Numerical Algorithm for Simulation of Hybrid-Degrees of Freedom Belt-Pulley Systems: Application to X-Y Positioning Mechanism

Document Type : Research Article

Authors

Faculty of Mechanical Engineering, K. N. Toosi University of Technology, Tehran, Iran

Abstract

This paper presents a comprehensive investigation into the modeling and dynamic analysis of a XY mechanism, considering the potential occurrence of motor pulley slipping. The research commenced with the establishment of kinematic relationships among system components and the definition of virtual pulleys. By characterizing static and kinetic frictions for individual system elements, various rolling and slipping states were explored. The study unveiled that the system, excluding motor pulleys, experiences a stick-slip phenomenon due to friction between actuator components and the ground, resulting in deadzones during motion initiation. To address this, a novel friction model encompassing deadzones was introduced, and equations accounting for the stick-slip phenomenon were derived. Moreover, recognizing that each actuator motor can be in either a rolling or slipping state, it was established that the mechanism represents a hybrid-DOF dynamic system. The equations of motion switch between four modes, denoted as RR, SR, RS, and SS, contingent on input voltages, kinematic and dynamic variables, and friction coefficients between motor pulleys and belts. Calculating the required friction to maintain rolling was essential; insufficient friction between motor pulleys and belts leads to motor slipping. The determination of the system's subsequent dynamics considered different motor states, varying DOF, and the interplay of stick-slip phenomena with deadzones. Ultimately, dynamic analyses of the mechanism were conducted through simulations in three distinct scenarios. This study effectively highlights the nonlinear effects and complexities inherent in this mechanism, offering valuable insights into its behavior under different conditions.

