含干摩擦多体系统Lagrange方程的数值算法

利用第一类Lagrange方程建立了固定约束面含干摩擦的多体系统动力学方程,将摩擦力的广义力用矩阵形式描述．利用增广法。将微分-代数方程转换成常微分方程,并用矩阵形式给出,提高了计算效率．最后用算例说明该方法的有效性．     

含摩擦滑移铰及驱动约束多刚体系统数值算法

研究了具有驱动约束及非光滑滑移铰多体系统动力学方程的建模与数值计算方法．将驱动约束视为非定常约束，非光滑滑移铰视为双边定常约束，滑移铰的摩擦模型采用库仑摩擦模型；应用第一类Lagrange方程建立系统的动力学方程，应用距离函数建立滑移铰的约束方程；将线性互补方法和Baumgarte约束稳定化方法引入，以解决滑移铰法向约束力的计算以及约束方程违约问题．最后应用曲柄摇杆机构作为算例，说明该方法的有效性．     

复杂非线性电路系统的动力学方程模型

Lagrange和Hamilton运动方程是分析力学的基本原理之一和方法论。应用Lagrange和Hamilton原理建立复杂非线性电路保守动力学方程模型是一种形式化可行的方法。对非保守的动力学系统,定义描述电路系统的荷控支路和链控支路的微观结构概念,应用Hamilton结构的方法,可以得到与La-grange结构等价的方程组;考虑大规模电路系统的复杂性,依据电路系统荷控支路和链控支路微观结构的概念,给出具有控制参量的Lagrange和Hamilton函数,以及具有相应关联矩阵和联接矩阵形式的Lagrange和Hamilton的动态方程;分析了保守和非保守复杂系统拓扑结构关系的描述和其动力学系统的建模,其建模过程具有规范性和方程具有对称性。虽然数学推导过程繁琐,但适合于计算机辅助形式化分析;基于Hamilton方法建立的电路模型为一阶微分动态方程组,特别适合进行理论分析和数值仿真计算。     

柔性机械手系统的动力学方程

本文应用动力学普遍方程,导出了单链柔性机械手系统的动力学方程;并以递推形式分析该方程的求解过程,递推的每一步只须解低维的方程组,因而便于计算.还讨论了多链柔性树状系统动力学方程的求解方案,它与单链柔性机械手系统具有相似性,便于编制程序.     

两柔性机器人协调操作的动力学模型及其逆动力学分析

柔性机器人动力学是当前机器人研究的热点,而其协调操作问题目前仍为空白．本 文首次建立了柔性机器人协调操作刚性负载的动力学模型,利用有限元法和Lagrange方程, 在柔性机器人协调操作的运动学和动力学协调约束条件基础上,推导出系统的动力学方程, 提出了其逆动力学问题的解决方案,并成功给出了平面两3R柔性臂协调操作的数值算例．     

基于Lagrange插值多项式拟合的力学系统的变分积分子

变分积分子是通过直接离散变分原理得到的一类特殊的动力学系统的数值差分格式,较之传统差分格式呈现出明显的计算优越性.由离散Euler-Lagrange方程的形式可知,变分积分子的构造过程最终归结为计算离散Lagrange函数的偏导数,其中离散Lagrange函数是Lagrange函数在单个时间步长的积分,通常由经典求积公式近似得到.根据离散Lagrange函数的积分表达式,解析计算其偏导数会随之衍生一个新的且与连续Euler-Lagrange方程密切关联的积分,因此,构造变分积分子就可以不再以通过经典求积公式得到的具体形式的离散Lagrange函数为前提,而是可以直接基于一组离散结点近似新衍生的积分.在这些离散结点处,如果进一步让系统的拟合轨迹严格满足Euler-Lagrange方程,即运动方程,那么新的积分自动为零,相应地,计算离散Lagrange函数的偏导数就简化为计算连续Lagrange函数关于速度变量的偏导数.这种新的构造方式同时结合了连续和离散的Euler-Lagrange方程,不仅让最终得到的差分格式仍然继承了变分积分子特有的优越计算性能,而且在同阶精度的情况下具有更小的局部误差.     

机器人手臂弹性动力学分析的Kane方法

本文将 Kane 动力学方法与假设模态法相结合.给出一种分析机器人手臂弹性动力学的新方法.首先基于 Kane 方法的运动学概念,并应用假设模态法建立了手臂弹性运动学.推导出完整的弹性动力学方程.并以一简例说明了其应用过程.这种方法比较简洁,兼具 Lagrange 法和 Newton-Euler 法的优点而克服了其不足,便于计算机数值分析.     

