Research Papers

Tool Orientation Planning in Milling With Process Dynamic Constraints: A Minimax Optimization Approach

[+] Author and Article Information
Tao Huang, Han Ding

State Key Laboratory of Digital Manufacturing
Equipment and Technology,
Huazhong University of
Science and Technology,
Wuhan 430074, China

Xiao-Ming Zhang

State Key Laboratory of Digital Manufacturing
Equipment and Technology,
Huazhong University of
Science and Technology,
Wuhan 430074, China
e-mail: cheungxm@hust.edu.cn,

Jürgen Leopold

TBZ Pariv GmbH,
Postfach 1108,
Chemnitz 09070, Germany

1Corresponding author.

Manuscript received January 18, 2018; final manuscript received July 10, 2018; published online July 31, 2018. Assoc. Editor: Radu Pavel.

J. Manuf. Sci. Eng 140(11), 111002 (Jul 31, 2018) (13 pages) Paper No: MANU-18-1041; doi: 10.1115/1.4040872 History: Received January 18, 2018; Revised July 10, 2018

In five-axis milling process, the tool path generated by a commercial software seldom takes the dynamics of the machining process into account. The neglect of process dynamics may lead to milling chatter, which causes overcut, quick tool wear, etc., and thus damages workpiece surface and shortens tool life. This motivates us to consider dynamic constraints in the tool path generation. Tool orientation variations in five-axis ball-end milling influence chatter stability and surface location error (SLE) due to the varying tool-workpiece immersion area and cutting force, which inversely provides us a feasible and flexible way to suppress chatter and SLE. However, tool orientations adjustment for suppression of chatter and SLE may cause drastic changes of the tool orientations and affects surface quality. The challenge is to strike a balance between the smooth tool orientations and suppression of chatter and SLE. To overcome the challenge, this paper presents a minimax optimization approach for planning tool orientations. The optimization objective is to obtain smooth tool orientations, by minimizing the maximum variation of the rotational angles between adjacent cutter locations, with constraints of chatter-free and SLE threshold. A dedicated designed ball-end milling experiment is conducted to validate the proposed approach. The work provides new insight into the tool path generation for ball-end milling of sculpture surface; also it would be helpful to decision-making for process parameters optimization in practical complex parts milling operations at shop floor.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


