留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

牛顿碰撞恢复系数评价下的碰撞力研究进展

王旭鹏 林文周 刘更 马尚君 佟瑞庭

王旭鹏,林文周,刘更, 等. 牛顿碰撞恢复系数评价下的碰撞力研究进展[J]. 机械科学与技术,2020,39(10):1526-1533 doi: 10.13433/j.cnki.1003-8728.20200179
引用本文: 王旭鹏,林文周,刘更, 等. 牛顿碰撞恢复系数评价下的碰撞力研究进展[J]. 机械科学与技术,2020,39(10):1526-1533 doi: 10.13433/j.cnki.1003-8728.20200179
Wang Xupeng, Lin Wenzhou, Liu Geng, Ma Shangjun, Tong Ruiting. Advance in Impact Force Model Research with Evolution of Newton Restitution Coefficient[J]. Mechanical Science and Technology for Aerospace Engineering, 2020, 39(10): 1526-1533. doi: 10.13433/j.cnki.1003-8728.20200179
Citation: Wang Xupeng, Lin Wenzhou, Liu Geng, Ma Shangjun, Tong Ruiting. Advance in Impact Force Model Research with Evolution of Newton Restitution Coefficient[J]. Mechanical Science and Technology for Aerospace Engineering, 2020, 39(10): 1526-1533. doi: 10.13433/j.cnki.1003-8728.20200179

牛顿碰撞恢复系数评价下的碰撞力研究进展

doi: 10.13433/j.cnki.1003-8728.20200179
基金项目: 国家自然科学基金项目(51275423,51505381,51675429)、陕西省教育厅自然专项基金项目(17JK0551)及西安理工大学博士启动基金项目(106-451117002)资助
详细信息
    作者简介:

    王旭鹏(1981−),副教授,研究方向为机械系统动力学,wangxupeng@xaut.edu.cn

    通讯作者:

    刘更,教授,博士生导师,npuliug@nwpu.edu.cn

  • 中图分类号: TG156

Advance in Impact Force Model Research with Evolution of Newton Restitution Coefficient

  • 摘要: 为了辨识间隙铰链处碰撞力的适用范围,更加准确地描述机械系统中普遍存在的碰撞现象及其对机械系统动态特性的影响规律,以牛顿碰撞恢复系数作为评价指标,以间隙铰链处轴、轴承间的碰撞和恢复过程为例,在不同恢复系数下和碰撞力模型下进行数值模拟及对比分析。研究发现,不同碰撞恢复系数下各模型碰撞过程的最大碰撞力、最大变形量及实际碰撞恢复系数差异较大。因此,实际选择碰撞力模型时应依据碰撞初始条件和材料特性等进行综合考虑。
  • 图  1  碰撞模型

    图  2  含阻尼碰撞-恢复模型

    图  3  轴-轴承接触碰撞模型

    图  4  碰撞力-变形量关系图

    图  5  碰撞速度-变形量关系图

    图  6  不同碰撞力模型实际碰撞恢复系数对比

    表  1  不同碰撞力模型在3种恢复系数值下的最大碰撞力

    碰撞力模型最大碰撞力/N
    Cr = 0.3Cr = 0.5Cr = 0.8
    Hertz 2136.033 2136.033 2136.033
    Liu 2305.168 2305.168 2305.168
    H-C 1943.499 1929.073 1975.844
    L-N 1928.888 1933.646 1986.405
    Gonthier 2207.553 1993.206 1945.774
    Flores 2308.516 2006.623 1952.949
    Bai 1459.471 1382.348 1405.777
    Wang 2362.823 2166.395 2111.053
    下载: 导出CSV

    表  2  不同碰撞力模型在3种恢复系数值下的最大变形量

    碰撞力模型最大变形量/mm
    Cr = 0.3Cr = 0.5Cr = 0.8
    Hertz0.005850.005850.00585
    Liu0.005380.005380.00538
    H-C0.004780.005000.00545
    L-N0.005060.005170.00548
    Gonthier0.003870.004500.00528
    Flores0.003680.004440.00534
    Bai0.006770.007520.00871
    Wang0.003630.004120.00490
    下载: 导出CSV

