Engineering Science and Technology, an International Journal 19 (2016) 1971–1984

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Engineering Science and Technology,an International Journal

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Short Communication

Static structural analysis of great five-axis turning–milling complex CNCmachine

http://dx.doi.org/10.1016/j.jestch.2016.07.0132215-0986/� 2016 Karabuk University. Publishing services by Elsevier B.V.This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

⇑ Corresponding author.E-mail addresses: cchong@mail.hust.edu.tw (C.C. Hong), clchang@mail.hust.edu.

tw (C.-L. Chang), george@llmachinery.com.tw (C.-Y. Lin).

Peer review under responsibility of Karabuk University.

C.C. Hong ⇑, Cheng-Long Chang, Chien-Yu LinDepartment of Mechanical Engineering, Hsiuping University of Science and Technology, Taichung 412-80, Taiwan, ROC

a r t i c l e i n f o a b s t r a c t

Article history:Received 22 April 2016Revised 9 June 2016Accepted 22 July 2016Available online 1 August 2016

Keywords:CAEStaticConstructionDeformationCNCMachinery bed

The design and analysis experiences of computer aided engineering (CAE) used in the heavy industry isnovel for conventional company before prepare going to execute the fourth industrial revolution. Theresearch purpose is to provide a utilization results of computation and automation in the third industrialrevolution. The CAE with commercial software is used as the research method to analyze the linear staticconstruction, stress and deformation for secondary shaft system, primary shaft system and machinerybed in great five-axis turning–milling complex CNC machine. It is desirable to reduce most weight ofCNC machine and maintain good enough stress to resist external loads in the process of researches.The linear results and conclusion for static stresses and displacements of secondary shaft system, primaryshaft system and machinery bed are obtained with the commercial computer software SOLIDWORKS�

2014 simulation module.� 2016 Karabuk University. Publishing services by Elsevier B.V. This is an open access article under the CC

BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction

Heavy industry machines usually modern designed in less cost,time, manpower and with more efficient when compared withconventional design ways. Uriarte et al. [11] presented the design,principles and applications for heavy industry manufacturingmachines. There are some manufacturing means: cutting, turningand milling etc., introduced by Black et al. [2] products at the low-est cost are desired. For the general descriptions of five-axis turn-ing–milling complex computer numerical control (CNC) machine,Mao et al. [8] provided an automatic collection of machining preci-sion for a CNC turn-mill machining center. Kara and Budak [6] usedan orthogonal turn-milling to optimize machining processes on amulti-tasking CNC machine tool. Majerik and Jambo [9] used com-puter commercial software CATIA� V5 to simulate tool-paths onhard milling process. Bohez [3] presented the kinematic of five-axis CNC machining center with the work piece by four axes: X-axis, Y-axis, A-axis, B-axis and one Z-axis: tool. Wagner [13] usedthe AUTOLISP program (a commercial AUTOCAD� component) tosimulate the cutting tool path in the 5 axes CNC machining.

Doyle and Case [4] presented the CAE commercial software forthe students’ education in the manufacturing engineering. Zaehand Siedl [14] used finite element method (FEM) to simulate andpredict the machine tools in large deformation behavior. Mackerle[7] reviewed the 1976–1996 analysis and simulation of machiningby using FEM. There are some commercial CAE software: genera-tive structural analysis software of CATIA�, structural analysis soft-ware of ANSYS�, simulation software of SOLIDWORKS�, simulationsoftware of Creo�, simulation software of Inventor�, simulationsoftware of FreeCAD (an open-source), simulation software of NXTM

Nastran�, simulation software of Abaqus�, composite analysis andstructural sizing software of HyperSizer�, NFX simulation softwareof midas� etc. Vivekananda et al. [12] used commercial softwareANSYS� (one of the FEM codes) to compute the natural frequencyof vibration for ultrasonic assisted turning (UAT) machiningprocess.

Ananthavel et al. [1] used the numerical simulation software(Matlab�/Simulink) to investigate the power transfer capacity sys-tem. Mohammed et al. [10] used software ANSYS to simulate ther-mal history for welding UNS S31803 duplex stainless steel joints.Euan et al. [5] used the Matlab� graphical user interface (GUI) soft-ware to simulate static cutting forces for ceramic milling tools. Thedesign and analysis experiences of CAE used in the heavy industry isnovel for conventional company before prepare going to executethe fourth industrial revolution. The research purpose is to providea utilization results of computation and automation in the third

Fig. 1. Great five-axis turning–milling complex CNC machine assembling 3D parts.

