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

Area of Science:

• Optical Engineering
• Materials Science
• Computational Mechanics

Background:

• Midspatial frequency errors (MSFRs) are critical in optical surface finishing.
• Mehta's bridging model is insufficient for irregular surfaces.
• Accurate pressure distribution prediction is key to controlling MSFRs.

Purpose of the Study:

• To develop a generalized numerical model for predicting pressure distribution in smoothing polishing (SP).
• To overcome limitations of existing models for irregular surfaces.
• To enhance control over MSFRs.

Main Methods:

• A 3D elastic structural finite element method (FEM) model was developed for the SP process.
• Governing matrix equations were derived and solved using boundary conditions.
• Iterative methods were employed for partial contact conditions.

Main Results:

• The generalized FEM model accurately predicts pressure distribution for various irregular surface morphologies.
• Simulations showed good agreement with experimental data, validating the model's practicability.
• The model effectively predicted the SP process on a large parabolic surface.

Conclusions:

• The proposed generalized numerical model is an effective tool for predicting SP processes.
• This FEM-based approach offers improved control over MSFRs.
• The model has practical applications in finishing complex optical surfaces.