hne

hinain 150

Received in revised form 16 October 2014Accepted 3 March 2015Available online 14 March 2015

Keywords:

that the vibration was assumed as a steady simple harmonic motion and was only mea-

especially in the case of precision mold inserts of opticalparts used for injection molding process. On the otherhand, SPDT is a complicated process inuenced easily by

achining theory,cial inteln uniqueachining

based approach together with the experimental invtion approach appears to be the most promising appCombining the two approaches allows the accuratetion of surface roughness along with this approach aidingwith the evaluation and improvement of machine toolperformance.

http://dx.doi.org/10.1016/j.measurement.2015.03.0040263-2241/ 2015 Elsevier Ltd. All rights reserved.

Corresponding author at: No. 438, Hebei Avenue, Qinhuangdao, HebeiProvince, China. Tel.: +86 15227248304.

E-mail address: sophiacjy@ysu.edu.cn (J. Chen).

Measurement 69 (2015) 2030

Contents lists available at ScienceDirect

Measurement

journal homepage: www.elseviproducts, surface roughness is an important index ofproduct quality and technical requirement [2]. In somecases, the surface roughness is required to be kept withina certain range rather than the possible lowest value,

through the use of approaches based on mexperimental investigation and arti[2,48]. Each approach possesses its owtages and disadvantages. However, mligenceadvan-theoryestiga-roach.predic-Single point diamond turning (SPDT) is a promising toolbased machining technology, which can be used for manu-facturing optical components and precision molds. Themain feature of SPDT is its ability to produce high-qualitysurface nish on the order of nanometers while meetingtight form tolerances on the order of micrometers [1]. For

and high spindle speed [3]. Consequently, the investigationon prediction of surface roughness in SPDT is signicantand necessary in order to control the desired surfaceroughness of product in a fast and effective manner.

Many researchers are interested in the prediction ofsurface roughness and research in this eld has yieldedsome useful ndings along with successful experiencePrediction modelRelative tool-work vibrationSwelling effectSurface roughnessSingle-point diamond turning

1. Introductionsured before turning process. In this study, an improved method is presented to evaluatethe actual relative tool-work vibration. By using this method the vibration informationobtained is more credible, as it contains the components caused by machine tool error,cutting force, material property and changing of cutting parameters. Moreover, the swel-ling effect is analyzed using a new evaluating method and taken into account for predictingsurface roughness. On the basis of analyzing both the relative vibration and the swellingeffect, a model is proposed for predicting surface roughness Ra in single point diamondturning. Prediction results prove that this model is a closer approximation of the actualturning process as compared to the previous models and shows a higher predictingaccuracy of surface roughness.

2015 Elsevier Ltd. All rights reserved.

the material swelling effect because of a ne feed rateArticle history:Received 9 June 2014

The relative tool-work vibration is not generalized enough to represent the actual displace-ment between tool and workpiece in previous prediction models. This is due to the factA model for predicting surface rougdiamond turning

Junyun Chen a,, Qingliang Zhao baCollege of Vehicles and Energy, Yanshan University, Qinhuangdao 150001, CbCenter for Precision Engineering (CPE), Harbin Institute of Technology, Harb

a r t i c l e i n f o a b s t r a c tss in single-point

001, China

er .com/ locate /measurement

empirical data suggests and supports that material swel-

achieve both the required hardness and goodmachinability,

J. Chen, Q. Zhao /Measurement 69 (2015) 2030 21In machining theory based approach, a model based onthe theory of machining is used to simulate the creation ofthe machined surface prole and visualize the surfacetopography along with assessing surface roughness [2].The surface roughness prole is generated with the rep-etition of the tool tip prole at intervals of feed per rev-olution (ideal surface roughness prole) plus a relativedisplacement between the tool and workpiece. Sata et al.[9] found that the roughness prole was composed of toolfeed component, swelling of workpiece, spindle rotationerror and chatter vibration error using spectrum analysismethod. Takasu et al. [10] estimated the surface roughnessprole as a function of both the ratio of vibration ampli-tude to geometrical roughness and the phase shift of thevibration to work rotation. He established a theoreticalmodel for creation of roughness prole and also indicatedthat, due to the tool interference, surface roughness inthe tool feed direction can be made much ner than thesum of whole vibration amplitude and geometrical rough-ness. On the basis of the model created by Takasu et al.,Cheung et al. [11] established a three-dimensional surfacetopography simulation model, which takes into accountthe tool geography, the machining condition as well asthe relative tool-work vibration in the kinematics of dia-mond turning process. The surface topography was gener-ated by a linear mapping of the predicted surfaceroughness proles on the surface elements of a cross lat-tice. Lee et al. [12] presented a dynamic surface topographymodel for the prediction of nano-surface generation inwhich an additional displacement caused by materialinduced vibration was introduced into the model as com-pared to the previous model.

2. Previous theoretical models

The basic idea for the theoretical models mentionedabove is the fact that the actual surface roughness proleis formed by an ideal surface roughness prole plus a rela-tive displacement between the tool and workpiece, whichis achieved by theoretic calculation. Ideal surface rough-ness prole is determined by cutting conditions, while arelative displacement between tool and workpiece wasconsidered as the relative tool-work vibration. In the caseof the primary models, materials were assumed ashomogeneous and isotropic and the relative vibrationwas assumed as a steady simple harmonic motion. For ani-sotropy of crystalline materials, an enhanced model, whichadds material induced vibration to the primary model, wasused. Although, they are able to predict surface roughnesswith low error, there are two major issues impacting pre-diction accuracy in previous theoretical models. First, therelative tool-work vibration was assumed as invariable,and it was measured before turning process. The secondis related to the material swelling effect, which wasignored in previous models.