Keywords

Main Subjects

References

[1]         M. Moeen and M. Reza, “Numerical algorithm for nonlinearity compensation of hardly constrained actuation for trajectory tracking control of deadzone-included dynamic systems,” ISA Trans., no. xxxx, 2024, doi: 10.1016/j.isatra.2024.07.025.
[2]         M. Ebrahimi and M. Homaeinezhad, “Compensation of friction and stick-slip uncertainties in trajectory tracking control of servo DC machines considering actuation constraints,” https://doi.org/10.1177/09596518231196830, Oct. 2023, doi: 10.1177/09596518231196830.
[3]         M. Lahoud, G. Marchello, M. D’Imperio, A. Müller, and F. Cannella, “A Deep Learning Framework for Non-Symmetrical Coulomb Friction Identification of Robotic Manipulators,” Proc. - IEEE Int. Conf. Robot. Autom., pp. 10510–10516, 2024, doi: 10.1109/ICRA57147.2024.10610737.
[4]         S. Mahajan and A. Cicirello, “Governing Equation Identification of Nonlinear Single Degree-of-Freedom Oscillators With Coulomb Friction Using Explicit Stick and Slip Temporal Constraints,” ASCE-ASME J. Risk Uncertain. Eng. Syst. Part B Mech. Eng., vol. 9, no. 4, Dec. 2023, doi: 10.1115/1.4063070/1166116.
[5]         A. Amthor, S. Zschaeck, and C. Ament, “High precision position control using an adaptive friction compensation approach,” IEEE Trans. Automat. Contr., vol. 55, no. 1, pp. 274–278, 2010, doi: 10.1109/TAC.2009.2036307.
[6]         A. Shahhosseini, M. H. Tien, and K. D’Souza, “Efficient Hybrid Symbolic-Numeric Computational Method for Piecewise Linear Systems With Coulomb Friction,” J. Comput. Nonlinear Dyn., vol. 18, no. 7, Jul. 2023, doi: 10.1115/1.4062203/1160344.
[7]         J. Shah, B. Snider, T. Clarke, S. Kozutsky, M. Lacki, and A. Hosseini, “Large-scale 3D printers for additive manufacturing: design considerations and challenges,” Int. J. Adv. Manuf. Technol., vol. 104, no. 9–12, pp. 3679–3693, 2019, doi: 10.1007/s00170-019-04074-6.
[8]         J. O. Jang, “Deadzone compensation of an XY-positioning table using fuzzy logic,” IEEE Trans. Ind. Electron., vol. 52, no. 6, pp. 1696–1701, 2005, doi: 10.1109/TIE.2005.858702.
[9]         Z. Zhao et al., “Adaptive Quantized Control of Flexible Manipulators Subject to Unknown Dead Zones,” IEEE Trans. Syst. Man, Cybern. Syst., vol. 53, no. 10, pp. 6438–6447, Oct. 2023, doi: 10.1109/TSMC.2023.3283268.
[10]       K. S. Sollmann, M. K. Jouaneh, and D. Lavender, “Dynamic modeling of a two-axis, parallel, H-frame-type XY positioning system,” IEEE/ASME Trans. Mechatronics, vol. 15, no. 2, pp. 280–290, 2010, doi: 10.1109/TMECH.2009.2020823.
[11]       S. He, H. Tang, Z. Zhu, P. Zhang, Y. Xu, and X. Chen, “A novel flexure piezomotor with minimized backward and nonlinear motion effect,” IEEE Trans. Ind. Electron., vol. 69, no. 1, pp. 652–662, 2022, doi: 10.1109/TIE.2020.3048320.
[12]       L. Yuan, L. Wang, R. Qi, Z. Zhao, J. Jin, and C. Zhao, “A novel hollow-type XY piezoelectric positioning platform,” Int. J. Mech. Sci., vol. 255, p. 108496, Oct. 2023, doi: 10.1016/J.IJMECSCI.2023.108496.
[13]       M. Miyasaka, M. Haghighipanah, Y. Li, J. Matheson, A. Lewis, and B. Hannaford, “Modeling Cable-Driven Robot with Hysteresis and Cable-Pulley Network Friction,” IEEE/ASME Trans. Mechatronics, vol. 25, no. 2, pp. 1095–1104, 2020, doi: 10.1109/TMECH.2020.2973428.
[14]       M. R. Homaeinezhad and M. M. Ebrahimi, “Numerical Approach for Nonlinear Dynamics Simulation of Belt- Pulley XY Positioning Mechanism,” pp. 352–373, 2024, doi: 10.37256/est.5220244538.
[15]       M. R. Homaeinezhad, M. Homaeinezhad, S. Akbari, and D. Nayeb Ghanbar Hosseini, “Input-decoupled discrete-time sliding mode control algorithm for servo multi-field multi-armature DC machine,” ISA Trans., vol. 127, no. xxxx, pp. 283–298, 2022, doi: 10.1016/j.isatra.2021.08.037.
[16]       A. Izadbakhsh, N. Nassiri, and M. B. Menhaj, “Linear/Nonlinear PID Control of Cooperative Multiple Robot Manipulators: A Robust Approach,” AUT J. Model. Simul., vol. 55, no. 1, pp. 5–5, Jun. 2023, doi: 10.22060/MISCJ.2023.21867.5305.
[17]       E. Ostertag, N. Bakri, and N. Becker, “Functional Disturbance Observer for Simultaneous Control and Dry Friction Compensation,” IFAC Proc. Vol., vol. 22, no. 6, pp. 421–426, 1989, doi: 10.1016/s1474-6670(17)54412-2.
[18]       H. Ahmadian, I. Sharifi, and H. A. Talebi, “Robust Distributed Lasso-Model Predictive Control Design: A Case Study on Large-Scale Multi-Robot Systems,” AUT J. Model. Simul., vol. 55, no. 1, pp. 8–8, Jun. 2023, doi: 10.22060/MISCJ.2023.22087.5312.
[19]       E. Jahanbazi, F. Jahangiri, and M. R. Mohammadi, “Neural Network based Fault Tolerant LQR Control for Orbital Maneuvering in LEO Satellites using Hall Effect Thrusters,” AUT J. Model. Simul., vol. 55, no. 1, pp. 11–11, Jun. 2023, doi: 10.22060/MISCJ.2023.22482.5326.
[20]       W. W. Yao, X. P. Zhou, D. Dias, Y. Jia, and Y. J. Li, “Frictional contact and stick-slip: Mechanism and numerical technology,” Int. J. Solids Struct., vol. 274, p. 112289, Jul. 2023, doi: 10.1016/J.IJSOLSTR.2023.112289.
[21]       B. Shi, F. Wang, C. Han, Z. Huo, and Y. Tian, “Design of a precise positioning stage actuated by a double-layer stick-slip actuator used for precise assembly,” Mech. Mach. Theory, vol. 185, p. 105336, Jul. 2023, doi: 10.1016/J.MECHMACHTHEORY.2023.105336.
[22]       G. S. Mfoumou, G. D. Kenmoé, and T. C. Kofané, “Computational algorithms of time series for stick-slip dynamics and time-delayed feedback control of chaos for a class of discontinuous friction systems,” Mech. Syst. Signal Process., vol. 119, pp. 399–419, 2019, doi: 10.1016/j.ymssp.2018.09.034.
[23]       G. Qiao, H. Li, X. Lu, J. Wen, and T. Cheng, “Piezoelectric stick-slip actuators with flexure hinge mechanisms: A review,” https://doi.org/10.1177/1045389X211072244, vol. 33, no. 15, pp. 1879–1901, Jan. 2022, doi: 10.1177/1045389X211072244.
[24]       W. Liu, F. Yang, X. Zhu, and X. Chen, “Stick-slip vibration behaviors of BHA and its control method in highly-deviated wells,” Alexandria Eng. J., vol. 61, no. 12, pp. 9757–9767, 2022, doi: 10.1016/j.aej.2022.01.039.
[25]       Y. Lu et al., “Experimental investigation of stick-slip behaviors in dry sliding friction,” Tribol. Int., vol. 201, p. 110221, Jan. 2025, doi: 10.1016/J.TRIBOINT.2024.110221.
[26]       Q. Huang, Z. Xie, and H. Liu, “Active control for stick-slip behavior of the marine propeller shaft subjected to friction-induced vibration,” Ocean Eng., vol. 268, no. September 2022, p. 113302, 2023, doi: 10.1016/j.oceaneng.2022.113302.
[27]       M. R. Homaeinezhad, M. M. Ebrahimi, and M. M. M. Alvar, “Discrete-Time Nonlinear Control Technique for Trajectory Tracking of Hybrid Reluctance Actuator,” pp. 1–27, 1999, doi: 10.24200/sci.2024.63806.8606.
[28]       D. Zhang, L. Kong, S. Zhang, Q. Li, and Q. Fu, “Neural networks-based fixed-time control for a robot with uncertainties and input deadzone,” Neurocomputing, vol. 390, pp. 139–147, 2020, doi: 10.1016/j.neucom.2020.01.072.
[29]       G. Galuppini, L. Magni, and D. Martino, “Model predictive control of systems with deadzone and saturation Model Predictive Control of Systems with Deadzone and Saturation,” no. February 2023, 2018, doi: 10.1016/j.conengprac.2018.06.010.
AUT Journal of Modeling and Simulation
Volume 56, Issue 2
2024
Pages 129-154

Files

Share

How to cite

Statistics