EI、Scopus 收录
Cao Dengqing, Chu Shiming, Li Zhengfa, Liu Rongqiang. STUDY ON THE NON-SMOOTH MECHANICAL MODELS AND DYNAMICS FOR SPACE DEPLOYABLE MECHANISMS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(1): 3-15. doi: 10.6052/0459-1879-12-341
Citation: Cao Dengqing, Chu Shiming, Li Zhengfa, Liu Rongqiang. STUDY ON THE NON-SMOOTH MECHANICAL MODELS AND DYNAMICS FOR SPACE DEPLOYABLE MECHANISMS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(1): 3-15. doi: 10.6052/0459-1879-12-341


doi: 10.6052/0459-1879-12-341
Funds:  The project was supported by the National Natural Science Foundation of China (91216106, 50935002).
  • Received Date: 2012-12-03
  • Rev Recd Date: 2012-12-20
  • Publish Date: 2013-01-18
  • The space deployable mechanism is widely used to develop and support the flexible solar array and payloads including parabolic antenna, plane phased array radar, and synthetic aperture radar in the aerospace engineering field. Non-smooth characteristics and the corresponding dynamic phenomena play a very important role in the design of space deployable mechanism. This paper reviews the state-of-art of non-smooth mechanical modeling and nonlinear dynamics for the space deployable mechanisms. First of all, the non-smooth properties such as the contact impact forces and friction models are elaborated for hinges with clearances. Then, the dynamical modeling methods, analytical approach, and parametric design are systematically presented for the mechanisms with clearances. Moreover, the nonlinear dynamic phenomena such as harmonic resonance, existence and stability of periodic motions, and various kinds of bifurcations are presented for the space deployable mechanisms whose joints are with clearances. Finally, directions for further works on the dynamics, stability and control for the non-smooth dynamical system of space deployable mechanisms are proposed.


  • loading
  • 1 Jin M, Kazuhide A, Yumi S. Deployment analysis of large space antenna using flexible multibody dynamics simulation. Acta Astronautica,2000, 47(1): 19-26  
    2 Tana GEB, Pellegrino S. Nonlinear vibration of cable-stiffened pantographic deployable structures. Journal of Sound and Vibration,2008, 314: 783-802  
    3 Lopatin AV, Morozov EV. Modal analysis of the thin-walled composite spoke of an umbrella-type deployable space antenna. Composite Structures, 2009, 88: 46-55  
    4 Birhanu FF, Chen ZB, Ma WS. Modeling and simulation of satellite solar panel deployment and locking. Information Technology Journal,2010, 9: 600-604  
    5 阎绍泽, 申永胜, 陈洪彬. 考虑杆件柔性和铰间隙的可展结构动力 学数值模拟. 清华大学学报(自然科学版), 2003, 43(2): 145-148 (Yan Shaoze, Shen Yongsheng, Chen Hongbin. Dynamic performance of deployable structures with flexible members and clearance connections. J Tsinghua Univ (Sci & Tech), 2003, 43(2): 145-148 (in Chinese))
    6 Folar CL, Tinker ML, Nurre GS, et al. Solar- array-induced disturbance of hubble telescope pointing system. J Spacecraft and Rocket,1995, 32(4): 634-644  
    7 黄文虎, 曹登庆, 韩增尧. 航天器动力学与控制的研究进展与展 望. 力学进展, 2012, 42(4): 367-394 (HuangWenhu, Cao Dengqing, Han Zengyao. Advances and trends in dynamics and control of spacecrafts. Advances in Mechanics, 2012, 42(4): 367-394 (in Chinese))
    8 王巍, 于登云, 马兴瑞. 航天器铰接结构非线性动力学特性研究进 展. 力学进展, 2006, 36(2): 233-238 (Wang Wei, Yu Dengyun, Ma Xingrui. Advances and trends of non-linear dynamics of space joint dominated structure. Advances in Mechanic, 2006, 36(2): 233-238 (in Chinese))
    9 阎绍泽. 航天器中含间隙机构非线性动力学问题及其研究进展. 动力学与控制学报, 2004, 2(2): 48-52 (Yan Shaoze. Development and problems of nonlinear dynamics of the mechanisms with clearances for spacecrafts. Journal of Dynamics and Control, 2004, 2(2):48-52 (in Chinese))
    10 Schwab AL, Meijaard JP, Meijers P. A comparison of revolute joint clearance models in the dynamic analysis of rigid and elastic mechanical systems. Mechanism and Machine Theory, 2002, 37: 895-913  
