigure 15

It can be seen from Figure 17 that flexible cutting force issmaller than rigid cutting force in differential direction butthe value is more by 19N in the 119883 direction Consequentlyit is necessary that the flexible model of cutting force isanalyzed For the validation of the model another simulation(in Figure 18) is conducted in the same cutting condition[24] as follows 119886

119899= 0 spindle speed = 269 rmin 119877

0=

9526mm 1198940= 30 st = 00508mm and 119886

119901= 635mm

The predicted cutting forces are compared and matched wellwith the experiment [24] Therefore it provides a theoreticalfoundation and reference for the turn-milling mechanismresearch

6 Conclusions

In this paper the cutting force of blade by turn-milling wasstudied in cutting parameters A rigid model and a flexiblemodel of cutting force with ball-end cutter are establishedrespectively based on the analysis of space geometry of theball-end mill and blades Some suggestions are providedto choose cutting parameters to reduce cutting forces andreach high productivity This study will provide a theoreticalfoundation and reference for the turn-milling mechanismresearch Based on this work the following conclusions canbe drawn

(i) The influences of cutting parameters and geometryshape of cutter on the cutting forces are analyzedby turn-milling The deformation values of blade

Advances in Materials Science and Engineering 9

0 50 100 150 200 250 300 350 400minus300

minus200

minus100

0

100

200

300

400

500

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

(a) 119886119890is a multiple of the diameter

0 50 100 150 200 250 300 350 400minus400

minus300

minus200

minus100

0

100

200

300

400

500

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

(b) 119886119890is constant

Figure 14 Effect of cutter diameter on cutting force (big symbol119863 = 8mm small symbol119863 = 5mm)

0 50 100 150 200 250 300 350 400minus300

minus200

minus100

0

100

200

300

400

500

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

(Big symbol 120573 = small symbol 120573 = 18∘)38∘

Figure 15 Effect of helix angle on cutting force

and cutter on the engaged trajectory are calculatedrespectively by using the iterative algorithm

(ii) In milling blades case cutting force is sensitive to theamount of feed but the influence of helix angle is thesmallestThe amount of deformation of the blade willnot be the same in a different thickness position ofthe bladeThe thinner the thickness is the greater thebending deformation becomes And cutting force isalso affected by the deformation

(iii) In milling titanium blades case flexible cutting forceis smaller than rigid cutting force in each direction

0 50 100 150 200 250 300 350 4000

50

100

150

200

250

300

350

400

450

500

Cutter rotation angle (∘)

= 01mms

= 02mms

= 03mms

F (N

)

Figure 16 Effect of feed on cutting force

but it is less 20N Since stiffness of titanium alloy isrelatively large the deformation of titanium alloy issmall and deformation of the tool is of the order ofminus5 times

Nomenclature

119899119905 Rotation speed of cutter (rmin)

119899119887 Rotation speed of blade (rmin)

119886119901 Depth of cut (mm)

119891119911 Feed per tooth (mmz)

119905119888 Uncut chip thickness (mm)

] Poisson ratio of blade120575119905 Deflection value of tool

120575119887 Deflection value of blade

10 Advances in Materials Science and Engineering

0 50 100 150 200 250 300 350 400minus400

minus300

minus200

minus100

0

100

200

300

400

Flexible Rigid

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

Figure 17 Comparisons of cutting forces in flexible and rigidmodel

0 50 100 150 200minus1000

minus800

minus600

minus400

minus200

0

200

400

600

800

1000

Cutti

ng fo

rce (

N)

FxFyFz

Rotation angle (∘)

Figure 18 Simulated cutting forces in end milling

120575119908 Cutter bending deflection

120575119888 Clamping deflection

119870119903119888 119870119886119888 and119870

119905119888 Radial axial and tangential cutting forcecoefficients

119870119903119890119870119886119890 and119870

119905119890 Edge force coefficients

120595 Immersion angle of cutting point120601 Cutting element position angle120573 Angle between the 119884-axis and the

reference cutting flute120579 Angle between the cross-feed direction

and the cutting flute119870119888 Measured clamping stiffness of cutter

119903 Radius (mm)

119911 The number of teeth on the cutter119891119886 Axial feed (mmr)

119891119903 Radial feed (mmr)

119864 Elastic modulus of bladeℎ Thickness of blade119890119905119887 Surface error

119886119890 Radial depth of cut

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (NSFC) (51105072 and 51475087) sup-ported by the Fundamental Research Funds for the CentralUniversities (N150304005)

References

[1] U Karaguzel M Bakkal and E Budak ldquoProcess modeling ofturn-milling using analytical approachrdquo Procedia CIRP vol 4pp 131ndash139 2012

[2] U Karaguzel E Uysal E Budak and M Bakkal ldquoAnalyticalmodeling of turn-milling process geometry kinematics andmechanicsrdquo International Journal of Machine Tools amp Manufac-ture vol 91 pp 24ndash33 2015

[3] S Ekinovic E Begovic and A Silajdzija ldquoComparison ofmachined surface quality obtained by high-speed machiningand conventional turningrdquo Machining Science and Technologyvol 11 no 4 pp 531ndash551 2007

[4] S Skoric TUdiljak andDCiglar ldquoStudy of the suitability of themachining of rotating surfacesrdquoTransactions of Famena vol 32no 2 pp 69ndash83 2008

