Abstract
Nonlinear friction is the limiting factor in using motor current signals to estimate the load of machine tools. The inertia of the axis and the positional dependency of the friction add another degree of complexity. The work focuses on industrial machining centers with ball-screw driven stages as they are used in metal cutting. The approach uses Internal low-frequency signals from the NC controller to keep the barriers for an industrial application at a minimum. The contribution of this study is twofold: First, it extends conventional analytic friction models so that they incorporate positional dependency of friction, as well as the contribution of the inertia of the axis. Second, it proposes how to model the both effects jointly through support vector regression. This data-driven model outperforms the extended Stribeck and the generalized Maxwell-slip friction models, which serve as a representative benchmark for static and dynamic friction models respectively. However, this comes with the need for a careful selection of the data, on which the support vector machine is trained, in order to obtain an accurate and general model.






Similar content being viewed by others
References
Al-Bender, F., Lampaert, V., & Swevers, J. (2005). The generalized Maxwell-slip model: A novel model for friction Simulation and compensation. IEEE Transactions on Automatic Control, 50(11), 1883–1887. https://doi.org/10.1109/TAC.2005.858676.
Altintas, Y. (1992). Prediction of cutting forces and tool breakage in milling from feed drive current measurements. Journal of Engineering for Industry, 114(4), 386–392.
Auchet, S., Chevrier, P., Lacour, M., & Lipinski, P. (2004). A new method of cutting force measurement based on command voltages of active electro-magnetic bearings. International Journal of Machine Tools and Manufacture, 44(14), 1441–1449. https://doi.org/10.1016/j.ijmachtools.2004.05.009.
Boser, B. E., Guyon, I. M., & Vapnik, V. N. (1992). A training algorithm for optimal margin classifiers. In Proceedings of the fifth annual workshop on computational learning theory, ACM, New York, NY, USA, COLT ’92, pp. 144–152. https://doi.org/10.1145/130385.130401
Bui, B. D., Uchiyama, N., & Sano, S. (2015). Nonlinear friction modeling and compensation for precision control of a mechanical feed-drive system. Sensors and Materials, 27(10), 971–983. https://doi.org/10.18494/SAM.2015.1169.
Canudas de Wit, C., Olsson, H., Astrom, K. J., & Lischinsky, P. (1995). A new model for control of systems with friction. IEEE Transactions on Automatic Control, 40(3), 419–425.
Chang, C. C., & Lin, C. J. (2011). LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2:27:1–27:27, software available at http://www.csie.ntu.edu.tw/~cjlin/libsvm.
Cherkassky, V., & Ma, Y. (2004). Practical selection of SVM parameters and noise estimation for SVM regression. Neural Networks, 17(1), 113–126. https://doi.org/10.1016/S0893-6080(03)00169-2.
Denkena, B., & Hackelöer, F. L. (2010). Multi-sensor disturbance force measurement for compliant mechanical structures. IEEE, pp 2518–2524. https://doi.org/10.1109/ICSENS.2010.5690446.
Hong, Y. C., Ha, S. J., & Cho, M. W. (2012). Predicting of cutting forces in a micromilling process based on frequency analysis of sensor signals and modified polynomial neural network algorithm. International Journal of Precision Engineering and Manufacturing, 13(1), 17–23. https://doi.org/10.1007/s12541-012-0003-9.
Kim, T. Y., Woo, J., Shin, D., & Kim, J. (1999). Indirect cutting force measurement in multi-axis simultaneous NC milling processes. International Journal of Machine Tools and Manufacture, 39(11), 1717–1731. https://doi.org/10.1016/S0890-6955(99)00027-9.
Kurihara, D., Kakinuma, Y., & Katsura, S. (2010). Cutting force control applying sensorless cutting force monitoring method. Journal of Advanced Mechanical Design, Systems, and Manufacturing, 4(5), 955–965. https://doi.org/10.1299/jamdsm.4.955.
Lampaert, V., Swevers, J., & Al-Bender, F. (2002). Modification of the Leuven integrated friction model structure. IEEE Transactions on Automatic Control, 47(4), 683–687. https://doi.org/10.1109/9.995050.
Lee, W., Lee, C. Y., Jeong, Y. H., & Min, B. K. (2015). Friction compensation controller for load varying machine tool feed drive. International Journal of Machine Tools and Manufacture, 96, 47–54. https://doi.org/10.1016/j.ijmachtools.2015.06.001.
Rafan, N., Jamaludin, Z., Chiew, T., Abdullah, L., & Maslan, M. (2015). Contour error analysis of precise positioning for ball screw driven stage using friction model feedforward. Procedia CIRP, 26, 712–717. https://doi.org/10.1016/j.procir.2014.08.021.
Rebelein, C., & Zaeh, M. F. (2016). Friction in feed drives of machine tools: Investigation, modeling and validation. Production Engineering, 10(4–5), 497–507. https://doi.org/10.1007/s11740-016-0678-3.
