Online Deflection Estimation of X-Axis Beam on Positioning Machine

For high-precision devices, one of the most important factors that influence their positioning accuracy is the deflection in the mechanical structures. The finite-element method (FEM) is the most common method used to investigate deflections. However, it has such a high computational complexity that it cannot be used in real-time deflection correction applications. In this paper, to improve the accuracy of a positioning machine, an online deflection estimation method that has high accuracy and low computational complexity is proposed. First, by analyzing the mechanical characteristics of the beam, the effect of the positioning head on the beam is represented by four forces located at their contact points and a deflection estimation model is developed. Then, the uncertain parameters of this estimation model are identified by the use of the deflection values obtained from the FEM analysis. The final mathematical model is seen to result in deflection values that are very close to the values obtained by FEM analysis. The applicability of this novel method is discussed and algorithms are proposed that extend the approach to other general gantry structures. Finally, the approach is successfully verified under three typical cases indicating its advantages, w.r.t. estimation accuracy and decreased computational complexity.