[5] M Pogacnik and J Kopac ldquoDynamic stabilization of the turn-milling process by parameter optimizationrdquo Proceedings of theInstitution of Mechanical Engineers Part B vol 214 no 2 pp127ndash135 2000

[6] S K Choudhury and J B Bajpai ldquoInvestigation in orthogonalturn-milling towards better surface finishrdquo Journal of MaterialsProcessing Technology vol 170 no 3 pp 487ndash493 2005

[7] S K Choudhury and K S Mangrulkar ldquoInvestigation oforthogonal turn-milling for the machining of rotationallysymmetrical work piecesrdquo Journal of Materials Processing Tech-nology vol 99 no 1 pp 120ndash128 2000

[8] A Calleja A Fernandez A Rodriguez L N de Lacalle andA Lamikiz ldquoTurn-milling of blades in turning centres andmultitasking machines controlling tool tilt anglerdquo Proceedingsof the Institution of Mechanical Engineers Part B Journal ofEngineering Manufacture vol 229 no 8 pp 1324ndash1336 2015

[9] C M Lee S W Kim Y H Lee and D W Lee ldquoThe optimalcutter orientation in ball end milling of cantilever-shaped thinplaterdquo Journal of Materials Processing Technology vol 153ndash154pp 900ndash906 2004

[10] M Fontaine A Moufki A Devillez and D Dudzinski ldquoMod-elling of cutting forces in ball-end milling with tool-surfaceinclination Part I predictive force model and experimentalvalidationrdquo Journal of Materials Processing Technology vol 189no 1ndash3 pp 73ndash84 2007

Advances in Materials Science and Engineering 11

[11] D Biermann P Kersting and T Surmann ldquoA general approachto simulating workpiece vibrations during five-axis milling ofturbine bladesrdquo CIRP AnnalsmdashManufacturing Technology vol59 no 1 pp 125ndash128 2010

[12] I Lazoglu Y Boz and H Erdim ldquoFive-axis milling mechanicsfor complex free form surfacesrdquo CIRP Annals-ManufacturingTechnology vol 60 no 1 pp 117ndash120 2011

[13] E Budak E Ozturk and L T Tunc ldquoModeling and simulationof 5-axismilling processesrdquoCIRPAnnalsmdashManufacturing Tech-nology vol 58 no 1 pp 347ndash350 2009

[14] E Budak ldquoImproving 5-axis milling operations using processmodelsrdquoMM Science Journal pp 358ndash365 2012

[15] E Ozturk and E Budak ldquoDynamics and stability of five-axis ball-end millingrdquo Journal of Manufacturing Science andEngineering vol 132 no 2 2010

[16] E Ozturk L T Tunc and E Budak ldquoInvestigation of leadand tilt angle effects in 5-axis ball-end milling processesrdquoInternational Journal of Machine Tools amp Manufacture vol 49no 14 pp 1053ndash1062 2009

[17] E Budak A Comak and E Ozturk ldquoStability and highperformance machining conditions in simultaneous millingrdquoCIRP AnnalsmdashManufacturing Technology vol 62 no 1 pp403ndash406 2013

[18] S Herranz F J Campa L N L De Lacalle et al ldquoThemilling of airframe components with low rigidity a generalapproach to avoid static and dynamic problemsrdquo Proceedingsof the Institution of Mechanical Engineers Part B Journal ofEngineering Manufacture vol 219 no 11 pp 789ndash801 2005

[19] D Olvera L N L de Lacalle F I Compean A Fz-ValdivielsoA Lamikiz and F J Campa ldquoAnalysis of the tool tip radialstiffness of turn-milling centersrdquo The International Journal ofAdvancedManufacturing Technology vol 60 no 9 pp 883ndash8912012

[20] A Lamikiz L N Lopez de Lacalle O Ocerin D Dıez and EMaidagan ldquoThe Denavit and Hartenberg approach applied toevaluate the consequences in the tool tip position of geometricalerrors in five-axis milling centresrdquo The International Journal ofAdvanced Manufacturing Technology vol 37 no 1 pp 122ndash1392008

[21] G M Kim B H Kim and C N Chu ldquoEstimation ofcutter deflection and form error in ball-end milling processesrdquoInternational Journal ofMachine Tools andManufacture vol 43no 9 pp 917ndash924 2003

[22] E B Kivanc and E Budak ldquoStructural modeling of end millsfor form error and stability analysisrdquo International Journal ofMachine ToolsampManufacture vol 44 no 11 pp 1151ndash1161 2004

[23] Q Cao J Zhao S Han and X Chen ldquoForce coefficientsidentification considering inclination angle for ball-end finishmillingrdquo Precision Engineering vol 36 no 2 pp 252ndash260 2012

[24] P Lee and Y Altintas ldquoPrediction of ball-end milling forcesfrom orthogonal cutting datardquo International Journal of MachineTools and Manufacture vol 36 no 9 pp 1059ndash1072 1996

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

8 Advances in Materials Science and Engineering

0 50 100 150 200 250 300 350 400minus300

minus200

minus100

0

100

200

300

400

500(Small symbol l = 25∘ big symbol l = 15∘)