    表  3  Cr = 0.3时不同碰撞力模型实际恢复系数及相对误差

    碰撞力模型初始速度/
    (m·s−1
    分离速度/(m·s−1实际恢复系数及误差
    Cr误差/%
    Hertz 0.5 0.5 1 0
    Liu 0.5 0.5 1 0
    H-C 0.5 −0.2906 0.5812 93.7333
    L-N 0.5 −0.3421 0.6842 128.0667
    Gonthier 0.5 −0.1521 0.3042 1.4
    Flores 0.5 −0.1281 0.2562 14.6
    Bai 0.5 −0.1634 0.3268 8.9333
    Wang 0.5 −0.1634 0.3268 8.9333
    下载: 导出CSV

    表  4  Cr = 0.5时不同碰撞力模型实际恢复系数及相对误差

    碰撞力模型 初始速度/
    (m·s−1
    分离速度/
    (m·s−1
    实际恢复系数及误差
    Cr 误差/%
    Hertz 0.5 0.5 1 0
    Liu 0.5 0.5 1 0
    H-C 0.5 −0.3315 0.663 24.585
    L-N 0.5 −0.3626 0.7252 31.054
    Gonthier 0.5 −0.2439 0.4878 2.501
    Flores 0.5 −0.2352 0.4704 6.293
    Bai 0.5 −0.2413 0.4826 3.605
    Wang 0.5 −0.2413 0.4826 3.605
    下载: 导出CSV

    表  5  Cr = 0.8时不同碰撞力模型恢复系数及对应相对误差

    碰撞力模型 初始速度(m·s−1 分离速度(m·s−1 实际恢复系数及误差
    Cr 误差/%
    Hertz 0.5 0.5 1 0
    Liu 0.5 0.5 1 0
    H-C 0.5 −0.4164 0.8328 4.1
    L-N 0.5 −0.4236 0.8472 5.9
    Gonthier 0.5 −0.384 0.768 4
    Flores 0.5 −0.3943 0.7886 1.425
    Bai 0.5 −0.3937 0.7874 1.575
    Wang 0.5 −0.3937 0.7874 1.575
    下载: 导出CSV
  • [1] Flores P, Ambrósio J, Claro J C P, et al. A study on dynamics of mechanical systems including joints with clearance and lubrication[J]. Mechanism and Machine Theory, 2006, 41(3): 247-261 doi: 10.1016/j.mechmachtheory.2005.10.002
    [2] Erkaya S. Prediction of vibration characteristics of a planar mechanism having imperfect joints using neural network[J]. Journal of Mechanical Science and Technology, 2012, 26(5): 1419-1430 doi: 10.1007/s12206-012-0308-8
    [3] Wang X P, Lin W Z, Ji X M, et al. Dynamic analysis of a planar multibody system with multiple revolute clearance joints[J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2019, 233(10): 3429-3443 doi: 10.1177/0954406218819022
    [4] Wang X P, Zhang Y, Gao Z, et al. Modeling and analysis of impact based on numerical and experimental approaches[J]. Advances in Mechanical Engineering, 2018, 10(12): 1-13
    [5] Nurre G S, Sharkey J P, Nelson J D, et al. Preservicing mission - on-orbit modifications to hubble space telescope pointing control system[J]. Journal of Guidance, Control, and Dynamic, 1995, 18(2): 222-229 doi: 10.2514/3.21373
    [6] 姚文莉, 岳嵘. 有争议的碰撞恢复系数研究进展[J]. 振动与冲击, 2015, 34(19): 43-48