弹性细杆弯扭度有突变时的Lagrange方程

根据弹性细杆静力学的Kirchhoff动力学比拟方法,将弹性细杆截面的弯扭度和形心应变矢有突变的弹性变形比拟为动力学中的打击运动现象.分别从精确Cosserat弹性细杆和Kirchhoff弹性细杆静力学的Lagrange方程出发,导出了弯扭度和形心应变矢有突变时的Lagrange方程,其形式与打击运动的Lagrange方程形式相同.分析了弯扭度和形心应变矢的突变对挠曲线光滑性的影响.为弹性细杆弯扭度有突变时的平衡分析提供分析力学方法.     

二阶动力学系统高阶PI观测器的参数化设计方法

本文研究二阶动力学系统的高阶比例积分(PI)观测器设计问题．基于Sylvester矩阵方程的解，提出了该观测器设计的参数化方法．该参数化方法给出了该类观测器增益矩阵的参数化表达式，其所含参数除了满足两个约束条件之外是完全自由的．这些参数为控制系统设计提供了全部自由度，可通过优化等手段选择这些参数来满足某些性能要求，如干扰解耦、故障检测和鲁棒性等．此外，该PI观测器的参数化设计方法直接利用二阶动力学系统的原始参数矩阵，只涉及二阶动力学系统n维参数矩阵的运算．给出一个数值例子，以说明所提方法的简单性和有效性．     

旋转圆盘上可变摆长的单摆的分岔问题分析

讨论了旋转圆盘上可变摆长单摆模型的静态分岔问题．本文中提出的简化模型对于分析此类工程实际问题的静态分岔现象十分方便．简化模型中考虑了绳子弹性变形所引起的绳长的变化，并将绳子的轴向变形视为弹簧模型．文中采用Lagrange方程对系统进行动力学建模，计算出了系统的动能以及势能．随后采用奇异性理论方法，计算了系统平衡点的分岔情况，给出了它的范式．本文做了一些数值算例，用以说明理论的正确性．     

Modeling and simulation of longitudinal dynamics coupled with clutch engagement dynamics for ground vehicles

During the engagement of the dry clutch in automotive transmissions, clutch judder may occur. Vehicle suspension and engine mounts couple the torsional and longitudinal models, leading to oscillations of the vehicle body that are perceived by the driver as poor driving quality. This paper presents an effective formulation for the modeling and simulation of longitudinal dynamics and powertrain torsional dynamics of the vehicle based on non-smooth dynamics of multibody systems. In doing so friction forces between wheels and the road surface are modeled along with friction torque in the clutch using Coulomb’s friction law. First, bilateral constraint equations of the system are derived in Cartesian coordinates and the dynamical equations of the system are developed using the Lagrange multiplier technique. Complementary formulations are proposed to determine the state transitions from stick to slip between wheels and road surface and from the clutch. An event-driven scheme is used to represent state transition problem, which is solved as a linear complementarity problem (LCP), with Baumgarte’s stabilization method applied to reduce constraint drift. Finally, the numerical results demonstrate that the modeling technique is effective in simulating the vehicle dynamics. Using this method stick-slip transitions between driving wheel and the road surface and from the clutch, as a form of clutch judder, are demonstrated to occur periodically for certain values of the parameters of input torque from engine, and static and dynamic friction characteristics of tire/ground contact patch and clutch discs.     

Modeling and simulation of the nonsmooth planar rigid multibody systems with frictional translational joints

The main purpose of this paper is to present a modeling and simulation method for the rigid multibody system with frictional translational joints. The small clearance between a slider and guide is considered. The geometric constraints of the translational joints are treated as bilateral constraints and the impacts between sliders and guides are neglected when the clearance sizes of the translational joints are very small. The contact situations of the normal forces acting on the sliders are described by inequalities and complementarity conditions, while the frictional contacts are characterized by a set-valued force law of the type of Coulomb’s law for dry friction. The dynamic equations of the multibody systems with normal and tangential contact forces are written on the acceleration-force level using the Lagrange multiplier technique. The problem of the transitions of the contact situation of the normal forces acting on sliders and the transitions of the stick-slip of the sliders in the system is formulated as a horizontal linear complementarity problem (HLCP), which is solved by event-driven method. Baumgarte’s stabilization method is used to decrease the constraint drift. Finally, two typical mechanisms are considered as demonstrative application examples. The numerical results obtained show some dynamical behaviors of the systems with frictional translational joints and constraint stabilization effect.     

