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.
Trajectory planning of aspherical surfaces with appropriate cutting parameters is always a tedious task, especially on difficult-to-grind materials. Orthogonal experiments are usually designed and conducted first to get a full estimation of forces under different sets of grinding conditions (e.g. depth of cut and feeding velocity). However, all these data will change, as the grinding wheel becomes blunt. To reduce the work on the selection of grinding parameters and keep the grinding process stable, a new force-controlled grinding strategy for large optical grinding machine on brittle material is proposed. The grinding force is controlled by adjusting feeding velocity along the trajectories in real time. The grinding force model is established by analyzing the complex contact area between the arc-shaped wheel and the workpiece. The co-existing of brittle and ductile removal is also considered. For the longtime delay of the system, the controller foresees the grinding force in 0.4 s later based on the model proposed, to prevent the large overshoot of the force (up to 87.5%). The verification of the controller was conducted on silicon carbide ceramics. The force overshoot was reduced to 22.5%, and the motion accuracy was guaranteed by position servo within 5 µm. The subsurface damage along the trajectory was further analyzed and discussed.
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