0
Research Papers

Smooth Tool Path Optimization for Flank Milling Based on the Gradient-Based Differential Evolution Method

[+] Author and Article Information
YaoAn Lu

State Key Laboratory of Mechanical
System and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: luyaoan028@163.com

Ye Ding

State Key Laboratory of Mechanical
System and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: y.ding@sjtu.edu.cn

LiMin Zhu

State Key Laboratory of Mechanical
System and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: zhulm@sjtu.edu.cn

1Corresponding author.

Manuscript received August 10, 2015; final manuscript received March 3, 2016; published online April 7, 2016. Assoc. Editor: Laine Mears.

J. Manuf. Sci. Eng 138(8), 081009 (Apr 07, 2016) (11 pages) Paper No: MANU-15-1399; doi: 10.1115/1.4032969 History: Received August 10, 2015; Revised March 03, 2016

Flank milling is one of the most important technologies for machining of complex surfaces. A small change of the tool orientation in the part coordinate system (PCS) may produce a great rotation of the rotary axes of the machine tool. Therefore, this paper proposes a tool path optimization model for flank milling in the machine coordinate system (MCS). The tool path is computed to smooth the variation of the rotary axes while controlling the geometric deviation. The geometric deviation is measured by the signed distance between the design surface and the tool envelope surface in the PCS. The geometric accuracy is not an objective but a constraint in the proposed optimization model. Given a prescribed geometric tolerance, the tool path smoothness optimization model is reformulated as a constrained nonlinear programming problem. The ε constrained differential evolution with gradient-based mutation (εDEg) is adopted to solve this constrained problem. The validity of the proposed approach is confirmed by numerical examples.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.

