Predictive Modeling of Grinding Force Considering Wheel Deformation for Toric Fewer-Axis Grinding of Large Complex Optical Mirrors

Fewer-axis ultraprecision grinding has been recognized as an important means for manufacturing large complex optical mirrors. The research on grinding force is critical to obtaining a mirror with a high surface accuracy and a low subsurface damage. In this paper, a unified 3D geometric model of toric wheel–workpiece contact area and its boundaries are established based on the local geometric properties of the wheel and the workpiece at the grinding point (GP). Moreover, the discrete wheel deformation is calculated with linear superposition of force-induced deformations of single grit, resolving the difficulties of applying Hertz contact theory to irregular contact area. The new deformed wheel surface is then obtained by using the least squares method. Based on the force distribution within the contact area and the coupled relationship between grinding force and wheel deformation, the specific grinding energy and the final predicted grinding force are obtained iteratively. Finally, the proposed methods are validated through grinding experiments.