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Research Papers

General Modeling and Calibration Method for Cutting Force Prediction With Flat-End Cutter

[+] Author and Article Information
Xing Zhang, Wei Zhang, Jun Zhang, Bo Pang

State Key Laboratory for Manufacturing
Systems Engineering,
Xi'an Jiaotong University,
Xi'an 710054, Shaanxi Province, China

Wanhua Zhao

State Key Laboratory for Manufacturing
Systems Engineering,
Xi'an Jiaotong University,
Xi'an 710054, Shaanxi Province, China
e-mail: whzhao@xjtu.edu.cn

1Corresponding author.

Manuscript received March 31, 2017; final manuscript received October 31, 2017; published online December 18, 2017. Assoc. Editor: Jaydeep Karandikar.

J. Manuf. Sci. Eng 140(2), 021007 (Dec 18, 2017) (18 pages) Paper No: MANU-17-1206; doi: 10.1115/1.4038371 History: Received March 31, 2017; Revised October 31, 2017

A general calibration method of cutter runout and specific cutting force coefficients (SCFCs) for flat-end cutter is proposed in this paper, and a high accuracy of cutting force prediction during peripheral milling is established. In the paper, the cutter runout, the bottom-edge cutting effect, and the actual feedrate with limitation during large tool path curvature are concerned comprehensively. First, based on the trochoid motion, a tooth trajectory model is built up and an analytical instantaneous uncut chip thickness (IUCT) model is put forward for describing the cutter/workpiece engagement (CWE). Second, a noncontact identification method for cutter runout including offset and inclination is given, which constructs an objective function by using the cutting radius relative variation between adjacent teeth, and identifies through a numerical optimization method. Thirdly, with consideration of bottom-edge cutting effect, the paper details a three-step calibration procedure for SCFCs based on an enhanced thin-plate milling experiment. Finally, a series of milling tests are performed to verify the effectiveness of the proposed method. The results show that the approach is suitable for both constant and nonconstant pitch cutter, and the generalization has been proved. Moreover, the paper points out that the cutter runout has a strong spindle speed-dependent effect, the milling force in cutter axis direction exists a switch-direction phenomenon, and the actual feedrate will be limited by large tool path curvature. All of them should be considered for obtaining an accurate milling force prediction.

