Abstract: Repeatability is an essential index for judging the moving accuracy and stability. A precise linear stage widely used in precise/super-precision engineering region is analyzed, and a series of researches are proposed to solve these problems including repeatability characterization unclearly and error compensation inaccurately. Firstly, the structure of precise linear stage is analyzed, and sensitive error terms are developed; secondly, the equivalent stiffness of the bearing-screw joint, the equivalent stiffness of the screw nut pair, the equivalent friction of the screw nut pair and the equivalent friction of the linear guides are calculated, respectively. The micro-dynamics of precise linear stage (<0.1 mm) is analyzed, and the dynamic equation of the precise linear stage is established. Finally, a comprehensive error model for repeatability of precise linear stage is established, and the distribution characteristic of repeatability based on statistics is computed. A series of measurement experiments are proposed in different displacement scales (10 mm, 0.1 mm, 0.01 mm). The width of repeatability is in coincidence with theoretical value in full stroke, which means the values of repeatability are not related to displacement. The relationships of displacement-time and velocity-time have the same trend with simulated results. in micro-scale displacement, and the error model accuracy is proved. By changing the material property, the value of repeatability is closed to predicted value, and the results are better than former stage, so that the error model can be adopted in repeatability prediction and compensation. This method has significantly meaning for repeatability improvement in micro displacement scale of precise linear stage.

Key words: precise linear stage, repeated positioning accuracy, dynamic, stiffness, friction