一种基于变恢复系数的接触碰撞力模型
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摘要
为了有效描述机械系统中的接触-碰撞现象,在考虑材料屈服强度和初始碰撞速度的基础上,提出一种变恢复系数模型,进而建立了一种改进的、变恢复系数的接触-碰撞模型;随后,分别以轴-轴承、球-球以及平面曲柄滑块机构为例,通过大量数值模拟和实验测试,以及二者间的对比分析,对改进模型的有效性、准确性进行了验证。研究结果表明,改进的模型能够更加准确的描述间隙铰链处的接触碰撞效应,以及间隙铰链对机械系统动态特性的影响规律。
In order to effectively describe contact-impact phenomena in mechanical systems, an improved contact-impact force model based on variable recovery coefficient was proposed. The variable recovery coefficient model was proposed considering material yield strength and initial impact velocity. Then, taking shaft-bearing, sphere-sphere, and a planar crank-slider mechanism as examples, a great number of numerical simulations and test measurements and their contrastive analyses were used to verify the correctness and effectiveness of the improved model. The results showed that the improved model can more accurately describe contact-impact effects in clearance joints and the influence law of clearance joints on dynamic characteristics of mechanical systems.
In order to effectively describe contact-impact phenomena in mechanical systems, an improved contact-impact force model based on variable recovery coefficient was proposed. The variable recovery coefficient model was proposed considering material yield strength and initial impact velocity. Then, taking shaft-bearing, sphere-sphere, and a planar crank-slider mechanism as examples, a great number of numerical simulations and test measurements and their contrastive analyses were used to verify the correctness and effectiveness of the improved model. The results showed that the improved model can more accurately describe contact-impact effects in clearance joints and the influence law of clearance joints on dynamic characteristics of mechanical systems.
引文
[1] FLORES P, AMBRóSIO J. Revolute joints with clearance in Multibody systems[J]. Computers and Structures, 2004, 82(17): 1359-1369.
[2] FLORES P. A parametric study on the dynamic response of planar Multibody systems with multiple clearance joints[J]. Nonlinear Dynamics, 2010, 61(4): 633-653.
[3] 郝雪清,陈江义.不同运动副材料对间隙机构动力学特性的影响[J].振动与冲击,2012, 31(12): 19-21. HAO Xueqing, CHEN Jiangyi. Effects of different materials in joints on dynamic characteristics of a mechanism with clearance[J]. Journal of Vibration and Shock, 2012,31(12): 19-21.
[4] HERTZ H. über dies Berührung fester elasticher K?rper[J]. Journal reine und angewandte Mathematik, 1881, 92: 156-171.
[5] CIAVARELLA M, DECUZZI P. The state of stress induced by the Plane frictionless cylindrical contact 1: the case of elastic similarity[J]. International Journal of Solid and Structures, 2001, 38: 4507-4523.
[6] LIU Caishan, ZHANG Ke, YANG Lei. The compliance contact model of cylindrical joints with clearance[J]. Acta Mechanica Sinica, 2005, 21(5):451-458.
[7] GOLDSMITH W. Impact: The theory and physical behaviour of colliding solids[M]. London: Edward Arnold Ltd, 1960.
[8] HUNT K H, CROSSLEY F R E. Coefficient of restitution interpreted as damping in vibroimpact[J]. Journal of Applied Mechanics, 1975, 7: 440-445.
[9] LANKARANI H M, NIKRAVESH P E. A contact force model with hysteresis damping for impact analysis of multi-body systems[J]. Journal of Mechanical Design, 1990, 112: 368-376.
[10] GONTHIER Y, MCPHEE J, LANGE C, et al. A regularized contact model with asymmetric damping and dwell-time dependent friction[J]. Multibody system dynamics, 2004, 11: 209-233.
[11] 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): 294-298. QIN Zhiying, LU Qishao. Analysis of impact process based on restitution coefficient[J]. Journal of Dynamics and Control, 2006(4): 294-298.
[12] 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: 357-375.
[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: 183-197.
[14] 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.
[15] 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. BAI Zhengfeng,ZHAO Yang,ZHAO Zhigang. Dynamic characteristics of mechanisms with joint clearance[J]. Journal of Vibration and Shock, 2011, 30(11):17-20.
[16] 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 Xupeng, LIU Geng, MA Shangjun. Study on dynamic characteristics of mechanisms with clearance joint[J]. Journal Vibration and Shock, 2016, 35(7) : 110-115.
[17] WANG Xupeng, LIU Geng, MA Shangjun. Dynamic analysis of planar mechanical systems with clearance joints using a new nonlinear contact force model[J]. Journal of Mechanical Science Technology, 2016, 30(4):1537-1545.
