Coulomb干摩擦模型与LuGre摩擦模型的分析与比较
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摘要
分析比较Coulomb干摩擦模型和LuGre摩擦模型的特点。Coulomb干摩擦模型形式简单,能较好地反映stick-slip运动状态的切换,但不能反映对系统动态响应有直接影响的不同的摩擦现象,且其不连续性也给数值仿真带来了困难。LuGre摩擦模型能捕捉滑动速度变化时摩擦力的变化,使其适用于stick-slip运动的研究,然而其参数的确定十分困难,且在数值计算时需要取较小的步长才能进行求解,计算效率较低。分别应用这两种模型仿真分析含摩擦滑移铰平面刚体的stick-slip现象,通过具体算例对数值方法进行说明,并给出了结论。
An analysis and comparison are carried out to show the characteristics of the Coulomb dry friction model and LuGre friction model.The Coulomb dry friction model is simple and can better reflect the switching of stick-slip motion.However,this model cannot reflect different friction phenomena that have direct influence on the dynamic response of the sys' em.This model is not continuous,which leads to numerical simulation difficulties.The LuGre friction model can capture the variation of friction force with slip velocity,thus making it suitable for studies on stick-slip motions.However,the model parameters of the LuGre frictional model can hardly be determined from any experiment.It is necessary to take small time step sizes to solve the numerical calculation,and the computation efficiency is low.The Coulomb friction model and the LuGre friction model are applied respectively to analyze the stick-slip phenomenon of the plane rigid body with friction-affected sliding joints.The numerical examples are given to illustrate the numerical method,andthe conclusion is summarized.
An analysis and comparison are carried out to show the characteristics of the Coulomb dry friction model and LuGre friction model.The Coulomb dry friction model is simple and can better reflect the switching of stick-slip motion.However,this model cannot reflect different friction phenomena that have direct influence on the dynamic response of the sys' em.This model is not continuous,which leads to numerical simulation difficulties.The LuGre friction model can capture the variation of friction force with slip velocity,thus making it suitable for studies on stick-slip motions.However,the model parameters of the LuGre frictional model can hardly be determined from any experiment.It is necessary to take small time step sizes to solve the numerical calculation,and the computation efficiency is low.The Coulomb friction model and the LuGre friction model are applied respectively to analyze the stick-slip phenomenon of the plane rigid body with friction-affected sliding joints.The numerical examples are given to illustrate the numerical method,andthe conclusion is summarized.
引文
[1]MUVENGEI O,KIHIU J,IKUA B.Dynamic analysis of planar multi-body systems with LuGre friction at differently located revolute clearance joints[J].Multibody Syst Dyn,2012,28(4):369-393.
[2]BHUSHAN B.摩擦学导论[M].葛世荣,译.北京:机械工业出版社,2007.
[3]刘丽兰,刘宏昭,吴子英,等.机械系统中摩擦模型的研究进展[J].力学进展,2008,38(2):201-213.
[4]PFEIFFER F,GLOCKER C.Multibody dynamics with unilateral contacts[M].New York:John Wiley&Sons.Inc,1996.
[5]FLORES P,AMBRSIO J,PIMENTA CLARO J C P,et al.Kinematics and dynamics of multibody systems with imperfect joints[M].Berlin:Springer,2008.
[6]丁千,翟红梅.机械系统摩擦动力学研究进展[J].力学进展,2013,43(1):112-131.
[7]MARQUES F,FLORES P,LANKARAN H M.On the Frictional Contacts in Multibody System Dynamics[M]//JOSEP M,FONTL.Multibody Dynamics Computational Methods and Applications.Switzerland:Springer International Publishing,2016:67-91.
[8]FLORES P,AMBRSIO J,CLARO J C P,et al.Translational joints with clearance in rigid multibody systems[J].Journal of Computational and Nonlinear Dynamics,2008,3:011007(1-10).
[9]PAULO F,LEINE R,GLOCKER C.Modeling and analysis of planar rigid multibody systems with translational clearance joints based on the non-smooth dynamics approach[J].Multibody Syst Dyn,2010,23(2):165-190.
[10]王琪,庄方方,郭易圆,等.非光滑多体系统动力学数值算法的研究进展[J].力学进展,2013,43(1):101-111.
[11]PFEIFFER F,FOERG M,Uibrich H.Numerical aspects of nonsmooth multibody dynamics[J].Computer Methods in Applied Mechanics and Engineering,2006,195:6891-6908.
[12]庄方方,王琪.含摩擦柱铰链平面多体系统动力学的建模和数值方法[J].工程力学,2012,29(5):193-199.
[13]WANG Q,PENG H,ZHUANG F F.A constraint-stabilized method for multibody dynamics with friction-affected translational joints based on HLCP[J].Discrete and Continuous Dynamical Systems Series B,2011,16(2):589-605.
[14]ZHUANG F F,WANG Q.Modeling and simulation of the nonsmooth planar rigid multibody systems with frictional translational joints[J].Multibody Syst Dyn,2013,29(4):403-423.
