A New Grey Box Approach for Friction Modelling of Machine Tool Drives
1
Manufacturing Technology Institute (MTI), RWTH Aachen University, Germany
2
Fraunhofer Institute for Production Technology (IPT), Germany
Submission date: 2024-02-14
Final revision date: 2024-03-19
Acceptance date: 2024-03-19
Online publication date: 2024-03-20
Publication date: 2024-04-02
Corresponding author
Journal of Machine Engineering 2024;24(1):5-16
KEYWORDS
TOPICS
ABSTRACT
Measurement of the process force in milling is usually conducted by using piezo-electric dynamometers which are costly and reduce the stiffness of the system. A less invasive alternative is an indirect estimation of cutting forces based on the power of the servo drives. However, a correction of frictional effects from the transmission system is necessary to achieve accurate results. Most machine tools are equipped with ball-screw drives whose friction behavior is highly nonlinear due to dependency on both velocity and position. This study provides a novel approach to consider all frictional and inertial effects in transmission behavior of ball-screw drives by utilizing the well-established generalized MAXWELL slip (GMS) model and combines it with a data-based approach, namely support vector regression (SVR). The approach acquires the internal states of the GMS model and uses them as an additional input for the SVR. The model is validated on different experiments conducted on a five-axis machining center and compared to established friction models, as well as a sole SVR. The results show the model to have errors between 7 % and 12 % over the full working range of the x- and y-axes, respectively, outperforming the benchmark models significantly.
REFERENCES (34)
1.
STEMMLER S., ABEL D., SCHWENZER M., ADAMS O., KLOCKE F., 2017, Model Predictive Control for Force Control in Milling, IFAC-PapersOnLine, 50/ 1, 15871–15876.
2.
SCHWENZER M., STEMMLER S., AY M., RÜPPEL A.K., BERGS T., ABEL D., 2022, Model Predictive Force Control in Milling Based on an Ensemble Kalman Filter, Journal of Intelligent Manufacturing, 33/7, 1907–1919.
3.
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.
4.
RAFAN N.A., JAMALUDIN Z., CHIEW T.H., ABDULLAH L., MASLAN M.N., 2015, Contour Error Analysis of Precise Positioning for Ball Screw Driven Stage Using Friction Model Feedforward, Procedia CIRP, 26, 712–717.
5.
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.
6.
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, https://doi.org/10.18494/ SAM.2015.1134.
7.
ARMSTRONG-HELOUVRY B., DUPONT P., de WIT C.C., 1994, A Survey of Models, Analysis Tools and Compensation Methods for the Control of Machines with Friction, Automatica, 30/7, 1083–1138, https://doi.org/10.1016/0005-1....
8.
COULOMB C.A., 1785, Theorie des Machines Simples, en Ayant Egard au Frottement de Leurs Parties, et a la Roideur Dews Cordages, Mémoires de Mathématique et de Physique, x, 161–342.
9.
REYNOLDS O., 1886, IV. on the Theory of Lubrication and its Application to Mr. Beauchamp Tower’s Experiments, Including an Experimental Determination of the Viscosity of Olive Oil, Philosophical Transactions of the Royal Society of London, 177, 157–234.
10.
SOMMERFELD A., 1904, Zur Hydrodynamischen Theorie der Schmiermittelreibung, Zeitschrift für Mathematik und Physik, 50, 97–155.
11.
HERSEY M.D., 1914, The Laws of Lubrication of Horizontal Journal Bearings, Journal of the Washington Academy of Sciences, 4/19, 542–552.
12.
STRIBECK R., 1902, Die wesentlichen Eigenschaften der Gleit- und Rollenlager, Zeitschrift des Vereines Deutscher Ingenieure, 46, 1341–1348.
13.
DAHL P.R., 1968, A Solid Friction Model, Technical rept. Published byAerospace Corp. el segundo CA, https://apps.dtic.mil/sti/cita..., last checked: 20.01.2024.
14.
RABINOWICZ E., 1958, The Intrinsic Variables Affecting the Stick-Slip Process, Proceedings of the Physical Society, 71/4, 668–675.
15.
