The present paper describes the sensitivity coefficient of measurement in the three-dimensional circular interpolation movement that is equivalent to cone-frustum cutting in five-axis machining centers with a tilting rotary table. The sensitive direction of a ball bar having a one-dimensional displacement sensor is parallel to its telescopic bar. In the present paper, the ratio of the measurement value to the actual error is defined as the sensitivity coefficient of measurement. The sensitivity coefficient of each axis is calculated by changing the apex angle and location of the cone-frustum. Different trajectories are obtained according to the attitude of the ball bar. This is due to the resulting variation in the sensitivity coefficient of the ball bar. If the ball bar is set parallel to the base circle of the cone-frustum, and if the center of the cone-frustum is positioned away from the centerline of the rotary table (in the positive direction of the linear axis that is perpendicular to the tilting axis of the table), the trajectory can be obtained appropriately.

NC data for machining the cone-frustum by means of five-axis machining centers with a tilting rotary table are analyzed in detail. The cone-frustum is machined by using a milling cutter at simultaneous five-axis control for inspecting the machining accuracy. However, the NC data have to be changed corresponding to the setting position of the workpiece on the rotary table. Thus, the moving range and velocity of each axis are analyzed by changing the apex angle and center position of the cone. It is found from the analyzed results that the larger apex angle gives the larger moving range and the higher velocity to all axes. When the center position moves along the Y-direction, every reversal point independently appears on a circular path. Therefore, it is recommended to offset the center position of the cone frustum along Y-direction to give the large moving ranges and the high velocities to the axes.

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

Influence oftest conditions on motion trajectories of three −dime 皿 sio 衂 circular interpo 且 ation in 5 −axis Machining Centers