浮放物体平面多刚体动力学建模与算法研究

采用非光滑多体系统动力学的方法研究浮放物体与基础平台组成的多体系统,建立其非光滑接触的动力学方程与数值算法.浮放物体由主体部分和支撑腿组成,其间通过含黏弹性阻力偶的转动铰连接.支撑腿与基础平台间的接触力简化为接触点的法向接触力和摩擦力,采用扩展的赫兹接触力模型描述接触点的法向接触力,采用库伦干摩擦模型描述其摩擦力.采用笛卡尔坐标系下的位形坐标作为系统的广义坐标.首先,将基础平台运动看作非定常约束,用第一类拉格朗日方程建立系统的动力学方程,并采用鲍姆加藤约束稳定化的方法解决违约问题.随后给出基于事件驱动法和线性互补方法的数值算法.当相对切向速度为零时,构造静滑动摩擦力的正负余量和正、负向加速度的互补关系,从而将接触点黏滞-滑移切换的判断以及静滑动摩擦力的计算转化为线性互补问题进行求解,并采用Lemke算法求解线性互补问题.最后,通过数值仿真选择合适的步长;通过仿真结果说明浮放物体运动中存在的黏滞-滑移切换现象以及基础平台运动、质心位置对浮放物体运动的影响.     

RESEARCH ON MODELING AND NUMERICAL METHOD OF FREE STANDING BODY ON PLANAR RIGID MULTIBODY DYNAMICS

采用非光滑多体系统动力学的方法研究浮放物体与基础平台组成的多体系统,建立其非光滑接触的动力学方程与数值算法.浮放物体由主体部分和支撑腿组成,其间通过含黏弹性阻力偶的转动铰连接.支撑腿与基础平台间的接触力简化为接触点的法向接触力和摩擦力,采用扩展的赫兹接触力模型描述接触点的法向接触力,采用库伦干摩擦模型描述其摩擦力.采用笛卡尔坐标系下的位形坐标作为系统的广义坐标.首先,将基础平台运动看作非定常约束,用第一类拉格朗日方程建立系统的动力学方程,并采用鲍姆加藤约束稳定化的方法解决违约问题.随后给出基于事件驱动法和线性互补方法的数值算法.当相对切向速度为零时,构造静滑动摩擦力的正负余量和正、负向加速度的互补关系,从而将接触点黏滞——滑移切换的判断以及静滑动摩擦力的计算转化为线性互补问题进行求解,并采用Lemke算法求解线性互补问题.最后,通过数值仿真选择合适的步长;通过仿真结果说明浮放物体运动中存在的黏滞-滑移切换现象以及基础平台运动、质心位置对浮放物体运动的影响.     

车辆纵向非光滑多体动力学建模与数值算法研究

在建立车辆纵向多体系统的动力学模型中, 将车身与车轮视为刚体, 两者通过减振器链接; 将传动系统视为一个圆盘通过扭簧和阻尼器与驱动轮连接; 将车轮与路面间的接触力简化为法向约束力、摩擦力和滚阻力偶,其中摩擦力的模型采用库仑干摩擦模型. 采用笛卡尔坐标作为该系统的广义坐标用于描述该系统的位形, 给出系统单双边的约束方程, 应用第一类拉格朗日方法建立了系统的动力学方程. 由于摩擦与滚阻的非光滑性, 使得该系统动力学方程不连续. 为便于计算, 建立了车轮与路面接触点的相对切向加速度与摩擦力余量的互补条件、车轮角加速度与滚阻力偶余量的互补条件, 以及车轮轮心法向加速度与路面法向约束力的互补条件. 将接触—分离、黏滞—滑移的判断问题转化成线性互补问题的求解, 并给出了具有约束稳定化的基于事件驱动法的数值计算方法. 最后, 应用该方法对车辆纵向多体系统进行了仿真, 分析了输出扭矩、摩擦及滚阻系数对其动力学行为的影响.      

