EI、Scopus 收录
中文核心期刊
Fu Li, Hu Hongkui, Fu Teng. CONTACT-IMPACT ANALYSIS IN MULTI-BODY SYSTEMS BASED ON NEWTON-EULER LCP APPROACH[J]. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(5): 1115-1125. DOI: 10.6052/0459-1879-17-023
Citation: Fu Li, Hu Hongkui, Fu Teng. CONTACT-IMPACT ANALYSIS IN MULTI-BODY SYSTEMS BASED ON NEWTON-EULER LCP APPROACH[J]. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(5): 1115-1125. DOI: 10.6052/0459-1879-17-023

CONTACT-IMPACT ANALYSIS IN MULTI-BODY SYSTEMS BASED ON NEWTON-EULER LCP APPROACH

  • Received Date: January 17, 2017
  • Available Online: June 19, 2017
  • The contact-impact analysis in multibody systems based on the nonsmooth dynamics approach is a hot topic in the research of multibody system dynamics. Newton-Euler approach is adopted to develop dynamics model of contactimpact analysis in non-smooth multi-body systems, and a new LCP formula is presented in this work. Different from Lagrange methods, Newton-Euler modeling method incorporate equality constraints into dynamic models with noninterpenetration constraints and frictional constraints together. In Newton-Euler modeling method, the basic system is derived by removing the non-interpenetration constraints and frictional constraints from the original multi-body system. Newton-Euler eqution of basic system is established by using the maximum coordinates method. Because the coordinates of the basic system are not independent of each other, equality constraints are involved in modeling, the basic system dynamic equations is a set of DAE (differential algebra equation). With the aid of constraint Jacobian matrix, Lagrangian multipliers corresponding to the non-interpenetration constraint forces and Coulomb friction forces are added to the basic system DAE to obtain the dynamic equations of global motion of the multi-body system with characteristics of variable topological structure. The complete dynamic model is composed of basic system DAE, equality and inequality constraints. In order to simplify the derivation process of LCP, a decomposed matrix form is built. The LCP -based Time-stepping method is adopted for numerical simulation. Time-stepping algorithm is a popular non-smooth numerical algorithm, Its prominent feature is that it can avoid the tedious event-detection process in numerical integration. In the process of numerical integration, the contact-detachment state of the system can be determined by solving the LCP. Our method is carried out in slider-crank mechanism with a translational clearance joint, the simulation results indicate that this method is effective.
  • [1]
    Moreau JJ. Unilateral contact and dry friction in finite freedom dynamics. In:Moreau JJ, Panagiotopoulos PD. Non-smooth Mechanics and Applications//International Centre for Mechanical Sciences, Courses and Lectures, Vol. 302, New York, Springer-Verlag, 1988:1-82
    [2]
    Panagiotopoulos PD. Inequality Problems in Mechanics and Applications. Boston:Stuttgart, Birkháuser, 1985
    [3]
    Brogliato B. Nonsmooth Mechanics:Models, Dynamics and Control, 2nd ed. London:Springer-Verlag, 1999
    [4]
    富立.非光滑多体系统动力学线性互补方法.北京:清华大学出版社, 2016