1972 C.C. Hong et al. / Engineering Science and Technology, an International Journal 19 (2016) 1971–1984

industrial revolution. For the construction of great five-axis turn-ing–milling complexmachine in this paper, the linear static stressesand displacements of secondary shaft system, primary shaft systemand machinery bed of CNC machines are obtained with the SOLID-WORKS� 2014 simulation module. The maximum values of stressand displacement are provided to give a reference and predictionfor the future construction of complex CNC machine. In theadvanced future works, when the boundary condition is appliedto the calculating model, the nonlinear state of the contact surfacewould be considered, which has a great influence on the calculationresults. In addition to gravity, other dynamic loads, such as inertialforce, cutting vibration and impact force, can be translated into sta-tic loads, which can be applied to the calculation model.

2. Method of simulations

2.1. Mathematical model and software

In the linear static structural analysis without considering iner-tial force, damping force and impact force, also the nonlinear stateof the contact surface would not be considered, a general matrixequation of mathematical model is used in the computer programto solve for stress and displacement results as follow,

½M�fug ¼ ffg ð1Þwhere ½M� is material stiffness matrix, fug is displacement vector,ffg is external load vector. The method of simulation with the soft-ware SOLIDWORKS� simulation module is followed in its steps.Step one, preparing and assembling all three dimensional parts(3D) that wanted to be simulated. Step two, choosing the individualmaterials of 3D parts that defined the properties wanted to be ana-lyzed. Step three, setting up the corresponding boundary conditionsfor the restrictions on the 3D parts. Step four, external loadingsapplied on the 3D parts. Step five, mesh of grids generated for the

3D parts. Step six, computation. Step seven, displacement, strainand stress results found.

2.2. Assembling 3D parts

To use the commercial CAE software and run the static resultsfor complex CNC machine, it is necessary to prepare the assem-bling 3D parts of great five-axis turning–milling complex CNCmachine as shown in Fig. 1. The dimensions of main parts are pro-vided respectively, for machinery bed is 8470 mm � 1463 mm �783 mm, for primary shaft system is 1190.5 mm � 940 mm �860 mm, for secondary shaft system is 1397 m � 845 mm � 1426mm, for work piece is cylindrical column with diameter u950mm and length 5000 mm. The positions of secondary shaft systemcan be moved from 0 mm to 6900 mm, there are three locations(0 mm, 4000 mm and 6900 mm) of positions used to computedand analyzed for the CNC machine.

2.3. Materials of 3D parts

It is necessary to define the individual material of assembling3D parts for great five-axis turning–milling complex CNC machine.The materials of main parts are given, for machinery bed, shaft sys-tems and work piece are cast iron. The yield stress of cast ironmaterial is 275 MPa. To prevent failure in the CNC machine, thevalue of working stress in each material of components shouldunder its yield stress value.

2.4. Boundary conditions of machinery bed

Five types of clamp (4, 8, 14, 20 and 36 positions) boundary con-ditions of machinery bed are used to computed and analyzed forthe second principal axes of CNC machine locates at three kindsof position (0 mm, 4000 mm and 6900 mm). Total 36 positions

(a) Bottom view of 36 positions clamp boundary conditions

(b) Initial displacement and external gravity loads

Fig. 2. Total 36 positions clamp of machinery bed in CNC machine. (a) Bottom view of 36 positions clamp boundary conditions. (b) Initial displacement and external gravityloads.

C.C. Hong et al. / Engineering Science and Technology, an International Journal 19 (2016) 1971–1984 1973

(18 positions at each side) clamp of machinery bed in CNC machineis shown in Fig. 2 for secondary shaft system locates at 0 mm, typ-ically. In Fig. 2(a), bottom view of 36 positions clamp boundaryconditions is shown. In Fig. 2(b), the initial displacement (displace-ment is 0 mm at each position of clamps) and the external gravityloads (acceleration of gravity 9.81 m/s2 perpendicular to X–Zplane) are shown.

2.5. Convergence study of meshes

A typical mesh of grids with secondary shaft system at4000 mm location for the CNC machine is shown in Fig. 3. To findthe more suitable number meshes used in the computation andanalyses for the CNC machine, it is necessary to make convergencestudy of meshes. There are 200.00 mm, 160.00 mm, 155.00 mm,

Fig. 3. Typical mesh of grids for the CNC machine.

Table 1Convergence results.

Maximum mesh grid sizes (mm) Maximum displacement values (mm)

200.00 8.454160.00 8.463155.00 8.465150.00 8.472140.00 8.470

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150.00 mm and 140.00 mm of maximum size lengths of five typemeshes used to find the maximum displacement converged valuesof machinery bed.

3. Results and discussions

3.1. Convergence results

Convergence results of maximum displacement values of total36 clamp positions machinery bed with secondary shaft systemat 0 mm location in CNC machine are listed in the Table 1. Themaximum size length 150.00 mm of mesh grids can be consideredin good convergence condition and used these grids to calculatethe stresses and displacements for further static computation withthe SOLIDWORKS� 2014 simulation module.

