Journal Article

Optimized dwell time algorithm in magnetorheological finishing

Zheng, Ligong, Li, Longxiang, Wang, Xu, Wang, Xiaokun, Zhang, Binzhi, Bai, Yang, Hu, Haixiang, Deng, Weijie, Zhang, Xuejun

2015

Overview

An optimized dwell time algorithm for magnetorheological finishing (MRF) is discussed. Based on the D-shape of the removal function of MRF, an optimized non-negative least-squares method is introduced to get dwell time from a linear matrix equation transferred from the de-convolution operation. Moreover, one kind of general surface error map extension is developed for any shape of optics to obtain a more precise optical surface in MRF. The simulation results show that the non-negative least-squares method of the constrained generalized minimal residual (GMRES) method with adaptive Tikhonov regulation is much faster to get highly stable dwell time distribution. In combination with the general surface error map extension, the peak to valley (PV) and root mean square (RMS) of the surface error of the diameter 400 mm converge from 184.41 and 21.26 nm to 7.56 and 0.632 nm with the consistency of the edge and the aperture inside. Finally, a fabricating experiment proves the validity of the optimized algorithm. Therefore, the algorithm developed and presented in this paper can facilitate the MRF process effectively.

• Publisher: Springer London,Springer Nature B.V
• Subject: Algorithms / Apertures / CAE) and Design / Computer simulation / Computer-Aided Engineering (CAD / Convolution / Dwell time / Engineering / Errors / Industrial and Production Engineering / Least squares method / Magnetorheological fluids / Mathematical analysis / Matrix methods / Mechanical Engineering / Media Management / Original Article