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References

Duan, X. Y. , Peng, F. Y. , Yan, R. , Zhu, Z. R. , Huang, K. , and Li, B. , 2016, “ Estimation of Cutter Deflection Based on Study of Cutting Force and Static Flexibility,” ASME J. Manuf. Sci. Eng., 138(4), p. 041001. [CrossRef]
Desai, K. A. , and Rao, P. V. M. , 2012, “ On Cutter Deflection Surface Errors in Peripheral Milling,” J. Mater. Process. Technol., 212(11), pp. 2443–2454. [CrossRef]
Yang, Y. , Zhang, W. H. , Ma, Y. C. , and Wan, M. , 2016, “ Chatter Prediction for the Peripheral Milling of Thin-Walled Workpieces With Curved Surfaces,” Int. J. Mach. Tool Manuf., 109, pp. 36–48. [CrossRef]
Altintas, Y. , Kersting, P. , Biermann, D. , Budak, E. , Denkena, B. , and Lazoglu, I. , 2014, “ Virtual Process Systems for Part Machining Operations,” CIRP Ann. Manuf. Technol., 63(2), pp. 585–605. [CrossRef]
Ko, J. H. , Yun, W. S. , Cho, D. W. , and Ehmann, K. F. , 2002, “ Development of a Virtual Machining System—Part 1: Approximation of the Size Effect for Cutting Force Prediction,” Int. J. Mach. Tool Manuf., 42(15), pp. 1595–1605. [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]
Zhang, X. , Zhang, J. , Zheng, X. , Pang, B. , and Zhao, W. , 2017, “ Tool Orientation Optimization of 5-Axis Ball-End Milling Based on an Accurate Cutter/Workpiece Engagement Model,” CIRP J. Manuf. Sci. Technol., 19, pp. 106–116.
Martellotti, M. E. , 1941, “ An Analysis of the Milling Process,” Trans. ASME, 63(8), pp. 677–700. http://www.meccanicamente.org/varie_corsi/archivio/martellotti_1941.pdf
Martellotti, M. E. , 1945, “ An Analysis of the Milling Process—Part 2: Down Milling,” Trans. ASME, 67, pp. 233–251.
Sutherland, J. W. , and DeVor, R. E. , 1986, “ An Improved Method for Cutting Force and Surface Error Prediction in Flexible End Milling Systems,” ASME J. Eng. Ind., 108(4), pp. 269–279. [CrossRef]
Wang, J. J. , and Liang, S. Y. , 1996, “ Chip Load Kinematics in Milling With Radial Cutter Runout,” ASME J. Eng. Ind., 118(1), pp. 111–116. [CrossRef]
Zhang, L. , and Zheng, L. , 2005, “ Prediction of Cutting Forces in End Milling of Pockets,” Int. J. Adv. Manuf. Technol., 25(3–4), pp. 281–287. [CrossRef]
Wei, Z. C. , Wang, M. J. , Ma, R. G. , and Wang, L. , 2010, “ Modeling of Process Geometry in Peripheral Milling of Curved Surfaces,” J. Mater. Process Technol., 210(5), pp. 799–806. [CrossRef]
Desai, K. A. , and Rao, P. V. M. , 2008, “ On Cutter Deflection Surface Errors in Peripheral Milling,” Int. J. Mach. Tool Manuf., 48(2), pp. 249–259. [CrossRef]
Han, X. , and Tang, L. M. , 2015, “ Precise Prediction of Forces in Milling Circular Corners,” Int. J. Mach. Tool Manuf., 88, pp. 184–193. [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]
Sun, Y. , 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]
Desai, K. A. , Agarwal, P. K. , and Rao, P. V. M. , 2009, “ Process Geometry Modeling With Cutter Runout for Milling of Curved Surfaces,” Int. J. Mach. Tool Manuf., 49(12–13), pp. 1015–1028. [CrossRef]
Yang, Y. , Zhang, W. H. , and Wan, M. , 2011, “ Effect of Cutter Runout on Process Geometry and Forces in Peripheral Milling of Curved Surfaces With Variable Curvature,” Int. J. Mach. Tool Manuf., 51(5), pp. 420–427. [CrossRef]
Dang, J. W. , Zhang, W. H. , Yang, Y. , and Wan, M. , 2010, “ Cutting Force Modeling for Flat End Milling Including Bottom Edge Cutting Effect,” Int. J. Mach. Tool Manuf., 50(11), pp. 986–997. [CrossRef]
Wan, M. , Zhang, W. H. , and Yang, Y. , 2011, “ Phase Width Analysis of Cutting Forces Considering Bottom Edge Cutting and Cutter Runout Calibration in Flat End Milling of Titanium Alloy,” J. Mater. Process. Technol., 211(11), pp. 1852–1863. [CrossRef]
Wan, M. , Lu, M. S. , Zhang, W. H. , and Yang, Y. , 2012, “ A New Ternary Mechanism Model for the Prediction of Cutting Forces in Flat End Milling,” Int. J. Mach. Tool Manuf., 57, pp. 34–45. [CrossRef]
Li, Z. L. , and Zhu, L. M. , 2016, “ Mechanistic Modeling of Five-Axis Machining With a Flat End Mill Considering Bottom Edge Cutting Effect,” ASME J. Manuf. Sci. Eng., 138(11), p. 111012. [CrossRef]
