Mathematical modeling of surface roughness in magnetic abrasive finishing of BK7 optical glass.

Magnetic abrasive finishing (MAF) is one of the advanced machining processes efficiently used to finish hard-to-machine materials. Simulation and modeling of the process is of particular importance to understand the mechanics of material removal and consequently achieve a high-quality surface with a minimum of surface defects. Hence, in this paper, we performed a numerical-experimental study to mathematically model the surface roughness during the MAF of BK7 optical glass. For this purpose, the initial roughness profile was estimated using fast Fourier transform (FFT) and a Gaussian filter. We obtained the final surface profile based on the material removal mechanisms and the corresponding chipping depth values evaluated by finite element analysis. We then validated experimentally the simulation results in terms of the arithmetic average surface roughness (R(a ). The comparison between the obtained results demonstrates that the theoretical and experimental findings are in good agreement when predicting the parameters' effect on surface roughness behavior.