0
Research Papers

Discrete-Time Prediction of Chatter Stability, Cutting Forces, and Surface Location Errors in Flexible Milling Systems

[+] Author and Article Information
Z. M. Kilic

Ph.D. Candidate

Y. Altintas

Professor
Fellow ASME
e-mail: altintas@mech.ubc.ca
Department of Mechanical Engineering,
The University of British Columbia,
2054-6250 Applied Science Lane,
Vancouver, BC, V6T 1Z4, Canada

Contributed by the Manufacturing Engineering Division of ASME for publication in the Journal of Manufacturing Science and Engineering. Manuscript received April 12, 2012; final manuscript received September 7, 2012; published online November 1, 2012. Assoc. Editor: Tony Schmitz.

J. Manuf. Sci. Eng 134(6), 061006 (Nov 12, 2012) (13 pages) doi:10.1115/1.4007622 History: Received April 12, 2012; Revised September 07, 2012

This paper presents a discrete-time modeling of dynamic milling systems. End mills with arbitrary geometry are divided into differential elements along the cutter axis. Variable pitch and helix angles, as well as run-outs can be assigned to cutting edges. The structural dynamics of the slender end mills and thin-walled parts are also considered at each differential element at the tool-part contact zone. The cutting forces include static chip removal, ploughing, regenerative vibrations, and process damping components. The dynamic milling system is modeled by a matrix of delay differential equations with periodic coefficients, and solved with an improved semidiscrete-time domain method in modal space. The chatter stability of the system is predicted by checking the eigenvalues of the time-dependent transition matrix which covers the tooth period for regular or spindle periods for variable pitch cutters, respectively. The same equation is also used to predict the process states such as cutting forces, vibrations, and dimensional surface errors at discrete-time domain intervals analytically. The proposed model is experimentally validated in down milling of a workpiece with 5% radial immersion and 30 mm axial depth of cut with a four fluted helical end mill.

FIGURES IN THIS ARTICLE
<>
Copyright © 2012 by ASME
Your Session has timed out. Please sign back in to continue.