    Yao W L, Yue R. Advance in controversial restitution coefficient study for impact problems[J]. Journal of Vibration and Shock, 2015, 34(19): 43-48 (in Chinese
    [7] Newton I. Philosophiae naturalis principia mathematica[M]. Apud. Guil. & Joh. Innys, 1726
    [8] Kilmister C W, Reeve J E. Rational mechanics [M]. Upper Saddle River, NJ: Prentice Hall Press, 1966
    [9] Stronge W J. Theoretical coefficient of restitution for planer impact of rough elasto-plastic bodies[R]. CONF-950686-TRN: 95: 006111-0385, 1995, 205: 351-362.
    [10] 王旭鹏, 张艳, 吉晓民, 等. 一种基于变恢复系数的接触碰撞力模型[J]. 振动与冲击, 2019, 38(5): 198-202

    Wang X P, Zhang Y, Ji X M, et al. A contact-impact force model based on variable recovery coefficient[J]. Journal of Vibration and Shock, 2019, 38(5): 198-202 (in Chinese
    [11] Hertz H. Über dies Berührung fester elasticher Körper[J]. Journal Reine und Angewandte Mathematik, 1881(92): 156-171
    [12] Liu C S, Zhang K, Yang L. The compliance contact model of cylindrical joints with clearances[J]. Acta Mechanica Sinica, 2005, 21(5): 451-458 doi: 10.1007/s10409-005-0061-7
    [13] Liu C S, Zhang K, Yang R. The FEM analysis and approximate model for cylindrical joints with clearances[J]. Mechanism and Machine Theory, 2007, 42(2): 183-197 doi: 10.1016/j.mechmachtheory.2006.02.006
    [14] Tian Q, Liu C, Machado M, et al. A new model for dry and lubricated cylindrical joints with clearance in spatial flexible multibody systems[J]. Nonlinear Dynamics, 2011, 64(1): 25-47
    [15] 王旭鹏. 含间隙铰链机构非线性接触力和碰撞动力学研究[D]. 西安: 西北工业大学, 2016.

    Wang X P. Research on nonlinear contact forces and impact dynamics of mechanism with clearance joints[D]. Xi′an: Northwestern Polytechnical University, 2016 (in Chinese).
    [16] Goldsmith W. Impact-the theory and physical behaviour of colliding solids[M]. London, England: Edward Arnold Ltd., 1960.
    [17] Machado M, Moreira P, Flores P, et al. Compliant contact force models in multibody dynamics: Evolution of the Hertz contact theory[J]. Mechanism and Machine Theory, 2012, 53: 99-121 doi: 10.1016/j.mechmachtheory.2012.02.010
    [18] Hunt K H, Crossley F R E. Coefficient of restitution interpreted as damping in vibroimpact[J]. Journal of Applied Mechanics, 1975, 42(2): 440-445 doi: 10.1115/1.3423596
    [19] Lankarani H M, Nikravesh P E. A contact force model with hysteresis damping for impact analysis of multibody systems[J]. Journal of Mechanical Design, 1990, 112(3): 369-376 doi: 10.1115/1.2912617
    [20] Gonthier Y, McPhee J, Lange C, Piedboeuf J C. A regularized contact model with asymmetric damping and dwell-time dependent friction[J]. Multibody system dynamics, 2004, 11: 209-233.
    [21] 秦志英, 陆启韶. 基于恢复系数的碰撞过程模型分析[J]. 动力学与控制学报, 2006, 4(4): 294-298

