ADVANCES IN THE RESEARCH ON NUMERICAL METHODS FOR NON-SMOOTH DYNAMICS OF MULTIBODY SYSTEMS

WANG Qi; ZHUANG Fangfang; GUO Yiyuan; ZHANG Jie; FANG Jie

doi:10.6052/1000-0992-12-024

Volume 43 Issue 1

Jan. 2013

Turn off MathJax

Article Contents

Article Navigation > Advances in Mechanics > 2013 > 43(1): 101-111

WANG Qi, ZHUANG Fangfang, GUO Yiyuan, ZHANG Jie, FANG Jie. ADVANCES IN THE RESEARCH ON NUMERICAL METHODS FOR NON-SMOOTH DYNAMICS OF MULTIBODY SYSTEMS[J]. Advances in Mechanics, 2013, 43(1): 101-111. doi: 10.6052/1000-0992-12-024

Citation:

WANG Qi, ZHUANG Fangfang, GUO Yiyuan, ZHANG Jie, FANG Jie. ADVANCES IN THE RESEARCH ON NUMERICAL METHODS FOR NON-SMOOTH DYNAMICS OF MULTIBODY SYSTEMS[J]. Advances in Mechanics, 2013, 43(1): 101-111. doi: 10.6052/1000-0992-12-024

Citation:

PDF( 523 KB)

ADVANCES IN THE RESEARCH ON NUMERICAL METHODS FOR NON-SMOOTH DYNAMICS OF MULTIBODY SYSTEMS

doi: 10.6052/1000-0992-12-024

School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China

Funds: The project was supported by the National Natural Science Foundation of China (11072014, 10832004).

More Information

Corresponding author: WANG Qi
Received Date: 2012-02-29
Rev Recd Date: 2012-05-03
Publish Date: 2013-01-24

Abstract

Abstract

The numerical method for the non-smooth dynamics of multibody systems is one of the hot topics of researches on the dynamics of multibody systems. In this paper, recent advances in the research on numerical methods are presented for the non-smooth dynamics of multibody systems with impact and friction. First, the Coulomb friction model, modified Coulomb friction model and the characteristics of the normal forces of multibody systems with unilateral and bilateral constraints are discussed. Second, recently developed numerical methods for the non-smooth dynamics of multibody systems based on continuous and discontinuous models are reviewed. The Event-driven scheme and time-stepping method for the non-smooth dynamics of multibody systems are described in detail based on the complementarity concept. These numerical methods are then analysed and compared. Finally, the problems in need of further studies are pointed out.
- friction,
- impact,
- non-smooth,
- multibody system

FullText(HTML)

References(61)

References

1 维滕伯格, 著. 多刚体系统动力学. 谢传锋译. 北京航空航天大学出版社, 1986

2 袁世杰. 多刚体系统动力学. 北京: 北京理工大学出版社,1988

3 Kane T R, Likins P W, Levionson D A, 著. 航天飞行器动力学. 黄克累, 张安厚译. 北京: 科学出版社, 1988

4 洪嘉振. 计算多体系统动力学. 北京: 高等教育出版社, 2001

5 Shabana A A. Dynamics of Multibody Systems. London: Cambridge University Press, 2005

6 潘振宽, 赵维加, 洪嘉振, 等. 多体系统动力学微分/ 代数方程组数值方法. 力学进展, 1996, 26(1): 28-40

7 王琪, 陆启韶. 多体系统Lagrange 方程数值算法的研究进展. 力学进展, 2001, 31(1): 9-17

8 Yang H, Hong J Z. Dynamics modeling of a flexible hubbeam system with a tip mass. Journal of Sound and Vibration, 2003, 266: 759-774

9 Ascher U M, Petzold L R. Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations. 北京: 科学出版社, 2009

10 洪嘉振, 刘锦阳. 机械系统计算动力学与建模. 北京: 高等教育出版社, 2011

11 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

12 Kunze M. Non-Smooth Dynamical Systems. New York: Springer, 2000

13 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

14 Flores P, Ambr ó sio J, Pimenta Claro J C, et al. Kinematics and Dynamics of Multibody Systems with Imperfect Joints. New York: Springer, 2008

15 Jonker J B, Waiboer R R, Aarts R G K M. Modelling of Joint Friction in Robotic Manipulators with Gear Transmissions, Multibody Dynamics. Computational Methods and Applications, Netherlands: Springer, 2007. 221-243

16 Tomlinson S E, Lewis R, Carr é M J. The effect of normal force and roughness on friction in human finger contact. Wear, 2009, 267: 1311-1318

17 彭慧莲, 郭易圆, 王琪. 用第一类Lagrange 方程求解平面多体系统约束力的方法. 工程力学, 2008, 25(12): 65-71

18 Blajer W. On the determination of joint reactions in multibody mechanisns. Journal of Mechanical Design, 2004,126: 341-350

19 齐朝晖. 多体系统动力学. 北京: 科学出版社, 2008

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

21 Flores P, Ambr ó sio J, Pimenta Claro J C, et al. Translational joints with clearance in rigid multibody systems. Journal of Computational and Nonlinear Dynamics, 2008, (3): 011007(1-10)

22 Kosenko I, Aleksandrov E. Volumetric modification of the Hertz contact problem and its application to the multibody dynamics simulation. Journal of Mechanical Science and Technology, 2009, 23: 931-937

23 Bai Z F, Zhao Y. Dynamic behavior analysis of planar mechanical systems with clearance in revolute joints using a new hybrid contact force model. International Journal of Mechanical Sciences, 2012, (54): 190-205

24 Machado M, Flores P. Pimenta Claro J C, et al. Development of a planar multibody model of the human knee joint. Nonlinear Dyn., 2010, 60: 459-478