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

Figure 11 Effect of tilt angle on cutting force

0 50 100 150 200 250 300 350 400minus100

minus50

0

50

100

150

200

250

300

350

400

450

N = 2N = 3

Cutter rotation angle (∘)

F (N

)

Figure 12 Effect of tooth number on cutting force

When the cutting depth is reduced cutting forces in threedirections119883 119884 and 119885 are all decreased and the total cuttingforce becomes smaller from Figure 13 But when the cuttingdepth decreases entrance angle and exit angle are constant

513 The Influence of Cutter Diameter on Cutting ForceWhen focusing on the effect of cutter diameter on cuttingforce the larger the cutter diameter is the larger the cuttingforce becomes no matter whether it is a given value or not inFigure 14 With the change of cutter diameter entrance angleremains unchanged while exit angle changes

514 The Influence of Cutter Diameter and Feed on CuttingForce It can be noticed from Figure 15 that cutting forceand cutting-in angle are not affected by different helix angleBut the cutting-out angle will be bigger when the helix angleincreases The last parameter is the rational speed Feed has

0 50 100 150 200 250 300 350 4000

100

200

300

400

500

600

Cutter rotation angle (∘)

ap = 08mm

ap = 10mm

ap = 12mm

F (N

)

Figure 13 Effect of cutting depth on cutting force

a great impact on the maximum cutting force as shown inFigure 16 And slight increase can cause large changes ofthe total cutting force so that the amount of feed should beselected with season during processing

52 Comparison of Rigid and Flexible Cutting Force Inorder to illustrate the contribution of flexible cutting forcecomparison of flexible cutting forces and rigid cutting forceswas simulated based on the same cutting conditions inFigure 15

It can be seen from Figure 17 that flexible cutting force issmaller than rigid cutting force in differential direction butthe value is more by 19N in the 119883 direction Consequentlyit is necessary that the flexible model of cutting force isanalyzed For the validation of the model another simulation(in Figure 18) is conducted in the same cutting condition[24] as follows 119886

119899= 0 spindle speed = 269 rmin 119877

0=

9526mm 1198940= 30 st = 00508mm and 119886

119901= 635mm

The predicted cutting forces are compared and matched wellwith the experiment [24] Therefore it provides a theoreticalfoundation and reference for the turn-milling mechanismresearch

6 Conclusions

In this paper the cutting force of blade by turn-milling wasstudied in cutting parameters A rigid model and a flexiblemodel of cutting force with ball-end cutter are establishedrespectively based on the analysis of space geometry of theball-end mill and blades Some suggestions are providedto choose cutting parameters to reduce cutting forces andreach high productivity This study will provide a theoreticalfoundation and reference for the turn-milling mechanismresearch Based on this work the following conclusions canbe drawn

(i) The influences of cutting parameters and geometryshape of cutter on the cutting forces are analyzedby turn-milling The deformation values of blade

Advances in Materials Science and Engineering 9

0 50 100 150 200 250 300 350 400minus300

minus200

minus100

0

100

200

300

400

500

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

(a) 119886119890is a multiple of the diameter

0 50 100 150 200 250 300 350 400minus400

minus300

minus200

minus100

0

100

200

300

400

500

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

(b) 119886119890is constant

Figure 14 Effect of cutter diameter on cutting force (big symbol119863 = 8mm small symbol119863 = 5mm)

0 50 100 150 200 250 300 350 400minus300

minus200

minus100

0

100

200

300

400

500

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

(Big symbol 120573 = small symbol 120573 = 18∘)38∘

Figure 15 Effect of helix angle on cutting force

and cutter on the engaged trajectory are calculatedrespectively by using the iterative algorithm

(ii) In milling blades case cutting force is sensitive to theamount of feed but the influence of helix angle is thesmallestThe amount of deformation of the blade willnot be the same in a different thickness position ofthe bladeThe thinner the thickness is the greater thebending deformation becomes And cutting force isalso affected by the deformation

(iii) In milling titanium blades case flexible cutting forceis smaller than rigid cutting force in each direction

0 50 100 150 200 250 300 350 4000

50

100

150

200

250

300

350

400

450

500

Cutter rotation angle (∘)

= 01mms

= 02mms

= 03mms

F (N

)

Figure 16 Effect of feed on cutting force

but it is less 20N Since stiffness of titanium alloy isrelatively large the deformation of titanium alloy issmall and deformation of the tool is of the order ofminus5 times

Nomenclature

119899119905 Rotation speed of cutter (rmin)

119899119887 Rotation speed of blade (rmin)

119886119901 Depth of cut (mm)

119891119911 Feed per tooth (mmz)

119905119888 Uncut chip thickness (mm)

] Poisson ratio of blade120575119905 Deflection value of tool

120575119887 Deflection value of blade

10 Advances in Materials Science and Engineering

0 50 100 150 200 250 300 350 400minus400

minus300

minus200

minus100

0

100

200

300

400

Flexible Rigid

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

Figure 17 Comparisons of cutting forces in flexible and rigidmodel

0 50 100 150 200minus1000

minus800

minus600

minus400

minus200

0

200

400

600

800

1000

Cutti

ng fo

rce (

N)

FxFyFz

Rotation angle (∘)

