Analysis of circular trajectory equivalent to cone-frustum milling in five-axis machining centers using motion simulator

The present paper describes the effect of the half apex angle of the cone-frustum on the motion trajectory under simultaneous five-axis motion and the effect of the sensitive direction of the ball bar when the motion trajectory is measured along the three-dimensional circular conical path. In the present paper, simulation of the measurement by means of a ball bar instrument is mainly conducted using a motion simulator developed previously. In particular, a precise mathematical model was developed to express the pitch errors of the axes of rotation of the five-axis machining center having a tilting rotary table driven by worm gears. In the experiment and simulation, primarily the center position and half apex angle of the cone-frustum were varied. In addition, two sensitive directions of the ball bar were investigated. The motion simulator incorporating the pitch error model can express the detailed trajectories obtained by the ball bar, even if the half apex angle and center position of the cone-frustum and the sensitive direction of the ball bar were changed. Then, the influence of the frictional force of the linear axes of motion, and the backlash and pitch error of the axes of rotation on the circular trajectories were analyzed. In particular, for the case of a half apex angle of 45°, the trajectory due to the errors of the axis of rotation is strongly affected by the sensitive direction of the ball bar.

► A detailed model of the pitch errors of the axes of rotation was proposed. ► Simulation results were confirmed to be in agreement with the measured results. ► The measured result depends on the sensitive direction of the ball bar. ► For a half apex angle of 45°, the sensitive direction strongly influences result.