Modeling and elastic deformation compensation of flexural feed drive system

This paper develops a novel interpolation algorithm to compensate the error caused by elastic deformation which can achieve higher tracking accuracy even without the signal from the linear scale on the table. First, a dynamic model which considers flexural modes of a feed drive system, servo control loops, and friction effects simultaneously is constructed. Based on the dynamic model, the equation of elastic deformation is then derived. The equation is further simplified to form a formulation in computing the deformations which is mainly caused by inertial and viscous forces during motion. Experiments and simulations are conducted to validate both dynamic model and the simplified elastic deformation equation. Based on the simplified equation, a novel elastic deformation compensation interpolation (MEDCI) algorithm is proposed to generate the modified position commands such that the tracking errors caused by elastic deformation can be reduced. Experimental results on the linear trajectory demonstrate that the proposed algorithm could reduce the maximum elastic deformation error from 23.4 μm to 6.4 μm and the root mean square (RMS) error from 19.5 μm to 3.1 μm which correspond to 84.1% and 72.6% reduction, respectively. Furthermore, the MEDCI can achieve more than 10% reduction as compared to the results in published literature.