A systematic approach on analyzing the relationship between straightness & angular errors and guideway surface in precise linear stage

In this paper, a systematic approach on how to calculate the straightness and angular errors based on measuring guideway surface and fitting curve is introduced. Straightness and angular errors play an important role in precise system, which can undermine the system accuracy, especially in multi-axis motion structure. Conventional method adopts a periodic function to represent the guideway surface. However, for majority environments, the guideway surface curve is random depending on different machining processes. Thus, it is necessary to develop a precise method to obtain the guideway surface curve for calculating the straightness & angular errors. Instead of adopting trigonometric function to represent the guideway surface, this paper measures the guideway first. By analyzing the characteristics of machining process for guide rail, the proper characteristic functions are selected in curve fitting based on the measurement results, and an accurate analytical expression of guideway surface is obtained. Therefore, the SaA error values can be calculated with corresponding formulas based on the expression. Compared with previous method, the new approach is more accurate in curve fitting and error calculation, which can be applied in other similar environment through the same procedure. Furthermore, by analyzing the measured results of guideway surface, the new approach procedure can be regarded as a bridge between the pattern of measured guideway surface and corresponding manufacture process, which is seldom discussed in other research works. This new approach is also comprehensive and systematic in error analysis in precise linear stages, which is beneficial to derive the distribution of straightness and angular errors for engineers before installation in design part. A case study of a precise linear stage by following the procedure in the new approach is developed, and the comparison between calculation and measured results proves the validation of the new approach.