Generalized numerical pressure distribution model for smoothing polishing of irregular midspatial frequency errors.

The smoothing effect of the rigid lap plays an important role in controlling midspatial frequency errors (MSFRs). At present, the pressure distribution between the polishing pad and processed surface is mainly calculated by Mehta's bridging model. However, this classic model does not work for the irregular MSFR. In this paper, a generalized numerical model based on the finite element method (FEM) is proposed to solve this problem. First, the smoothing polishing (SP) process is transformed to a 3D elastic structural FEM model, and the governing matrix equation is gained. By virtue of the boundary conditions applied to the governing matrix equation, the nodal displacement vector and nodal force vector of the pad can be attained, from which the pressure distribution can be extracted. In the partial contact condition, the iterative method is needed. The algorithmic routine is shown, and the applicability of the generalized numerical model is discussed. The detailed simulation is given when the lap is in contact with the irregular surface of different morphologies. A well-designed SP experiment is conducted in our lab to verify the model. A small difference between the experimental data and simulated result shows that the model is totally practicable. The generalized numerical model is applied on a Φ500  mm parabolic surface. The calculated result and measured data after the SP process have been compared, which indicates that the model established in this paper is an effective method to predict the SP process.