Freeform surface topography model for ultraprecision turning under the influence of various errors

Abstract

This work establishes an accurate freeform surface topography model considering geometric errors, tracking errors, and cutting forces. Regarding geometric errors, based on the theory of multibody systems and homogeneous coordinate transformation, the transfer relationship between various geometric errors and the tool error in the workpiece coordinate system is described. Using the continuous acceleration Position-Velocity-Time (PVT) interpolation method, the offset discrete points caused by geometric errors are interpolated and rediscretized, and the accurate mathematical model between the tool errors (position and posture) in the workpiece coordinate system and the topography of the freeform surface is established. Based on the model, the influence of geometric errors on the contour errors of freeform surfaces is accurately calculated, and the contribution and similarity of the effects of various geometric errors on the contour errors of freeform surfaces are analyzed. For dynamic-dependent factors, a second-order system with two degrees of freedom on the X or Z axis is established. According to the simplified result of the equivalent system, the contour error of the freeform surface caused by the tracking error and cutting force is analyzed. For the tracking error, under the condition of constant rotation velocity of the spindle, the change of the slope of the freeform surface along the circumferential direction causes the change in the velocity and acceleration of the motion axis; thus, the corresponding area of the surface has a larger contour error. For cutting force, the change of the slope of the freeform surface along the circumferential direction changes the tool working rake angle, the tool working clearance angle, and the shearing angle, resulting in a change in the cutting force. Moreover, the change of cutting speed is accompanied by the change of cutting force. An experiment verifies the effectiveness of the proposed modeling method. In addition, the modeling method provides an effective solution for the calculation of the contribution rate of different error sources to the contour error of the freeform surface.