含摩擦与碰撞平面多刚体系统动力学线性互补算法

王晓军; 王琪

doi:10.6052/0459-1879-15-168

含摩擦与碰撞平面多刚体系统动力学线性互补算法

doi: 10.6052/0459-1879-15-168

王晓军¹,
王琪^2, ,

1.
常州工学院机电学院, 常州213002
2. 北京航空航天大学航空科学与工程学院, 北京100191

基金项目: 国家自然科学基金资助项目(11372018).

详细信息

通讯作者:
王琪,教授,主要研究方向:多体系统动力学与控制.E-mail:bhwangqi@sina.com

中图分类号: O313.7
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- 被引次数: 0
出版历程
- 收稿日期: 2015-05-11
- 修回日期: 2015-06-24
- 刊出日期: 2015-09-18

A LCP METHOD FOR THE DYNAMICS OF PLANAR MULTIBODYSYSTEMS WITH IMPACT AND FRICTION

Wang Xiaojun¹,
Wang Qi^{2
, ,}

1.
Department of Electron and Machine, Changzhou Institute of Technology, Changzhou 213002, China
2. School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China

Funds: The project was supported by the National Natural Science Foundation of China (11372018).

摘要

摘要: 基于接触力学理论和线性互补问题的算法, 给出了一种含接触、碰撞以及库伦干摩擦, 同时具有理想定常约束(铰链约束) 和非定常约束(驱动约束) 的平面多刚体系统动力学的建模与数值计算方法. 将系统中的每个物体视为刚体, 但考虑物体接触点的局部变形, 将物体间的法向接触力表示成嵌入量与嵌入速度的非线性函数,其切向摩擦力采用库伦干摩擦模型. 利用摩擦余量和接触点的切向加速度等概念, 给出了摩擦定律的互补关系式; 并利用事件驱动法, 将接触点的黏滞-滑移状态切换的判断及黏滞状态下摩擦力的计算问题转化成线性互补问题的求解. 利用第一类拉格朗日方程和鲍姆加藤约束稳定化方法建立了系统的动力学方程, 由此可降低约束的漂移, 并可求解该系统的运动、法向接触力和切向摩擦力, 还可以求解理想铰链约束力和驱动约束力. 最后以一个类似夯机的平面多刚体系统为例, 分析了其动力学特性, 并说明了相关算法的有效性.
- 多体系统 /
- 库伦干摩擦 /
- 接触力 /
- 线性互补问题 /
- 非光滑
Abstract: This paper is presented to show the modeling and numerical method for the dynamics of the planar multi-rigid-body system with contact, impact and Coulomb's dry friction. The multibody system consists of the rigid bodies which are linked with ideal joints and driving motors, so the system constraint equations included two parts, scleronomic constraint equations and rheonomic constraint equations. Based on the theory of contact mechanics, the local deformations in contact bodies are taken into account and the normal forces of contact surfaces are expressed as nonlinear functions of relative penetration depth and its speed during impact between two bodies. The Coulomb dry friction model is used to describe the tangential frictional forces of contact surfaces. Using the concept of friction saturation and the relative acceleration of the contact point in the tangential direction, the complementarity conditions and formulations about the friction law are given. The problems of detecting stick-slip transitions of contact points and solving frictional forces in stick situation are formulated and solved as a linear complementarity problem (LCP) by the event-driven scheme. The dynamical equations of the system are obtained by Lagrange's equations of the first kind and Baumgarte stabilization method in order to reduce the constraint drift and solve the system motion, normal contact forces and tangential friction forces as well as ideal joint constraint forces and driven constraint forces in the system. Finally, the numerical example of a planar multi-rigid-body like flat beater is given to analyze its dynamical behavior and show the availability of the method in this paper.
- multibody system /
- Coulomb dry friction /
- contact force /
- linear complementarity problem /
- non-smooth

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参考文献(26)

董富祥, 洪嘉振.多体系统动力学碰撞问题研究综述.力学进展, 2009, 39(3): 352-359 (Dong Fuxiang, Hong Jiazhen. Review of impact problem for dynamics of multibody system. Advances in Mechanics, 2009, 39(3): 352-359 (in Chinese))

曹登庆, 初世明, 李郑发, 等. 空间可展机构非光滑力学模型和动力学研究. 力学学报, 2013, 45(1): 4-14 (Cao Dengqing, Chu Shiming, Li Zhengfa, et al. Study on the non-smooth mechanical model and dynamics for space deployable mechanism. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(1): 4-14 (in Chinese))

王琪, 庄方方, 郭易圆, 等. 非光滑多体系统动力学数值算法的研究进展. 力学进展, 2013, 43(1): 101-111 (Wang Qi, Zhuang Fangfang, Guo Yiyuan, et al. Advances in the research on numerical methods for non-smooth dynamics of multibody systems. Advances in Mechanics. 2013, 43(1): 101-111 (in Chinese))

王庚祥, 刘宏昭. 多体系统动力学中关节效应模型的研究进展. 力学学报, 2015, 47(1): 31-50 (Wang Gengxiang, Liu Hongzhao. Research progress of joint effects model in multibody system dynamics. Journal of Theoretical and Applied Mechanics, 2015, 47(1): 31-50 (in Chinese))

