含摩擦柱铰链平面多体系统动力学的建模和数值方法

以含摩擦柱铰链平面多体系统为研究对象,建立其动力学方程并给出相应的数值计算方法。首先,建立了含摩擦转动柱铰链的力学模型。在此基础上,应用第一类Lagrange方程给出了该类系统的动力学方程,将Lagrange乘子与柱铰链的法向约束力建立了对应关系,并给出了柱铰链摩擦力的广义力。由于摩擦力的存在,使得该方程是关于Lagrange乘子的分段连续的非线性代数方程组,该文对此采用混合算法:对于连续段(物体相对转动的角速度不为零时),采用拟牛顿算法和龙格-库塔法求解方程;在不连续点(物体相对转动的角速度为零时),通过粒子群算法(PSO)、试算法和龙格-库塔法求解方程,克服了方程在不连续处Lagrange乘子(法向约束力)的初值不易选取的困难。最后,通过算例说明了该算法的有效性和可行性。

MODELING AND NUMERICAL ALGORITHM FOR PLANAR MULTIBODY SYSTEM WITH FRICTION ON REVOLUTE JOINTS

The modeling and numerical algorithm for a planar multi-body system with friction on revolute joints are developed.Based on the model of a revolute joint,the dynamic equations of the system are derived by the first kind of Lagrange’s equations,then the relationship between Lagrange multipliers and the normal constraint force acting on the joint is obtained and the generalized force of friction is given.For the equations are piecewise continuous nonlinear algebraic equations about Lagrange multipliers,Quasi-Newton and Runge-Kutta algorithms are used to simulate the dynamical systems during the continuous interval(the relative angular velocity of the body does not equal to zero),and Particle Swarm Optimization,the trial and error method and Runge-Kutta algorithm are applied to solve the equations at the discontinuity points(the relative angular velocity of the body equals to zero).This algorithm overcomes the difficulty of choosing the initial values of Lagrange multipliers at discontinuity points.A numerical example is provided to demonstrate the validity and feasibility of the method.