References

Altintas, Y., and Weck, M., 2004, “Chatter Stability of Metal Cutting and Grinding,” CIRP Ann. - Manuf. Technol., 53(2), pp. 619–642. [CrossRef]
Tlusty, J., and Polacek, M., 1963, “The Stability of the Machine Tool Against Self-Excited Vibration in Machining,” Proc. Int. Res. in Production Engineering, Pittsburgh, ASME, pp. 465–474.
Tobias, S., and FishwickW., 1958, “Theory of Regenerative Machine Tool Chatter,” Engineer, 205, pp. 199–203.
Minis, I., and Yanushevsky, R., 1993, “A New Theoretical Approach for the Prediction of Machine Tool Chatter in Milling,” ASME J. Eng. Industry, 115(1), pp. 1–8. [CrossRef]
Altintas, Y., and Budak, E., 1995, “Analytical Prediction of Stability Lobes in Milling,” CIRP Ann. - Manuf. Technol., 44(1), pp. 357–362. [CrossRef]
Budak, E., and Altintas, Y., 1998, “Analytical Prediction of Chatter Stability in Milling—Part I: General Formulation,” ASME J. Dyn. Sys., Meas., Control, 120(1), pp. 22–30. [CrossRef]
Merdol, S. D., and Altintas, Y., 2004, “Multi Frequency Solution of Chatter Stability for Low Immersion Milling,” ASME J. Manuf. Sci. Eng., 126(3), pp. 459–466. [CrossRef]
Altintas, Y., and Lee, P., 1996, “A General Mechanics and Dynamics Model for Helical End Mills,” CIRP Ann. - Manuf. Technol., 45(1), pp. 59–64. [CrossRef]
Altintas, Y., Engin, S., and Budak, E., 1999, “Analytical Stability Prediction and Design of Variable Pitch Cutters,” ASME J. Manuf. Sci. Eng., 121, pp. 173–178. [CrossRef]
Tlusty, J., and Ismail, F., 1981, “Basic Non-Linearity in Machining Chatter,” CIRP Ann. - Manuf. Technol., 30(1), pp. 299–304. [CrossRef]
Smith, S., and Tlusty, J., 1991, “An Overview of Modeling and Simulation of the Milling Process,” ASME J. Eng. Industry, 113(2), pp. 169–175. [CrossRef]
Montgomery, D., and Altintas, Y., 1991, “Mechanism of Cutting Force and Surface Generation in Dynamic Milling,” ASME J. Eng. Industry, 113(2), pp. 160–168. [CrossRef]
Kline, W., DeVor, R., and Shareef, I., 1982, “The Prediction of Surface Accuracy in End Milling,” ASME J. Eng. Industry, 104(3), pp. 272–278. [CrossRef]
Budak, E., and Altintas, Y., 1995, “Modeling and Avoidance of Static Form Errors in Peripheral Milling of Plates,” Int. J. Mach. Tools Manuf., 35(3), pp. 459–476. [CrossRef]
Insperger, T., and Stépán, G., 2002, “Semi-Discretization Method for Delayed Systems,” Int. J. Numer. Methods Eng., 55, pp. 503–518. [CrossRef]
Insperger, T., and Stépán, G., 2004, “Updated Semi-Discretization Method for Periodic Delay-Differential Equations With Discrete Delay,” Int. J. Numer. Math. Eng., 61, pp. 117–141. [CrossRef]
Bayly, P. V., Halley, J. E., Mann, B. P., and Davies, M. A., 2003, “Stability of Interrupted Cutting by Temporal Finite Element Analysis,” ASME J. Manuf. Sci. Eng., 125(2), pp. 220–225. [CrossRef]
Altintas, Y., Stepan, G., Merdol, D., and Dombovari, Z., 2008, “Chatter Stability of Milling in Frequency and Discrete Time Domain,” CIRP J. Manuf. Sci. Technol., 1(1), pp. 35–44. [CrossRef]
Bachrathy, D., Insperger, T., and Stépán, G., 2009, “Surface Properties of the Machined Workpiece for Helical Mills,” Mach. Sci. Technol., 13(2), pp. 227–245. [CrossRef]
Schmitz, T. L., and Mann, B. P., 2006, “Closed-Form Solutions for Surface Location Error in Milling,” Int. J. Mach. Tools Manuf., 46(12-13), pp. 1369–1377. [CrossRef]
Budak, E., 2006, “Analytical Models for High Performance Milling. Part I: Cutting Forces, Structural Deformations and Tolerance Integrity,” Int. J. Mach. Tools Manuf., 46(12-13), pp. 1478–1488. [CrossRef]
Budak, E., 2006, “Analytical Models for High Performance Milling. Part II: Process Dynamics and Stability,” Int. J. Mach. Tools Manuf., 46(12-13), pp. 1489–1499. [CrossRef]
Ding, Y., Zhu, L., Zhang, X., and Ding, H., 2011, “Numerical Integration Method for Prediction of Milling Stability,” ASME J. Manuf. Sci. Eng., 133(3), p. 031005. [CrossRef]