An extended divide-and-conquer algorithm for a generalized class of multibody constraints

An extension to the divide-and-conquer algorithm (DCA) is presented in this paper to model constrained multibody systems. The constraints of interest are those applied to the system due to the inverse dynamics or control laws rather than the kinematically closed loops which have been studied in the literature. These imposed constraints are often expressed in terms of the generalized coordinates and speeds. A set of unknown generalized constraint forces must be considered in the equations of motion to enforce these algebraic constraints. In this paper dynamics of this class of multibody constrained systems is formulated using a Generalized-DCA. In this scheme, introducing dynamically equivalent forcing systems, each generalized constraint force is replaced by its dynamically equivalent spatial constraint force applied from the appropriate parent body to the associated child body at the connecting joint without violating the dynamics of the original system. The handle equations of motion are then formulated considering these dynamically equivalent spatial constraint forces. These equations in the GDCA scheme are used in the assembly and disassembly processes to solve for the states of the system, as well as the generalized constraint forces and/or Lagrange multipliers.     

Comparison of two slideline methods using ADINA

Two general methods of treating sliding interface problems were implemented in ADINA. The first method uses constraint equations and is based on the work of Taylor, Hughes et al. The second method is a penalty function method where finite stiffnesses are used to simulate the contact forces. This is similar to the method used by Hallquist in NIKE2D. These may be used as notension sliding interfaces, with or without friction, or as a non-sliding interface to interpolate between different mesh regions. We briefly review the theory behind these methods and describe the implementation in ADINA. Several application problems have been run, including metal forming problems. Based on this experience the methods are compared in terms of ease of use, accuracy, reliability, influence on bandwidth, and solution time. Neither method is ideal. The penalty method is generally more efficient but may be inaccurate, whereas the constraint equations are accurate but less efficient.     

Constraint Forces and Undetermined Multipliers in Constrained Multibody Systems

This paper addresses the relation between constraining forces, constraint equations, and undetermined multipliers, used in studying constrained multibody systems. A formalism is developed establishing the undetermined multiplier method through the concept of a generalized constraint force, partial velocities, and kinematic constraint equations.     

Chain Vibration and Dynamic Stress in Three-Dimensional Multibody Tracked Vehicles

A three-dimensional computational finite element procedure for the vibration and dynamic stress analysis of the track link chains of off-road vehicles is presented in this paper. The numerical procedure developed in this investigation integrates classical constrained multibody dynamics methods with finite element capabilities. The nonlinear equations of motion of the three-dimensional tracked vehicle model in which the track link s are considered flexible bodies, are obtained using the floating frame of reference formulation. Three-dimensional contact force models are used to describe the interaction of the track chain links with the vehicle components and the ground. The dynamic equations of motion are first presented in terms of a coupled set of reference and elastic coordinates of the track links. Assuming that the structural flexibility of the track links does not have a significant effect on their overall rigid body motion as well as the vehicle dynamics, a partially linearized set of differential equations of motion of the track links is obtained. The equations associated with the rigid body motion are used to predict the generalized contact, inertia, and constraint forces associated with the deformation degrees of freedom of the track links. These forces are introduced to the track link flexibility equations which are used to calculate the deformations of the links resulting from the vehicle motion. A detailed three-dimensional finite element model of the track link is developed and utilized to predict the natural frequencies and mode shapes. The terms that represent the rigid body inertia, centrifugal and Coriolis forces in the equations of motion associated with the elastic coordinates of the track link are described in detail. A computational procedure for determining the generalized constraint forces associated with the elastic coordinates of the deformable chain links is presented. The finite element model is then used to determine the deformations of the track links resulting from the contact, inertia, and constraint forces. The results of the dynamic stress analysis of the track links are presented and the differences between these results and the results obtained by using the static stress analysis are demonstrated.     

A computer-oriented method for reducing linearized multibody system equations by incorporating constraints

Consider a spatial multibody system with rigid and elastic bodies. The bodies are linked by rigid interconnections (e.g. revolute joints) causing constraints, as well as by flexible interconnections (e.g. springs) causing applied forces. Small motions of the system with respect to a given nominal configuration can be described by linearized dynamic equations and kinematic constraint equations. We present a computer-oriented procedure which allows to develop a minimum number of these equations. There are three problems. First: algorithmic selection of position coordinates; second: condensation of the dynamic equations; third: evaluation of the constraint forces. To demonstrate the procedure, a closed loop multibody system is used as an example.