基于LuGre摩擦模型的接触约束法旋转柔性梁斜碰撞研究

基于接触约束法和LuGre摩擦模型对在重力场作用下作大范围旋转运动的柔性梁系统和斜坡发生含摩擦斜碰撞的动力学问题进行研究. 首先运用刚柔耦合的多体系统动力学理论对大范围运动的柔性梁进行离散化和动力学建模, 在碰撞时采用冲量动量法求出跳跃速度, 其次在法向上引入接触约束求解出碰撞力, 在切向上采用LuGre摩擦模型分两种方式求解摩擦力, 第一种是在滑动时摩擦力由摩擦系数和碰撞力计算得出, 黏滞状态下引入切向约束计算拉格朗日乘子反应实际摩擦力, 根据黏滞/滑动切换判断计算出碰撞过程摩擦力(与Coulomb摩擦模型计算摩擦力一致); 第二种根据LuGre摩擦模型摩擦系数和法向碰撞力计算其摩擦力, 从而在碰撞时无需黏滞/滑动切换, 采用相同的摩擦力计算公式. 通过与Coulomb摩擦模型对比发现, LuGre摩擦模型描述碰撞切向摩擦过程更精确, LuGre摩擦模型黏滞时建立约束方程和碰撞采用统一的摩擦力公式这两种建模方式描述的斜碰撞动力学特性没有区别, 进而说明采用法向接触约束和LuGre摩擦模型具有满足碰撞非嵌入情况、避免黏滞/滑动切换、描述摩擦力相对准确的优势.      

含摩擦滑移铰平面多刚体系统动力学的数值算法

基于LuGre摩擦模型和线性互补问题(LCP)的数值算法,给出了具有双边约束含摩擦滑移铰平面多体系统动力学的数值算法.首先,根据滑移铰的特点,当间隙充分小时,将其视为双边约束,给出了滑移铰中滑道作用于滑块上的法向接触力的互补关系;LuGre摩擦模型能有效地描述机械系统中的黏滞与滑移运动,将该模型用于描述滑块与滑道间的摩擦力.其次,结合Baumgarte约束稳定化方法,应用第一类Lagrange方程,建立了该多体系统的动力学方程,给出了Lagrange乘子与滑移铰中作用于滑块上的法向接触力的关系式.然后,将滑块与滑道间多种接触状态的判断以及作用于滑块上的法向接触力的计算转换为线性互补问题的求解,并用常微分方程的数值算法求解该多体系统的动力学方程.最后,通过数值仿真算例揭示了滑移铰中滑块的黏滞与滑移现象,以及滑块在滑道内的多种接触状态;另外,在文中分别采用Coulomb干摩擦模型和LuGre摩擦模型,对算例中的某些工况进行了数值仿真,并且分别用本文方法得到的数值仿真结果与已有方法得到的数值仿真结果对比,表明了本文给出的方法的有效性.      

含摩擦滑移铰平面多刚体系统动力学的数值算法

基于LuGre摩擦模型和线性互补问题(LCP)的数值算法,给出了具有双边约束含摩擦滑移铰平面多体系统动力学的数值算法.首先,根据滑移铰的特点,当间隙充分小时,将其视为双边约束,给出了滑移铰中滑道作用于滑块上的法向接触力的互补关系;LuGre摩擦模型能有效地描述机械系统中的黏滞与滑移运动,将该模型用于描述滑块与滑道间的摩擦力.其次,结合Baumgarte约束稳定化方法,应用第一类Lagrange方程,建立了该多体系统的动力学方程,给出了Lagrange乘子与滑移铰中作用于滑块上的法向接触力的关系式.然后,将滑块与滑道间多种接触状态的判断以及作用于滑块上的法向接触力的计算转换为线性互补问题的求解,并用常微分方程的数值算法求解该多体系统的动力学方程.最后,通过数值仿真算例揭示了滑移铰中滑块的黏滞与滑移现象,以及滑块在滑道内的多种接触状态;另外,在文中分别采用Coulomb干摩擦模型和LuGre摩擦模型,对算例中的某些工况进行了数值仿真,并且分别用本文方法得到的数值仿真结果与已有方法得到的数值仿真结果对比,表明了本文给出的方法的有效性.     

含摩擦滑移铰平面多刚体动力学的HLCP方法

给出了一种基于水平线性互补问题(HLCP)的双边约束滑移铰含摩擦平面多刚体系统动力学的数值计算方法.首先从系统的约束方程出发建立了每个双边约束中两个约束面的法向约束力的互补关系;并利用摩擦余量的概念给出了库仑摩擦定律的互补表达式.然后针对事件驱动算法将该类非光滑多体系统动力学方程中双边约束中法向约束力切换和系统"stick-slip"运动状态切换的判断统一成HLCP的求解,通过定义一组变维数矩阵给出了HLCP形式的一般表达式,便于编程计算.最后通过一个两自由度多体系统的算例验证了该方法的有效性.     