    Qin Z Y, Lu Q S. Analysis of impact process model based on restitution coefficien[J]. Journal of Dynamics and Control, 2006, 4(4): 294-298 (in Chinese
    [22] Flores P, Machado M, Silva M T, et al. On the continuous contact force models for soft materials in multibody dynamics[J]. Multibody System Dynamics, 2011, 25(3): 357-375 doi: 10.1007/s11044-010-9237-4
    [23] Flores P, Koshy C S, Lankarani H M, et al. Numerical and experimental investigation on multibody systems with revolute clearance joints[J]. Nonlinear Dynamics, 2011, 65(4): 383-398 doi: 10.1007/s11071-010-9899-8
    [24] Flores P, Lankarani H M. Dynamic response of multibody systems with multiple clearance joints[J]. Journal of Computational and Nonlinear Dynamics, 2012, 7(3): 031003 doi: 10.1115/1.4005927
    [25] Koshy C S, Flores P, Lankarani H M. Study of the effect of contact force model on the dynamic response of mechanical systems with dry clearance joints: computational and experimental approaches[J]. Nonlinear Dynamics, 2013, 73(1-2): 325-338 doi: 10.1007/s11071-013-0787-x
    [26] Machado M, Costa J, Seabra E, et al. The effect of the lubricated revolute joint parameters and hydrodynamic force models on the dynamic response of planar multibody systems[J]. Nonlinear Dynamics, 2012, 69(1-2): 635-654 doi: 10.1007/s11071-011-0293-y
    [27] 王旭鹏, 刘更, 马尚君. 含间隙运动副机构的动力学特性研究[J]. 振动与冲击, 2016, 35(7): 110-115

    Wang X P, Liu G, Ma S J. Dynamic characteristics of mechanisms with revolute clearance joints[J]. Journal of Vibration and Shock, 2016, 35(7): 110-115 (in Chinese
    [28] 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.

    Bai Z F. Research on dynamic characteristics of mechanism with joint clearance[D]. Harbin: Harbin Institute of Technology, 2011 (in Chinese).
    [29] Bai Z F, Zhao Y. Dynamic behaviour analysis of planar mechanical systems with clearance in revolute joints using a new hybrid contact force model[J]. International Journal of Mechanical Sciences, 2012, 54(1): 190-205 doi: 10.1016/j.ijmecsci.2011.10.009
    [30] Bai Z F, Zhao Y. Dynamics modeling and quantitative analysis of multibody systems including revolute clearance joint[J]. Precision Engineering, 2012, 36(4): 554-567 doi: 10.1016/j.precisioneng.2012.04.002
    [31] Bai Z F, Zhao Y. A hybrid contact force model of revolute joint with clearance for planar mechanical systems[J]. International Journal of Non-Linear Mechanics, 2013, 48: 15-36 doi: 10.1016/j.ijnonlinmec.2012.07.003
    [32] 白争锋, 赵阳, 赵志刚. 考虑运动副间隙的机构动态特性研究[J]. 振动与冲击, 2011, 30(11): 17-20, 41

    Bai Z F, Zhao Y, Zhao Z G. Dynamic characteristics of mechanisms with joint clearance[J]. Journal of Vibration and Shock, 2011, 30(11): 17-20, 41 (in Chinese
    [33] Bai Z F, Zhao Y. Research on dynamic wear of revolution joint with clearance for mechanical system[J]. Applied Mechanics and Materials, 2011, 55-57: 488-493 doi: 10.4028/www.scientific.net/AMM.55-57.488
    [34] 王旭鹏, 刘更, 马尚君, 等. 间隙铰链对平面机构碰撞动力学特性影响分析[J]. 振动与冲击, 2017, 36(17): 74-78

