机床动力学建模的拓展传递矩阵法

Extended Transfer Matrix Method for Dynamic Modeling of Machine Tools

针对现代高性能数控机床动力学建模与优化问题,提出一种适合机床动态分析的拓展传递矩阵法,该方法将机械系统划分为刚体、柔体和结合面三类元件,并以矩阵的形式给出元件数学模型。而整机的动力学模型则是由这三类元件组成的复杂网络,应用状态矢量传递思想对元件网络进行整合,最终得到用一个高维矩阵表示的整机模型,求解该高维矩阵能够方便地得到整机的动态特性。最后应用该建模方法对数控机床中一种直线电动机驱动进给功能部件进行动力学建模与分析,给出该功能部件频响函数的仿真与试验对比,并作了相应的分析。分析表明该方法对于数控机床整机的建模、动态特性分析具有很好的建模精度。该方法简化机床动力学的建模过程,更适合于工程应用。

An extended transfer matrix method （E-TMM） which is fit for dynamic analysis is proposed to meet the demand of dynamic modeling and optimization of high-performance machine tools. In E-TMM a mechanical system is divided into three types of element,rigid body,flexible body and joint. And the model of each element is described by a matrix. Thus the whole machine can be described by a complicated network of elements. By using the idea of state vector transmission,the network of elements can be deduced into a higher dimensional matrix,which is the model of the whole machine. It is convenient to get the dynamic characters of the whole machine by solving the higher dimensional matrix. As an instantiate,a linear motor driving feed unit used in machine tools is modeled by using the proposed method. Experiment verifications in frequency response functions are carried out,which indicates that the E-TMM is valid with enough accuracy in the dynamic analysis. The E-TMM simplifies the dynamic modeling process of machine tools,and it is more appropriate for engineering applications.