计及二阶效应的刚柔耦合连杆系统动力学分析

根据虚功原理和达郎伯原理推导了计及二阶效应的柔性单元运动方程,并利用刚化条件得到了刚性梁单元运动方程,给出了刚柔耦合连杆系统动力学建模与分析的方法.对构件刚度相差悬殊的多体系统进行动力学分析时,如若当作多刚体系统分析,会因忽略弹性变形导致结果不准确；当作多柔体系统建模分析求解,则因自由度太多导致方程庞大难求解.可行的方法是:将刚性单元与柔性单元耦合建模,在多柔体系统基础上,引入刚性单元和刚性约束条件,对刚性构件自身的动力学特性进行等效,然后按照一般弹性系统有限元方法集成得到虚拟柔性系统动力学方程,建立过渡坐标与广义坐标关系,消除非独立坐标,得到真实的系统运动方程,降低系统方程维数,提高分析效率.以曲柄滑块机构为例,介绍了计及二阶效应的刚柔耦合系统动力学的建模分析过程.

Dynamical analysis on rigid-flexible-coupled connecting rod system via second-order effects

By applying the virtual work and d＇Alembert principles, a kinematical equation of flexible elements is deduced via second-order effects. Meanwhile, a kinematical equation of rigid beam elements is derived from rigid conditions. Accordingly, a dynamical modeling-analysis method is proposed for rigid-flexi- ble-coupled connecting rod systems. When a dynamical analysis is conducted on the multi-body system with significant differences among component rigidities, e. g. a multi-body rigid system is assumed, the ignorance of elastic deformations leads to inaccurate outcomes. Whilst a multi-body flexible system is supposed, the equation can scarcely be solved due to overwhelming DOFs. As such, a feasible approach, i. e. coupling between rigid and flexible elements, is proposed. Based on the multi-body flexible system, the rigid elements and constraints are introduced. In this manner, the dynamical property equivalence is first undertaken for rigid components. Then, the dynamical equation of virtual flexible system is obtained using an integrated FEM for elastic systems. Next, the relation between transition and generic coordinates is estab- lished to eliminate the dependent coordinates. Mterwards, a practical kinematical system equation is attained to reduce the equation dimension and enhance the analysis efficiency. Finally, a case study on crank sliding block is used to illustrate the dynamical modeling and analysis processes of rigid-flexible-coupled systems via second-order effects.