含非理想空间棱柱铰的多体系统接触分析

传统的接触分析方法通过物体间的相对运动确定接触位置. 将这种方法用于多体系统中铰内的接触分析时, 无论铰内间隙是否十分微小都必须解除铰的运动学约束, 从而导致求解效率和求解精度方面的诸多弊端. 基于铰约束反力与铰内接触力之间的力系等效关系, 以及铰内可能接触点运动之间内在的运动学关系, 以矩形截面的棱柱铰为例, 提出了一种对空间棱柱铰进行摩擦接触分析的方法, 可在不解除铰的运动学约束的前提下得到铰内接触模式和接触力. 数值算例验证了方法的可行性.      

三相驱动下非光滑振动驱动系统的动力学分析

可移动式机器人已成为机器人研究领域的重要分支,为实现其在狭小特殊环境中的运动, 学者们提出并研究了振动驱动移动系统.本文基于二维LuGre摩擦模型和拉格朗日方程,给出了一类振动驱动系统在各向同性摩擦环境中的动力学建模方法和数值算法.这类振动驱动系统结构简单且密封性好,依靠箱体与地面间的摩擦力实现自身的定向运动.该系统由一个外部箱体和两个内部质量块构成,两个质量块在箱体内的两个平行轨道上作三相振动驱动,箱体通过三个刚性支撑足与地面保持接触. 二维LuGre摩擦模型的利用,可有效避免库伦摩擦模型的不连续性给动力学方程的数值求解带来的困难,且可有效揭示该系统在运动过程中的黏滞-滑移切换现象. 数值仿真结果表明,通过调整其内部质量块的驱动参数,可实现箱体的直线平移、定轴转动和平面一般运动,且箱体在移动和转动过程中会出现擦滑、穿滑、回滑和不黏等4种现象; 另外,通过调节驱动参数, 不仅可以改变箱体移动和转动的快慢,还可以改变箱体形心运动轨迹的曲率半径.      

KINETICS ANALYSIS OF NON-SMOOTH VIBRATION-DRIVEN SYSTEM WITH THREE-PHASE CONTROL 1)

可移动式机器人已成为机器人研究领域的重要分支,为实现其在狭小特殊环境中的运动, 学者们提出并研究了振动驱动移动系统.本文基于二维LuGre摩擦模型和拉格朗日方程,给出了一类振动驱动系统在各向同性摩擦环境中的动力学建模方法和数值算法.这类振动驱动系统结构简单且密封性好,依靠箱体与地面间的摩擦力实现自身的定向运动.该系统由一个外部箱体和两个内部质量块构成,两个质量块在箱体内的两个平行轨道上作三相振动驱动,箱体通过三个刚性支撑足与地面保持接触. 二维LuGre摩擦模型的利用,可有效避免库伦摩擦模型的不连续性给动力学方程的数值求解带来的困难,且可有效揭示该系统在运动过程中的黏滞-滑移切换现象. 数值仿真结果表明,通过调整其内部质量块的驱动参数,可实现箱体的直线平移、定轴转动和平面一般运动,且箱体在移动和转动过程中会出现擦滑、穿滑、回滑和不黏等4种现象; 另外,通过调节驱动参数, 不仅可以改变箱体移动和转动的快慢,还可以改变箱体形心运动轨迹的曲率半径.     

LCP method for a planar passive dynamic walker based on an event-driven scheme

The main purpose of this paper is to present a linear complementarity problem (LCP) method for a planar passive dynamic walker with round feet based on an event-driven scheme. The passive dynamic walker is treated as a planar multi-rigid-body system. The dynamic equations of the passive dynamic walker are obtained by using Lagrange’s equations of the second kind. The normal forces and frictional forces acting on the feet of the passive walker are described based on a modified Hertz contact model and Coulomb’s law of dry friction. The state transition problem of stick-slip between feet and floor is formulated as an LCP, which is solved with an event-driven scheme. Finally, to validate the methodology, four gaits of the walker are simulated: the stance leg neither slips nor bounces; the stance leg slips without bouncing; the stance leg bounces without slipping; the walker stands after walking several steps.     

Modeling and analysis of rigid multibody systems with driving constraints and frictional translation joints

An approach is proposed for modeling and anal- yses of rigid multibody systems with frictional translation joints and driving constraints. The geometric constraints of translational joints with small clearance are treated as bilat- eral constraints by neglecting the impact between sliders and guides. Firstly, the normal forces acting on sliders, the driv- ing constraint forces （or moments） and the constraint forces of smooth revolute joints are all described by complementary conditions. The frictional contacts are characterized by a set- valued force law of Coulomb＇s dry friction. Combined with the theory of the horizontal linear complementarity problem （HLCP）, an event-driven scheme is used to detect the transi- tions of the contact situation between sliders and guides, and the stick-slip transitions of sliders, respectively. And then, all constraint forces in the system can be computed easily. Secondly, the dynamic equations of multibody systems are written at the acceleration-force level by the Lagrange multiplier technique, and the Baumgarte stabilization method is used to reduce the constraint drift. Finally, a numerical example is given to show some non-smooth dynamical behaviors of the studied system. The obtained results validate the feasibility of algorithm and the effect of constraint stabilization.     