Lee, C. M. , Kim, S. W. , Lee, Y. H. , and Lee, D. W. , 2004, “The Optimal Cutter Orientation in Ball End Milling of Cantilever-Shaped Thin Plate,” J. Mater. Process. Technol., 153–154, pp. 900–906. [CrossRef]
Wan, M. , Zhang, W. , Qiu, K. , Gao, T. , and Yang, Y. , 2005, “Numerical Prediction of Static Form Errors in Peripheral Milling of Thin-Walled Workpieces With Irregular Meshes,” ASME J. Manuf. Sci. Eng., 127(1), p. 13. [CrossRef]
Smith, S. , Wilhelm, R. , Dutterer, B. , Cherukuri, H. , and Goel, G. , 2012, “Sacrificial Structure Preforms for Thin Part Machining,” CIRP Ann. Manuf. Technol., 61(1), pp. 379–382. [CrossRef]
Koike, Y. , Matsubara, A. , and Yamaji, I. , 2013, “Design Method of Material Removal Process for Minimizing Workpiece Displacement at Cutting Point,” CIRP Ann. Manuf. Technol., 62(1), pp. 419–422. [CrossRef]
Layegh K, S. E. , Yigit, I. E. , and Lazoglu, I. , 2015, “Analysis of Tool Orientation for 5-Axis Ball-End Milling of Flexible Parts,” CIRP Ann. Manuf. Technol., 64(1), pp. 97–100. [CrossRef]
Soori, M. , Arezoo, B. , and Habibi, M. , 2016, “Tool Deflection Error of Three-Axis Computer Numerical Control Milling Machines, Monitoring and Minimizing by a Virtual Machining System,” ASME J. Manuf. Sci. Eng., 138(8), p. 081005. [CrossRef]
Prat, D. , Fromentin, G. , Poulachon, G. , and Duc, E. , 2016, “Modeling and Analysis of Five-Axis Milling Configurations and Titanium Alloy Surface Topography,” ASME J. Manuf. Sci. Eng., 138(6), p. 061006. [CrossRef]
Zhang, X.-M. , Zhang, D. , Cao, L. , Huang, T. , Leopold, J. , and Ding, H. , 2017, “Minimax Optimization Strategy for Process Parameters Planning: Toward Interference-Free Between Tool and Flexible Workpiece in Milling Process,” ASME J. Manuf. Sci. Eng., 139(5), p. 051010. [CrossRef]
Yan, R. , Li, H. , Peng, F. , Tang, X. , Xu, J. , and Zeng, H. , 2017, “Stability Prediction and Step Optimization of Trochoidal Milling,” ASME J. Manuf. Sci. Eng., 139(9), p. 091006. [CrossRef]
Comak, A. , Ozsahin, O. , and Altintas, Y. , 2016, “Stability of Milling Operations With Asymmetric Cutter Dynamics in Rotating Coordinates,” ASME J. Manuf. Sci. Eng., 138(8), p. 081004. [CrossRef]
Honeycutt, A. , and Schmitz, T. , 2017, “A Numerical and Experimental Investigation of Period-n Bifurcations in Milling,” ASME J. Manuf. Sci. Eng., 139(1), p. 011003. [CrossRef]
Honeycutt, A. , and Schmitz, T. L. , 2017, “Milling Stability Interrogation by Subharmonic Sampling,” ASME J. Manuf. Sci. Eng., 139(4), p. 041009. [CrossRef]
Singh, K. K. , Kartik, V. , and Singh, R. , 2017, “Modeling of Dynamic Instability Via Segmented Cutting Coefficients and Chatter Onset Detection in High-Speed Micromilling of Ti6al4v,” ASME J. Manuf. Sci. Eng., 139(5), p. 051005. [CrossRef]
Altintas, Y. , Shamoto, E. , Lee, P. , and Budak, E. , 1999, “Analytical Prediction of Stability Lobes in Ball-End-Milling,” ASME J. Manuf. Sci. Eng., 121(4), pp. 586–592. [CrossRef]
Ozturk, E. , Tunc, L. T. , and Budak, E. , 2009, “Investigation of Lead and Tilt Angle Effects in 5-Axis Ball-End Milling Processes,” Int. J. Mach. Tools Manuf., 49(14), pp. 1053–1062. [CrossRef]
Shamoto, E. , and Akazawa, K. , 2009, “Analytical Prediction of Chatter Stability in Ball End Milling With Tool Inclination,” CIRP Ann. Manuf. Technol., 58(1), pp. 351–354. [CrossRef]
Budak, E. , Ozturk, E. , and Tunc, L. T. , 2009, “Modeling and Simulation of 5-Axis Milling Processes,” CIRP Ann. Manuf. Technol., 58(1), pp. 347–350. [CrossRef]
Ozturk, E. , and Budak, E. , 2010, “Dynamics and Stability of Five-Axis Ball-End Milling,” ASME ASME J. Manuf. Sci. Eng., 132(2), p. 021003. [CrossRef]
Insperger, T. , Gradišek, J. , Kalveram, M. , Stépán, G. , Winert, K. , and Govekar, E. , 2006, “Machine Tool Chatter and Surface Location Error in Milling Processes,” ASME J. Manuf. Sci. Eng., 128(4), p. 913. [CrossRef]
Honeycutt, A. , and Schmitz, T. L. , 2017, “Surface Location Error and Surface Roughness for Period-n Milling Bifurcations,” ASME J. Manuf. Sci. Eng., 139(6), p. 061010. [CrossRef]
Kiran, K. , Rubeo, M. , Kayacan, M. C. , and Schmitz, T. , 2017, “Two Degree of Freedom Frequency Domain Surface Location Error Prediction,” Precis. Eng., 48, pp. 234–242. [CrossRef]
Sun, C. , and Altintas, Y. , 2016, “Chatter Free Tool Orientations in 5-Axis Ball-End Milling,” Int. J. Mach. Tools Manuf., 106, pp. 89–97. [CrossRef]
Huang, T. , Zhang, X. , Zhang, X. , and Ding, H. , 2013, “An Efficient Linear Approximation of Acceleration Method for Milling Stability Prediction,” Int. J. Mach. Tools Manuf., 74(8), pp. 56–64. [CrossRef]
Huang, T. , Zhang, X. , and Ding, H. , 2017, “A Novel Approach With Smallest Transition Matrix for Milling Stability Prediction,” Nonlinear Dyn., 90(1), pp. 95–104. [CrossRef]
Huang, T. , Zhang, X. , and Ding, H. , 2013, “Decoupled Chip Thickness Calculation Model for Cutting Force Prediction in Five-Axis Ball-End Milling,” Int. J. Adv. Manuf. Technol., 69(5–8), pp. 1203–1217. [CrossRef]
Lee, P. , and Altintas, Y. , 1996, “Prediction of Ball-End Milling Forces From Orthogonal Cutting Data,” Int. J. Mach. Tools Manuf., 36(9), pp. 1059–1072. [CrossRef]
Marcotte, P. , and Dussault, J.-P. , 1989, “A Sequential Linear Programming Algorithm for Solving Monotone Variational Inequalities,” SIAM J. Control Optim., 27(6), pp. 1260–1278. [CrossRef]
Jun, C.-S. , Cha, K. , and Lee, Y.-S. , 2003, “Optimizing Tool Orientations for 5-Axis Machining by Configuration-Space Search Method,” Comput.-Aided Des., 35(6), pp. 549–566. [CrossRef]
Yang, J. , and Altintas, Y. , 2013, “Generalized Kinematics of Five-Axis Serial Machines With Non-Singular Tool Path Generation,” Int. J. Mach. Tools Manuf., 75, pp. 119–132. [CrossRef]
Wright, S. , and Nocedal, J. , 1999, Numerical Optimization, Springer Series in Operations Research, New York, p. 164.