Ding, Y., Zhu, L., Zhang, X., and Ding, H., 2011, “On a Numerical Method for Simultaneous Prediction of Stability and Surface Location Error in Low Radial Immersion Milling,” ASME J. Dyn. Sys., Meas., Control, 133(2), p. 024503. [CrossRef]
Engin, S., and Altintas, Y., 2001, “Mechanics and Dynamics of General Milling Cutters. Part I: Helical End Mills,” Int. J. Mach. Tools Manuf., 41(15), pp. 2195–2212. [CrossRef]
Kaymakci, M., Kilic, Z. M., and Altintas, Y., 2012, “Unified Cutting Force Model for Turning, Boring, Drilling and Milling Operations,” Int. J. Mach. Tools Manuf., 54-55, pp. 34–45. [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]
Insperger, T., Mann, B. P., Edes, B., and Stépán, G., 2006, “The Effect of RunOut on the Chatter Frequencies of Milling Processes,” Proceedings of the 9th CIRP International Workshop on Modeling of Machining Operations, Bled, Slovenia.
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, pp. 216–224. [CrossRef]
Chiou, R. Y., and Liang, S. Y., 1998, “Chatter Stability of a Slender Cutting Tool in Turning With Tool Wear Effect,” Int. J. Mach. Tools Manuf., 38(4), pp. 315–327. [CrossRef]
Altintas, Y., Eynian, M., and Onozuka, H., 2008, “Identification of Dynamic Cutting Force Coefficients and Chatter Stability With Process Damping,” CIRP Ann. – Manuf. Technol., 57(1), pp. 371–374. [CrossRef]
Ahmadi, K., and Ismail, F., 2011, “Analytical Stability Lobes Including Nonlinear Process Damping Effect on Machining Chatter,” Int. J. Mach. Tools Manuf., 51(4), pp. 296–308. [CrossRef]
Huang, C. Y., and Wang, J. J. J., 2007, “Mechanistic Modeling of Process Damping in Peripheral Milling,” ASME J. Manuf. Sci. Eng., 129(1), pp. 12–20. [CrossRef]
Budak, E., and Tunc, L. T., 2009, “A New Method for Identification and Modeling of Process Damping in Machining,” ASME J. Manuf. Sci. Eng., 131, p. 051019. [CrossRef]
Eynian, M., and Altintas, Y., 2010, “Analytical Chatter Stability of Milling With Rotating Cutter Dynamics at Process Damping Speeds,” ASME J. Manuf. Sci. Eng., 132(2), p. 021012. [CrossRef]
Aguilar, J. C., 2007, “An Unconditionally A-Stable Method for Initial Value Problems Based on Simpson's Rule,” Int. Math. Forum, 2(56), pp. 2771–2779. Available at http://www.m-hikari.com/imf-password2007/53-56-2007/aguilarIMF53-56-2007.pdf
cutpro, 2000, “CUTPRO© UBC Advanced Machining Simulation System (Ver.9.3).”
Park, S. S., and Altintas, Y., 2004, “Dynamic Compensation of Spindle Integrated Force Sensors With Kalman Filter,” ASME J. Dyn. Sys., Meas., Control, 126(3), pp. 443–452. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Peripheral milling with varying geometry and structural dynamics along the axial depth of cut

Grahic Jump Location
Fig. 2

Process damping mechanism

Grahic Jump Location
Fig. 3

Structural dynamic model of a flexible cutter milling a flexible part

Grahic Jump Location
Fig. 4

SLE on the workpiece

Grahic Jump Location
Fig. 5

Measured FRF along the slender end mill axis: (a) measurement points; (b) measured FRF in feed (x) direction; (c) measured FRF in normal (y) direction. (Note: Impact location is kept constant at Point 3 to avoid hammer bounces; the vibrations are measured with laser at points 1 to 4.)

Grahic Jump Location
Fig. 6

Experimental validation of stability models. (a) Unstable cut at 10,500 rev/min spindle speed with 30 mm depth of cut. (b) Stable cut at 12,700 rev/min spindle speed with 25 mm depth of cut.

Grahic Jump Location
Fig. 7

Comparison of predicted and measured cutting forces. Prediction includes run-out parameters. Cutting conditions: spindle speed = 12,700 rev/min; axial depth of cut = 25 mm; radial depth of cut = 0.9525 mm down milling. See Table 1 for dynamic parameters.

Grahic Jump Location
Fig. 8

SLE measurement: (a) setup and (b) comparison of experimental and simulated SLE results. See Fig. 7 for cutting conditions.

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