In the cutting process, the actual relative tool-workvibration was caused by machine tool error, cutting force,material property and change in cutting parameters.Some scholars have tried to analyze the relative vibrationusing the spectrum method or by measuring the force incutting process [9,1315]. However, no research workthe compounding of coating solutionwas optimized to gen-erate medium-phosphorus NiP, which possesses a coatingdepth of more than 50 lm and a hardness of 50HRC.Table 1 tabulates the cutting conditions in the tests study-ing relative tool-work vibration and the swelling effect.

The surface prole was measured about 10 mm inlength by contact probe prolometer, Form Talysurf PGI1240 (Taylor Hobson Ltd.) in 2D, while the surface topogra-phy was measured by a non-contact type surface measure-ment system, White Light Interferometer Veeco NT1100(WLI, Veeco Metrology Group) in 3D for each sample. Themeasurement data was then processed with MATLAB soft-ware. The diamond tool wear was observed by a scanningelectronic microscope (SEM, Hitachi S-4700) and an opticalmeasuring microscope (STM6, Olympus, Japan).

4. The relative tool-work vibration

4.1. Evaluating the relative tool-work vibration

Relative vibration may be caused by machine tool error,cutting force, material properties and change in cuttingling obviously changes the surface roughness prole [3].However, no report predicts surface roughness while con-sidering the effect of material swelling.

In the present study, a prediction model is presented topredict the surface roughness in the SPDT process, whichtakes both actual tool-work vibration and material swel-ling into account. It is almost impossible to measure theactual tool-work vibration directly in cutting process. Toovercome this challenge, a concept of equivalent ampli-tude was proposed to aid with the evaluation of the actualtool-work vibration with the assistance of experiments.Furthermore, the swelling proportion of every materialwas dened to quantify the swelling effect, and the rela-tion between the swelling effect and cutting parameterswas investigated by means of experiments.

3. Experimental setup

A series of face cutting tests were conducted on a four-axis CNC ultra-precision machine tool (made by Nachi-Fujikoshi Corp., Japan) shown in Fig. 1 (left). A diamondtool used in tests is shown in Fig. 1 (right), with a rakeangle of 0, a front clearance angle of 6 and a tool-noseradius of 0.5 mm.

The tests were carried out on three kinds of materialsincluding copper (Cu), aluminum alloy (Al7075-T6) andelectroless-nickel (NiP) during studying relative tool-workvibration and the swelling effect. Aluminum alloy and cop-per were available in market, while samples of NiP wereprepared on an aluminum alloy rod (7075-T6). In order tohas been reported which takes the actual relative tool-work vibration into account when establishing a model.On the other hand, according to the results of roughnessprole based on the spectrum analysis, it can be concludedthat the material swelling is an important part contribut-ing to the surface roughness prole [9,13]. Additionally,

(left)

Tn

1111111122

22 J. Chen, Q. Zhao /Measurement 69 (2015) 2030Fig. 1. CNC ultra-precision machine tool

Table 1Cutting conditions for experiments.

TermNo.

Spindle speed(rpm)

Feed rate(mm/min)

Depth of cut(lm)

Tool-noseradius (mm)

1 1000 25 2 0.52 1000 30 2 0.53 1000 35 2 0.54 1000 40 2 0.55 1000 40 4 0.56 1000 40 6 0.57 1000 40 8 0.58 1500 25 2 0.59 1500 30 2 0.5

10 1500 35 2 0.511 1500 40 2 0.5parameters during the cutting process. The relative vibra-tion between the tool and workpiece translates onto themachined surface and is very difcult to be measureddirectly. Therefore it is feasible and applicable to extractthe vibration information from the machined surface.After which, the relationship between the relative vibra-tion and each corresponding factor can be analyzed to pre-dict the surface roughness.

Previous models consider the amplitude of basic fre-quency of spindle to be the amplitude of simple harmonicmotion, which indicates that the amplitude of relativevibration rather than frequency has a dominant impacton surface roughness. As a result, considerable attentionneeds to be given to the amplitude of actual tool-workvibration, and then a denition of equivalent amplitudewas proposed to evaluate it.

A part of measured surface prole was shown in Fig. 2.The location of diamond tool tip xi;Yixi can be extractedfrom the measured surface roughness prole to form thetool locus in radial direction, which represents the dis-placement between the tool and workpiece, i.e., the rela-tive tool-work vibration.

By taking X-axis along the tool feed and Y-axis along theinfeed cutting direction, the number of cutting edgesduplicated on the machined surface along radial directionis given as

N dL x1=se 1where L is the length of measured surface roughness pro-le, s is tool feed per work revolution, and de meansand diamond tools used in tests (right).

ermo.