    11 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 (Ding Wangcai, Xie Jianhua. Advances of research on bifurcations. Advances in Mechanics, 2005, 35(4):513-524 (in Chinese))
    12 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))
    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 Syst Dyn, 2010, 23:165-190  
    14 Kane TR, Levinson DA. Dynamics: Theory and Applications. New York: Mcgraw-Hill, 1985. 231-241
    15 韩维, 侯志强. 碰撞-振动系统动力学的研究进展. 海军航空工程 学院学报, 2004, 19(5): 501-509 (HanWei,Hou, Zhiqiang. Review on dynamics of the vibro-impact system. Journal of Naval Aeronautical Engineering Institute, 2004, 19(5): 501-509 (in Chinese))
    16 Earles SWE, Wu CLS. Motion analysis of a rigid-link mechanism with clearance at a bearing using Lagrangian mechanism and digital computation. In: Proceeding of Conference on Mechanisms, IME, London, England, 1972: 83-89
    17 Furuhashi T, Morita N, Matsuura M. Research on dynamics of fourbar linkage with clearances at turning pairs. Bull JSME, 1978, 21:518-523  
    18 Gilardi G., Sharf I. Literature survey of contact dynamics modeling. Mechanism and Machine Theory, 2002, 37: 1213-1239  
    19 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 (Jin Dongping, Hu Haiyan. Vibro-impacts and their typical behaviors of mechanical systems. Advances in Mechanics, 1999,29(2): 155-164 (in Chinese))
    20 Bai ZF, Zhao Y. A hybrid contact force model of revolute joint with clearance for planar mechanical systems. International Journal of Non-Linear Mechanics, 2013, 48: 15-36  
    21 Machado M, Moreira P, Flores P, et al. Compliant contact force models in multibody dynamics: Evolution of the Hertz contact theory. Mechanism and Machine Theory, 2012, 53: 99-121  
    22 Zhang LX, Bai ZF, Zhao Y, et al. Dynamic response of solar panel deployment on spacecraft system considering joint clearance. Acta Astronautica, 2012, 81: 174-185  
    23 Dubowsky S, Freudenstein F. Dynamic analysis of mechanical systems with clearance, Part 1: Formation of dynamic model. ASME Journal Engineering for Industry, 1971, 93B: 305-309  
    24 Dubowsky S. Gardner TN. Dynamic interactions of link elasticity and clearance connections in planar mechanical systems. ASME Journal of Engineering for Industry, 1975, 97B (2): 652-661
    25 Hunt. KH. Crossley FR. Coeffcient of restitution interpreted as damping in vibroimpact. Journal of Applied Mechanics, 1975, 42:440-445  
    26 Herbert RG, Whannell DC. Shape and frequency composition of pulses from an impact pair. Journal of Engineering for Industry,1977, 99: 513-518  
    27 Lankarani HM, Nikavesh PE. A contact force model with hysteresis damping for impact analysis of multibody systems. ASME Journal of Mechanical Design, 1990, 112: 369-376  
    28 秦志英, 陆启韶. 基于恢复系数的碰撞过程模型分析. 动力学与 控制学报, 2006, 4: 294-298 (Qin Zhiying, Lu Qishao. analysis of impact process model based on restitution coeffcient. Journal of Dynamics and Control, 2006, 4: 294-298 (in Chinese))
    29 Yigit AS, Ulsoy AG, Scott RA. Spring-dashpot models for the dynamics of a radically rotating beam with impact. Journal of Sound and Vibration, 1990, 142 (3): 515-525  
    30 Bai ZF, 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  
    31 Liu CS, Zhang K, Yang R. The FEM analysis and approximate model for cylindrical joints with clearances. Mech Mach Theory,2007, 42: 183-197  
    32 Mishra BK,Murty CVR.On the determination of contact parameters for realistic DEM simulations of ball mills.Powder Technology,2001, 115: 290-297  
    33 Mishra BK,Thornton C.An improved contact model for ball mill simulation by the discrete element method.Advanced Powder Technology,2002, 13: 25-41
    34 Ciavarella M, Decuzzi P. The state of stress induced by the plane frictionless cylindrical contact 1: The case of elastic similarity. International Journal of Solids and Structures, 2001, 38: 4507-4523  
