Theoretical Analysis and Experimental Study of Material Removal Characteristics in Bonnet Tool Polishing Process

Abstract

To achieve ultra-precision optical elements, this paper research on removal-function of bonnet tool polishing from the theoretical and experimental aspects. Firstly, based on the principle of bonnet tool polishing, we calculate the velocity distribution through the geometric relationship, the pressure distribution through finite element model. Then, according to Preston formula, the removal function model is built. Finally, experimental system of bonnet tool polishing is built to accomplish removal-function experiment. And the experimental result indicates that removal-function model is reliable.

An adaptive bonnet polishing approach based on dual-mode contact depth TIF

“…The non-negative least square method is used to expand the 2-dimension convolution between the removal function and dwell time into a matrix equation [14]. Each line is equivalent to a linear constraint, and the objective function is nonlinear:…”

“…With the removal function moving on the surface of workpiece, if the removal amount of each point on the workpiece surface is added up, the total material removal amount of the whole surface can be calculated [11]. According to this differential idea, the removal function of the polishing tool is differentiated to 𝛿𝛼, the dwell time function of the workpiece surface is differentiated to 𝛿𝛽 , the removal amount of the area scanned by the polishing tool is superimposed in infinite differential elements [12]: (13) When 𝛿𝛼, 𝛿𝛽 ∝ 0，𝛿𝛼, 𝛿𝛽 can be infinitely reduced to area microelement 𝑑𝛼, 𝑑𝛽： (14) The total material removal amount of the workpiece surface is regarded as 2-dimension spatial convolution of the removal function 𝑅(𝑥, 𝑦) and dwell time 𝐷(𝑥, 𝑦) [13]: (15) With certain removal function 𝑅(𝑥, 𝑦) related to TIF and total material removal amount 𝐻(𝑥, 𝑦), the aim of BP dwell time algorithms is to figure out dwell time distribution 𝐷(𝑥, 𝑦) on each dwell point during processing.…”