Virtual Computer Numerical
12.3 Application Examples
12.3.3 Accurate Contouring at Sharp Corners
Two tool-path modification strategies have been adopted for smoothing the motion around sharp corners. The under-corner approach is suitable for machining corners in a shorter time while remain-ing within a specified tolerance. This technique can be applied with high bandwidth servo controllers that are capable of accurately tracking the reference toolpath, such as adaptive sliding mode control.
The over-corner approach is based on smoothing the tool path outside the corner while remaining within the given tolerance. This approach is suitable for correcting the under-cut problem, caused by the large phase lag in low bandwidth controllers such as P, P-PI, or PID. The cornering feedrate is adjusted iteratively such that contour error violation does not occur. Both techniques have been experimentally validated, as shown in Figures 12.11 and 12.12. Full details of these algorithms are provided in Reference [27].
FIGURE 12.9 Hierarchical auto-tuning strategy.
High-Level Fuzzy Logic Control (intelligent supervisor)
Trajectory Generation
Upper Layer
Axis
Control Amplifier
Servomotor Feedback Measurement
Bottom Layer Intermediate Layer
Back-And-Forth Motion Commands
Control Parameter Adjustment (turning actions) CNC Feed Drive Control System
Feedback
Performance Evaluation Level (information abstraction and system
performance evaluation)
λ KS ρ
λ
KS ρ
0775_C012.fm Page 10 Tuesday, September 4, 2007 9:41 AM
Virtual Computer Numerical Control System 12-11
FIGURE 12.10 System performance before and after fuzzy tuning: (a) initially noisy system, (b) initially highly stable and sluggish system, (c) initially unstable system.
FIGURE 12.11 Contouring performance for 90° under-corner spline with sliding mode control.
0.010
Tracking error (mm) Tracking error (mm)Tracking error (mm)
Time (sec)
Tracking error (mm)Tracking error (mm)
Initial Response – Highly Stable System Initial Response – Noisy System
Time (sec)
Initial Response – Unstable System 0.100 (a) Original Toolpath Cornering Performance
(c) Original Toolpath Contour Error Profile
(b) Modified Toolpath Cornering Performance
y Axis y Axis
(d) Modified Toolpath Contour Error Profile
Tolerance
Contour error (μm) Contour error [μm]
12
0775_C012.fm Page 11 Tuesday, September 4, 2007 9:41 AM
12-12 Mechatronic Systems: Devices, Design, Control, Operation and Monitoring
12.4 Conclusion
CNC machines are mechatronic systems. Control plays a crucial role in their operation. A comprehensive virtual model of a modular CNC was presented in this chapter. The VCNC allows integration of trajectory planning and interpolation routines, mathematical models of ball-screw and linear drives, friction, feedback sensors, amplifiers, D/A converters, and flexible motion control laws. The system allows the designer to try out various feed-drive design alternatives, control laws, and sensors with different reso-lutions. Accurate modeling of drives allows realistic prediction of the machine’s high-speed contouring capability. Auto-tuning of sophisticated axis control laws allows tracking performance to be optimized prior to implementation on the real machine. Modification of sharp corners with smooth spline segments allows desired contouring tolerances to be maintained while traveling sharp corners in minimum time.
These features have all been verified experimentally on a three-axis machining center.
Acknowledgment
This research is sponsored by NSERC and Pratt & Whitney Canada under research chair and strategic grant agreements.
References
1. Altintas, Y., Manufacturing Automation: Metal Cutting Mechanics, Machine Tool Vibrations, and CNC Design, Cambridge University Press, Cambridge, England, 2000.
2. Erkorkmaz, K. and Altintas, Y., High speed CNC system design: Part I—Jerk Limited Trajectory Generation and Quintic Spline Interpolation, International Journal Machine Tools and Manufacture, Vol. 41, No. 9, 1323–1345, 2001.
FIGURE 12.12 Contouring performance for 90° over-corner spline with P-PI servo control.
Modified toolpath
x Axis
y Axis
(a) Original Toolpath Cornering Performance
y Axis
(c) Original Toolpath Contour Error Profile (d) Modified Toolpath Contour Error Profile
Experiment
Simulation Simulation
Experiment
Contour error (μm) Contour error (μm)
Time (sec) Time (sec) (b) Modified Toolpath Cornering Performance
Experiment Simulation
Maximum 289 (μm)
0775_C012.fm Page 12 Tuesday, September 4, 2007 9:41 AM
Virtual Computer Numerical Control System 12-13
3. Altintas, Y., Erkorkmaz, K., and Zhu, W.-H., Sliding mode controller design for high speed drives, Annals of CIRP, Vol. 49, No. 1, 265–270, 2000.
4. Boucher, P., Dumur, D., and Rahmani, K.F., Generalized predictive cascade control (GPCC) for machine tool drives, Annals of CIRP, Vol. 39, No. 1, 357–360, 1990.
5. Erkorkmaz, K. and Altintas, Y., High speed CNC system design: Part III—high speed tracking and contouring control of feed drives, International Journal of Machine Tools and Manufacture, Vol. 41, No. 11, 1637–1658, 2001.