References

Liu, X. W. , 1995, “ Five-Axis NC Cylindrical Milling of Sculptured Surfaces,” Comput. Aided Des., 27(12), pp. 887–894. [CrossRef]
Redonnet, J. , Rubio, W. , and Dessein, G. , 1998, “ Side Milling of Ruled Surfaces: Optimum Positioning of the Milling Cutter and Calculation of Interference,” Int. J. Adv. Manuf. Technol., 14(7), pp. 459–465. [CrossRef]
Der Min, T. , and Her, M. J. , 2001, “ Accurate 5-Axis Machining of Twisted Ruled Surfaces,” ASME J. Manuf. Sci. Eng., 123(4), pp. 731–738. [CrossRef]
Gong, H. , and Wang, N. , 2009, “ Optimize Tool Paths of Flank Milling With Generic Cutters Based on Approximation Using the Tool Envelope Surface,” Comput. Aided Des., 41(12), pp. 981–989. [CrossRef]
Ding, H. , and Zhu, L. M. , 2009, “ Global Optimization of Tool Path for Five-Axis Flank Milling With a Cylindrical Cutter,” Sci. China Ser. E, 52(8), pp. 2449–2459. [CrossRef]
Zhu, L. , Zheng, G. , Ding, H. , and Xiong, Y. , 2010, “ Global Optimization of Tool Path for Five-Axis Flank Milling With a Conical Cutter,” Comput. Aided Des., 42(10), pp. 903–910. [CrossRef]
Lartigue, C. , Duc, E. , and Affouard, A. , 2003, “ Tool Path Deformation in 5-Axis Flank Milling Using Envelope Surface,” Comput. Aided Des., 35(4), pp. 375–382. [CrossRef]
Chiou, J. C. J. , 2004, “ Accurate Tool Position for Five-Axis Ruled Surface Machining by Swept Envelope Approach,” Comput. Aided Des., 36(10), pp. 967–974. [CrossRef]
Gong, H. , Cao, L. X. , and Liu, J. , 2005, “ Improved Positioning of Cylindrical Cutter for Flank Milling Ruled Surfaces,” Comput. Aided Des., 37(12), pp. 1205–1213. [CrossRef]
Zhu, L. M. , Ding, H. , and Xiong, Y. L. , 2012, “ Simultaneous Optimization of Tool Path and Shape for Five-Axis Flank Milling,” Comput. Aided Des., 44(12), pp. 1229–1234. [CrossRef]
Sun, Y. W. , and Guo, Q. , 2012, “ Analytical Modeling and Simulation of the Envelope Surface in Five-Axis Flank Milling With Cutter Runout,” ASME J. Manuf. Sci. Eng., 134(2), p. 021010. [CrossRef]
Li, Z. L. , and Zhu, L. M. , 2014, “ Envelope Surface Modeling and Tool Path Optimization for Five-Axis Flank Milling Considering Cutter Runout,” ASME J. Manuf. Sci. Eng., 136(4), p. 041021. [CrossRef]
Hsieh, H. T. , and Chu, C. H. , 2011, “ Particle Swarm Optimisation (PSO)-Based Tool Path Planning for 5-Axis Flank Milling Accelerated by Graphics Processing Unit (GPU),” Int. J. Comput. Integr. Manuf., 24(7), pp. 676–687. [CrossRef]
Castagnetti, C. , Duc, E. , and Ray, P. , 2008, “ The Domain of Admissible Orientation Concept: A New Method for Five-Axis Tool Path Optimisation,” Comput. Aided Des., 40(9), pp. 938–950. [CrossRef]
Plakhotnik, D. , and Lauwers, B. , 2014, “ Graph-Based Optimization of Five-Axis Machine Tool Movements by Varying Tool Orientation,” Int. J. Adv. Manuf. Technol., 74(1–4), pp. 307–318. [CrossRef]
Srijuntongsiri, G. , and Makhanov, S. S. , 2015, “ Optimisation of Five-Axis Machining G-Codes in the Angular Space,” Int. J. Prod. Res., 53(11), pp. 3207–3227. [CrossRef]
Pechard, P. Y. , Tournier, C. , Lartigue, C. , and Lugarini, J. P. , 2009, “ Geometrical Deviations Versus Smoothness in 5-Axis High-Speed Flank Milling,” Int. J. Mach. Tools Manuf., 49(6), pp. 454–461. [CrossRef]
Zheng, G. , Bi, Q. Z. , and Zhu, L. M. , 2012, “ Smooth Tool Path Generation for Five-Axis Flank Milling Using Multi-Objective Programming,” Proc. Inst. Mech. Eng., Part B, 226(2), pp. 247–254. [CrossRef]
Chu, C. H. , Hsieh, H. T. , Lee, C. H. , and Yan, C. y. , 2015, “ Spline-Constrained Tool-Path Planning in Five-Axis Flank Machining of Ruled Surfaces,” Int. J. Adv. Manuf. Technol., 80(9), pp. 2097–2104. [CrossRef]
Tulsyan, S. , and Altintas, Y. , 2015, “ Local Toolpath Smoothing for Five-Axis Machine Tools,” Int. J. Mach. Tools Manuf., 96, pp. 15–26. [CrossRef]
Tournier, C. , Castagnetti, C. , Lavernhe, S. , and Avellan, F. , 2006, “ Tool Path Generation and Post-Processor Issues in Five-Axis High Speed Machining of Hydro Turbine Blades,” Fifth International Conference on High Speed Machining, Metz, France.
Beudaert, X. , Pechard, P. Y. , and Tournier, C. , 2011, “ 5-Axis Tool Path Smoothing Based on Drive Constraints,” Int. J. Mach. Tools Manuf., 51(12), pp. 958–965. [CrossRef]
Hsieh, H. T. , and Chu, C. H. , 2013, “ Improving Optimization of Tool Path Planning in 5-Axis Flank Milling Using Advanced PSO Algorithms,” Rob. Comput. Integr. Manuf., 29(3), pp. 3–11. [CrossRef]
Hsieh, H. T. , and Chu, C. H. , 2012, “ Optimization of Tool Path Planning in 5-Axis Flank Milling of Ruled Surfaces With Improved PSO,” Int. J. Precis. Eng. Manuf., 13(1), pp. 77–84. [CrossRef]
Chu, C. H. , and Hsieh, H. T. , 2012, “ Generation of Reciprocating Tool Motion in 5-Axis Flank Milling Based on Particle Swarm Optimization,” J. Intell. Manuf., 23(5), pp. 1501–1509. [CrossRef]
Hsieh, H. T. , Tsai, Y. C. , and Chu, C. H. , 2013, “ Multi-Pass Progressive Tool Path Planning in Five-Axis Flank Milling by Particle Swarm Optimisation,” Int. J. Comput. Integr. Manuf., 26(10), pp. 977–987. [CrossRef]
Kuo, C. L. , Chu, C. H. , Li, Y. , Li, X. y. , and Gao, L. , 2015, “ Electromagnetism-Like Algorithms for Optimized Tool Path Planning in 5-Axis Flank Machining,” Comput. Ind. Eng., 84, pp. 70–78. [CrossRef]
Takahama, T. , and Sakai, S. , 2010, “ Constrained Optimization by the ε Constrained Differential Evolution With an Archive and Gradient-Based Mutation,” IEEE Congress on Evolutionary Computation, pp. 1–9.
Takahama, T. , and Sakai, S. , 2006, “ Constrained Optimization by the ε Constrained Differential Evolution With Gradient-Based Mutation and Feasible Elites,” IEEE Congress on Evolutionary Computation, pp. 1–8.
Erkorkmaz, K. , and Altintas, Y. , 2001, “ High Speed CNC System Design. Part I: Jerk Limited Trajectory Generation and Quintic Spline Interpolation,” Int. J. Mach. Tools Manuf., 41(9), pp. 1323–1345. [CrossRef]
Ferry, W. , and Altintas, Y. , 2008, “ Virtual Five-Axis Flank Milling of Jet Engine Impellers—Part II: Feed Rate Optimization of Five-Axis Flank Milling,” ASME J. Manuf. Sci. Eng., 130(1), p. 011013. [CrossRef]
Ferry, W. , and Altintas, Y. , 2008, “ Virtual Five-Axis Flank Milling of Jet Engine Impellers—Part I: Mechanics of Five-Axis Flank Milling,” ASME J. Manuf. Sci. Eng., 130(1), p. 011005. [CrossRef]
Merdol, S. D. , and Altintas, Y. , 2008, “ Virtual Simulation and Optimization of Milling Applications—Part II: Optimization and Feedrate Scheduling,” ASME J. Manuf. Sci. Eng., 130(5), p. 051005. [CrossRef]
Merdol, S. D. , and Altintas, Y. , 2008, “ Virtual Simulation and Optimization of Milling Operations—Part I: Process Simulation,” ASME J. Manuf. Sci. Eng., 130(5), p. 051004. [CrossRef]
Erkorkmaz, K. , 2015, “ Efficient Fitting of the Feed Correction Polynomial for Real-Time Spline Interpolation,” ASME J. Manuf. Sci. Eng., 137(4), p. 044501. [CrossRef]
Karandikar, J. , Traverso, M. , Abbas, A. , and Schmitz, T. , 2014, “ Bayesian Inference for Milling Stability Using a Random Walk Approach,” ASME J. Manuf. Sci. Eng., 136(3), p. 031015. [CrossRef]
dos Santos, R. G. , and Coelho, R. T. , 2014, “ A Contribution to Improve the Accuracy of Chatter Prediction in Machine Tools Using the Stability Lobe Diagram,” ASME J. Manuf. Sci. Eng., 136(2), p. 021005. [CrossRef]
Zheng, C. , Wang, J.-J. J. , and Sung, C. , 2014, “ Analytical Prediction of the Critical Depth of Cut and Worst Spindle Speeds for Chatter in End Milling,” ASME J. Manuf. Sci. Eng., 136(1), p. 011003. [CrossRef]
Ding, Y. , Zhang, X. , and Ding, H. , 2015, “ Harmonic Differential Quadrature Method for Surface Location Error Prediction and Machining Parameter Optimization in Milling,” ASME J. Manuf. Sci. Eng., 137(2), p. 024501. [CrossRef]
Zhu, L. M. , Zhang, X. M. , Zheng, G. , and Ding, H. , 2009, “ Analytical Expression of the Swept Surface of a Rotary Cutter Using the Envelope Theory of Sphere Congruence,” ASME J. Manuf. Sci. Eng., 131(4), p. 041017. [CrossRef]
Marquardt, D. W. , 1963, “ An Algorithm for Least-Squares Estimation of Nonlinear Parameters,” J. Soc. Ind. Appl. Math., 11(2), pp. 431–441. [CrossRef]
Langeron, J. M. , Duc, E. , Lartigue, C. , and Bourdet, P. , 2004, “ A New Format for 5-Axis Tool Path Computation, Using Bspline Curves,” Comput. Aided Des., 36(12), pp. 1219–1229. [CrossRef]
Anotaipaiboon, W. , and Makhanov, S. S. , 2011, “ Minimization of the Kinematics Error for Five-Axis Machining,” Comput. Aided Des., 43(12), pp. 1740–1757. [CrossRef]
Chen, H. P. , Kuo, H. H. , and Tsay, D. M. , 2009, “ Removing Tool Marks of Blade Surfaces by Smoothing Five-Axis Point Milling Cutter Paths,” J. Mater. Process. Technol., 209(17), pp. 5810–5817. [CrossRef]
Qin, J.-Y. , Jia, Z.-Y. , Ma, J.-W. , Ren, Z.-J. , and Song, D.-N. , “ An Efficient 5-Axis Toolpath Optimization Algorithm for Machining Parts With Abrupt Curvature,” Proc. Inst. Mech. Eng., Part C (online).

