Matrix perturbation method for predicting dynamic modal shapes of the workpiece in high-speed machining

Machining is a material removal process that changes the dynamic properties during machining operations. The variations in the dynamic properties of the workpiece have all important effect oil the integrated machining system dynamics which determines the stability of the system. This paper presents the matrix perturbation method for analytical prediction of the dynamic modal shape of the workpiece in high-speed machining. A finite element model of the workpiece is developed first. Based oil the finite element model, the matrix perturbation method is adopted to compute the modal shapes of the workpiece at different machining stages, which are reasonable-approximation modal shapes of the real workpiece. In order to validate the proposed method, numerical simulation and hammer impact experiments of thin-walled workpieces at different machining stages are conducted, and the experimentally measured modal frequencies are compared with the present analytical method.