6. Pritschow, G., On the influence of the velocity gain factor on the path deviation, Annals of the CIRP, Vol. 45, No. 1, 367–371, 1996.
7. Tomizuka, M., Zero phase error tracking algorithm for digital control, ASME Journal of Dynamic Systems, Measurement, and Control, Vol. 109, 65–68, 1987.
8. Armstrong, H.B., Dupont, P., and Canudas De Wit, C., A survey of models, analysis tools and compensation methods for the control of machines with friction, Automatica, Vol. 30, No. 7, 1083–1138, 1994.
9. Erkorkmaz, K. and Altintas, Y., High speed CNC system design: Part II—modeling and identifi-cation of feed drives, International Journal of Machine Tools and Manufacture, Vol. 41, No. 10, 1487–1509, 2001.
10. Erkorkmaz, K., Optimal Trajectory Generation and Precision Tracking Control for Multi-Axis Machines, Ph.D. thesis, University of British Columbia, Department of Mechanical Engineering, Vancouver, BC, Canada, 2004.
11. Kao, J.Y., Yeh, Z.M., Tarng, Y.S., and Lin, Y.S., A study of backlash on the motion accuracy of CNC lathes, International Journal of Machine Tools and Manufacture, Vol. 36, No. 5, 539–550, 1996.
12. de Silva, C.W., Intelligent Control–Fuzzy Logic Applications, CRC Press, Boca Raton, FL, 1995.
13. Goulet, J.-F., de Silva, C.W., and Modi, V.J., Hierarchical knowledge-based control of a deployable orbiting manipulator, Acta Astronautica, Vol. 50, No. 3, 139–148, 2002.
14. Weck, M., Meylahn, A., and Hardebusch, C., Innovative algorithms for spline-based CNC control-ler, Production Engineering Research and Development in Germany; Annals of the German Academic Society for Production Engineering, Vol. 6, No. 1, 83–86, 1999.
15. Bobrow, J.E., Dubowsky, S., and Gibson, J.S., Time-optimal control of robotic manipulators along specified paths, International Journal of Robotics Research, Vol. 4, No. 3, 3–17, 1985.
16. Butler, J., Haack, B., and Tomizuka, M., Reference generation for high speed coordinated motion of a two axis system, Symposium on Robotics, ASME Winter Annual Meeting, Chicago, IL, DSC-11, 1988, pp. 457–470.
17. Erkorkmaz, K. and Altintas, Y., High speed contouring control algorithm for CNC machine tools, Proceedings of ASME Dynamic Systems and Control Division, IMECE’98, DSC-64, 1998, pp. 463–469.
18. Jouaneh, M.K., Wang, Z., and Dornfeld, D.A., Trajectory planning for coordinated motion of a robot and a positioning table: Part 1—path specification, IEEE Transactions on Robotics and Auto-mation, Vol. 6, No. 6, 735–745, 1990.
19. Jouaneh, M.K., Dornfeld, D.A., and Tomizuka, M., Trajectory planning for coordinated motion of a robot and a positioning table: Part 2—optimal trajectory specification, IEEE Transactions on Robotics and Automation, Vol. 6, No. 6, 746–759, 1990.
20. Weck, M. and Ye, G., Sharp corner tracking using the IKF control strategy, Annals of the CIRP, Vol. 39, No. 1, 437–441, 1990.
21. Wang, F.-C. and Yang, D.C.H., Nearly arc-length parameterized quintic-spline interpolation for precision machining, Computer Aided Design, Vol. 25, No. 5, 281–288, 1993.
22. Erkorkmaz, K. and Altintas, Y., Quintic spline interpolation with minimal feed fluctuation, ASME Journal of Manufacturing Science and Engineering, Vol. 127, No. 2, 339–349, 2005.
23. Altintas, Y. and Erol, N.A., Open architecture modular tool kit for motion and machining process control, Annals of the CIRP, Vol. 47, No. 1, 295–300, 1998.
0775_C012.fm Page 13 Tuesday, September 4, 2007 9:41 AM
12-14 Mechatronic Systems: Devices, Design, Control, Operation and Monitoring
24. Yeung, C.H., A Three-Axis Virtual Computer Numerical Control (CNC) System, M.A.Sc. thesis, University of British Columbia, Department of Mechanical Engineering, Vancouver, BC, Canada, 2004.
25. Astrom, K.J. and Wittenmark, B., Computer-Controlled Systems: Theory and Design, 3rd ed., Prentice-Hall, Upper Saddle River, NJ, 1997.
26. Yeung, C.-H., Altintas, Y., and Erkorkmaz, K., Virtual CNC system—Part I: system architecture, International Journal of Machine Tools and Manufacture, Vol. 46, No. 10, 1107–1123, 2006.
27. Erkorkmaz, K., Yeung, C.-H., and Altintas, Y., Virtual CNC system—Part II: high speed contouring application, International Journal of Machine Tools and Manufacture, Vol. 46, No. 10, 1124–1138, 2006.
0775_C012.fm Page 14 Tuesday, September 4, 2007 9:41 AM
13-1