含有随机参数的机械多体系统动力学建模与仿真

在工程中,机械多体系统的参数往往具有不确定性,如设计公差、制造和装配误差、磨损等因素导致零件的几何尺寸具有随机性;工作温度的影响使得弹性模量、泊松比等参数产生变异.传统的多体系统动力学研究往往忽略了参数的随机性,因此存在局限性.文章基于Kane方程,采用随机理论处理参数的不确定性问题,讨论了含随机参数的多体系统建模问题;并采用Monte-Carlo方法进行解算,最终得到统计意义上的结果.对一含随机参数的柔性机械臂进行了仿真计算,验证了本方法的正确性和有效性.

Dynamic Modeling and Simulation of Mechanical Multibody Systems with Probabilistic Parameters

In engineering, uncertain characteristics exist in nearly all the mechanical multibody systems. The dynamic parameters of mechanical parts such as dimension, Young's Modulus, density, Poisson's ratio etc is usually probabilistic due to design tolerance, assembly errors, wear and operating temperature. Previous modeling methods of mechanical multibody systems usually ignored the probabilistic characteristics of the dynamic parameters. So they have some limitations. In this paper probabilistic parameters are considered in modeling and simulating of mechanical multibody systems and they are treated as probabilistic variables, probabilistic process and probabilistic fields respectively. Thus the responses of the mechanical system are also probabilistic ones. Based on Kane equation and Monte-Carlo method, computer code called XJ-MBS is developed to simulate general mechanical multibody systems with probabilistic parameters. The simulation results are expressed in statistic. As an illustrative example, a flexible mechanical arm with probabilistic parameters is simulated by XJ-MBS and some useful results were obtained. The accuracy and validity of the theory presented in the paper is proved.