Abstract: 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.

Key words: Dynamics, Higher dimensional matrix, NC machine tools, Transfer matrix method