Wang, J. J. J. , and Zheng, C. M. , 2003, “ Identification of Cutter Offset in End Milling Without a Prior Knowledge of Cutting Coefficients,” Int. J. Mach. Tool Manuf., 43(7), pp. 687–697. [CrossRef]
Wan, M. , Zhang, W. H. , Qin, G. H. , and Tan, G. , 2007, “ Efficient Calibration of Instantaneous Cutting Force Coefficients and Runout Parameters for General End Mills,” Int. J. Mach. Tool Manuf., 47(11), pp. 1767–1776. [CrossRef]
Ko, J. H. , and Cho, D. W. , 2005, “ Determination of Cutting-Condition-Independent Coefficients and Runout Parameters in Ball-End Milling,” Int. J. Adv. Manuf. Technol., 26(11–12), pp. 1211–1221. [CrossRef]
Wan, M. , Zhang, W. H. , Qin, G. H. , and Wang, Z. P. , 2008, “ Consistency Study on Three Cutting Force Modeling Methods for Peripheral Milling,” Proc. Inst. Mech. Eng. B, 222(6), pp. 665–676. [CrossRef]
Zhang, X. , Zhang, J. , and Zhao, W. H. , 2016, “ A New Method for Cutting Force Prediction in Peripheral Milling of Complex Curved Surface,” Int. J. Adv. Manuf. Technol., 86(1–4), pp. 117–128. [CrossRef]
Budak, E. , Altintas, Y. , and Armarego, E. J. A. , 1996, “ Prediction of Milling Force Coefficients From Orthogonal Cutting Data,” ASME J. Manuf. Sci. Eng., 118(2), pp. 216–224. [CrossRef]
Wang, J. J. J. , and Zheng, C. M. , 2002, “ Identification of Shearing and Ploughing Cutting Constants From Average Forces in Ball-End Milling,” Int. J. Mach. Tool Manuf., 42(6), pp. 695–705. [CrossRef]
Yoon, M. C. , and Kim, Y. G. , 2004, “ Cutting Dynamic Force Modelling of End Milling Operation,” J. Mater. Process Technol., 155–156, pp. 1383–1389. [CrossRef]
Gradišek, J. , Kalveram, M. , and Weinert, K. , 2004, “ Mechanistic Identification of Specific Force Coefficients for a General End Mill,” Int. J. Mach. Tool Manuf., 44(4), pp. 401–414. [CrossRef]
Wang, M. H. , Gao, L. , and Zheng, Y. H. , 2014, “ An Examination of the Fundamental Mechanics of Cutting Force Coefficients,” Int. J. Mach. Tool Manuf., 78, pp. 1–7. [CrossRef]
Gonzalo, O. , Beristain, J. , Jauregi, H. , and Sanz, C. , 2010, “ A Method for the Identification of the Specific Force Coefficients for Mechanistic Milling Simulation,” Int. J. Mach. Tool Manuf., 50(9), pp. 765–774. [CrossRef]
Edouard, R. L. , and Enrico, F. , 2009, “ Mechanistic Cutting Force Model Parameters Evaluation in Milling Taking Cutter Radial Runout Into Account,” Int. J. Adv. Manuf. Technol., 45(1–2), pp. 8–15. [CrossRef]
Shin, Y. C. , and Waters, A. J. , 1997, “ A New Procedure to Determine Instantaneous Cutting Force Coefficients for Machining Force Prediction,” Int. J. Mach. Tool Manuf., 37(9), pp. 1337–1351. [CrossRef]
Yun, W. S. , and Cho, D. W. , 2001, “ Accurate 3-D Cutting Force Prediction Using Cutting Condition Independent Coefficients in End Milling,” Int. J. Mach. Tool Manuf., 41(4), pp. 463–478. [CrossRef]
Feng, H. Y. , and Su, N. , 2001, “ A Mechanistic Cutting Force Model for 3D Ball-End Milling,” ASME J. Manuf. Sci. Eng., 123(1), pp. 23–29. [CrossRef]
Wan, M. , Zhang, W. H. , Dang, J. W. , and Yang, Y. , 2009, “ New Procedures for Calibration of Instantaneous Cutting Force Coefficients and Cutter Runout Parameters in Peripheral Milling,” Int. J. Mach. Tool Manuf., 49(14), pp. 1144–1151. [CrossRef]
Wan, M. , Zhang, W. H. , Dang, J. W. , and Yang, Y. , 2010, “ A Novel Cutting Force Modeling Method for Cylindrical End Mill,” Appl. Math Model, 34(3), pp. 823–836. [CrossRef]
Zhang, X. , Zhang, J. , Pang, B. , and Zhao, W. H. , 2016, “ An Accurate Prediction Method of Cutting Forces in 5-Axis Flank Milling of Sculptured Surface,” Int. J. Mach. Tool Manuf., 104, pp. 26–36. [CrossRef]
Zhang, X. , Zhang, J. , Zhang, W. , Li, J. , and Zhao, W. , 2017, “ A Non-Contact Calibration Method for Cutter Runout With Spindle Speed Dependent Effect and Analysis of Its Influence on Milling Process,” Precis. Eng., epub.
Wan, M. , Wang, Y. T. , Zhang, W. H. , Yang, Y. , and Dang, J. W. , 2011, “ Prediction of Chatter Stability for Multiple-Delay Milling System Under Different Cutting Force Models,” Int. J. Mach. Tool Manuf., 51(4), pp. 281–295. [CrossRef]

