不同广义坐标动力学建模方法及应用

Dynamics modeling methods and applications based on different generalized coordinate

为快速搭建多部件机械结构的动力学模型,分析了两种不同广义坐标对建模过程的影响,并对两种动力学模型进行了一致性验证。为简化刚度矩阵形式,采用相对坐标为广义自由度建立直线进给系统和机床整机动力学模型,并基于固有频率对模型的可靠性进行验证。结果证明,两种建模思路得到的动力学模型在形式上有所不同,但具有结果一致性;所建立的整机动力学模型能够很好的预测系统的首阶固有频率,与实测值误差为3.16%,可以充当低阶固有频率优化的便捷模型,快速的完成质量及刚度优化及分配。

It is of great importance,dynamic modeling and analysis,for structural design and performance analysis of mechanical systems.The adoption of convenient dynamic modeling methods and ideas can quickly build the system dynamics model and provide a foundation for the subsequent research.In order to build the dynamic model of multi-component mechanical structure quickly,the influences of two kind of different generalized coordinates on the modeling process was analyzed,and the consistency of the two dynamic models was verified.In order to simplify the stiffness matrix form,the linear feed system and the machine tool dynamic model were established with the relative coordinates as the generalized degrees of freedom,and the reliability of the model was verified based on the natural frequency.The results show that the dynamic models obtained by the two modeling ideas are different in form,but the results are consistent.The dynamic model of the whole machine can well predict the first natural frequency of the system,with an error of 3.16%compared with the measured value.It can serve as a convenient model for the optimization of low-order natural frequency,and can quickly complete the optimization and allocation of mass and stiffness.