Figure 18 Simulated cutting forces in end milling

120575119908 Cutter bending deflection

120575119888 Clamping deflection

119870119903119888 119870119886119888 and119870

119905119888 Radial axial and tangential cutting forcecoefficients

119870119903119890119870119886119890 and119870

119905119890 Edge force coefficients

120595 Immersion angle of cutting point120601 Cutting element position angle120573 Angle between the 119884-axis and the

reference cutting flute120579 Angle between the cross-feed direction

and the cutting flute119870119888 Measured clamping stiffness of cutter

119903 Radius (mm)

119911 The number of teeth on the cutter119891119886 Axial feed (mmr)

119891119903 Radial feed (mmr)

119864 Elastic modulus of bladeℎ Thickness of blade119890119905119887 Surface error

119886119890 Radial depth of cut

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (NSFC) (51105072 and 51475087) sup-ported by the Fundamental Research Funds for the CentralUniversities (N150304005)

References

[1] U Karaguzel M Bakkal and E Budak ldquoProcess modeling ofturn-milling using analytical approachrdquo Procedia CIRP vol 4pp 131ndash139 2012

[2] U Karaguzel E Uysal E Budak and M Bakkal ldquoAnalyticalmodeling of turn-milling process geometry kinematics andmechanicsrdquo International Journal of Machine Tools amp Manufac-ture vol 91 pp 24ndash33 2015

[3] S Ekinovic E Begovic and A Silajdzija ldquoComparison ofmachined surface quality obtained by high-speed machiningand conventional turningrdquo Machining Science and Technologyvol 11 no 4 pp 531ndash551 2007

[4] S Skoric TUdiljak andDCiglar ldquoStudy of the suitability of themachining of rotating surfacesrdquoTransactions of Famena vol 32no 2 pp 69ndash83 2008

[5] M Pogacnik and J Kopac ldquoDynamic stabilization of the turn-milling process by parameter optimizationrdquo Proceedings of theInstitution of Mechanical Engineers Part B vol 214 no 2 pp127ndash135 2000

[6] S K Choudhury and J B Bajpai ldquoInvestigation in orthogonalturn-milling towards better surface finishrdquo Journal of MaterialsProcessing Technology vol 170 no 3 pp 487ndash493 2005

[7] S K Choudhury and K S Mangrulkar ldquoInvestigation oforthogonal turn-milling for the machining of rotationallysymmetrical work piecesrdquo Journal of Materials Processing Tech-nology vol 99 no 1 pp 120ndash128 2000

[8] A Calleja A Fernandez A Rodriguez L N de Lacalle andA Lamikiz ldquoTurn-milling of blades in turning centres andmultitasking machines controlling tool tilt anglerdquo Proceedingsof the Institution of Mechanical Engineers Part B Journal ofEngineering Manufacture vol 229 no 8 pp 1324ndash1336 2015

[9] C M Lee S W Kim Y H Lee and D W Lee ldquoThe optimalcutter orientation in ball end milling of cantilever-shaped thinplaterdquo Journal of Materials Processing Technology vol 153ndash154pp 900ndash906 2004

[10] M Fontaine A Moufki A Devillez and D Dudzinski ldquoMod-elling of cutting forces in ball-end milling with tool-surfaceinclination Part I predictive force model and experimentalvalidationrdquo Journal of Materials Processing Technology vol 189no 1ndash3 pp 73ndash84 2007

Advances in Materials Science and Engineering 11

[11] D Biermann P Kersting and T Surmann ldquoA general approachto simulating workpiece vibrations during five-axis milling ofturbine bladesrdquo CIRP AnnalsmdashManufacturing Technology vol59 no 1 pp 125ndash128 2010

[12] I Lazoglu Y Boz and H Erdim ldquoFive-axis milling mechanicsfor complex free form surfacesrdquo CIRP Annals-ManufacturingTechnology vol 60 no 1 pp 117ndash120 2011

[13] E Budak E Ozturk and L T Tunc ldquoModeling and simulationof 5-axismilling processesrdquoCIRPAnnalsmdashManufacturing Tech-nology vol 58 no 1 pp 347ndash350 2009

[14] E Budak ldquoImproving 5-axis milling operations using processmodelsrdquoMM Science Journal pp 358ndash365 2012

[15] E Ozturk and E Budak ldquoDynamics and stability of five-axis ball-end millingrdquo Journal of Manufacturing Science andEngineering vol 132 no 2 2010

[16] E Ozturk L T Tunc and E Budak ldquoInvestigation of leadand tilt angle effects in 5-axis ball-end milling processesrdquoInternational Journal of Machine Tools amp Manufacture vol 49no 14 pp 1053ndash1062 2009

[17] E Budak A Comak and E Ozturk ldquoStability and highperformance machining conditions in simultaneous millingrdquoCIRP AnnalsmdashManufacturing Technology vol 62 no 1 pp403ndash406 2013

[18] S Herranz F J Campa L N L De Lacalle et al ldquoThemilling of airframe components with low rigidity a generalapproach to avoid static and dynamic problemsrdquo Proceedingsof the Institution of Mechanical Engineers Part B Journal ofEngineering Manufacture vol 219 no 11 pp 789ndash801 2005