3.2. Static results due to gravity force of machinery bed and externalloads

Firstly, only the machinery bed gravity force (weight 13 tons)itself on the machinery bed are considered, static stress and dis-placement results of total 36 positions clamp of machinery bedare shown in Figs. 4(a) and (b), respectively. The maximum valueof stresses is 2 MPa and the maximum value of displacements is0.0038 mm in the machinery bed. Secondly for the simplicity, themachinery bed gravity forces (weight 13 tons) and uniform pres-

sure external loads (10 MPa) on the machinery bed are considered.Static stress and displacement results of total 36 positions clamp ofmachinery bed are shown in Figs. 4(c) and (d), respectively. Themaximum value of stresses is 396 MPa and the maximum valueof displacements is 0.89 mm in the machinery bed. The maximumvalue (396 MPa) of stress due to gravity force and uniform pressureexternal loads (10 MPa) are greater than yield stress value275 MPa, so the machinery bed are in un-safety condition. Donot suggest the machinery bed to stand greater and over than10 MPa external loads. Fortunately, the total actual gravity loadsof primary shaft system, secondary shaft system, work piece andend supporter upon the machinery bed are around 0.1 MPa(10 tons/m2), it is less than 10 MPa and can be considered in safetycondition.

3.3. Static results due to gravity force of main parts

For the precision, all the gravity force loads of main parts inmachinery bed, primary shaft system, secondary shaft system,work piece and end supporter are considered. Static stress and dis-placement results of total 36 positions clamp of machinery bed(weight 13 tons) with secondary shaft system at three locationsof X axis: 0 mm, 4000 mm and 6900 mm in CNC machine due togravity force effect are shown in Figs. 5–7, respectively. Whenthe secondary shaft system located at X axis: 0 mm, the maximumvalue of stresses is 154 MPa and the maximum value of displace-ments is 0.17 mm. When the secondary shaft system moved andlocated at X axis: 4000 mm, the maximum value of stresses is137 MPa and the maximum value of displacements is also0.17 mm. In order to express even clear of the simulation results,resultant displacement (URES) for chosen nine nodes at the bottomline of secondary shaft system is depicted with the curve picture asshown in Fig. 6(c), they are linearly decreasing from value0.011 mm. When the secondary shaft system moved and locatedat X axis: 6900 mm, the maximum value of stresses is 129 MPaand the maximum value of displacements is same as 0.17 mm.

(a) Stress for machinery bed due to gravity force

(b) Displacement for machinery bed due to gravity force

Fig. 4. Stress and displacement for machinery bed due to gravity force and external loads. (a) Stress for machinery bed due to gravity force. (b) Displacement for machinerybed due to gravity force. (c) Stress for machinery bed due to gravity force and external loads. (d) Displacement for machinery bed due to gravity force and external loads.

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The maximum values of stress due to gravity force effect for sec-ondary shaft system at X axis: 0 mm, 4000 mm and 6900 mm areall smaller than yield stress value 275 MPa, so the CNC machinecan be considered in safety condition.

3.4. Static maximum values for five types of clamp

For secondary shaft system locates at X axis: 0 mm, the com-pared results of static maximum stress and displacement for

(c) Stress for machinery bed due to gravity force and external loads

(d) Displacement for machinery bed due to gravity force and external loads

Fig. 4 (continued)

1976 C.C. Hong et al. / Engineering Science and Technology, an International Journal 19 (2016) 1971–1984

five types of clamp (36, 20, 14, 8 and 4 positions) boundaryconditions of machinery bed are shown in Tables 2 and 3,respectively. The static maximum stress (154 MPa) and dis-placement (0.17 mm) in total 36 positions clamp boundary con-ditions of machinery bed are found in smaller values than theothers. The static stress and displacement for other four typesof clamp (20, 14, 8 and 4 positions) boundary conditions of

machinery bed are shown in Figs. 8–11 with enlarge amplifica-tion scale, respectively.

3.5. Reduced weight for machinery bed

Usually it is desirable to reduce most weight of CNC machineand maintain good enough stress to resist external loads. The

(a) Stress for secondary shaft system at x axis: 0mm

(b) Displacement for secondary shaft system at x axis: 0mm

Fig. 5. Stress and displacement for secondary shaft system at X axis: 0 mm. (a) Stress for secondary shaft system at X axis: 0 mm (b) Displacement for secondary shaft systemat X axis: 0 mm.

C.C. Hong et al. / Engineering Science and Technology, an International Journal 19 (2016) 1971–1984 1977

reduced weight for machinery bed (weight 12 tons) with tunneltype is shown in Fig. 12. The ribs in the two sides of bed areremoved, formed as a tunnel shape and reduced 1 ton weight.Compared results of static stress and displacement in total 36 posi-tions clamp for two types of machinery beds (weight 13 tons and12 tons) with secondary shaft system at three locations of X axis:

0 mm, 4000 mm and 6900 mm in CNCmachine due to gravity forceeffect are shown in Tables 4 and 5, respectively. Also the maximumvalues of stress due to gravity force effect for secondary shaft sys-tem at X axis: 0 mm, 4000 mm and 6900 mm are all smaller thanyield stress value 275 MPa, so the two type’s beds of CNC machinescan be considered in safety condition.

