Position-dependent geometric errors measurement and identification for rotary axis of multi-axis machine tools based on optimization method using double ball bar

Abstract

Geometric errors measurement and identification for rotary table are important. However, precisely adjustment for the setup position of a double ball bar in each measurement pattern is inconvenient. This study proposes a novel optimization identification method using a double ball bar to recognize the position-dependent geometric errors (PDGEs) of rotary axis. A mathematical model for ball bar measurement is firstly constructed to map the relationship between measurement direction and position of the double ball bar. And then, the setup positions of the double ball bar for PDGEs identification are analyzed. According to analysis for setup positions of the double ball bar, simplified measurement patterns would be conducted by adjusting only two setup positions for the ball bar and thus reduce the procedure of accurate adjustment for the ball bar. The PDGEs can be fitted as an nth B-spline curve, on the account of its being smooth and continuous. To identify the PDGEs, an optimization method, by computing the suitable value of control points of nth B-spline curve of errors to minimize the optimal value of the target function between the actual measured value and the value derived from a theoretical measurement model, is proposed. Moreover, in order to obtain the accurate value of control points of the error curve, the sensitivity analysis is conducted to acquire the sensitivity matrix with respect to control points of errors. The PDGEs are able to be identified simultaneously after calculating the appropriate values of control points of errors. The proposed identification method is validated by simulation and experiment. The results prove the effectiveness of the proposed method.