Ruderman, M., & Bertram, T. (2011). Modified Maxwell-slip model of presliding friction. IFAC Proceedings Volumes, 44(1), 10764–10769. https://doi.org/10.3182/20110828-6-IT-1002.00309.
Sato, R., Shirase, K., & Hayashi, A. (2017). Energy consumption of feed drive systems based on workpiece setting position in five-axis machining center. Journal of Manufacturing Science and Engineering, 140(2), 021008. https://doi.org/10.1115/1.4037427.
Shinno, H., Hashizume, H., & Yoshioka, H. (2003). Sensor-less monitoring of cutting force during ultraprecision machining. CIRP Annals, 52(1), 303–306. https://doi.org/10.1016/S0007-8506(07)60589-7.
Smola, A. J., & Schölkopf, B. (2004). A tutorial on support vector regression. Statistics and Computing, 14(3), 199–222. https://doi.org/10.1023/B:STCO.0000035301.49549.88.
Stein, J., Colvin, D., Clever, G., & Wang, C. (1986). Evaluation of DC servo machine-tool feed drives as force sensors. Journal of Dynamic Systems Measurement and Control-Transactions of the ASME, 108(4), 279–288.
Stemmler, S., Abel, D., Schwenzer, M., Adams, O., & Klocke, F. (2017). Model predictive control for force control in milling. IFAC-Papers OnLine, 50(1), 15871–15876. https://doi.org/10.1016/j.ifacol.2017.08.2336.
Swevers, J., Al-Bender, F., Ganseman, C., & Projogo, T. (2000). An integrated friction model structure with improved presliding behavior for accurate friction compensation. IEEE Transactions on Automatic Control, 45(4), 675–686. https://doi.org/10.1109/9.847103.
Tjahjowidodo, T., Al-Bender, F., & Van Brussel, H. (2005). Friction identification and compensation in a DC motor. IFAC Proceedings Volumes, 38(1), 554–559. https://doi.org/10.3182/20050703-6-CZ-1902.00093.
Tjahjowidodo, T., Al-Bender, F., Van Brussel, H., & Symens, W. (2007). Friction characterization and compensation in electro-mechanical systems. Journal of Sound and Vibration, 308(3–5), 632–646. https://doi.org/10.1016/j.jsv.2007.03.075.
Tsirikoglou, P., Abraham, S., Contino, F., Lacor, C., & Ghorbaniasl, G. (2017). A hyperparameters selection technique for support vector regression models. Applied Soft Computing, 61, 139–148. https://doi.org/10.1016/j.asoc.2017.07.017.
Vapnik, V., Golowich, S. E., & Smola, A. J. (1996). Support vector method for function approximation, regression estimation and signal processing. In NIPS.
Villegas, F. J., Hecker, R. L., Peña, M. E., Vicente, D. A., & Flores, G. M. (2014). Modeling of a linear motor feed drive including pre-rolling friction and aperiodic cogging and ripple. The International Journal of Advanced Manufacturing Technology, 73(1–4), 267–277. https://doi.org/10.1007/s00170-014-5795-6.
Wu, X., Kumar, V., Ross Quinlan, J., Ghosh, J., Yang, Q., Motoda, H., et al. (2008). Top 10 algorithms in data mining. Knowledge and Information Systems, 14(1), 1–37. https://doi.org/10.1007/s10115-007-0114-2.
Yamada, Y., Kakinuma, Y., Ito, T., Fujita, J., & Matsuzaki, H. (2016). Sensorless monitoring of cutting force variation with fractured tool under heavy cutting condition. In ASME, p V003T08A025. https://doi.org/10.1115/MSEC2016-8820.
Yamada, Y., & Kakinuma, Y. (2016a). Mode decoupled cutting force monitoring by applying multi encoder based disturbance observer. Procedia CIRP, 57, 643–648. https://doi.org/10.1016/j.procir.2016.11.111.
Yamada, Y., & Kakinuma, Y. (2016b). Sensorless cutting force estimation for full-closed controlled ball-screw-driven stage. The International Journal of Advanced Manufacturing Technology, 87(9), 3337–3348. https://doi.org/10.1007/s00170-016-8710-5.
Yamada, Y., Yamato, S., & Kakinuma, Y. (2017). Mode decoupled and sensorless cutting force monitoring based on multi-encoder. The International Journal of Advanced Manufacturing Technology, 92(9–12), 4081–4093. https://doi.org/10.1007/s00170-017-0427-6.
Yang, M., Yang, J., & Ding, H. (2018). A two-stage friction model and its application in tracking error pre-compensation of CNC machine tools. Precision Engineering, 51, 426–436. https://doi.org/10.1016/j.precisioneng.2017.09.014.
Acknowledgements
The authors would like to thank the German Research Foundation DFG for the kind support within the Cluster of Excellence “Internet of Production”.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Schwenzer, M., Auerbach, T., Miura, K. et al. Support vector regression to correct motor current of machine tool drives. J Intell Manuf 31, 553–560 (2020). https://doi.org/10.1007/s10845-019-01464-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10845-019-01464-1