Mathematical Model of Feed Drive Mechanical System and Friction for CNC Machine Tools.

The response of the feed drive system consisting of a CNC controller and a feed mechanism has been simulated by using a simple mathematical model that is a single degree of freedom. However, this model has not been able to represent some behaviors. In this paper, a new model, a multi degree of freedom is proposed. The model consists of a work table, a ball screw shaft and nut, and support bearings. The experimental results demonstrate that the proposed model well expresses the actual frequency response of the work table in the feed direction. The proposed model also has a useful function that friction can be easily introduced to each mechanical component. A model representing friction is also proposed. The influence of friction can not be generally investigated in the feed drive system. The measurement of the circular movement was conducted by using a special equipment. As a result, the simulated circular trajectory was in agreement with the actual trajectory and the quadrant glitch caused by stiction was well expressed.