Figures

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Fig. 1

Cutting force model in peripheral milling: (a) CWE; (b) side-edge cutting force and (c) bottom-edge cutting force

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Fig. 2

(a) Cutter offset, (b) cutter offset and inclination, and (c) cutter pitch angle

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Fig. 3

(a) Calculation model of IUCT and (b) calculation model of tooth start/end angle

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Fig. 4

(a) Noncontact measurement with eddy current sensors, (b) measurement schematic diagram of the jth cutting disk element and (c) measured results of target distance

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Fig. 5

(a) Thin-plate milling with side edge, (b) measured milling force during thin-plate milling with side edge, (c) thin-plate milling with bottom edge, and (d) measured milling force during thin-plate milling with bottom edge

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Fig. 7

Measured voltage: (a) first sensor at position 1 with n = 6 krpm, (b) first sensor at position 3 with n = 6 krpm, and (c) first sensor at position 1 with n = 1 krpm, and (d) first sensor at position 1 with n = 8 krpm

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Fig. 8

Identification result of cutter runout: (a) Offset for the first cutter and (b) offset and inclination for the first cutter

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Fig. 6

(a) Milling experiment setup, (b) noncontact measurement of cutter runout, and (c) thin-plate milling

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Fig. 9

Milling force of three teeth cutter: (a) measured, (b) predicted, and (c) comparison in one revolution; milling force of four teeth cutter: (d) measured, (e) predicted, and (f) comparison in one revolution

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Fig. 10

(a) Tool path curvature and actual feedrate, (b) tooth start/end angle and feed direction angle, (c) measured milling force, and (d) predicted milling force

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Fig. 11

(a) Tool path curvature and actual feedrate, (b) tooth start/end angle and feed direction angle, (c) measured milling force, and (d) predicted milling force

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Fig. 12

Comparison results of measured and predicted milling force: (a) test 1, (b) test 2, and (c) test 3

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Fig. 15

(a) Actual cutting radius with position from bottom, (b) maximum IUCT with position from bottom; comparison results of measured and predicted milling force: (c) test 8 and (d) test 9

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Fig. 13

Comparison results of measured and predicted milling force: (a) test 4, (b) test 5, (c) milling force in z direction under different axial depth of cuts, and (d) relative prediction error under different axial depth of cuts

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Fig. 14

(a) Actual cutting radius under different spindle speeds, (b) maximum IUCT under different spindle speeds; comparison results of measured and predicted milling force: (c) test 6 and (d) test 7

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Fig. 17

Milling force with F = 2400/min: (a) measured, (b) predicted; milling force with F = 4800/min: (c) measured; (d) predicted; milling force with F = 7200/min: (e) measured and (f) predicted

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Fig. 16

Actual feedrate after interpolation under different nominal feed speeds

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