    Fu Li. LCP Method for Non-smooth Multibody System Dynamics. Beijing:Tsinghua University Press, 2016 (in Chinese)
    [5]
    Lötstedt P. Mechanical systems of rigid bodies subject to unilateral constraints. Siam Journal on Applied Mathematics, 1982, 42(2):281-296 doi: 10.1137/0142022
    [6]
    Baraff D. Issues in computing contact forces for nonpenetrating rigid bodies. Algorithmica, 1993, 10:292-352 doi: 10.1007/BF01891843
    [7]
    Pfeiffer F, Glocker C. Multibody Dynamics with Unilateral Contacts//Non-linear Dynamics. Weinheim:John Wiley & Sons, 1996
    [8]
    Glocker, C, Set-Valued Force Laws-Dynamics of Non-Smooth Systems. Berlin:Springer, 2001
    [9]
    Stewart DE. Rigid body dynamics with friction and impact. Siam Review, 2000, 42(1):3-39 doi: 10.1137/S0036144599360110
    [10]
    Anitescu M, Potra FA. Formulationg dynamics multi-rigid-body contact problems with friction as solvable linear complementarity problems. Nonlinear Dynamics, 1997, 14:231-247 doi: 10.1023/A:1008292328909
    [11]
    Acary V, Brogliato B. Numerical Methods for Nonsmooth Dynamical Systems//Applications in Mechanics and Electronics. Berlin:Springer-Verlag, 2008
    [12]
    Blumentals A, Brogliato B. The contact problem in Lagrangian sys-tems subject to bilateral and unilateral constraints, with or without sliding Coulomb's friction:A tutorial. Multibody System Dynamics, 2016, 1:1-34
    [13]
    Zhao Z, Liu CS, Chen B, et al. Asymptotic analysis of Painlevës paradox. Multibody System Dynamics, 2015, 35(3):299-319 doi: 10.1007/s11044-014-9448-1
    [14]
    Glocker Ch. Energetic consistency conditions for standard impacts. In:Part Ⅱ:Poisson-type inequality impact laws. Multibody System Dynamics, 2014, 32(1):445-509
    [15]
    Dietmayer K. Modelling of unilateral constraints using power-based restriction functions within Lagrangian mechanics. Mathematical & Computer Modelling of Dynamical System, 2015, 21(3):1-26
    [16]
    Glocker C. Simulation of Hard Contacts with Friction. In:An Iterative Projection Method. Recent Trends in Dynamical Systems, Springer, Basel, Switzerland, 2013:493-515
    [17]
    Schindler T, Rezaei S, Kursawe J, et al. Half-explicit timestepping schemes on velocity level based on time-discontinuous Galerkin methods. Computer Methods in Applied Mechanics and Engineering, 2015, 290(15):250-276
    [18]
    Kikuuwe R, Brogliato B. A new representation of systems with frictional unilateral constraints and its Baumgarte-like relaxation. Multibody System Dynamics, 2015, 34(7):1-24
    [19]
    Pournaras A, Karaoulanis F, Natsiavas S. Dynamics of mechanical systems involving impact and friction using an efficient contact detection algorithm. http://dx.doi.org/10.1016/j.ijnonlinmec.2016.08.007, 2016-8-24
    [20]
    王晓军, 王琪.含摩擦与碰撞平面多刚体系统动力学线性互补算法.力学学报, 2015, 47(2):814-821 http://lxxb.cstam.org.cn/CN/abstract/abstract145449.shtml

    Wang Xiaojun, Wang Qi. A LCP method for the dynamics of planar multibody systems with impact and friction. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(2):814-821(in Chinese) http://lxxb.cstam.org.cn/CN/abstract/abstract145449.shtml
    [21]
    Ferrari F, Tasora A, Masarati P, et al. N-body gravitational and contact dynamics for asteroid aggregation. Multibody System Dynamics, 2017, 39(1):3-20 doi: 10.1007%2Fs11044-016-9547-2.pdf
    [22]
    张韵, 李俊峰.碎石堆小行星的散体动力学建模与仿真方法综述.力学学报, 2015, 47(1):1-7 doi: 10.6052/0459-1879-14-329

    Zhangyun, Li Junfeng. A survey of granular dynamics modeling and simulation methods for rubble-pile asteroids. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(1):1-7 (in Chinese) doi: 10.6052/0459-1879-14-329
    [23]
    Zhao Zhen, Liu Caishan, Chen Tao. Docking dynamics between two spacecrafts with APDSes. Multibody System Dynamics, 2016, 37(3):245-270 doi: 10.1007/s11044-015-9477-4
    [24]
    Yaqubi S, Dardel M. Daniali HM. Modeling and control of crank-slider mechanism with multiple clearance joints. Multibody System Dynamics, 2016, 36(2):1-25
    [25]
    Abdallah MAB, Khemili I, Aifaoui N. Numerical investigation of a flexible slider-crank mechanism with multijoints with clearance. Multibody System Dynamics, 2016, 38(2):173-199 doi: 10.1007/s11044-016-9526-7
    [26]
    Lim KW, Krabbenhoft K, José E, et al. A contact dynamics approach to the Granular Element Method. Computer Methods in Applied Mechanics and Engineering, 2014, 268(1):557-573 http://adsabs.harvard.edu/abs/2014CMAME.268..557L
    [27]
    Leine RI, Schweizer A, Christen M, et al. Simulation of rockfall trajectories with consideration of rock shapein. Multibody System Dynamics, 2014, 32:241-271 doi: 10.1007/s11044-013-9393-4
    [28]
    Zobova AZ, Nicolas TH, Noot V, et al. Multi-physics modelling of a compliant humanoid robot. Multibody System Dynamics, 2017, 39(1):95-114 doi: 10.1007/s11044-016-9545-4
    [29]
    Shourijeh MS, Mcphee J. Foot-ground contact modeling within human gait simulations:From Kelvin-Voigt to hyper-volumetric models. Multibody System Dynamics, 2015, 35(1):393-407 doi: 10.1007%2Fs11044-015-9467-6.pdf
    [30]
    Josep JR, Font-Llagunes M, Plaza A, et al. Dynamic considerations of heel-strike impact in human gait. Multibody System Dynamics, 2015, 35(3):215-232 doi: 10.1007/s11044-015-9460-0
    [31]
    洪嘉振.计算多体系统动力学.北京:高等教育出版社, 1999