Grahic Jump Location
Fig. 1

Schematic diagram of feasible tool orientation at CLi

Grahic Jump Location
Fig. 2

Coordinate representation of milling process: WCS XYZ, PCS FCN and TCS xyz. The tool orientation is defined by inclination angles α and γ.

Grahic Jump Location
Fig. 3

Flow chart of the optimization procedures

Grahic Jump Location
Fig. 4

Critical DOC with respect to the inclination angles in the slot milling with fixed spindle speed Ω = 9000 rpm, (a) three-dimensional diagram and (b) contour map, to verify that tool orientation adjustment can be used to avoid chatter. For example, specify that DOC is 0.3 mm, if α=20deg and γ=0deg, then the critical DOC is under the specified one, which means unstable (x-label), by changing α=30 deg and γ=0 deg, the critical one is over the specified one, then cutting process become stable (o-label).

Grahic Jump Location
Fig. 5

Schematic of the tool paths, tool orientations and the machined workpiece

Grahic Jump Location
Fig. 6

Spectral analysis of the acceleration signals of the experiments and the estimated critical times

Grahic Jump Location
Fig. 7

Comparison of the critical DOCs between the simulations and experiments

Grahic Jump Location
Fig. 8

The predicted feasible tool orientations and experimental verification: ap=0.32 mm, Ω = 9 krpm

Grahic Jump Location
Fig. 9

The predicted SLEs with respect to the variation of inclination angles: (a) the stability lobes under α=40 deg,γ=40 deg and the corresponding SLEs at DOC ap=0.3 mm and 0.25 mm; (b) the SLEs at DOC ap=0.25 mm under α=40 deg,γ=−40 deg for comparison: (a) α=40 deg,γ=40 deg and (b) α=40 deg,γ=−40 deg

Grahic Jump Location
Fig. 10

Experimental setup and the tool path generated by Unigraphics NX

Grahic Jump Location
Fig. 11

Experimental comparison between the optimized and original tool orientations

Grahic Jump Location
Fig. 12

The definition of SLE in ball-end milling



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