The static and dynamic analysis of machine tools using dynamic matrix reduction technique

An approach, for condensing the system matrices of machine-tool structures, based on dynamiccondensation, is presented. The selection of the number of degrees of freedom to be retained in the condensed system, is based on the accurate representation of the first five modes of the original system. This is illustrated by an example of a lathe spindle-workpiece system. In this example, the system inertia, the damping and the stiffness matrices, which are orginally of the dimension 25×25, are condensed to a dimension of 12×12. Thus economy in the computation time and computer memory storage is realized. It is shown that this condensation technique is valid for the static case also.