Comparison and analysis of two Coulomb friction models on the dynamic behavior of slider-crank mechanism with a revolute clearance joint

The objective of this study is to investigate the effects of the Coulomb dry friction model versus the modified Coulomb friction model on the dynamic behavior of the slider-crank mechanism with a revolute clearance joint. The normal and tangential forces acting on the contact points between the journal and the bearing are described by using a Hertzian-based contact force model and the Coulomb friction models, respectively. The dynamic equations of the mechanism are derived based on the Lagrange equations of the first kind and the Baumgarte stabilization method. The frictional force is solved via the linear complementarity problem (LCP) algorithm and the trial-and-error algorithm. Finally, three numerical examples are given to show the influence of the two Coulomb friction models on the dynamic behavior of the mechanism. Numerical results show that due to the stick friction, the slider-crank mechanism may exhibit stick-slip motion and can balance at some special positions, while the mechanism with ideal joints cannot.     

Application of the nonsmooth dynamics approach to model and analysis of the contact-impact events in cam-follower systems

The dynamic modeling and analysis of planar rigid multibody systems that experience contact-impact events is presented and discussed throughout this work. The methodology is based on the nonsmooth dynamics approach, in which the interaction of the colliding bodies is modeled with multiple frictional unilateral constraints. Rigid multibody systems are stated as an equality of measures, which are formulated at the velocity-impulse level. The equations of motion are complemented with constitutive laws for the forces and impulses in the normal and tangential directions. In this work, the unilateral constraints are described by a set-valued force law of the type of Signorini??s condition, while the frictional contacts are characterized by a set-valued force law of the type of Coulomb??s law for dry friction. The resulting contact-impact problem is formulated and solved as an augmented Lagrangian approach, which is embedded in the Moreau time-stepping method. The effectiveness of the methodologies presented in this work is demonstrated throughout the dynamic simulation of a cam-follower system of an industrial cutting file machine.     

Formulating Three-Dimensional Contact Dynamics Problems

ABSTRACT

Complementarity formulations are a promising approach for solving dynamic multi-rigid-body contact problems. Two aspects of simulating contact in a complementarity setting are addressed here. First, an explicit formulation of the differential equations governing contact points for bodies of general surface geometry is developed. These equations may be used to integrate the contact position and to set up the basic dynamics equations. Second, an efficient method for handling frictionless planar contacts of arbitrary boundary shape is presented. Throughout, the problem is set up as explicitly as possible, with special attention being given to the way that the contact geometry is related to the dynamics.     

Numerical method for dynamics of multi-body systems with two-dimensional Coulomb dry friction and nonholonomic constraints

Based on the dynamical theory of multi-body systems with nonholonomic constraints and an algorithm for complementarity problems, a numerical method for the multi-body systems with two-dimensional Coulomb dry friction and nonholonomic constraints is presented. In particular, a wheeled multi-body system is considered. Here,the state transition of stick-slip between wheel and ground is transformed into a nonlinear complementarity problem(NCP). An iterative algorithm for solving the NCP is then presented using an event-driven method. Dynamical equations of the multi-body system with holonomic and nonholonomic constraints are given using Routh equations and a constraint stabilization method. Finally, an example is used to test the proposed numerical method. The results show some dynamical behaviors of the wheeled multi-body system and its constraint stabilization effects.     

干气密封滑动摩擦界面切向接触刚度分形模型

为揭示干气密封滑动摩擦界面高频微幅自激摩擦振动规律，用分形参数表征摩擦界面形貌特性，根据重新建立的微凸体接触变形方式，以及对非协调弹性体在切向力作用下初始滑动问题的研究，建立了干气密封滑动摩擦界面切向接触刚度分形模型. 通过数值对切向接触刚度的影响因素进行了分析，研究结果表明:切向接触刚度随分形维数、真实接触面积和材料特性系数的增大而增大；切向接触刚度随特征尺度、摩擦系数的增大逐渐减小. 相比于分形维数、特征尺度和材料特性系数对切向接触刚度的影响，摩擦系数的影响相对较小. 这些研究结果为进一步研究干气密封高频微幅自激摩擦振动奠定了基础.