A Method of Calculating Motion Error in a Linear Motion Bearing Stage

Abstract

We report a method of calculating the motion error of a linear motion bearing stage. The transfer function method, which exploits reaction forces of individual bearings, is effective for estimating motion errors; however, it requires the rail-form errors. This is not suitable for a linear motion bearing stage because obtaining the rail-form errors is not straightforward. In the method described here, we use the straightness errors of a bearing block to calculate the reaction forces on the bearing block. The reaction forces were compared with those of the transfer function method. Parallelism errors between two rails were considered, and the motion errors of the linear motion bearing stage were measured and compared with the results of the calculations, revealing good agreement.

Improvement of Position Repeatability of a Linear Stage with Yaw Minimization

“…The balls recirculate, enabling the block to perform a linear motion along the rail. The stiffness between the block and rail is analogous to a set of springs that resist external forces applied to the block in horizontal and vertical directions, as shown in Figure 3b [3][4][5][6][7][8][9][10][11][12][13][14][15].…”

“…Major studies have simplified the balls of the LM Guide, which are the most elastic parts deformed by force, to spring models. Such simplification has been used to predict the translational error motions of stages with the LM Guide rail shape error and ball stiffness [3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Linear stages for electrical test machines are designed with high acceleration and deceleration capabilities for productivity.…”

A novel error equivalence model on the kinematic error of the linear axis of high-end machine tool

“…In view of the difficulty in obtaining the geometric error of guide rail, Khim et al [15] further substituted the geometric error of guide rail with the straightness error of base, and analyzed the motion error of linear guide rail. As for the aerostatic bearings, Ekinci et al [16] proposed an equation system, aiming at investigating the relationship from the geometric errors of guideway to the motion errors of axis.…”

A Novel Error Equivalence Model on the Kinematic Error of the Linear Axis of High-End Machine Tool

“…Ma et al [13] proposed a method of combining the geometric error of rolling guide and the elastic deformation of rolling ball, aiming to study the motion error rule of slider under different working situations. Khim et al [14] In view of the difficulty in obtaining the geometric error of guide rail, Khim et al [15] further substituted the geometric error of guide rail with the straightness error of base, and analyzed the motion error of linear guide rail. As for the aerostatic bearings, Ekinci et al [16] proposed an equation system, aiming at investigating the relationship from the geometric errors of guideway to the motion errors of axis.…”