Dynamic Modeling and Analysis of Rigid Multi-body System with Clearance Joints Based on Deep Learning

doi:10.3901/JME.2022.09.136

Abstract

Abstract: The contact force of the joint in the mechanical system is strongly nonlinear, which is influenced by the amount of clearance in the joint, the material property of the parts of the kinematic pair and the contact state during movement. Traditional theoretical models of friction mainly focus on the universality of the description of friction phenomenon, but it is difficult to accurately describe the nonlinear characteristics of friction in the motion. Based on the data obtained from the physical prototype test, the neural network model of the nonlinear contact force of the clearance joint is established by using the deep learning method. The contact friction data set is generated by the friction experiment, and the contact impact force data set is generated by the mixed model of revolute hinge clearance. After training and testing, a neural network model describing the contact dynamics of revolute clearance hinge is obtained. Combined with Lagrange equation, a "rigid-body-to-clearance-to-rigid-body" dynamic model of a slider crank mechanism with clearance joint is established. The dynamic responses of the key parameters of the system are obtained through simulation and compared with the results of physical tests. The correctness of the clearance joint model based on deep learning method is verified, which provided a feasible idea for the application of deep learning method in the direction of nonlinear system dynamics modelling.

Key words: joint clearance, friction experiment, nonlinear contact force model, multi-body system, dynamics, deep learning

CLC Number:

TH113

LIU Zhen, HU Sanbao, HU Junhua, XIANG Chao. Dynamic Modeling and Analysis of Rigid Multi-body System with Clearance Joints Based on Deep Learning[J]. Journal of Mechanical Engineering, 2022, 58(9): 136-146.