25 Flores P, Pereira R, Machado M, et al. Investigation on the Baumgarte stabilization method for dynamic analysis of constrained multibody systems. Proceedings of EUCOMES, 2008. 305-312

26 陈萌, 张新访, 张云清, 等. 对接机构隔框锁的接触碰撞动力学研究及仿真. 宇航学报, 2002, 3(6): 43-49

27 Ambr ó sio J , Verissimo P. Improved bushing models for general multibody systems and vehicle dynamics. Multibody Systems Dynamics, 2009, 22: 341-365

28 Flores P. Modeling and simulation of wear in revolute clearance joints in multibody systems. Mechanism and Machine Theory, 2009, 44: 1211-1222

29 Tian Q, Zhang Y Q, Chen L P, et al. Simulation of planar flexible multibody systems with clearance and lubricated revolute joints. Nonlinear Dyn, 2010, 60: 489-511

30 Leine R I, VanCampen D H, Glocker C. Nonlinear dynamics and modeling of various wooden toys with impact and friction. Journal of Vibration and Control, 2003, 9: 25-78

31 Piedboeuf J, Carufel J, Hurteau R. Friction and stick-slip in robots: Simulation and Experimentation. Multibody System Dynamics, 2000, 4: 341-354

32 Nozaki K , Terumichi Y, Nishimura K, et al. Study of rocking motion of rigid body with slide contact. Journal of Mechanical Science and Technology, 2009, 23: 1001-1007

33 彭慧莲, 王士敏, 王琪, 等. 具有固定双边约束多点摩擦的多体系统的动力学建模和数值算法. 力学学报, 2009, 41(1):105-111

34 彭慧莲, 王琪, 庄方方. 含摩擦滑移铰平面多刚体动力学的HLCP方法. 力学学报, 2010, 42(5): 943-950

35 韩继业, 修乃华, 戚厚铎. 非线性互补理论与算法. 上海: 上海科学出版社, 2006

36 张培爱, 何素艳, 张兴新. 互补问题的一种光滑迭代算法, 大连理工大学学报, 2003, 43(1): 16-19

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

38 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

39 Moreau J J. Numerical aspects of the sweeping process. Computer Methods in Applied Mechanics and Engineering, 1999, 177: 329-349

40 Brogliato B, Dam A A, Paoli L, et al. Numerical simulation of finite dimensional multibody non-smooth mechanical systems. Applied Mechanics Reviews, 2002, 55(2):107-150

41 Anitescu M, Hart G D. A constraint-stabilized timestepping approach for rigid multibody dynamics with joints, contact and friction. International Journal for Numerical Methods in Engineering, 2004, 60: 2335-2371

42 段文杰, 王琪、王天舒. 圆弧足被动行走器非光滑动力学仿真研究. 力学学报, 2011, 43(4): 765-774

43 Collins S, Ruina A, Tedrake R, et al. Efficient bipedal robots based on passive-dynamic walkers. Science Magazine, 2005, 307(5712): 1082-1085

44 Liu N, Li J F, Wang T S. The effects of parameter variation on the gaits of passive walking models: simulations and experiments. Robotica, 2009, 27(4): 511-528

45 高海平. 受约束多体系统线性互补建模及相关问题研究. [博士论文]. 北京: 北京航空航天大学, 2010

46 Zhang H W, Li J Y, Pan S H. New second-order cone linear complementarity formulation and semi-smooth Newton algorithm for finite element analysis of 3D frictional contact problem. Comput. Methods Appl. Mech. Engrg,2011, 200: 77-88

47 Theodosiou C, Natsiavas S. Dynamics of finite element structural models with multiple unilateral constraints. International Journal of Non-Linear Mechanics, 2009, 44:371-382

48 Acary V, Brogliato B. Numerical Methods for Non-smooth Dynamical Systems-Applications in Mechanics and Electronics. Berlin: Springer, 2008

49 董富祥, 洪嘉振. 平面柔性多体系统正碰撞动力学建模理论研究. 计算力学学报, 2010, 27(6): 1042-1048

50 韩石磊, 洪嘉振. 柔性多体碰撞问题的多变量方法. 力学学报, 2011, 43(5): 886-893

51 Arczewski K, Fraczek J. Friction models and stress recovery methods in vehicle dynamics modelling. Multibody System Dynamics, 2005, 14: 205-224

52 赵振, 刘才山, 陈滨. 三维含摩擦多刚体碰撞问题的数值计算方法. 中国科学G辑, 2006, 36(1): 72-88

53 Leonesio M, Bianchi G. Self-locking analysis in closed kinematic chains. Mechanism and Machine Theory, 2009,44: 2038-2052

54 Fraczek J, Wojtyra M. On the unique solvability of a direct dynamics problem for mechanisms with redundant constraints and Coulomb friction in joints. Mechanism and Machine Theory, 2011, 46: 312-334

55 Pfeiffer F. On impacts with friction. Applied Mathematics and Computation, 2010, 217: 1184-1192

56 刘才山, 陈滨. 多柔体系统碰撞动力学研究综述. 力学进展,2000, 30(1): 7-14

57 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

58 胡海岩. 分段非光滑机械系统动力学的进展. 振动工程学报,1995, 8(4): 331-341

59 金栋平, 胡海岩. 碰撞振动及其典型现象. 力学进展, 1999,29(2): 155-164

60 韩石磊, 洪嘉振. 柔性多体系统接触/碰撞动力学的若干关键问题. 力学与实践, 2011, 33(2): 1-7

61 丁旺才, 谢建华. 碰撞振动系统分岔与混沌的研究进展. 力学进展, 2005, 35(4): 513-524

Relative Articles

Supplements(0)

Cited By

Proportional views