    Wang X P, Liu G, Ma S J, et al. Effects of clearance joint on impact dynamic characteristics of planar mechanisms[J]. Journal of Vibration and Shock, 2017, 36(17): 74-78 (in Chinese
    [35] Wang X P, Liu G, Ma S J. Dynamic analysis of planar mechanical systems with clearance joints using a new nonlinear contact force model[J]. Journal of Mechanical Science and Technology, 2016, 30(4): 1537-1545 doi: 10.1007/s12206-016-0308-1
    [36] Wang X P, Liu G. Modeling and simulation of revolute joint with clearance in planar multi-body systems[J]. Journal of Mechanical Science and Technology, 2015, 29(10): 4113-4120 doi: 10.1007/s12206-015-0905-4
    [37] Wang X P, Liu G, Ma S J, et al. Study on dynamic responses of planar multibody systems with dry revolute clearance joint: Numerical and experimental approaches[J]. Journal of Sound and Vibration, 2019, 438: 116-138 doi: 10.1016/j.jsv.2018.08.052
    [38] Xu B C, Wang X P, Ji X M, et al. Dynamic and motion consistency analysis for a planar parallel mechanism with revolute dry clearance joints[J]. Journal of Mechanical Science and Technology, 2017, 31(7): 3199-3209 doi: 10.1007/s12206-017-0609-z
    [39] Lee T W, Wang A C. On the dynamics of intermittent-motion mechanisms. Part 1: dynamic model and response[J]. Journal of Mechanisms, Transmissions, and Automation in Design, 1983, 105(3): 534-540 doi: 10.1115/1.3267392
    [40] Herbert R G, McWhannell D C. Shape and frequency composition of pulses from an impact pair[J]. Journal of Engineering for Industry, 1977, 99(3): 513-518 doi: 10.1115/1.3439270
    [41] Anagnostopoulos A S. Pounding of buildings in series during earthquakes[J]. Earthquake Engineering and Structural Dynamics, 1988, 16(3): 443-456 doi: 10.1002/eqe.4290160311
    [42] Tsuji Y, Tanaka T, Ishida T. Lagrangian numerical simulation of plug flow of cohesionless particles in a horizontal pipe[J]. Powder Technology, 1992, 71(3): 239-250 doi: 10.1016/0032-5910(92)88030-L
    [43] Brilliantov N V, Spahn F, Hertzsch J M, et al. The collision of particles in granular systems[J]. Physica A: Statistical Mechanics and its Applications, 1996, 231(4): 417-424 doi: 10.1016/0378-4371(96)00099-4
    [44] Hu S W, Guo X L. A dissipative contact force model for impact analysis in multibody dynamics[J]. Multibody System Dynamics, 2015, 35(2): 131-151 doi: 10.1007/s11044-015-9453-z
    [45] Yigit A S, Christoforou A P, Majeed M A. A nonlinear visco-elastoplastic impact model and the coefficient of restitution[J]. Nonlinear Dynamics, 2011, 66(4): 509-521 doi: 10.1007/s11071-010-9929-6
    [46] Thornton C. Coefficient of restitution for collinear collisions of elastic-perfectly plastic spheres[J]. Journal of Applied Mechanics, 1997, 64(2): 383-386 doi: 10.1115/1.2787319
    [47] Kagami J, Yamada K, Hatazawa T. Contact between a sphere and rough plates[J]. Wear, 1983, 87(1): 93-105 doi: 10.1016/0043-1648(83)90025-X
    [48] Wu C Y, Li L Y, Thornton C. Energy dissipation during normal impact of elastic and elastic-plastic spheres[J]. International Journal of Impact Engineering, 2005, 32(1-4): 593-604 doi: 10.1016/j.ijimpeng.2005.08.007
    [49] Burgin L V, Aspden R M. Impact testing to determine the mechanical properties of articular cartilage in isolation and on bone[J]. Journal of Materials Science: Materials in Medicine, 2008, 19(2): 703-711 doi: 10.1007/s10856-007-3187-2
    [50] Shi X, Polycarpou A A. Measurement and modeling of normal contact stiffness and contact damping at the meso scale[J]. Journal of Vibration and Acoustics, 2005, 127(1): 52-60 doi: 10.1115/1.1857920
  • 加载中
图(6) / 表(5)
计量
  • 文章访问数:  228
  • HTML全文浏览量:  92
  • PDF下载量:  21
  • 被引次数: 0
出版历程
  • 收稿日期:  2019-08-15
  • 网络出版日期:  2020-11-07
  • 刊出日期:  2020-10-05

目录

    /

    返回文章
    返回