(a) Stress for secondary shaft system at x axis: 4000mm

(b) Displacement for secondary shaft system at x axis: 4000mm

(c) Resultant displacement (URES) for chosen nodes of secondary shaft system

Fig. 6. Stress and displacement for secondary shaft system at X axis: 4000 mm. (a) Stress for secondary shaft system at X axis: 4000 mm. (b) Displacement for secondary shaftsystem at X axis: 4000 mm (c) Resultant displacement (URES) for chosen nodes of secondary shaft system.

1978 C.C. Hong et al. / Engineering Science and Technology, an International Journal 19 (2016) 1971–1984

(a) Stress for secondary shaft system at x axis: 6900mm

(b) Displacement for secondary shaft system at x axis: 6900mm

Fig. 7. Stress and displacement for secondary shaft system at X axis: 6900 mm. (a) Stress for secondary shaft system at X axis: 6900 mm. (b) Displacement for secondary shaftsystem at X axis: 6900 mm.

Table 2Compared static maximum stresses for five types of clamp.

Maximum stresses Clamp positions of bed

Total 36 Total 20 Total 14 Total 8 Total 4

154 MPa 157 MPa 155 MPa 159 MPa 191 MPa

C.C. Hong et al. / Engineering Science and Technology, an International Journal 19 (2016) 1971–1984 1979

Table 3Compared static maximum displacements for five types of clamp.

Maximum displacements Clamp positions of bed

Total 36 Total 20 Total 14 Total 8 Total 4

0.17 mm 0.17 mm 0.18 mm 0.21 mm 0.49 mm

(a) Stress for total 20 clamp positions of bed

(b) Displacement for total 20 clamp positions of bed

Fig. 8. Stress and displacement for total 20 clamp positions of bed with amplification scale 4863. (a) Stress for total 20 clamp positions of bed. (b) Displacement for total 20clamp positions of bed.

1980 C.C. Hong et al. / Engineering Science and Technology, an International Journal 19 (2016) 1971–1984

(a) Stress for total 14 clamp positions of bed

(b) Displacement for total 14 clamp positions of bed

Fig. 9. Stress and displacement for total 14 clamp positions of bed with amplification scale 4714. (a) Stress for total 14 clamp positions of bed. (b) Displacement for total 14clamp positions of bed.

C.C. Hong et al. / Engineering Science and Technology, an International Journal 19 (2016) 1971–1984 1981

(a) Stress for total 8 clamp positions of bed

(b) Displacement for total 8 clamp positions of bed

Fig. 10. Stress and displacement for total 8 clamp positions of bed with amplification scale 3934. (a) Stress for total 8 clamp positions of bed. (b) Displacement for total 8clamp positions of bed.

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(a) Stress for total 4 clamp positions of bed

(b) Displacement for total 4 clamp positions of bed

Fig. 11. Stress and displacement for total 4 clamp positions of bed with amplification scale 1763. (a) Stress for total 4 clamp positions of bed. (b) Displacement for total 4clamp positions of bed.

C.C. Hong et al. / Engineering Science and Technology, an International Journal 19 (2016) 1971–1984 1983

Fig. 12. Reduced weight for machinery bed (weight 12 tons).

Table 4Compared static maximum stresses for two types of beds.

Maximumstresses

Machinery beds(Tons)

Secondary shaft system locations

0 mm 4000 mm 6900 mm

13 150 MPa 137 MPa 129 MPa12 150 MPa 159 MPa 157 MPa

Table 5Compared static maximum displacements for two types of beds.

Maximumdisplacements

Machinery beds(Tons)

Secondary shaft system locations

0 mm 4000 mm 6900 mm

13 0.17 mm 0.17 mm 0.17 mm12 0.19 mm 0.21 mm 0.20 mm

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4. Conclusions

In this paper, the static stresses and displacements of secondaryshaft system, primary shaft system and machinery bed of CNCmachines are obtained with the SOLIDWORKS� 2014 simulation

module. The static stress and displacement for other four typesof clamp boundary conditions of machinery bed are studied. It isdesirable to reduce most weight of CNC machine and maintaingood enough stress to resist external loads. The maximum valuesof stress due to gravity force effect are all smaller than yieldstress value, so the CNC machine can be considered in safetycondition.

Acknowledgements

The completion of this paper was made possible by a grantMOST 103-302-2-004 from Ministry of Science and Technology,Taiwan, ROC.

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