Spindlespeed (rpm)

Feed rate(mm/min)

Depth of cut(lm)

Tool-noseradius (mm)

2 1500 40 4 0.53 1500 40 6 0.54 1500 40 8 0.55 2000 25 2 0.56 2000 30 2 0.57 2000 35 2 0.58 2000 40 2 0.59 2000 40 4 0.50 2000 40 6 0.51 2000 40 8 0.5rounding down to the nearest whole unit. In the measuredsurface roughness prole, the location of every point form-ing tool locus can be extracted according to X value, asfollows:

xi x1 i 1Dx x1 i 1s 2with i 1;2; . . . ;N. Consequently, the location of everypoint xi;Yixi can be achieved from the measured rough-ness prole, as shown in Fig. 2. The tool locus, i.e. the actualrelative tool-work vibration can be dened as

Ytxi Yixi minfyixig 3with i 1;2; . . . ;N. This vibration will increase the surfaceroughness of machined surface. In order to evaluate thevibration easily, the actual relative tool-work vibrationwas simplied as a simple harmonic motion. The principleof simplication lies on an assumption that both the rela-tive tool-work vibration and simple harmonic motion havethe same impact on surface roughness. That is, both theprole of tool locus and the curve of simple harmonicmotion were regarded as surface roughness proles andhad the same arithmetic roughness value Ra. As a result,the amplitude of simple harmonic motion is dened asequivalent amplitude, which represents the degree ofchanging surface roughness with respect to the actual rela-tive tool-work vibration. The simplication procedure forthe vibration is described below.

Assuming a simple harmonic motion as

Yhx A1 cos2pfx 4

TMillime

e mea

J. Chen, Q. Zhao /Measurement 69 (2015) 2030 23Rah 1N1XN1i1

Yhxi Yhxi

7

Let Eq. (6) equal Eq. (7), then the equivalent amplitudeA can be calculated as

A N21PN

i1 NYtxi PN

i1Ytxi

N2PN1

i1 N1 1 cos pDxi1s

PN1i1 1 cos pDxi1s

8

4.2. Effect of cutting parameters

When depth of cut is set as 2 lm, the actual relativetool-work vibration as a function of the change of feed rateis shown in Fig. 3 at different spindle speeds. It can be seenthat the equivalent amplitude has no obvious uctuationexcept for Al7075 under spindle speed of 2000 r/min,which may be caused by the inhomogeneous materialproperties of the aluminum alloy. As the feed rate can onlydetermine the overlap of the tool prole in radial direction,it does not contribute to the amplitude. Therefore, theactual relative tool-work vibration can be regarded as con-and its discretization form can be expressed as

Yhxi A1 cos2pfDxi 1 5where Dx 1=mf and f was assumed as 1=2s, m is an opti-mized positive integer, i 1;2; . . . ;N1, N1 dNs=Dxe. Thearithmetic roughness value Rat calculated from the proleof tool locus and the arithmetic roughness value Rah calcu-lated from the curve of simple harmonic motion can begiven as Eqs. (6) and (7) respectively.

Rat 1NXN

i1Ytxi

PNi1YtxiN

6

xYx))(,( 222 xYx

Mic

rom

eter

sFig. 2. Extract tool locus from thstant with increasing feed rate for each material under anidentical spindle speed.

Fig. 4 presents the relationship between the equivalentamplitude and depth of cut under feed rate of 40 mm/min.It is known that depth of cut determines the contact condi-tion between tool and workpiece and it would have adirect effect on cutting force resulting in the relative vibra-tion. However, the depth of cut in SPDT is too small toinuence the cutting force and the friction conditionbetween tool and chip. So no direct relationship betweendepth of cut and the relative vibration was found accordingto the results shown in Fig. 4, which indicates that theequivalent amplitude is maintained within a smaller rangeas the depth of cut is changed. In other words, the relativevibration during cutting process is almost unaffected bythe change in depth of cut for each material.

During cutting process, the increase of spindle speedcan augment spindle vibration contributing to the relativevibration between tool and workpiece, but also increasesthe cutting times at the same location to reduce the cuttingforce and further reduce the relative vibration. Fig. 5 showsthe effect of spindle speed on the relative vibration at dif-ferent feed rates and depths of cut for three materials.Fig. 5(a) shows that the equivalent amplitude has no dis-tinct change under a certain spindle speed for NiP, butchanges from less than 5 nm to near 15 nmwith increasingspindle speed, which means spindle speed affects the rela-tive vibration more signicantly than feed rate and depthof cut for NiP. It can be explained that spindle speed mainlyinuences spindle vibration in cutting homogeneous NiP.The evaluated equivalent amplitude is found to remain inthe range of 1018 nm for machining Cu at different spin-dle speeds, as shown in Fig. 5(b). During the cutting of Cumaterial, the increase of spindle speed may lead to largerspindle vibration and smaller cutting force at the sametime. Whereas, for Al7075 shown in Fig. 5(c), there is a sig-nicant change in the equivalent amplitude at differentspindle speeds while the equivalent amplitude decreaseswith increasing spindle speed. It is inferred that theincrease of spindle speed mainly reduces the cutting force,as Al7075 is a typical inhomogeneous alloy.

