Equivalent stiffness modeling of linear motion guideways for stage systems

In this work, an 8-spring equivalent stiffness model for the linear motion (LM) guideways of a positioning stage system is studied. In the model, eight springs connect the LM block to the LM rail. The equivalent model can satisfy the static and dynamic characteristics of typical LM guideways. Based on a finite element model of an LM guideway, the static deflection and normal mode analysis of a 1-axis stage system is evaluated. The simulation results match the experimental results with more than 90% accuracy. The static deflection of a 3-axis stage is also tested. The deflection of the tool plate is measured by a coordinate measuring machine. The amount of deflection with respect to the location of the tool plate can be predicted within an error of approximately 4~6 μm.