基于数字图像处理方法的弹塑性倾斜接触冲击动力学试验与数值分析
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摘要
针对弹塑性倾斜冲击问题,测量和预测冲击对象在接触冲击过程中的运动参数及接触力仍然是一个难点。考虑振动响应的影响,结合假设模态法和广义动量定理建立冲击对象的运动模型;根据Jackson-Green模型,将振动响应考虑到接触变形中,系统探讨和研究了弹塑性接触冲击过程中的接触力变化;基于数字图像处理方法,通过设计多标识点的冲击试验,描述与跟踪冲击对象在接触冲击过程中的运动规律,并对恢复系数和冲击后的运动参数进行试验与仿真对比分析。试验与仿真结果表明:滑动摩擦判断条件Δ呈W形分布,且存在3个临界冲击角,分别为27.5°、42.5°和58.4°;对于初始冲击角θ=45°,接触点冲击后反弹速度、角速度和恢复系数的仿真与试验结果基本吻合,其相对误差均小于5%,验证了所建模型的正确性。
For the elasto-plastic oblique impact problems,it is still difficult to measure and predict the motion parameters and contact force of the impact object during the contact impact events.With consideration of vibration responses,the kinetic model of impact object is established based on the assumed mode method and generalized momentum theorem.Considering the vibration responses in the contact deformation,the changes of contact force during the elasto-plastic contact impact has been studied theoretically based on the Jackson-Green model.The impact test with multi-markers is performed.The digital image processing method is used to describe and track the motion law of the impact object during the contact impact.Experimental results for the coefficient of restitution and the motion parameters after impact have been compared with simulations.The experimental and simulation results show that the judgment condition for sliding friction,Δ,presents the W-distribution;and,three critical initial impact angles,27.5°,42.5°,and 58.4°are found to determine whether the impact object slides or not.For the impact angleθ=45°,simulation results are found to be in good agreement with the experimental data in terms of the rebound velocity of the contact point,the angular velocity and the coefficient of restitution.All the relative error is less than 5%.Thus,it can be verified that the established model is relatively accurate.
For the elasto-plastic oblique impact problems,it is still difficult to measure and predict the motion parameters and contact force of the impact object during the contact impact events.With consideration of vibration responses,the kinetic model of impact object is established based on the assumed mode method and generalized momentum theorem.Considering the vibration responses in the contact deformation,the changes of contact force during the elasto-plastic contact impact has been studied theoretically based on the Jackson-Green model.The impact test with multi-markers is performed.The digital image processing method is used to describe and track the motion law of the impact object during the contact impact.Experimental results for the coefficient of restitution and the motion parameters after impact have been compared with simulations.The experimental and simulation results show that the judgment condition for sliding friction,Δ,presents the W-distribution;and,three critical initial impact angles,27.5°,42.5°,and 58.4°are found to determine whether the impact object slides or not.For the impact angleθ=45°,simulation results are found to be in good agreement with the experimental data in terms of the rebound velocity of the contact point,the angular velocity and the coefficient of restitution.All the relative error is less than 5%.Thus,it can be verified that the established model is relatively accurate.
引文
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[29]陈健美,宋庆余,朱峰.数字图像处理与分析[M].镇江:江苏大学出版社,2015.CHEN Jianmei,SONG Qingyu,ZHU Feng.Digital image processing and analysis[M].Zhenjiang:Jiangsu University Press,2015.
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[33]MACHADO M,MOREIRA P,FLORES P,et al.Compliant contact force models in multi-body dynamics:Evolution of the Hertz contact theory[J].Mechanism and Machine Theory,2012,53:99-121.
[34]WANG H,YIN X C,QI X L,et al.Experimental and theoretical analysis of the elastic-plastic normal repeated impacts of a sphere on a beam[J].International Journal of Solids and Structures,2017,109:131-142.
[35]王尧,项丹,孟文俊.ZChSnSb11-6/20钢复合材料不同结合界面结合强度仿真与试验[J].中国机械工程,2017,28(1):101-106,112.WANG Yao,XIANG Dan,MENG Wenjun.Simulation and experiments of binding strength of different binding interfaces on ZChSnSb11-6/20 steel composites[J].China Mechanical Engineering,2017,28(1):101-106,112.