In general, it can be concluded that the actual relativetool-work vibration is signicantly inuenced by thechange in spindle speed, but not by feed rate and depthof cut. Thus, among the cutting parameters, we only needto take into account the effect of spindle speed on thevibration when a model is established for predicting sur-face roughness.

ool locus))(,( iii xYx

Measured surface profile

ters

sured surface roughness prole.4.3. Effect of material property

The surface topography and surface prole of themachined surfaces are shown in Fig. 6 for every materialunder same cutting parameters (spindle speed: 1000 r/min, feed rate: 25 mm/min, depth of cut: 2 lm). A dash-dot-line was drawn by connecting a series of tool noselocations in the prole to observe the relative tool-workvibration directly. It can be observed that the dash-dot-lineis almost straight for material NiP, which implies that themeasured prole is close to the ideal prole and the rela-tive tool-work vibration is negligible. Moreover, based on

0 rate (

Spind

24 J. Chen, Q. Zhao /Measurement 69 (2015) 203025 30

5

10

15

20

Equi

vale

nt a

mpl

itude

(nm

)

Equi

vale

nt a

mpl

itude

(nm

)

25 30 35 400

10

20

30

40

50

NiPCuAl7075

Feed rate (mm/min) Feed(a)

Fig. 3. Relationship between the equivalent amplitude and feed rate. (a)2000 r/min.

15

20

25

30

30

40

50

NiPCum

plitu

de (n

m)

ampl

itude

(nm

)analyzed results, the equivalent amplitude was less than10 nm for a spindle speed of 1000 r/min, as shown inFig. 7. This phenomenon can be explained from the mate-rial property of NiP shown in Fig. 8. NiP has amorphousstructure, in which the atomic arrangement does not fea-ture with long-range order and translation cyclicity. As aresult, the solid solution structure of NiP is homogeneousand does not have grain boundaries, dislocations, twincrystals and other defects. In addition, the passivating lmcovered on the surface of NiP basal body also has homoge-neous structure without any dislocation. Therefore, therelative vibration is very small in the case of machiningNiP because of the high isotropy of this material.

It can be observed from Fig. 6(b), that there is a largeuctuation for the displacement between tool and work-piece when machining Cu as compared to NiP. The resultsof equivalent amplitude also support this conclusion and itcan be seen that, the magnitude of all the values wasgreater than 10 nm, as shown in Fig. 7. This fact can be

2 3 4 50

5

10

2 3 4 5 6 7 80

10

20 Al7075

Equi

vale

nt a

Equi

vale

nt

Depth of cut (m) Depth of (a)

Fig. 4. Relationship between equivalent amplitude and depth of cut. (a) Spind2000 r/min.

1000 1200 1400 1600 1800 20000

5

10

15

20

Equi

vale

nt a

mpl

itude

(nm

)

Equi

vale

nt a

mpl

itude

(nm

)

(a)1000 1200 14000

5

10

15

20

Spindle speSpindle speed (r/min)

Fig. 5. Relationship between equivalent amplitude and spindle speEqui

vale

nt a

mpl

itude

(nm

)

25 30 35 400

5

10

15

20

NiPCuAl7075

(c)35 40

NiPCuAl7075

(b) Feed rate (mm/min)mm/min)

le speed: 1000 r/min; (b) spindle speed: 1500 r/min; (c) spindle speed:

10

15

20

mpl

itude

(nm

)

NiPCuAl7075explained on the basis that copper (Cu) is a polycrystallinealloy material and does not have a similar homogeneousstructure as NiP. However, copper has some deoxidizingelements and other elements in the bulk material besidespure Cu in order to improve material performance, as seenfrom the metallurgical structure of Cu shown in Fig. 9.

As shown in Table 2, Al, Zn, Mg and Cu are the main ele-ments that make up Al7075. It can form solid solutionstructure or a chemical compound in the basal body of Altermed as trapped phase, which has a different physicaland mechanical property from the basal body. As a result,this material was strengthened by the trapped phase,thereby increasing the hardness. However, the existenceof trapped phase makes the material non-homogeneous.The metallurgical structure in Fig. 9 shows the trappedphase in Al7075 has a higher proportion and a bigger sizeas compared to Cu. The machined surface prole ofAl7075 exhibits the largest displacement between tooland workpiece along with the largest equivalent

2 3 4 5 6 7 80

5 NiPCuAl7075

Equi

vale

nt a

(c)6 7 8

(b)cut (m) Depth of cut (m)

le speed: 1000 r/min; (b) spindle speed: 1500 r/min; (c) spindle speed:

1000 1200 1400 1600 1800 20000

10

20

30

40

50

(c)(b)

Equi

vale

nt a

mpl

itude

(nm

)

1600 1800 2000

ed (r/min) Spindle speed (r/min)

ed. (a) Material: NiP; (b) material: Cu; (c) material: Al7075.

(a)Millimeters

J. Chen, Q. Zhao /Measurement 69 (2015) 2030 25crom

eter

s M

icro

met

ers amplitude, i.e., Al7075 exhibits the biggest relative tool-work vibration among the three materials as shown inFigs. 6 (c) and 7. It can be concluded that material proper-ties can largely inuence the actual relative tool-workvibration in SPDT, thus we must consider the effect ofmaterial properties on the vibration behavior when pre-dicting surface roughness.

4.4. Effect of tool wear

In the machining process for Al7075, serious wear ofdiamond tool occurred due to its higher hardness. Fig. 10shows the degree of tool wear when the machining wascompleted. It can be seen that the circular part of diamond

(b)

(c)

Millimeters

Mi

Millimeters

Mic

rom

eter

s

Fig. 6. Three-dimensional topography and surface prole of machined surface. (a) Material: NiP; (b) material: Cu; (c) material: Al7075.

0

10

20

30

40

50

NiP Cu Al7075

Equi

vale

nt a

mpl

itude

(nm

)

Fig. 7. Relationship between equivalent amplitude and materialproperty.