    Hong Jiazhen. Computational Dynamics of Multibody Systems. Beijing:Higher Education Press, 1999(in Chinese)
    [32]
    齐朝晖.多体系统动力学.大连:科学出版社, 2008

    Qi zhaohui. Multi-body System Dynamics. Dalian:Science Press, 2008 (in Chinese)
    [33]
    Shabana AA. Computational Dynamics 3rd ed. West Sussex:John Wiley, 2010
    [34]
    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 doi: 10.6052/0459-1879-14-323

    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) doi: 10.6052/0459-1879-14-323
  • Related Articles

    [1]Wang Gengxiang, Ma Daolin, Liu Yang, Liu Caishan. RESEARCH PROGRESS OF CONTACT FORCE MODELS IN THE COLLISION MECHANICS OF MULTIBODY SYSTEM[J]. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(12): 3239-3266. DOI: 10.6052/0459-1879-22-266
    [2]Tang Zijian, Du Wei, Du Peng, Hu Haibao, Chen Xiaopeng, Wen Jun, Xie Luo. STUDY ON THE BEHAVIOR OF BUBBLES COLLIDING WITH HYDROPHILIC AND HYDROPHOBIC CURVED WALLS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(9): 2401-2408. DOI: 10.6052/0459-1879-22-116
    [3]Yang Ming, Liu Jubao, Yue Qianbei, Ding Yuqi, Wang Ming. NUMERICAL SIMULATION ON THE VORTEX-INDUCED COLLISION OF TWO SIDE-BY-SIDE CYLINDERS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(6): 1785-1796. DOI: 10.6052/0459-1879-19-224
    [4]Wang Xiaojun, Lü Jing, Wang Qi. A NUMERICAL METHOD FOR DYNAMICS OF PLANAR MULTI- RIGID-BODY SYSTEM WITH FRICTIONAL TRANSLATIONAL JOINTS BASED ON LUGRE FRICTION MODEL[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(1): 209-217. DOI: 10.6052/0459-1879-18-222
    [5]Wang Xiaojun, Wang Qi. A LCP METHOD FOR THE DYNAMICS OF PLANAR MULTIBODYSYSTEMS WITH IMPACT AND FRICTION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(5): 814-821. DOI: 10.6052/0459-1879-15-168
    [6]Fu Li Yue Yuefengtong. DAE-LCP mixed method for multibody system dynamics with frictional contacts[J]. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(2): 400-407. DOI: 10.6052/0459-1879-2011-2-lxxb2009-574
    [7]Junbo Zhang, Xikui Li. A mesh-free method based on linear complementary model for gradient plasticity continuum[J]. Chinese Journal of Theoretical and Applied Mechanics, 2009, 41(6): 888-897. DOI: 10.6052/0459-1879-2009-6-2008-376
    [8]THELINEAR COMPLEMENTARYPROBLEM FOR ELASTO-PLASTIC ANALYSIS[J]. Chinese Journal of Theoretical and Applied Mechanics, 1995, 27(1): 38-47. DOI: 10.6052/0459-1879-1995-1-1995-403
  • Cited by

    Periodical cited type(6)

    1. 冯盖亚,贾山,陈金宝,周向华. 可行走着陆器的牛顿-欧拉法动力学研究. 航天返回与遥感. 2024(01): 53-64 .
    2. 冯盖亚,贾山,陈金宝,周向华. 可行走着陆机构牛顿-欧拉动力学分析和能耗优化. 空天技术. 2024(04): 1-12 .
    3. 郑鹏,王琪,吕敬,郑旭东. 摩擦与滚阻对被动行走器步态影响的研究. 力学学报. 2020(01): 162-170 . 本站查看
    4. 李乾,徐华,张越,程芳. 基于约束的刚体碰撞响应仿真研究与应用. 计算机仿真. 2020(03): 338-342 .
    5. 李华杰,刘宏昭. 考虑磨损影响的含间隙机构仿真与试验研究. 机械科学与技术. 2020(04): 539-546 .
    6. 王晓军,吕敬,王琪. 含摩擦滑移铰平面多刚体系统动力学的数值算法. 力学学报. 2019(01): 209-217 . 本站查看

    Other cited types(7)

Catalog

    Article Metrics

    Article views (1431) PDF downloads (501) Cited by(13)
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return