HESS D.P., SOOM A., 1991, Normal Vibrations and Friction Under Harmonic Loads: Part I—Hertzian Contacts, Journal of Tribology, 113/1, 80–86.
16.
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.
17.
SWEVERS J., AL-BENDER F., GANSEMAN C.G., 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.
18.
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.
19.
SCHWENZER M., AUERBACH T., MIURA K., DÖBBELER B., BERGS T., 2020, Support Vector Regression to Correct Motor Current of Machine Tool Drives, Journal of Intelligent Manufacturing, 31/3, 553–560.
20.
BOSER B.E., GUYON I.M., VAPNIK V.N., 1992, A Training Algorithm for Optimal Margin Classifiers, Haussler, D. (Hrsg.): Proceedings of the Fifth Annual Workshop on Computational Learning Theory, Pittsburgh Pennsylvania USA, 27 07 1992–29 07 1992. New York, NY, USA, ACM, 144–152.
21.
VAPNIK V., GOLOWICH S., SMOLA A., 1996, Support Vector Method for Function Approximation, Regression Estimation and Signal Processing, Mozer M.C., Jordan M., Petsche T., (Hrsg.), Advances in Neural Information Processing Systems, 9, NeurIPS Proceedings.
22.
KIM G.D., CHU C.N., 1999, Indirect Cutting Force Measurement Considering Frictional Behaviour in a Machining Centre Using Feed Motor Current, The International Journal of Advanced Manufacturing Technology, 15/7, 478–484.
23.
FUJITA T., XI T., IKEDA R., KEHNE S., FEY M., BRECHER C., 2022, Identification of a Practical Digital Twin for Simulation of Machine Tools, International Journal of Automation Technology, 16/3, 261–268.
24.
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.
25.
SHINNO H., HASHIZUME H., YOSHIOKA H., 2003, Sensor-less Monitoring of Cutting Force during Ultraprecision Machining, CIRP Annals, 52/1, 303–306.
26.
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.
27.
DENKENA B., HACKELO F.L., 2010, Multi-sensor Disturbance Force Measurement for Compliant Mechanical Structures, IEEE Sensors, Kona, HI, 01.11.2010–04.11.2010, IEEE, 2518–2524.
28.
MIURA K., BERGS T., 2019, A Method of Cutting Power Monitoring for Feed Axes in Milling by Power Measurement Device, IFAC-PapersOnLine, 52/13, 2471–2476.
29.
YAMADA Y., KAKINUMA Y., 2016, Sensorless Cutting Force Estimation for Full-Closed Controlled Ball-Screw-Driven Stage, The International Journal of Advanced Manufacturing Technology, 87/9–12, 3337–3348.
30.
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.
31.
XI T., FUJITA T., KEHNE S., IKEDA R., FEY M., BRECHER C., 2022, An Extended Lugre Model for Estimating Nonlinear Frictions in Feed Drive Systems of Machine Tools, Procedia CIRP, 107, 452–457.
32.
CARLSON F.B., ROBERTSSON A., JOHANSSON R., 2015, Modeling and Identification of Position and Temperature Dependent Friction Phenomena Without Temperature Sensing, 2015, IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Hamburg, Germany, 28.09.2015–02.10.2015, IEEE, 3045–3051.
33.
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.
34.
ZSCHACK S., BUCHNER S., AMTHOR A., AMENT C., 2012, Maxwell Slip Based Adaptive Friction Compensation in High Precision Applications, IECON 2012 – 38th Annual Conference on IEEE Industrial Electronics Society, Montreal, QC, Canada, 25.10.2012–28.10.2012, IEEE, 2331–2336.
| eISSN: | 2391-8071 |
| ISSN: | 1895-7595 |
We process personal data collected when visiting the website. The function of obtaining information about users and their behavior is carried out by voluntarily entered information in forms and saving cookies in end devices. Data, including cookies, are used to provide services, improve the user experience and to analyze the traffic in accordance with the Privacy policy. Data are also collected and processed by Google Analytics tool (more).
You can change cookies settings in your browser. Restricted use of cookies in the browser configuration may affect some functionalities of the website.
You can change cookies settings in your browser. Restricted use of cookies in the browser configuration may affect some functionalities of the website.