References

[1] FLORES P, AMBRóSIO J. Revolute joints with clearance in multibody systems[J]. Computers & Structures, 2004, 82(17-19): 1359-1369.
[2] ZHENG Enlai, CHU Lei, JIANG Shuyun, et al. Multi-body dynamic modeling and error analysis of planar flexible multi-link mechanism with lubricated revolute clearance joints and crankshaft-bearing structure[J]. Journal of Mechanical Engineering, 2020, 56(3): 106-120. 郑恩来, 储磊, 蒋书运, 等. 含润滑间隙和曲轴转子-轴承结构的平面柔性多连杆机构多体动力学建模与动态误差分析[J]. 机械工程学报, 2020, 56(3): 106-120.
[3] YAN Shaoze, XIANG Wuweikai, HUANG Tieqiu. Advances in modeling of clearance joints and dynamics of mechanical systems with clearances[J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2016, 52(4): 741-755. 阎绍泽, 向吴维凯, 黄铁球. 计及间隙的运动副和机械系统动力学的研究进展[J]. 北京大学学报(自然科学版), 2016, 52(4): 741-755.
[4] DING Qian, ZHAI Hongmei. The advance in researches of friction dynamics in mechanics system[J]. Advances in Mechanics, 2013, 43(1): 112-131. 丁千, 翟红梅. 机械系统摩擦动力学研究进展[J]. 力学进展, 2013, 43(1): 112-131.
[5] FLORES P. A parametric study on the dynamic response of planar multibody systems with multiple clearance joints[J]. Nonlinear Dynamics, 2010, 61(4): 633-653.
[6] ERKAYA S, UZMAY İ. Determining link parameters using genetic algorithm in mechanisms with joint clearance[J]. Mechanism and Machine Theory, 2009, 44(1): 222-234.
[7] ERKAYA S, UZMAY İ. Investigation on effect of joint clearance on dynamics of four-bar mechanism[J]. Nonlinear Dynamics, 2009, 58(1): 179-198.
[8] RZINE B, MOUJIBI N, SAKA A, et al. Subsystem interaction of mechatronic system with clearance[J]. International Journal of Systems Control, 2010, 44(1): 222-234.
[9] MUKRAS S, KIM N, MAUNTLER N, et al. Analysis of planar multibody systems with revolute joint wear[J]. Wear, 2010, 268(5-6): 643-652.
[10] SHIAU T, TSAI Y, TSAI M. Nonlinear dynamic analysis of a parallel mechanism with consideration of joint effects[J]. Mechanism and Machine Theory, 2008, 43(4): 491-505.
[11] HUNT K, CROSSLEY E. Coefficient of restitution interpreted as damping in vibro impact[J]. Journal of Applied Mechanics, 1975, 42(2): 440-445.
[12] LANKARANI H M, NIKRAVESH P. A contact force model with hysteresis damping for impact analysis of multibody systems[J]. Journal of Mechanical Design, 1990, 112(3): 369-376.
[13] BAI Zhengfeng, TIAN Hao, ZHAO Yang. Dynamics modeling and simulation of mechanism with joint clearance[J]. Journal of Harbin Institute of Technology, 2020, 17(5): 706-710.
[14] STRIBECK R. Die wesentlichen eigenschaften der gleit-und rollenlager: The key qualities of sliding and roller bearings[J]. Zeitschrift des Vereins Deutscher Ingenieure, 1902, 46(38-39): 1342-1348, 1432-1437.
[15] HESS D, SOOM A. Friction at a lubricated line contact operating at oscillating sliding velocities[J]. Journal of Tribology, 1990, 112(1): 147-152.
[16] COURTNEY-PRATT J, EISNER E. The effect of a tangential force on the contact of metallic bodies[J]. Proceedings of the Royal Society of London, 1957, 238(A): 529-550.
[17] RABINOWICZ E. The nature of the static and kinetic coefficients of friction[J]. Journal of Applied Physics, 1951, 22(11): 1373-1379.
[18] DUAN Shuyong, LI Changluo, HAN Xu, et al. Forward-inverse dynamics analysis of robot arm trajectories and development of a nonlinear friction model for robot joints[J]. Journal of Mechanical Engineering, 2020, 56(9): 18-28. 段书用, 李昌洛, 韩旭, 等. 机械臂动力学分析及关节非线性摩擦模型建立[J]. 机械工程学报, 2020, 56(9): 18-28.
[19] SU Yuewen, ZHU Aibin, CHEN Wei, et al. Effect of friction and contact in clearance joint on dynamics of multibody system[J]. Lubrication Engineering, 2008, 3(8): 16-19. 宿月文, 朱爱斌, 陈渭, 等. 间隙约束副摩擦接触对多体系统动态特性的影响[J]. 润滑与密封, 2008, 3(8): 16-19.
[20] SHI Qun, LÜ Lei, XIE Jiajun. Intelligent posture control of humanoid robot in variable environment[J]. Journal of Mechanical Engineering, 2020, 56(3): 64-72. 施群, 吕雷, 谢家骏. 可变环境下仿人机器人智能姿态控制[J]. 机械工程学报, 2020, 56(3): 64-72.
[21] RUECKERT E, NAKATENUS M, TOSATTO S, et al. Learning inverse dynamics models in O(n) time with LSTM networks[C]// 2017 IEEE-RAS 17th International Conference on Humanoid Robotics (Humanoids), November 15-17, 2017, Birmingham, UK. New York: IEEE, 2017: 811-816.
[22] CHOI H, AN J, KIM J, et al. Data-driven simulation for general purpose multibody dynamics using deep neural networks[J]. Multibody System Dynamics, 2021, 51(4): 419-454.
[23] PANG Tao. Position-dependent dynamics prediction based on deep learning for five-axis machine tools[D]. Chengdu: University of Electronic Science and Technology of China, 2020. 庞涛. 基于深度学习的五轴机床变姿态下动力学特性预测[D]. 成都: 电子科技大学, 2020.
[24] BAI Zhengfeng. Research on dynamic characteristics of mechanism with joint clearance[D]. Harbin: Harbin Institute of Technology, 2011. 白争锋. 考虑铰间间隙的机构动力学特性研究[D]. 哈尔滨: 哈尔滨工业大学, 2011.
[25] HARTOG J. Forced vibrations with combined coulomb and viscous friction[J]. Transaction of the American Society of Mechanical Engineering, 1931, 53(9): 107-115.
[26] BO L, PAVELESCU D. The friction-speed relation and its influence on the critical velocity of the stick-slip Motion[J]. Wear, 1982, 82(3): 277-289.
[27] KARNOPP D. Computer simulation of stick-slip friction in mechanical dynamic systems[J]. Journal of Dynamic Systems Measurement and Control, 1985, 107(1): 100-103.
[28] ARMSTRONG-HéLOUVRY B, DUPONT P, WIT C C D. A survey of models, analysis tools and compensation methods for the control of machines with friction[J]. Automatica, 1994, 30(7): 1083-1138.
[29] FLORES P. Dynamic analysis of mechanical systems with imperfect kinematic joints[D]. Guimaraes: University of Minho, 2004.