Pfeiffer F, Glocker C. Multibody Dynamics with Unilateral Contacts. New York: John Wiley & Sons. Inc.1996

Flores P, mbrosio J. Kinematics and Dynamics of Multibody Systems with Imperfect Joints. Berlin: Springer, 2008

刘丽兰, 刘宏昭, 吴子英, 等. 机械系统中摩擦模型的研究进展. 力学进展, 2008, 38(2): 200-213 (Liu Lilan, Liu Hongzhao, Wu Ziying, et al. An overview of friction models in mechanical systems. Advances in Mechanics, 2008, 38(2): 200-213 (in Chinese))

Machado M, Moreira P, Flores P. Compliant contact force models in multibody dynamics: Evolution of the Hertz contact theory. Mechanism and Machine Theory, 2012, 53: 99-121

刘才山, 陈滨, 王玉玲. 考虑摩擦作用的多柔体系统点面碰撞模型.中国机械工程, 2000, 11(6): 616-619 (Liu Caishan, Chen Bin, Wang Yuling. The point-surface impact model considering the friction effect in flexible multi-body system. China Mechanical Engineering, 2000, 11(6): 616-619 (in Chinese))

丁千, 翟红梅. 机械系统摩擦动力学研究进展. 力学进展, 2013, 43(1): 112-131 (Ding Qian, Zhai Hongmei. The advance in researches of friction dynamics in mechanics system. Advances in Mechanics, 2013, 43(1): 112-131 (in Chinese))

Pennestri E, Valentini P P, Vita L. Multibody dynamics simulation of planar linkages with Dahl friction. Multibody Syst. Dyn., 2007, 17: 321-347

Dopico D, Luaces A, Gonzalez M, et al. Dealing with multiple contacts in a human-in-the-loop application, Multibody System Dynamics, 2011, 25 (2):167-183

Flores P, Ambrosio J. Translational joints with clearance in rigid multibody systems. ASME Journal of Computational and Nonlinear Dynamics, 2008, 3: 011007(1-10)

Pfeiffer F, Foerg M. Uibrich H. Numerical aspects of non-smooth multibody dynamics. Computer Methods in Applied Mechanics and Engineering, 2006, 195: 6891-6908

Flores P, Leine R, Glocker C. Modeling and analysis of planar rigid multibody systems with translational clearance joints based on the non-smooth dynamics approach. Multibody System Dynamics, 2010, 23: 165-190

Anitescu1 M, Hart G D. A constraint-stabilized time-stepping approach for rigid multibody dynamics with joints, contact and friction. Int J Numer Meth Engng, 2004, 60: 2335-2371

Wang Q, Peng H L, Zhuang F F. A constraint-stabilized method for multibody dynamics with friction-affected translational joints based on HLCP. Discrete and Continuous Dynamical Systems Series B, 2011, 16(2): 589-605

Zhuang F F, Wang Q. Modeling and simulation of the nonsmooth planar rigid multibody systems with frictional translational joints. Multibody Syst Dyn, 2012, 29: 403-423

Zhuang F F, Wang Q. Modeling and analysis of rigid multibody systems with driving constraints and frictional translation joints. Acta Mechanica Sinica, 2014, 30(3): 437-446

王晓军, 王琪, 庄方方. 含摩擦滑移铰及驱动约束多刚体系统数值算法. 动力学与控制学报, 2014, 12(4): 335-340 (Wang Xiaojun, Wang Qi, Zhuang Fangfang. The numerical method for multibody system with frictional translational joints and driving constraints. Journal of Dynamics and Control, 2014, 12(4): 335-340 (in Chinese))

范新秀, 王琪. 车辆纵向非光滑多体动力学建模与数值算法研究. 力学学报, 2015, 47(2): 301-309 (Fan Xinxiu, Wang Qi. Research on modeling and simulation of longitudinal vehicle dynamics based on non-smooth dynamics of multibody systems. Journal of Theoretical and Applied Mechanics, 2015, 47(2): 301-309 (in Chinese))

洪嘉振. 多体系统动力学. 北京:高等教育出版社, 1999 (Hong Jiazhen. Computation Dynamics of Multi-body Systems. Beijin: Higher Education Press, 1999 (in Chinese))

Neto M A, Ambrósio J. Stabilization methods for the integration of DAE in the presence of redundant constraints. Multibody Syst. Dyn., 2003, 10: 81-105

Flores, P, Machado, M, Seabra, E, et al. A parametric study on the Baumgarte stabilization method for forward dynamics of constrained multibody systems. J. Comput. Nonlinear Dyn., 2011, 6(1): 011019-011027

杨孟余, 冯德成, 沙爱民, 等. 公路沥青路面设计规范. 北京: 人民交通出版社, 2006 (Yang Mengyu, Feng Decheng, Sha Aiming, et al. Specification for Design of Highway Asphalt Pavement. Beijing: China Communications Press, 2006 (in Chinese))

申爱琴, 张艳红, 郭寅川, 等. 三类沥青路面结构力学响应的对比分析.长安大学学报, 2009, 29(4):1-7 (Shen Aiqin, Zhang Yanhong, Guo Yinchuan, et al. Comparative analysis of mechanical response of three typical asphalt pavement structures. Journal of Chang'an University, 2009, 29(4): 1-7 (in Chinese))

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