20 40 60 80 1000

500

1000

1500

2000

Intensity (cps)

2theta (deg.)

Fig. 8. X-ray spectra of NiP.

Basal body

Trapped phase

Basal body

Trapped phase

Fig. 9. Metallurgical structure of Cu (left) and Al7075 (right).

tool has to cut the hard trapped phase and soft basal body

n

.3

26 J. Chen, Q. Zhao /Measurement 69 (2015) 2030of Al alternately, resulting in the repeating change of cut-ting state and cutting force in the turning process. The rela-tive tool-work vibration for cutting this material must begreater than cutting homogeneous materials. However,when the diamond tool wears out, the length of contactzone may increase to 100 lm, as shown in Fig. 10.Accordingly, the part of workpiece in contact with the dia-mond tool is composed of the hard trapped phase and softbasal body simultaneously, leading to a steadier materialremoval process as compared to before the tool wear.Therefore, the relative tool-work vibration gets smallerwith increase in tool wear, and the effect of tool wear onthe vibration must be considered in the turning process.

5. The material swelling effect

5.1. Method of quantifying the swelling effect

In the SPDT process, as the tool has two edges includingcutting edge and burnishing edge, the latter burnishes andindents the freshly machined surface besides cutting thematerials via cutting edge in turning process. Meanwhile,the metal left behind the cutting edge undergoes highpressure, which results in a material ow toward the sideof the active cutting edge [16]. The material left behindthe ank face recovers after burnishing [3]. Moreover, thecutting force along the main cutting edge pushes asidethe work material near the tool nose, causing it to owtoward the free surface [17]. The combined effect of plasticow, burnishing, and elastic recovery is called the swellingtool contacting the workpiece during the machining hasworn out into a straight shape. Further analysis of Fig. 10revealed that the worn part had a height of 7.6 lm and awidth of 95.8 lm. It is generally agreed that tool wearmay lead to a larger relative tool-work vibration. On thecontrary, it is found in this study that the equivalentamplitude becomes smaller with the increase in cuttingdistance and with the aggravation in tool wear, as shownin Fig. 11. The equivalent amplitude decreases from44 nm to 4 nm, indicating that the relative tool-workvibration was reduced gradually.

This can be explained from the metallurgical structureshown in Fig. 9 (right), in which the size of trapped phaseis about 20 lm in material of Al7075, while the length ofcontact zone between tool and workpiece during the turn-ing process is not larger than 10 lm. Thus, the diamond

Table 2Chemical composition of Al7075.

Composition Cu Si Fe M

Mass percent (%) 1.22.0 0.4 0.5 0effect [13], which causes the change of tool marks genera-tion on the machined surface, as shown in Fig. 12.

Liu et al. [18] showed plastic side ow could increasepeak-to-valley roughness due to the material piling up atthe trailing edge of the tool. Sata et al. [9] found workmaterial swells at the end of the active cutting edge caus-ing a greater tool mark on the machined surface becausethe swelling increases the peaks height of the feed compo-nents in spectrum. However, in some cases, the swellingeffect was found to decrease the surface roughness whenplastic ow for ductile materials is overwhelmed by theeffect of materials recovery [3]. The amount of recoveryis decided by the material properties and forces on theank face [13]. Previous research implies that the amountof swelling depends upon the properties of the materialbeing cut. Softer and more ductile material show higherswelling of the tool marks [9]. In order to quantify theswelling effect, Sata et al. [9] dened the swelling ratioas the ratio of power between the rst order feed compo-nent of the measured roughness spectrum and the idealroughness spectrum. Then, Cheung et al. [13] proposed alocal swelling ratio SRi at the ith radial section of themachined surface which is dened as the square root ofthe ratio of the power spectral density for the rst feedcomponents of the measured and the ideal surface rough-ness spectrum.

In present study, the effect of material swelling on sur-face roughness is required to consider in the predictionmodel, so it is not feasible to process the measured rough-ness prole by means of spectrum method. Therefore, aswelling proportion SP was proposed to quantify the swel-ling effect based directly on measured roughness prole. Itis dened as a proportion between the average height oftool mark on measured surface and the height of ideal toolmark:

SP Pn

i1HrinHc

9

where Hri is the height of the ith tool mark after both reco-vering and plastic owing on machined surface, as shownin Fig. 12, Hc is the calculated height of ideal tool markHc s2=8R; s is tool feed per work revolution, R is the toolnose radius) and n is the number of tool marks evaluated. Itcan be deduced that the effect of plastic ow will be largerthan the effect of recovery on roughness prole and thus toincrease the surface roughness, if SP > 1; while the effect ofplastic ow will be smaller than the effect of recovery onroughness prole and thus to reduce the surface rough-ness, if SP < 1.

5.2. Effect of cutting parameters

Sata et al. [9] studied the swelling ratio of C45 and brassat the different feed rates. It was found that the swelling

Mg Zn Cr Ti Al

2.12.9 5.16.1 0.4 0.06 90ratios remain nearly constant within a certain feed raterange. Cheung et al. [13] analyzed the distribution ofswelling ratio on machined surface of aluminum singlecrystal and Al6061 to evaluate the materials anisotropy.However, no report was found to predict surface roughnesstaking into account the swelling effect. Therefore, theeffect of cutting parameters on the material swelling and

0) an

J. Chen, Q. Zhao /Measurement 69 (2015) 2030 27Fig. 10. Image of tool wear (left, magnication 20the change of surface roughness caused by the swellingeffect is still far from understand very well and needs tobe further studied.

