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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. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a dynamics-based interpolator with real-time look-ahead (DBLA) algorithm is proposed to generate a smooth and jerk-limited acceleration/deceleration (ACC/DEC) feedrate profile. The interpolator consists of three modules: geometric, dynamics-based, and jerk-limited modules. The geometric module can detect the local maximum/minimum (max/min) curvatures, and divide a NURBS curve into small segments according to the information of sharp corners. The feedrates at the sharp corners are determined based on confined chord errors and curvatures of the curve. The dynamics-based module utilizes a dynamics feedrate modification equation (DFME) to estimate contour errors at the sharp corners and adjusts the feedrates at the locations of the sharp corners. The jerk-limited module plans the feedrate profile of the curve according to the segments’ length and the given jerk limit. Simulations are performed to verify real-time performance of the look-ahead algorithm. Experiments using a PC-based motion controller and an X–Y table are conducted to demonstrate that high-accuracy can be achieved with the proposed dynamics-based interpolator as compared to the adaptive-feedrate and the curvature-based feedrate interpolation algorithms. [Copyright &y& Elsevier]