Hierarchical error model to estimate motion error of linear motion bearing table

This study presents a general and systematic approach for motion error estimation of a linear motion bearing table based on hierarchical idea. The approach is implemented in the following four steps: (1) dividing the errors of a linear motion system into four tiers, namely Datum Tier, Guideway Tier, Slider Tier, and Table Tier; (2) measuring form errors of Guideway Tier using the proposed method that combines the displacement sensors and laser interferometer; (3) developing a map of the form errors of Guideway Tier and motion errors of Slider Tier using the Hertz contact theory and a transfer function method; and (4) formulating a map between the motion errors of Slider Tier and the error of Table Tier using a direction cosine matrix. The advantage of this approach is that it does not require the assumption that the form error phases of the two guide rails are the same, and thereby provides a more accurate model of motion error. A typical linear motion bearing table is considered as an example to illustrate the generality and effectiveness of the proposed approach.