[19] D Olvera L N L de Lacalle F I Compean A Fz-ValdivielsoA Lamikiz and F J Campa ldquoAnalysis of the tool tip radialstiffness of turn-milling centersrdquo The International Journal ofAdvancedManufacturing Technology vol 60 no 9 pp 883ndash8912012

[20] A Lamikiz L N Lopez de Lacalle O Ocerin D Dıez and EMaidagan ldquoThe Denavit and Hartenberg approach applied toevaluate the consequences in the tool tip position of geometricalerrors in five-axis milling centresrdquo The International Journal ofAdvanced Manufacturing Technology vol 37 no 1 pp 122ndash1392008

[21] G M Kim B H Kim and C N Chu ldquoEstimation ofcutter deflection and form error in ball-end milling processesrdquoInternational Journal ofMachine Tools andManufacture vol 43no 9 pp 917ndash924 2003

[22] E B Kivanc and E Budak ldquoStructural modeling of end millsfor form error and stability analysisrdquo International Journal ofMachine ToolsampManufacture vol 44 no 11 pp 1151ndash1161 2004

[23] Q Cao J Zhao S Han and X Chen ldquoForce coefficientsidentification considering inclination angle for ball-end finishmillingrdquo Precision Engineering vol 36 no 2 pp 252ndash260 2012

[24] P Lee and Y Altintas ldquoPrediction of ball-end milling forcesfrom orthogonal cutting datardquo International Journal of MachineTools and Manufacture vol 36 no 9 pp 1059ndash1072 1996

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Advances in Materials Science and Engineering 9

0 50 100 150 200 250 300 350 400minus300

minus200

minus100

0

100

200

300

400

500

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

(a) 119886119890is a multiple of the diameter

0 50 100 150 200 250 300 350 400minus400

minus300

minus200

minus100

0

100

200

300

400

500

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

(b) 119886119890is constant

Figure 14 Effect of cutter diameter on cutting force (big symbol119863 = 8mm small symbol119863 = 5mm)

0 50 100 150 200 250 300 350 400minus300

minus200

minus100

0

100

200

300

400

500

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

(Big symbol 120573 = small symbol 120573 = 18∘)38∘

Figure 15 Effect of helix angle on cutting force

and cutter on the engaged trajectory are calculatedrespectively by using the iterative algorithm

(ii) In milling blades case cutting force is sensitive to theamount of feed but the influence of helix angle is thesmallestThe amount of deformation of the blade willnot be the same in a different thickness position ofthe bladeThe thinner the thickness is the greater thebending deformation becomes And cutting force isalso affected by the deformation

(iii) In milling titanium blades case flexible cutting forceis smaller than rigid cutting force in each direction

0 50 100 150 200 250 300 350 4000

50

100

150

200

250

300

350

400

450

500

Cutter rotation angle (∘)

= 01mms

= 02mms

= 03mms

F (N

)

Figure 16 Effect of feed on cutting force

but it is less 20N Since stiffness of titanium alloy isrelatively large the deformation of titanium alloy issmall and deformation of the tool is of the order ofminus5 times

Nomenclature

119899119905 Rotation speed of cutter (rmin)

119899119887 Rotation speed of blade (rmin)

119886119901 Depth of cut (mm)

119891119911 Feed per tooth (mmz)

119905119888 Uncut chip thickness (mm)

] Poisson ratio of blade120575119905 Deflection value of tool

120575119887 Deflection value of blade

10 Advances in Materials Science and Engineering

0 50 100 150 200 250 300 350 400minus400

minus300

minus200

minus100

0

100

200

300

400

Flexible Rigid

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

Figure 17 Comparisons of cutting forces in flexible and rigidmodel

0 50 100 150 200minus1000

minus800

minus600

minus400

minus200

0

200

400

600

800

1000

Cutti

ng fo

rce (

N)

FxFyFz

Rotation angle (∘)

Figure 18 Simulated cutting forces in end milling

120575119908 Cutter bending deflection

120575119888 Clamping deflection

119870119903119888 119870119886119888 and119870

119905119888 Radial axial and tangential cutting forcecoefficients

119870119903119890119870119886119890 and119870

119905119890 Edge force coefficients

120595 Immersion angle of cutting point120601 Cutting element position angle120573 Angle between the 119884-axis and the

reference cutting flute120579 Angle between the cross-feed direction

and the cutting flute119870119888 Measured clamping stiffness of cutter

119903 Radius (mm)

119911 The number of teeth on the cutter119891119886 Axial feed (mmr)

119891119903 Radial feed (mmr)

119864 Elastic modulus of bladeℎ Thickness of blade119890119905119887 Surface error

119886119890 Radial depth of cut

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (NSFC) (51105072 and 51475087) sup-ported by the Fundamental Research Funds for the CentralUniversities (N150304005)

References

[1] U Karaguzel M Bakkal and E Budak ldquoProcess modeling ofturn-milling using analytical approachrdquo Procedia CIRP vol 4pp 131ndash139 2012

[2] U Karaguzel E Uysal E Budak and M Bakkal ldquoAnalyticalmodeling of turn-milling process geometry kinematics andmechanicsrdquo International Journal of Machine Tools amp Manufac-ture vol 91 pp 24ndash33 2015

[3] S Ekinovic E Begovic and A Silajdzija ldquoComparison ofmachined surface quality obtained by high-speed machiningand conventional turningrdquo Machining Science and Technologyvol 11 no 4 pp 531ndash551 2007