    35 Ciavarella M, Decuzzi P. The state of stress induced by the plane frictionless cylindrical contact. 2: The general case (elastic dissimilarity). International Journal of Solids and Structures, 2001, 38:4523-4533
    36 Flores P, Koshy CS, Lankarani HM, et al. Numerical and experimental investigation on multibody systems with revolute clearance joints. Nonlinear Dyn, 2011, 65: 383-398  
    37 Muvengei O, Kihiu J, Ikua B. Numerical study of parametric effects on the dynamic response of planar multi-body systems with di  
    erently located frictionless revolute clearance joints. Mechanism and Machine Theory, 2012, 53: 30-49  
    38 Wang X, Chen P. Planar Four-bar Mechanism Including Revolute Joints with Clearance. In: Proceeding of 2011 International Conference on Mechatronic Science, Electric Engineering and Computer,2011. 19-22
    39 Wang Y, Chen X, Gindy N, et al. Elastic deformation of a fixture and turbine blades system based on finite element analysis. Int J Adv Manuf Technol, 2008, (4): 79-96
    40 Bograd S, Reuss P, Schmidt A, et al. Modeling the dynamics of mechanical joints. Mechanical Systems and Signal Processing, 2011,25: 2801-2826  
    41 Brutti C, Coglitore G, Valentini PP. Modeling 3D revolute joint with clearance and contact stiffness. Nonlinear Dyn, 2011, 66: 531-548  
    42 Olivier A, Bauchau, Rodriguez J. Modeling of joints with clearance in flexible multibody systems. International Journal of Solids and Structures, 2002, 39: 41-63  
    43 Ibrahimbegovi A, Mamouri S. On rigid components and joint constraints in nonlinear dynamics of flexible multibody systems employing3D geometrically exact beam model. Comput Methods Appl Mech Engrg, 2000, 188: 805-831  
    44 Li T, Guo J, Cao Y. Dynamic characteristics analysis of deployable space structures considering joint clearance. Acta Astronautica,2011, 68: 974-983  
    45 Tian Q, Zhang Y, Chen L, et al. Dynamics of spatial flexible multibody systems with clearance and lubricated spherical joints. Computers and Structures, 2009, 87: 913-929  
    46 Erkaya S, Uzmay I. Effects of balancing and link flexibility on dynamics of a planar mechanism having joint clearance. Scientia Iranica,2012, 19(3): 483-490  
    47 Li Z, Cai G, Huang Q, et al. Analysis of nonlinear vibration of a motor-linkage mechanism system with composite links. Journal of Sound and Vibration, 2008, 311: 924-940  
    48 Gummer A, Sauer B. Influence of contact geometry on local friction energy and stiffness of revolute joints. Journal of Tribology, 2012,134: 1-9
    49 Den Hartog JP. Forced vibrations with combined coulomb and viscous friction. Transactions of the ASME, 1993, 19: 107-115
    50 Iwan WD. The Dynamics Response of Bilinear Hysteretic System. California: California Institute of Technology, 1961  
    51 Ernest R. The nature of the static and kinetic coeffcients of friction. Journal of Applied Physics, 1951, 22(11): 1373-79  
    52 Stribeck R. Die wesentlichen eigenschaften der gleit-und rollenlager-the key qualities of sliding and roller bearings. Zeitschrift des Vereins Deutscher Ingenieure,1902, 46 (38-39):1342-1348,1432-1437
    53 Rhee SK, Tsang PHS, Wang YS. Friction induced noise and vibration of disc brakes. Wear, 1989, 133: 39-45  
    54 Dahl P. Solid Friction Damping of Spacecraft Collations. Boston: Defense Technical Informat on Center, 1975  
    55 Canudas CW, Olsson H, Astrom KJ, et al. A new model for control of systems with friction. IEEE Transactions on Automatic Control,1995, 40(3): 419-425  
    56 Haessig DA, Friedland B. On the modeling and simulation of friction. Journal of Dynamic Systems, Measurement and Control, 1991,113(3): 354-362  
  • 加载中


    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (2483) PDF downloads(3389) Cited by()
    Proportional views


    DownLoad:  Full-Size Img  PowerPoint