Prediction and compensation of motion accuracy in a linear motion bearing table

In the present research, a corrective machining algorithm is introduced to improve the motion accuracy of linear motion bearing tables. The algorithm commences with reverse analysis, in which the rail form error is estimated from the measured linear and angular motion errors. In the next step, the rail is remachined to reduce the estimated form error. Then, the motion errors are measured again, and the procedure is repeated until the measured errors are sufficiently small. A transfer function, which represents the bearing force variation of a bearing block with respect to the spatial frequency components of the rail form error, is used to describe the characteristics of the linear motion bearings. Computations are carried out via the Hertz contact theory. From the theoretical evaluation, it is evident that the magnitude of the normalized transfer function quantitatively represents the accuracy averaging effect at each spatial frequency and that motion errors are not affected by the preload and the stiffness of the bearings. It is also clear that the algorithm can be used to estimate the equivalent rail form error in terms of motion errors. As a practical application, the algorithm is utilized to improve the motion errors of an XY table with linear motion bearings. The experimental results show that the motion accuracy of a linear motion bearing table can be improved to about 1 μm of linear motion error and about 1-2 arcsec of angular motion error by applying the proposed algorithm.