[4] S Skoric TUdiljak andDCiglar ldquoStudy of the suitability of themachining of rotating surfacesrdquoTransactions of Famena vol 32no 2 pp 69ndash83 2008

[5] M Pogacnik and J Kopac ldquoDynamic stabilization of the turn-milling process by parameter optimizationrdquo Proceedings of theInstitution of Mechanical Engineers Part B vol 214 no 2 pp127ndash135 2000

[6] S K Choudhury and J B Bajpai ldquoInvestigation in orthogonalturn-milling towards better surface finishrdquo Journal of MaterialsProcessing Technology vol 170 no 3 pp 487ndash493 2005

[7] S K Choudhury and K S Mangrulkar ldquoInvestigation oforthogonal turn-milling for the machining of rotationallysymmetrical work piecesrdquo Journal of Materials Processing Tech-nology vol 99 no 1 pp 120ndash128 2000

[8] A Calleja A Fernandez A Rodriguez L N de Lacalle andA Lamikiz ldquoTurn-milling of blades in turning centres andmultitasking machines controlling tool tilt anglerdquo Proceedingsof the Institution of Mechanical Engineers Part B Journal ofEngineering Manufacture vol 229 no 8 pp 1324ndash1336 2015

[9] C M Lee S W Kim Y H Lee and D W Lee ldquoThe optimalcutter orientation in ball end milling of cantilever-shaped thinplaterdquo Journal of Materials Processing Technology vol 153ndash154pp 900ndash906 2004

[10] M Fontaine A Moufki A Devillez and D Dudzinski ldquoMod-elling of cutting forces in ball-end milling with tool-surfaceinclination Part I predictive force model and experimentalvalidationrdquo Journal of Materials Processing Technology vol 189no 1ndash3 pp 73ndash84 2007

Advances in Materials Science and Engineering 11

[11] D Biermann P Kersting and T Surmann ldquoA general approachto simulating workpiece vibrations during five-axis milling ofturbine bladesrdquo CIRP AnnalsmdashManufacturing Technology vol59 no 1 pp 125ndash128 2010

[12] I Lazoglu Y Boz and H Erdim ldquoFive-axis milling mechanicsfor complex free form surfacesrdquo CIRP Annals-ManufacturingTechnology vol 60 no 1 pp 117ndash120 2011

[13] E Budak E Ozturk and L T Tunc ldquoModeling and simulationof 5-axismilling processesrdquoCIRPAnnalsmdashManufacturing Tech-nology vol 58 no 1 pp 347ndash350 2009

[14] E Budak ldquoImproving 5-axis milling operations using processmodelsrdquoMM Science Journal pp 358ndash365 2012

[15] E Ozturk and E Budak ldquoDynamics and stability of five-axis ball-end millingrdquo Journal of Manufacturing Science andEngineering vol 132 no 2 2010

[16] E Ozturk L T Tunc and E Budak ldquoInvestigation of leadand tilt angle effects in 5-axis ball-end milling processesrdquoInternational Journal of Machine Tools amp Manufacture vol 49no 14 pp 1053ndash1062 2009

[17] E Budak A Comak and E Ozturk ldquoStability and highperformance machining conditions in simultaneous millingrdquoCIRP AnnalsmdashManufacturing Technology vol 62 no 1 pp403ndash406 2013

[18] S Herranz F J Campa L N L De Lacalle et al ldquoThemilling of airframe components with low rigidity a generalapproach to avoid static and dynamic problemsrdquo Proceedingsof the Institution of Mechanical Engineers Part B Journal ofEngineering Manufacture vol 219 no 11 pp 789ndash801 2005

[19] D Olvera L N L de Lacalle F I Compean A Fz-ValdivielsoA Lamikiz and F J Campa ldquoAnalysis of the tool tip radialstiffness of turn-milling centersrdquo The International Journal ofAdvancedManufacturing Technology vol 60 no 9 pp 883ndash8912012

[20] A Lamikiz L N Lopez de Lacalle O Ocerin D Dıez and EMaidagan ldquoThe Denavit and Hartenberg approach applied toevaluate the consequences in the tool tip position of geometricalerrors in five-axis milling centresrdquo The International Journal ofAdvanced Manufacturing Technology vol 37 no 1 pp 122ndash1392008

[21] G M Kim B H Kim and C N Chu ldquoEstimation ofcutter deflection and form error in ball-end milling processesrdquoInternational Journal ofMachine Tools andManufacture vol 43no 9 pp 917ndash924 2003

[22] E B Kivanc and E Budak ldquoStructural modeling of end millsfor form error and stability analysisrdquo International Journal ofMachine ToolsampManufacture vol 44 no 11 pp 1151ndash1161 2004

[23] Q Cao J Zhao S Han and X Chen ldquoForce coefficientsidentification considering inclination angle for ball-end finishmillingrdquo Precision Engineering vol 36 no 2 pp 252ndash260 2012

[24] P Lee and Y Altintas ldquoPrediction of ball-end milling forcesfrom orthogonal cutting datardquo International Journal of MachineTools and Manufacture vol 36 no 9 pp 1059ndash1072 1996