[36]李淑君,王尧,项丹,等.ZChSnSb11-6/20钢复合材料结合界面影响因子研究[J].稀有金属材料与工程,2016,45(10):2555-2560.LI Shujun,WANG Yao,XIANG Dan,et al.Investigation of impact factor of binding interface on ZChSnSb11-6/20steel composites[J].Rare Metal Materials and Engineering,2016,45(10):2555-2560.
[2]黄意新,赵阳,郭剑,等.一种新型GEO卫星在轨捕获机构的设计与分析[J].振动与冲击,2016,35(24):132-138.HUANG Yixin,ZHAO Yang,GUO Jian,et al.Design and analysis of a novel on-orbit capture mechanism for GEOsatellites[J].Journal of Vibration and Shock,2016,35(24):132-138.
[3]ASKARI E,DABIRRAHMANI D,FLORES P,et al.Nonlinear vibration and dynamics of ceramic on ceramic artificial hip joints:A spatial multibody modelling[J].Nonlinear Dynamics,2014,76(2):1365-1377.
[4]王国彪,陈殿生,陈科位,等.仿生机器人研究现状[J].机械工程学报,2015,51(13):27-44.WANG Guobiao,CHEN Diansheng,CHEN Kewei,et al.The current research status and development strategy on biomimetic robot[J].Journal of Mechanical Engineering,2015,51(13):27-44.
[5]WU H N,WANG J W.Observer design and output feedback stabilization for nonlinear multivariable systems with diffusion PDE-governed sensor dynamics[J].Nonlinear Dynamics,2013,3(72):615-628.
[6]妥吉英,邓兆祥,张河山,等.新型扭转准零刚度的振动角度传感系统[J].西安交通大学学报,2017,51(8):1-7.TUO Jiying,DENG Zhaoxiang,ZHANG Heshan,et al.A new type of sensor system for angular vibration measurement of torsion quasi-zero-stiffness[J].Journal of Xi’an Jiaotong University,2017,51(8):1-7.
[7]CHEN Y,HOU S J,FU K K,et al.Low-velocity impact response of composite sandwich structures:modelling and experiment[J].Composite Structures,2017,168:322-334.
[8]STRONGE W J.Energetically consistent calculations for oblique impact in unbalanced systems with friction[J].Journal of Applied Mechanics,2015,82(8):081003.
[9]章孝顺,章定国,陈思佳,等.基于绝对节点坐标法的大变形柔性梁几种动力学模型研究[J].物理学报,2016,65(9):094501.ZHANG Xiaoshun,ZHANG Dingguo,CHEN Sijia,et al.Several dynamic models of a large deformation flexible beam based on the absolute nodal coordinate formulation[J].Acta Physica Sinica,2016,65(9):094501.
[10]WANG H,YIN X C,DENG Q M,et al.Experimental and theoretical analyses of elastic-plastic repeated impacts by considering wave effects[J].European Journal of Mechanics-A/Solids,2017,65:212-222.
[11]周建星,孙文磊,曹莉,等.行星齿轮传动系统碰撞振动特性研究[J].西安交通大学学报,2016,50(3):16-21.ZHOU Jianxing,SUN Wenlei,CAO Li,et al.Vibro-impact characteristics of planetary gear transmission[J].Journal of Xi’an Jiaotong University,2016,50(3):16-21.
[12]WRIGGERS P,RUST W T,REDDY B D.A virtual element method for contact[J].Computational Mechanics,2016,58(6):1039-1050.
[13]WANG Y,LI S J,XIANG D,et al.Experimental and theoretical analyses of contact-impact behavior of Babbitt ZChSnSb11-6[J].Proceedings of the Institution of Mechanical Engineers,Part L:Journal of Materials:Design and Applications,2017,http://doi.org/10.1177/1464420717739334.
[14]BAZRAFSHAN M,AHMADIAN H,JALALI H.Modeling the interaction between contact mechanisms in normal and tangential directions[J].International Journal of Non-Linear Mechanics,2014,58:111-119.
[15]LIU T,LI G B,WEI H J,et al.Experimental observation of cross correlation between tangential friction vibration and normal friction vibration in a running-in process[J].Tribology International,2016,97:77-88.
[16]AL-SHUKA H F N,CORVES B J,ZHU W H.Dynamic modeling of biped robot using Lagrangian and recursive Newton-Euler formulations[J].International Journal of Computer Applications,2014,101(3):1-8.