Figures

Grahic Jump Location
Fig. 1

C axis values according to i and j

Grahic Jump Location
Fig. 2

Two different tool paths

Grahic Jump Location
Fig. 3

Geometric model of a conical cutter

Grahic Jump Location
Fig. 4

A conical cutter in five-axis motion

Grahic Jump Location
Fig. 5

The table-tilting machine tool

Grahic Jump Location
Fig. 6

Schematic diagram of the geometric deviations

Grahic Jump Location
Fig. 8

Distribution of the geometric deviations of the initial tool path

Grahic Jump Location
Fig. 9

Angles between the tool orientations

Grahic Jump Location
Fig. 10

Distribution of the geometric deviations of the optimized tool path

Grahic Jump Location
Fig. 11

Evolutions of the A axis

Grahic Jump Location
Fig. 12

Evolutions of the C axis

Grahic Jump Location
Fig. 13

The CLs of the (a) initial tool path, (b) tool path optimized in the PCS, and (c) tool path optimized in the MCS

Grahic Jump Location
Fig. 14

Evolutions of A axis of the machine tool

Grahic Jump Location
Fig. 15

Evolutions of C axis of the machine tool

Grahic Jump Location
Fig. 16

C axis values along the tool paths

Grahic Jump Location
Fig. 17

Distribution of the geometric deviations of the optimized tool path

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In