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

10 Advances in Materials Science and Engineering

0 50 100 150 200 250 300 350 400minus400

minus300

minus200

minus100

0

100

200

300

400

Flexible Rigid

Cutter rotation angle (∘)

F (N

)

FxiFyi

FziF

Figure 17 Comparisons of cutting forces in flexible and rigidmodel

0 50 100 150 200minus1000

minus800

minus600

minus400

minus200

0

200

400

600

800

1000

Cutti

ng fo

rce (

N)

FxFyFz

Rotation angle (∘)

Figure 18 Simulated cutting forces in end milling

120575119908 Cutter bending deflection

120575119888 Clamping deflection

119870119903119888 119870119886119888 and119870

119905119888 Radial axial and tangential cutting forcecoefficients

119870119903119890119870119886119890 and119870

119905119890 Edge force coefficients

120595 Immersion angle of cutting point120601 Cutting element position angle120573 Angle between the 119884-axis and the

reference cutting flute120579 Angle between the cross-feed direction

and the cutting flute119870119888 Measured clamping stiffness of cutter

119903 Radius (mm)

119911 The number of teeth on the cutter119891119886 Axial feed (mmr)

119891119903 Radial feed (mmr)

119864 Elastic modulus of bladeℎ Thickness of blade119890119905119887 Surface error

119886119890 Radial depth of cut

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (NSFC) (51105072 and 51475087) sup-ported by the Fundamental Research Funds for the CentralUniversities (N150304005)

References

[1] U Karaguzel M Bakkal and E Budak ldquoProcess modeling ofturn-milling using analytical approachrdquo Procedia CIRP vol 4pp 131ndash139 2012

[2] U Karaguzel E Uysal E Budak and M Bakkal ldquoAnalyticalmodeling of turn-milling process geometry kinematics andmechanicsrdquo International Journal of Machine Tools amp Manufac-ture vol 91 pp 24ndash33 2015

[3] S Ekinovic E Begovic and A Silajdzija ldquoComparison ofmachined surface quality obtained by high-speed machiningand conventional turningrdquo Machining Science and Technologyvol 11 no 4 pp 531ndash551 2007

[4] S Skoric TUdiljak andDCiglar ldquoStudy of the suitability of themachining of rotating surfacesrdquoTransactions of Famena vol 32no 2 pp 69ndash83 2008

[5] M Pogacnik and J Kopac ldquoDynamic stabilization of the turn-milling process by parameter optimizationrdquo Proceedings of theInstitution of Mechanical Engineers Part B vol 214 no 2 pp127ndash135 2000

[6] S K Choudhury and J B Bajpai ldquoInvestigation in orthogonalturn-milling towards better surface finishrdquo Journal of MaterialsProcessing Technology vol 170 no 3 pp 487ndash493 2005

[7] S K Choudhury and K S Mangrulkar ldquoInvestigation oforthogonal turn-milling for the machining of rotationallysymmetrical work piecesrdquo Journal of Materials Processing Tech-nology vol 99 no 1 pp 120ndash128 2000

[8] A Calleja A Fernandez A Rodriguez L N de Lacalle andA Lamikiz ldquoTurn-milling of blades in turning centres andmultitasking machines controlling tool tilt anglerdquo Proceedingsof the Institution of Mechanical Engineers Part B Journal ofEngineering Manufacture vol 229 no 8 pp 1324ndash1336 2015

[9] C M Lee S W Kim Y H Lee and D W Lee ldquoThe optimalcutter orientation in ball end milling of cantilever-shaped thinplaterdquo Journal of Materials Processing Technology vol 153ndash154pp 900ndash906 2004

[10] M Fontaine A Moufki A Devillez and D Dudzinski ldquoMod-elling of cutting forces in ball-end milling with tool-surfaceinclination Part I predictive force model and experimentalvalidationrdquo Journal of Materials Processing Technology vol 189no 1ndash3 pp 73ndash84 2007

Advances in Materials Science and Engineering 11

[11] D Biermann P Kersting and T Surmann ldquoA general approachto simulating workpiece vibrations during five-axis milling ofturbine bladesrdquo CIRP AnnalsmdashManufacturing Technology vol59 no 1 pp 125ndash128 2010

[12] I Lazoglu Y Boz and H Erdim ldquoFive-axis milling mechanicsfor complex free form surfacesrdquo CIRP Annals-ManufacturingTechnology vol 60 no 1 pp 117ndash120 2011

[13] E Budak E Ozturk and L T Tunc ldquoModeling and simulationof 5-axismilling processesrdquoCIRPAnnalsmdashManufacturing Tech-nology vol 58 no 1 pp 347ndash350 2009

[14] E Budak ldquoImproving 5-axis milling operations using processmodelsrdquoMM Science Journal pp 358ndash365 2012

[15] E Ozturk and E Budak ldquoDynamics and stability of five-axis ball-end millingrdquo Journal of Manufacturing Science andEngineering vol 132 no 2 2010

[16] E Ozturk L T Tunc and E Budak ldquoInvestigation of leadand tilt angle effects in 5-axis ball-end milling processesrdquoInternational Journal of Machine Tools amp Manufacture vol 49no 14 pp 1053ndash1062 2009

[17] E Budak A Comak and E Ozturk ldquoStability and highperformance machining conditions in simultaneous millingrdquoCIRP AnnalsmdashManufacturing Technology vol 62 no 1 pp403ndash406 2013

