柔性机械系统动力学的变形耦合方法

采用弹性广义坐标耦合形式描述柔性构件的变形场 ,引入非线性位移 -应变关系确定新的形函数 ,使柔性体广义变形坐标 -应变成为线性关系 ,采用这种线性形式描述柔性体的应变能。将含变形广义坐标二阶项保留到求出偏 (角 )速度后再线性化 ,根据Kane方程建立了基于小变形的柔性机械系统动力学一致线性化模型。对含柔性梁的急回机构动力学进行了仿真研究。仿真结果表明曲柄在一些特定转速下 ,柔性梁出现失稳 ;在某些转速时 ,柔性梁动响应具有拍频特征。

DEFORMATION-COUPLING MODELING METHOD FOR DYNAMICS OF FLEXBLE MECHANICAL SYSTEMS

Coupling terms of elastic general coordinates are employed to describe a deformation field of a flexible body in order to obtain the consistent linearization dynamic model of flexible mechanical systems. Nonlinear strain-displacement relations of the flexible body are introduced to determine new mode functions, and an approximate linear relation between general deformation coordinates and strains of the body is obtained. So the strain energy of the flexible body can be given by using the conventional linear strain-displacement relation. The nonlinear terms of deformation coordinates in kinematic analysis can be linearized until partial velocities and partial angular ones are given. A consistent linearization dynamic model of the systems is developed by using Kane's equation. Dynamic responses of a flexible beam in a quick return mechanism are studied by using the model. Simulating results show that the behaviors of the beam are unstable at the certain angular velocities of the rigid crank, and an interesting periodic pattern is observed for some cases.