Analysis of Three-Dimensional Circular Motion Trajectories of Five-Axis Machining Centres Simulating Cone-Frustum Cutting

Abstract

In the present paper, a mathematical model was developed to represent the pitch error of the axes of rotation of five-axis machining centers having a tilting rotary table. The parameters used in the model were determined based on data measured for simultaneous three-axis motion. In experiments and simulations, the center offset and half apex angle of the cone-frustum are varied. In addition, the sensitive direction of the ball bar is varied to be either perpendicular to the conical surface or parallel to the bottom surface of the cone frustum. The simulation results obtained for different half apex angles, center positions of the cone-frustum, and sensitive directions of the ball bar are in good agreement with the experimental data. Then, the effects of the friction torque of the linear axes and the backlash and pitch error of the axes of rotation are simulated in order to analyze the experimentally obtained circular trajectories. When the center position of the cone-frustum is located far from the center line of the axis of rotation in the Y direction, the circular trajectory is affected by the sensitive direction of the ball bar and the half apex angle of the cone-frustum. In particular, for the case of a half apex angle of 45 degrees, the trajectory is strongly affected by the errors of the axis of rotation.