[18] S Herranz F J Campa L N L De Lacalle et al ldquoThemilling of airframe components with low rigidity a generalapproach to avoid static and dynamic problemsrdquo Proceedingsof the Institution of Mechanical Engineers Part B Journal ofEngineering Manufacture vol 219 no 11 pp 789ndash801 2005

[19] D Olvera L N L de Lacalle F I Compean A Fz-ValdivielsoA Lamikiz and F J Campa ldquoAnalysis of the tool tip radialstiffness of turn-milling centersrdquo The International Journal ofAdvancedManufacturing Technology vol 60 no 9 pp 883ndash8912012

[20] A Lamikiz L N Lopez de Lacalle O Ocerin D Dıez and EMaidagan ldquoThe Denavit and Hartenberg approach applied toevaluate the consequences in the tool tip position of geometricalerrors in five-axis milling centresrdquo The International Journal ofAdvanced Manufacturing Technology vol 37 no 1 pp 122ndash1392008

[21] G M Kim B H Kim and C N Chu ldquoEstimation ofcutter deflection and form error in ball-end milling processesrdquoInternational Journal ofMachine Tools andManufacture vol 43no 9 pp 917ndash924 2003

[22] E B Kivanc and E Budak ldquoStructural modeling of end millsfor form error and stability analysisrdquo International Journal ofMachine ToolsampManufacture vol 44 no 11 pp 1151ndash1161 2004

[23] Q Cao J Zhao S Han and X Chen ldquoForce coefficientsidentification considering inclination angle for ball-end finishmillingrdquo Precision Engineering vol 36 no 2 pp 252ndash260 2012

[24] P Lee and Y Altintas ldquoPrediction of ball-end milling forcesfrom orthogonal cutting datardquo International Journal of MachineTools and Manufacture vol 36 no 9 pp 1059ndash1072 1996

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Advances in Materials Science and Engineering 11

[11] D Biermann P Kersting and T Surmann ldquoA general approachto simulating workpiece vibrations during five-axis milling ofturbine bladesrdquo CIRP AnnalsmdashManufacturing Technology vol59 no 1 pp 125ndash128 2010

[12] I Lazoglu Y Boz and H Erdim ldquoFive-axis milling mechanicsfor complex free form surfacesrdquo CIRP Annals-ManufacturingTechnology vol 60 no 1 pp 117ndash120 2011

[13] E Budak E Ozturk and L T Tunc ldquoModeling and simulationof 5-axismilling processesrdquoCIRPAnnalsmdashManufacturing Tech-nology vol 58 no 1 pp 347ndash350 2009

[14] E Budak ldquoImproving 5-axis milling operations using processmodelsrdquoMM Science Journal pp 358ndash365 2012

[15] E Ozturk and E Budak ldquoDynamics and stability of five-axis ball-end millingrdquo Journal of Manufacturing Science andEngineering vol 132 no 2 2010

[16] E Ozturk L T Tunc and E Budak ldquoInvestigation of leadand tilt angle effects in 5-axis ball-end milling processesrdquoInternational Journal of Machine Tools amp Manufacture vol 49no 14 pp 1053ndash1062 2009

[17] E Budak A Comak and E Ozturk ldquoStability and highperformance machining conditions in simultaneous millingrdquoCIRP AnnalsmdashManufacturing Technology vol 62 no 1 pp403ndash406 2013

[18] S Herranz F J Campa L N L De Lacalle et al ldquoThemilling of airframe components with low rigidity a generalapproach to avoid static and dynamic problemsrdquo Proceedingsof the Institution of Mechanical Engineers Part B Journal ofEngineering Manufacture vol 219 no 11 pp 789ndash801 2005

[19] D Olvera L N L de Lacalle F I Compean A Fz-ValdivielsoA Lamikiz and F J Campa ldquoAnalysis of the tool tip radialstiffness of turn-milling centersrdquo The International Journal ofAdvancedManufacturing Technology vol 60 no 9 pp 883ndash8912012

[20] A Lamikiz L N Lopez de Lacalle O Ocerin D Dıez and EMaidagan ldquoThe Denavit and Hartenberg approach applied toevaluate the consequences in the tool tip position of geometricalerrors in five-axis milling centresrdquo The International Journal ofAdvanced Manufacturing Technology vol 37 no 1 pp 122ndash1392008

[21] G M Kim B H Kim and C N Chu ldquoEstimation ofcutter deflection and form error in ball-end milling processesrdquoInternational Journal ofMachine Tools andManufacture vol 43no 9 pp 917ndash924 2003

[22] E B Kivanc and E Budak ldquoStructural modeling of end millsfor form error and stability analysisrdquo International Journal ofMachine ToolsampManufacture vol 44 no 11 pp 1151ndash1161 2004

[23] Q Cao J Zhao S Han and X Chen ldquoForce coefficientsidentification considering inclination angle for ball-end finishmillingrdquo Precision Engineering vol 36 no 2 pp 252ndash260 2012

[24] P Lee and Y Altintas ldquoPrediction of ball-end milling forcesfrom orthogonal cutting datardquo International Journal of MachineTools and Manufacture vol 36 no 9 pp 1059ndash1072 1996

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials