Dynamic approximation method for removal function size in magnetorheological finishing

In magnetorheological finishing (MRF), predicting the size of a removal function plays an important role in determining the efficiency of optical material removal. The size of the removal function can be adjusted for different immersion depths of optical parts into the MRF ribbon, which enables the development of multiple MRF-processing algorithms: dwell-time calculation, path planning, or dynamic control of MRF instruments. However, few methods for such algorithms have been developed to dynamically approximate the size of removal functions with respect to various immersion depths. Thus, the ability to dynamically approximate the size of the MRF removal function is indeed of significance. A dynamic approximation method is designed after analyzing the generation mechanism of removal function and its size; establishing the equations for size, which are further numerically analyzed and simplified for common MRF configurations; and approximating the length and width of removal function dynamically. The approximation accuracy is verified through experimental tests where UBK7 optical parts are polished on a PKC1000-Q2 MRF installation. It is revealed that the approximation errors for the length and width are less than 6% and 8%, respectively.