For the purpose of correlating a prediction model of sur-face roughness with the swelling effect, it was analyzed atdifferent cutting parameters for NiP, as shown in Fig. 13.The swelling proportion is in the ranges of 1.211.39,1.041.11 and 0.961.08 at varying spindle speeds of1000 r/min, 1500 r/min and 2000 r/min respectively underdifferent feed rates and depths of cut. The result impliesthat the swelling proportion nearly keeps invariable withthe changing feed rates and cutting depths for a xed spin-dle speed. However, it decreases obviously when the spin-dle speed was increased, which means machined surface

5.5 6.0 6.5 7.0 7.5 8.0 8.50

10

20

30

40

50

Cutting distance (km)

Equi

vale

nt a

mpl

itude

(nm

)

Fig. 11. Relationship between equivalent amplitude and tool wear.

Hc

HrHfIdeal surface calculated

Surface after plastic flow Surface after recovery

Fig. 12. Schematic illustration for the effect of swelling on surfacegeneration (Hc height of ideal tool mark calculated, Hf height of toolmark after plastic ow, Hr height of tool mark after recovery).1

1.5

Swel

ling

prop

ortio

n

d size of worn part (right, magnication 1000).becomes smoother at a higher spindle speed. This can beexplained based on the fact that at higher spindle speedthe same position on the fresh machined surface will beburnished and indented many times, which cause a largerresidual stress onto the surface, with a larger recovery andthus a lower height of tool mark. The results reveal that thematerials swelling effect was mainly affected by thespindle speed, which is very useful and signicant forthe proposed prediction model in this study, because theroughness prole after plastic ow and recovery can beclearly known based on the swelling proportion at differ-ent spindle speeds.

6. A prediction model of surface roughness

6.1. Creation of a prediction model

Based on above analysis, the main factors affecting therelative tool-work vibration are spindle speed, materialproperty and tool wear. In addition, the swelling effect ofa material will change mainly with the change in spindlespeed. Therefore, in the prediction model, experimentsare necessary to determine the relative tool-work vibrationand the swelling effect at different spindle speeds for eachmaterial. As shown in Fig. 14, the roughness prole wasrst measured on the machined surface in radial direction,and then processed by the methods discussed in the

1000 1200 1400 1600 1800 20000.5

Spindle speed (r/min)

Fig. 13. The swelling ratio of NiP at different cutting parameters.

Then, both the roughness prole after the swellingeffect YSx and the curve of equivalent simple harmonicmotion Yhx were produced with the method of additionof waveforms on MATLAB/Simulink software, where Yhxis given by Eq. (4) and shown in Fig. 15(c). So, the additionof two waveforms resulted in a new roughness prole Y(x),as shown in Fig. 15(d). Finally, predicted arithmetic rough-ness value Ra was calculated with export data of the rough-ness prole Y(x) on MATLAB/Simulink software. It is notedthat the roughness prole Y(x) contains both the relativetool-work vibration and the swelling effect, is only usedto calculate roughness value but not actual roughness pro-le of machined surface.

In conclusion, there are three aspects of signicant fea-ture in the prediction model presented in this paper, as

Experiments Measure roughness profile

Data processing

Cutting parameters

Materials property

Relative tool-work vibration

The swelling proportion

Ideal roughness profile

Roughness profile after swelling effect

Equivalent vibration

Addition of waveforms and data processing

Surface roughness

28 J. Chen, Q. Zhao /Measurement 69 (2015) 2030previous section. As a result, the actual relative tool-workvibration was simplied as a simple harmonic motion tocalculate the equivalent amplitude A, while swelling pro-portion SP of each material can be determined accordingto Eq. (9).

Once the cutting parameters are conrmed, the idealroughness prole in radial direction shown in Fig. 15(a)can be expressed as

YIx x2

2Rif 0 6 x 6 s=2 10

YIx x ns2

2Rif x > s=2 11

where s is tool feed per work revolution, R is the tool noseradius and n = dx s=2=sede means rounding down tothe nearest whole unit). Since the swelling effect cannotbe avoided, both plastic ow and recovery of the materialwere taken into account to evaluate a roughness proleafter swelling effect YSx, which is calculated on the basisof the ideal roughness prole as well as the calculated

Fig. 14. A block diagram of the prediction model of surface roughness.swelling proportion SP, as shown in Fig. 15 (b).

YSx SPYIx 12

x0 s 2s 3s

Ys(x) (b)

After swelling effect

2s

(a)

x0 3s

c

Y (x)

H

cHrH

s

1

Fig. 15. The schematic diagram of predicting process of surface roughness. (a) Idshown in Fig. 12; (c) equivalent simple harmonic motion; (d) roughness prolefollows:

(1) The evaluated vibration is more credible and close tothe actual vibration in the turning process becauseof the relative tool-work vibration coming from themachined surface.

(2) The swelling effect, i.e., the material plastic ow andrecovery in turning is rst taken into account in theprediction of surface roughness.

(3) This prediction model adopts the approach combin-ing machining theory with experimentalinvestigation.