[15]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[J].力学学报,2015,47(5):814-821.
[16]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[J].力学学报,2015,47(2):303-309.
[17]PENNESTRI E,VALENTINI P P,VITA L.Multibody dynamics simulation of planar linkages with Dahl friction[J].Multibody Syst Dyn,2007,17(4):321-347.
[18]MUVENGEI O,KIHIU J,IKUA B.Dynamic analysis of planar rigid-body mechanical systems with two-clearance revolute joints[J].Nonlinear Dyn,2013,73:259-273.
[19]WANG Z,TIAN Q,HU H Y,et al.Nonlinear dynamics and chaotic control of a exible multibody system with uncertain joint clearance[J/OL].Nonlinear Dyn,2016,86(3):1571-1597.[2017-10-20].https://link.springer.com/article/10.1007%2Fs11071-016-2978-8.DOI:10.1007/s11071-016-2978-8.
[20]MARQUES F,FLORES P,PIMENTA CLARO J C,et al.Asurvey and comparison of several friction force models for dynamic analysis of multibody mechanical systems[J].Nonlinear Dyn,2016,86(3):1407-1443.
[21]PENNESTRI E.ROSSI V,SALVINI P,et al.Review and comparison of dry friction force models[J].Nonlinear Dyn,2016,83(4):1785-1801.责任编辑:杨子立
[2]BHUSHAN B.摩擦学导论[M].葛世荣,译.北京:机械工业出版社,2007.
[3]刘丽兰,刘宏昭,吴子英,等.机械系统中摩擦模型的研究进展[J].力学进展,2008,38(2):201-213.
[4]PFEIFFER F,GLOCKER C.Multibody dynamics with unilateral contacts[M].New York:John Wiley&Sons.Inc,1996.
[5]FLORES P,AMBRSIO J,PIMENTA CLARO J C P,et al.Kinematics and dynamics of multibody systems with imperfect joints[M].Berlin:Springer,2008.
[6]丁千,翟红梅.机械系统摩擦动力学研究进展[J].力学进展,2013,43(1):112-131.
[7]MARQUES F,FLORES P,LANKARAN H M.On the Frictional Contacts in Multibody System Dynamics[M]//JOSEP M,FONTL.Multibody Dynamics Computational Methods and Applications.Switzerland:Springer International Publishing,2016:67-91.
[8]FLORES P,AMBRSIO J,CLARO J C P,et al.Translational joints with clearance in rigid multibody systems[J].Journal of Computational and Nonlinear Dynamics,2008,3:011007(1-10).
[9]PAULO F,LEINE R,GLOCKER C.Modeling and analysis of planar rigid multibody systems with translational clearance joints based on the non-smooth dynamics approach[J].Multibody Syst Dyn,2010,23(2):165-190.
[10]王琪,庄方方,郭易圆,等.非光滑多体系统动力学数值算法的研究进展[J].力学进展,2013,43(1):101-111.
[11]PFEIFFER F,FOERG M,Uibrich H.Numerical aspects of nonsmooth multibody dynamics[J].Computer Methods in Applied Mechanics and Engineering,2006,195:6891-6908.
[12]庄方方,王琪.含摩擦柱铰链平面多体系统动力学的建模和数值方法[J].工程力学,2012,29(5):193-199.
[13]WANG Q,PENG H,ZHUANG F F.A constraint-stabilized method for multibody dynamics with friction-affected translational joints based on HLCP[J].Discrete and Continuous Dynamical Systems Series B,2011,16(2):589-605.
[14]ZHUANG F F,WANG Q.Modeling and simulation of the nonsmooth planar rigid multibody systems with frictional translational joints[J].Multibody Syst Dyn,2013,29(4):403-423.
[15]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[J].力学学报,2015,47(5):814-821.
[16]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[J].力学学报,2015,47(2):303-309.
[17]PENNESTRI E,VALENTINI P P,VITA L.Multibody dynamics simulation of planar linkages with Dahl friction[J].Multibody Syst Dyn,2007,17(4):321-347.
[18]MUVENGEI O,KIHIU J,IKUA B.Dynamic analysis of planar rigid-body mechanical systems with two-clearance revolute joints[J].Nonlinear Dyn,2013,73:259-273.
[19]WANG Z,TIAN Q,HU H Y,et al.Nonlinear dynamics and chaotic control of a exible multibody system with uncertain joint clearance[J/OL].Nonlinear Dyn,2016,86(3):1571-1597.[2017-10-20].https://link.springer.com/article/10.1007%2Fs11071-016-2978-8.DOI:10.1007/s11071-016-2978-8.
[20]MARQUES F,FLORES P,PIMENTA CLARO J C,et al.Asurvey and comparison of several friction force models for dynamic analysis of multibody mechanical systems[J].Nonlinear Dyn,2016,86(3):1407-1443.
[21]PENNESTRI E.ROSSI V,SALVINI P,et al.Review and comparison of dry friction force models[J].Nonlinear Dyn,2016,83(4):1785-1801.责任编辑:杨子立