[18] STAMMERS C W, GHAZAVI M. A theoretical and experimental study of the dynamics of a four-bar chain with bearing clearance: pin motion, contact loss and impact[J]. Journal of Sound and Vibration, 1991, 150(2):301-315.
[19] MINAMOTO H, KAWAMURA S. Effects of material strain rate sensitivity in low speed impact between two identical spheres[J].International Journal of Impact Engineering, 2009,36:680-686.
[20] 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.
[21] DUBOWSKY S, FREUDENSTEIN F. Dynamic analysis of mechanical systems with clearances, Part 1: formulation of dynamic model[J]. Journal of Engineering for Industry, 1971,93: 305-309.
[22] 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: 25-47.
[23] 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.
[24] ZHANG Y N, INNA S. Validation of nonlinear viscoelastic contact force models for low speed impact[J]. Journal of Applied Mechanics, 2009, 76(5):911-914.
[2] FLORES P. A parametric study on the dynamic response of planar Multibody systems with multiple clearance joints[J]. Nonlinear Dynamics, 2010, 61(4): 633-653.
[3] 郝雪清,陈江义.不同运动副材料对间隙机构动力学特性的影响[J].振动与冲击,2012, 31(12): 19-21. HAO Xueqing, CHEN Jiangyi. Effects of different materials in joints on dynamic characteristics of a mechanism with clearance[J]. Journal of Vibration and Shock, 2012,31(12): 19-21.
[4] HERTZ H. über dies Berührung fester elasticher K?rper[J]. Journal reine und angewandte Mathematik, 1881, 92: 156-171.
[5] CIAVARELLA M, DECUZZI P. The state of stress induced by the Plane frictionless cylindrical contact 1: the case of elastic similarity[J]. International Journal of Solid and Structures, 2001, 38: 4507-4523.
[6] LIU Caishan, ZHANG Ke, YANG Lei. The compliance contact model of cylindrical joints with clearance[J]. Acta Mechanica Sinica, 2005, 21(5):451-458.
[7] GOLDSMITH W. Impact: The theory and physical behaviour of colliding solids[M]. London: Edward Arnold Ltd, 1960.
[8] HUNT K H, CROSSLEY F R E. Coefficient of restitution interpreted as damping in vibroimpact[J]. Journal of Applied Mechanics, 1975, 7: 440-445.
[9] LANKARANI H M, NIKRAVESH P E. A contact force model with hysteresis damping for impact analysis of multi-body systems[J]. Journal of Mechanical Design, 1990, 112: 368-376.
[10] GONTHIER Y, MCPHEE J, LANGE C, et al. A regularized contact model with asymmetric damping and dwell-time dependent friction[J]. Multibody system dynamics, 2004, 11: 209-233.
[11] 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): 294-298. QIN Zhiying, LU Qishao. Analysis of impact process based on restitution coefficient[J]. Journal of Dynamics and Control, 2006(4): 294-298.
[12] 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: 357-375.
[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: 183-197.
[14] 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.
[15] 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. BAI Zhengfeng,ZHAO Yang,ZHAO Zhigang. Dynamic characteristics of mechanisms with joint clearance[J]. Journal of Vibration and Shock, 2011, 30(11):17-20.
[16] 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 Xupeng, LIU Geng, MA Shangjun. Study on dynamic characteristics of mechanisms with clearance joint[J]. Journal Vibration and Shock, 2016, 35(7) : 110-115.
[17] WANG Xupeng, LIU Geng, MA Shangjun. Dynamic analysis of planar mechanical systems with clearance joints using a new nonlinear contact force model[J]. Journal of Mechanical Science Technology, 2016, 30(4):1537-1545.
[18] STAMMERS C W, GHAZAVI M. A theoretical and experimental study of the dynamics of a four-bar chain with bearing clearance: pin motion, contact loss and impact[J]. Journal of Sound and Vibration, 1991, 150(2):301-315.
[19] MINAMOTO H, KAWAMURA S. Effects of material strain rate sensitivity in low speed impact between two identical spheres[J].International Journal of Impact Engineering, 2009,36:680-686.
[20] 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.
[21] DUBOWSKY S, FREUDENSTEIN F. Dynamic analysis of mechanical systems with clearances, Part 1: formulation of dynamic model[J]. Journal of Engineering for Industry, 1971,93: 305-309.
[22] 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: 25-47.
[23] 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.
[24] ZHANG Y N, INNA S. Validation of nonlinear viscoelastic contact force models for low speed impact[J]. Journal of Applied Mechanics, 2009, 76(5):911-914.