[17]SHAFEI A M,SHAFEI H R.Oblique impact of multi-flexible-link systems[J].Journal of Vibration and Control,2016,DOI:1077546316654854.
[18]REZVANIAN M,BAGHESTANI A M,DANESHPAZHOOH M,et al.Off-center impact of an elastic column by a rigid mass[J].Mechanics Research Communications,2015,63:21-25.
[19]KOGUT L,ETSION I.Elastic-plastic contact analysis of a sphere and a rigid flat[J].Journal of Applied Mechanics,2002,69(5):657-662.
[20]ETSION I,KLIGERMAN Y,KADIN Y.Unloading of an elastic-plastic loaded spherical contact[J].International Journal of Solids and Structures,2005,42(13):3716-3729.
[21]JACKSON R L,GREEN I,MARGHITU D B.Predicting the coefficient of restitution of impacting elastic-perfectly plastic spheres[J].Nonlinear Dynamics,2010,60(3):217-229.
[22]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):593-604.
[23]BOETTCHER R,KUNIK M,EICHMANN S,et al.Revisiting energy dissipation due to elastic waves at impact of spheres on large thick plates[J].International Journal of Impact Engineering,2017,104:45-54.
[24]KOGUT L,KOMVOPOULOS K.Analysis of the spherical indentation cycle for elastic-perfectly plastic solids[J].Journal of Materials Research,2004,19(12):3641-3653.
[25]YE N,KOMVOPOULOS K.Indentation analysis of elastic-plastic homogeneous and layered media:criteria for determining the real material hardness[J].Journal of Tribology,2003,125(4):685-691.
[26]BRAKE M R.An analytical elastic plastic contact model with strain hardening and frictional effects for normal and oblique impacts[J].International Journal of Solids and Structures,2015,62:104-123.
[27]GHAEDNIA H,MARGHITU D B,JACKSON R L.Predicting the permanent deformation after the impact of a rod with a flat surface[J].Journal of Tribology,2015,137(1):011403.
[28]GHEADNIA H,CERMIK O,MARGHITU D B.Experimental and theoretical analysis of the elasto-plastic oblique impact of a rod with a flat[J].International Journal of Impact Engineering,2015,86:307-317.
[29]陈健美,宋庆余,朱峰.数字图像处理与分析[M].镇江:江苏大学出版社,2015.CHEN Jianmei,SONG Qingyu,ZHU Feng.Digital image processing and analysis[M].Zhenjiang:Jiangsu University Press,2015.
[30]CROSS R.Oblique bounce of a rubber ball[J].Experimental Mechanics,2014,54(9):1523-1536.
[31]REZAEI A,VERHELST R,Van PAEPEGEM W,et al.Finite element modelling and experimental study of oblique soccer ball bounce[J].Journal of Sports Sciences,2011,29(11):1201-1213.
[32]闻邦椿,刘树英,张纯宇.机械振动学[M].2版.北京:冶金工业出版社,2011.WEN Bangchun,LIU Shuying,ZHANG Chunyu.Mechanical vibration[M].2nd ed.Beijing:Metallurgical Industry Press,2011.
[33]MACHADO M,MOREIRA P,FLORES P,et al.Compliant contact force models in multi-body dynamics:Evolution of the Hertz contact theory[J].Mechanism and Machine Theory,2012,53:99-121.
[34]WANG H,YIN X C,QI X L,et al.Experimental and theoretical analysis of the elastic-plastic normal repeated impacts of a sphere on a beam[J].International Journal of Solids and Structures,2017,109:131-142.
[35]王尧,项丹,孟文俊.ZChSnSb11-6/20钢复合材料不同结合界面结合强度仿真与试验[J].中国机械工程,2017,28(1):101-106,112.WANG Yao,XIANG Dan,MENG Wenjun.Simulation and experiments of binding strength of different binding interfaces on ZChSnSb11-6/20 steel composites[J].China Mechanical Engineering,2017,28(1):101-106,112.
[36]李淑君,王尧,项丹,等.ZChSnSb11-6/20钢复合材料结合界面影响因子研究[J].稀有金属材料与工程,2016,45(10):2555-2560.LI Shujun,WANG Yao,XIANG Dan,et al.Investigation of impact factor of binding interface on ZChSnSb11-6/20steel composites[J].Rare Metal Materials and Engineering,2016,45(10):2555-2560.