6.2. Verication of the prediction model

Verication tests of face cutting were carried out formaterials NiP and Cu. The tests were conducted on afour-axis CNC ultra-precision machine tool (made byNachi-Fujikoshi Corp., Japan) and a diamond tool used intests has a rake angle of 0, a front clearance angle of 6and a tool-nose radius of 0.5 mm. The cutting conditionsare tabulated as Table 3. By using the model proposed inthe present study, the equivalent amplitude A and swellingproportion SP were rst evaluated under varying cuttingparameters for NiP and Cu, as shown in Table 4. Then sur-face roughness values Ra were predicted.

The predicted values, measured values and ideal valuesare shown in Fig. 16, in which the ideal values were calcu-lated from the ideal roughness prole YIs given by Eqs.(10) and (11). It can be seen that there are three kinds of

x

Yh(x)

0

A2

A

x

Y(x)

0

Addition of waveforms

(c)

(d)

eal roughness prole; (b) roughness prole after swelling effect, Hc and Hrcontaining both the relative tool-work vibration and the swelling effect.

surface roughness values, which increases with theincrease in feed rate, as illustrated in Fig. 16(a) and (c).This can be explained that a bigger feed rate will makethe tool marks deeper and wider in ideal roughness prole,

and lead to a larger ideal value of surface roughness ascompared to a smaller feed rate. Additionally, it was foundthat there was a good accordance between the predictedand the measured values, indicating the prediction errorwas small or close to negligible in this case.

Fig. 16(b) and (d) presents the measured surface rough-ness having no obvious uctuation when the depth of cutincreases, which supports that the effect of depth of cuton the relative vibration and the swelling effect can beignored in the prediction model. The little uctuation formeasured surface roughness may be caused due to thechange of the machine tool error or the swelling propor-tion with the change in depth of cut. However, the resultsfor the measured and predicted values were in goodagreement.

It is noticed that the two materials (NiP and Cu) weremachined with the same diamond tool, the same machinetool and the same cutting parameters, theoretically,

Table 3Cutting conditions of verication tests.

Termno.

Spindle speed(rpm)

Feed rate(mm/min)

Depth of cut(lm)

Tool-noseradius (mm)

Termno.

Spindle speed(rpm)

Feed rate(mm/min)

Depth of cut(lm)

Tool-noseradius (mm)

1 1500 25 2 0.5 8 2000 25 2 0.52 1500 30 2 0.5 9 2000 30 2 0.53 1500 35 2 0.5 10 2000 35 2 0.54 1500 40 2 0.5 11 2000 40 2 0.55 1500 40 4 0.5 12 2000 40 4 0.56 1500 40 6 0.5 13 2000 40 6 0.57 1500 40 8 0.5 14 2000 40 8 0.5

Table 4Equivalent amplitude A and swelling proportion SP calculated by themodel.

A (nm) and SP Spindle speed (rpm)1500 2000

Material NiP

A 8 12

SP 1.11 1.08

Material Cu

A 13 14

SP 0.82 0.85

J. Chen, Q. Zhao /Measurement 69 (2015) 2030 29(nm

) 60

7025 30 35 400

10

20

30

40

Surf

ace

roug

hnes

s Ra

(nm

)Su

rfac

e ro

ughn

ess R

a

Ideal

NiP Cu

(c)

25 30 35 400

10

20

30

40

50

Feed rate (mm/min)

Feed rate (mm/min)

Ideal

NiP Cu

(a)

Fig. 16. Model predicted surface roughness (dash dot line), measured surface rouspeed: 1500 r/min, depth of cut: 2 lm; (b) spindle speed: 1500 r/min, feed rate: 4speed: 2000 r/min, feed rate: 40 mm/min.30

40

Surf

ace

roug

hnes

s Ra

(nm

)a

(nm

)

2 3 4 5 6 7 80

10

20

30

40

50

60

70

Depth of cut (m)

Ideal

NiP Cu

(b)(d)2 3 4 5 6 7 8

0

10

20

Ideal

NiP Cu Su

rfac

e ro

ughn

ess R

Depth of cut (m)

ghness (solid line) and ideal surface roughness for NiP and Cu. (a) Spindle0 mm/min; (c) spindle speed: 2000 r/min, depth of cut: 2 lm; (d) spindle

the ideal surface should be identical, but the measured sur-face roughness values were found to have a big differencein comparison to the corresponded ideal value. This differ-ence could be caused by the effect of material property onthe relative vibration and the swelling effect. Especially formaterial Cu, most of predicted surface roughness and mea-

the error is within 6.5%, which further proves the improve-ment of the model proposed in the present study.

Acknowledgments

The authors would like to express their sincere thanks

30 J. Chen, Q. Zhao /Measurement 69 (2015) 2030sured surface roughness are less than ideal value, which iscaused by the swelling proportion SP < 1, i.e., Hr < Hc inFig. 15(b). Therefore, it is necessary to consider the inu-ence of material property in order to achieve high predic-tion accuracy when predicting the surface roughness.Overall, using the prediction model in the present study,a good accordance between the measured and predictedvalues is realized. The average prediction error of surfaceroughness Ra is found to be 5.1% as well as the error iswithin 6.5% in most cases.

7. Conclusions

The actual relative tool-work vibration during the turn-ing process is different from the relative vibration mea-sured before turning. The swelling effect can obviouslyaffect the surface roughness prole through changing thesize of tool mark, thus have to be taken into account theprediction of surface roughness in SPDT.

