Mathematical model for active lap to achieve unsymmetrical fabrication

Haitao Liu; Zhige Zeng; Fan Wu; Bin Fan

doi:10.1117/12.975689

16 October 2012 Mathematical model for active lap to achieve unsymmetrical fabrication

Haitao Liu, Zhige Zeng, Fan Wu, Bin Fan

Proceedings Volume 8416, 6th International Symposium on Advanced Optical Manufacturing and Testing Technologies: Advanced Optical Manufacturing Technologies; 841622 (2012) https://doi.org/10.1117/12.975689
Event: 6th International Symposium on Advanced Optical Manufacturing and Testing Technologies (AOMATT 2012), 2012, Xiamen, China

Abstract

A new mathematical model is proposed to calculate the Material Removal (MR) on any point of the mirror’s surface during Computer Controlled Active Lap (CCAL)’s grinding and polishing. In this model, the workpiece rotation rate ω1, lap rotation rate ω₂ and the pressure P which applied on the workpiece surface by active lap are binary functions in the mirror polar coordinate system whose polar axis is from workpiece center to lap center’s initial position. The independent variables ρ and θ are the coordinates of lap center during fabrication, so the rotation rate and pressure is become to ω₁(ρ, θ), ω₂(ρ, θ) and P(ρ, θ). According to the simulation, this model can produce unsymmetrical material removal by choosing unsymmetrical ω1(ρ, θ), ω2(ρ, θ) or P(ρ, θ). This means it is possible to get the optimal ω₁, ω₂ and P functions for the demanded material removal map, and make the effects of single circle manufacture much better. This model can give active lap the unsymmetrical fabrication capability, and suitable for correcting the astigmatism or grinding off-axis aspheric surface.

Citation Download Citation

Haitao Liu, Zhige Zeng, Fan Wu, and Bin Fan "Mathematical model for active lap to achieve unsymmetrical fabrication", Proc. SPIE 8416, 6th International Symposium on Advanced Optical Manufacturing and Testing Technologies: Advanced Optical Manufacturing Technologies, 841622 (16 October 2012); https://doi.org/10.1117/12.975689

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