Removal Function Library for Spherical Polishing Tools Based on Super-Gaussian Function

Zirong Xu; Qitai Huang; Jianfeng Ren

doi:10.3788/LOP240764

Laser & Optoelectronics Progress, Volume. 61, Issue 17, 1714009(2024)

Removal Function Library for Spherical Polishing Tools Based on Super-Gaussian Function

Zirong Xu^1,2, Qitai Huang^1,2、*, and Jianfeng Ren^1,2

Author Affiliations

¹School of Optoelectronic Science and Engineering, Soochow University, Suzhou 215006, Jiangsu, China

²Key Lab of Advanced Optical Manufacturing Technologies of Jiangsu Province, Suzhou 215006, Jiangsu, China

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Figures & Tables(12)

Fig. 1. Flexible spherical polishing. (a) Schematic of continuous precession; (b) schematic of four-step discrete precession

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Fig. 2. Flow chart of removal function library model building

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Fig. 3. Physical image of fixed-point polishing device

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Fig. 4. Removal function of four-step discrete precession. (a) θ=30°; (b) θ=25°; (c) θ=20°; (d) θ=15°

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Fig. 5. Comparison of cross-section of removal function fitting data at different speeds with $θ = 20 °$ . (a) F=12 N; (b) F=10 N; (c) F=8 N; (d) F=6 N; (e) F=4 N

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Fig. 6. Comparison of cross-section of removal function fitting data at different precession angles with $F = 12 N$ .（a）S=600 r/min；（b）S=480 r/min；（c）S=360 r/min；（d）S=240 r/min

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Fig. 7. Correspondence between (a) parameter A, (b) parameter B, and three polishing parameters

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Fig. 8. Comparison of cross-section of experimental and predicted data

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Table 1. Experimental parameters of fixed-point polishing

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Table 1. Experimental parameters of fixed-point polishing

Experimental parameter	Value
Tool radius /mm	20
Shore hardness of tool /HA	40
Dwell time /s	4×20
Polishing fluid proportion	CeO₂ 1∶8
Polishing powder size /μm	3
Material	K9
Precession angle θ /（°）	30，25，20，15
Pressure F /N	12，10，8，6，4
Speed S /（r/min）	600，480，360，240
Detection instrument	ZYGO interferometer

Table 2. Statistics of goodness of fit
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Table 2. Statistics of goodness of fit
R² ≥0.99 0.98‒0.99 0.97‒0.98 0.96‒0.97
Number 54 20 3 3

Table 3. Relationship between fitting parameters and polishing parameters
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Table 3. Relationship between fitting parameters and polishing parameters
Parameter Precession angle θ Pressure F Speed S
A Nonlinear and monotonous Non-monotonous Nonlinear and monotonous
B Non-monotonous Monotonous No significant correlation

Table 4. Removal function prediction error

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Table 4. Removal function prediction error

No.	［α n F］	A	B	Relative error /%	R²
1	［22.5° 450 r/min 11 N］	0.9015	-3.4856×10^-4	5.27	0.9954
2	［22.5° 450 r/min 7 N］	0.8912	-0.0011	4.94	0.9962
3	［27.5° 570 r/min 9 N］	1.1972	-3.8419×10^-4	6.44	0.9938
4	［27.5° 300 r/min 5 N］	0.6400	-0.0018	5.49	0.9962

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Zirong Xu, Qitai Huang, Jianfeng Ren. Removal Function Library for Spherical Polishing Tools Based on Super-Gaussian Function[J]. Laser & Optoelectronics Progress, 2024, 61(17): 1714009

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