In machining a material with a homogeneous structure(e.g., NiP), the actual relative tool-work vibration causedwas very smaller when compared to inhomogeneousmaterials. This is due to the fact that homogeneous materi-als do not present grain boundaries, dislocations, com-pound twins and other defects. But for inhomogeneousmaterials (e.g., Cu and Al7075), material induced vibrationwas larger and mainly determined by the size of trappedphase and the length of contact zone between tool andworkpiece.

Among three types of cutting parameters, the spindlespeed has the most dominant inuence on the relativevibration and the swelling effect when compared to thatof the other two parameters of feed rate and depth of cut.Moreover, it was found that a higher spindle speed leadsto a lower swelling proportion and smoothermachined sur-face, because the larger residual stress and amount ofrecovery can be caused on the fresh machined surface.

Using the approach combining machining theory withexperimental investigation, a prediction model of surfaceroughness in SPDT was proposed. It takes into accountthe actual relative tool-work vibration extracted from themachined surface and the swelling effect, which representsthe complicated elastic and plastic deformation in cutting.Therefore, this model is further close to the actual cuttingprocess.

There is a good agreement between the model predictedand the measured values. The average prediction error ofsurface roughness Ra is found to be 5.1%while inmost casesto the National Scientic Foundation of China (NSFC)(Contract No. 51205343) and Postdoctoral ScienceFoundation of China (Contract No. 2012M520595) for theirnancial support of the research work.

References

[1] M. Tauhiduzzaman, S.C. Veldhuis, Effect of material microstructureand tool geometry on surface generation in single point diamondturning, Precis. Eng. 38 (2014) 481491.

[2] P.G. Benardos, G.C. Vosniakos, Predicting surface roughness inmachining: a review, Int. J. Mach. Tools Manuf. 43 (2003) 833844.

[3] M.C. Kong, W.B. Lee, C.F. Cheung, S. To, A study of materials swellingand recovery in single-point diamond turning of ductile materials, J.Mater. Process. Technol. 180 (2006) 210215.

[4] K.V. Rao, B.S.N. Murthy, N. Mohan Rao, Prediction of cutting toolwear, surface roughness and vibration of work piece in boring of AISI316 steel with articial neural network, Measurement 51 (2014) 6370.

[5] Z. Hessainia, A. Belbah, M.A. Yallese, T. Mabrouki, J.F. Rigal, On theprediction of surface roughness in the hard turning based on cuttingparameters and tool vibrations, Measurement 46 (2013) 16711681.

[6] V. Upadhyay, P.K. Jain, N.K. Mehta, In-process prediction of surfaceroughness in turning of Ti6Al4V alloy using cutting parametersand vibration signals, Measurement 46 (2013) 154160.

[7] A.M. Zain, H. Haron, S. Sharif, Prediction of surface roughness in theend milling machining using articial neural network, Expert Syst.Appl. 37 (2010) 17551768.

[8] D. Karayel, Prediction and control of surface roughness in CNC latheusing articial neural network, J. Mater. Process. Technol. 209 (2009)31253137.

[9] T. Sata, M. Li, S. Takata, H. Hiraoka, Q.Q. Li, X.Z. Xing, X.G. Xiao,Analysis of surface roughness generation in turning operation and itsapplications, Annals CIRP 34 (1985) 473476.

[10] S. Takasu, M. Masuda, T. Nishiguchi, Inuence of study vibrationwith small amplitude upon surface roughness in diamondmachining, Annals CIRP 34 (1985) 463467.

[11] C.F. Cheung, W.B. Lee, Modelling and simulation of surfacetopography in ultra-precision diamond turning, Proc. Inst. Mech.Eng. Part B: J. Eng. Manuf. 214 (2000) 463480.

[12] W.B. Lee, C.F. Cheung, A dynamic surface topography model for theprediction of nano-surface generation in ultra-precision machining,Int. J. Mech. Sci. 43 (2001) 961991.

[13] C.F. Cheung, W.B. Lee, A multi-spectrum analysis of surfaceroughness formation in ultra-precision machining, Precis. Eng. 24(2000) 7787.

[14] H. Wang, S. To, C.Y. Chan, C.F. Cheung, W.B. Lee, A theoretical andexperimental investigation of the tool-tip vibration and its inuenceupon surface generation in single-point diamond turning, Int. J.Mach. Tools Manuf. 50 (2001) 241252.

[15] W.B. Lee, C.F. Cheung, S. To, Materials induced vibration in ultra-precision machining, J. Mater. Process. Technol. 8990 (1999) 318325.

[16] M.C. Shaw, J.A. Crowell, Finish machining, Annals CIRP 13 (1965)(1965) 522.

[17] T. Sata, Surface nish in metal cutting, Annals CIRP 12 (1964) 190197.

[18] K. Liu, S.N. Melkote, Effect of plastic side ow on surface roughnessin micro-turning process, Int. J. Mach. Tools Manuf. 46 (2006) 17781785.

A model for predicting surface roughness in single-point diamond turning1 Introduction2 Previous theoretical models3 Experimental setup4 The relative tool-work vibration4.1 Evaluating the relative tool-work vibration4.2 Effect of cutting parameters4.3 Effect of material property4.4 Effect of tool wear

5 The material swelling effect5.1 Method of quantifying the swelling effect5.2 Effect of cutting parameters

6 A prediction model of surface roughness6.1 Creation of a prediction model6.2 Verification of the prediction model

7 ConclusionsAcknowledgmentsReferences