Improved analysis model for material removal mechanisms of bonnet polishing incorporating the pad wear effect

Chenchun Shi; Yunfeng Peng; Liang Hou; Zhenzhong Wang; Yinbiao Guo

doi:10.1364/AO.57.007172

Applied Optics
Vol. 57,
Issue 25,
pp. 7172-7186
(2018)
•https://doi.org/10.1364/AO.57.007172

Improved analysis model for material removal mechanisms of bonnet polishing incorporating the pad wear effect

Chenchun Shi, Yunfeng Peng, Liang Hou, Zhenzhong Wang, and Yinbiao Guo

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Chenchun Shi, Yunfeng Peng, Liang Hou, Zhenzhong Wang, and Yinbiao Guo, "Improved analysis model for material removal mechanisms of bonnet polishing incorporating the pad wear effect," Appl. Opt. 57, 7172-7186 (2018)

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Abstract

Bonnet polishing technology has been widely applied in precision optical machining. Until now, most of the research concerning the modeling for material removal mechanisms of bonnet polishing have been presented based on the well-known Preston model. However, the various parameters involved in the bonnet polishing process are not formulated into that model, such as slurry characteristics, pad properties, bonnet sizes, processing conditions, etc. Recently, several analysis models capturing those various parameters have been developed and are even capable of interpreting non-Prestonian behaviors, but the pad wear effect has still not been taken into account. Hence, the purpose of this paper is to establish an improved analysis model by incorporating the pad wear effect with the cumulative polishing time. Compared with the previous analysis model and Preston model, the predicted results of the improved analysis model are much closer to the experimental data and become more acceptable. According to the analysis of key parameters, the understanding of material removal mechanisms in bonnet polishing is further completed, and the time-dependent pad wear effect should no longer be neglected.

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Parameter	Value	Unit	References
$E$	$1 \times 10^{6}$	Pa	[27,28]
$η_{s}$	$4.3 \times 10^{7}$	$1 / m^{2}$	[29]
$v$	0.17	–	[30]
$k_{s}$	$3.33 \times 10^{- 4}$	m	[27]
$σ$	$3.03 \times 10^{- 6}$	m	[31]

Group	No.	$P_{b}$ (bar)	$h$ (mm)	$n_{1}$ (rpm)	$α$ (deg)
A	1	0.4	0.15	1200	15
	2	0.8
	3	1.2
	4	1.6
	5	2.0
B	1	1	0.1	1200	15
B	2	1	0.2	1200	15
C	1	1	0.15	300	15
	2			600
	3			900
	4			1200
	5			1500
	6			1800
D	1	1	0.15	1200	5
	2				10
	3				15
	4				20
	5				25
	6				30

Group	No.	$P (0, 0)$ (Mpa)	$U (0, 0)$ (m/s)	$d (0, 0, 0)$ (μm)	$d (0, 0, t)$ (μm)	R2
A	1	0.59	0.646	4.12	$d (t) = 4.13 - 5.68 \times 10^{- 3} t - 3.52 \times 10^{- 6} t^{2}$	0.9995
	2	0.67		3.89	$d (t) = 3.91 - 5.94 \times 10^{- 3} t - 2.67 \times 10^{- 6} t^{2}$	0.9994
	3	0.65		3.93	$d (t) = 3.94 - 5.90 \times 10^{- 3} t - 2.94 \times 10^{- 6} t^{2}$	0.9994
	4	0.76		3.73	$d (t) = 3.74 - 6.14 \times 10^{- 3} t - 2.21 \times 10^{- 6} t^{2}$	0.9993
	5	0.61		4.02	$d (t) = 4.03 - 5.80 \times 10^{- 3} t - 3.06 \times 10^{- 6} t^{2}$	0.9995
B	1	0.64	0.647	3.94	$d (t) = 3.95 - 5.90 \times 10^{- 3} t - 3.49 \times 10^{- 6} t^{2}$	0.9995
B	2	0.70	0.644	3.83	$d (t) = 3.84 - 6.00 \times 10^{- 3} t - 2.46 \times 10^{- 6} t^{2}$	0.9994
C	1	1.01	0.161	3.30	$d (t) = 3.30 - 1.44 \times 10^{- 3} t - 5.24 \times 10^{- 7} t^{2}$	1.0000
	2	1.21	0.323	3.06	$d (t) = 3.06 - 3.01 \times 10^{- 3} t - 1.62 \times 10^{- 6} t^{2}$	0.9999
	3	0.99	0.484	3.35	$d (t) = 3.36 - 4.53 \times 10^{- 3} t - 2.46 \times 10^{- 6} t^{2}$	0.9999
	4	1.02	0.646	3.32	$d (t) = 3.34 - 6.69 \times 10^{- 3} t - 2.71 \times 10^{- 7} t^{2}$	0.9988
	5	1.15	0.807	3.18	$d (t) = 3.22 - 9.59 \times 10^{- 3} t + 7.24 \times 10^{- 6} t^{2}$	0.9959
	6	1.34	0.968	2.98	$d (t) = 3.03 - 1.22 \times 10^{- 2} t + 1.64 \times 10^{- 5} t^{2}$	0.9956
D	1	1.19	0.217	3.08	$d (t) = 3.08 - 2.01 \times 10^{- 3} t - 8.76 \times 10^{- 7} t^{2}$	1.0000
	2	0.97	0.433	3.38	$d (t) = 3.38 - 3.96 \times 10^{- 3} t - 2.49 \times 10^{- 6} t^{2}$	0.9999
	3	0.70	0.646	3.83	$d (t) = 3.85 - 6.01 \times 10^{- 3} t - 2.63 \times 10^{- 6} t^{2}$	0.9994
	4	0.55	0.853	4.19	$d (t) = 4.22 - 8.47 \times 10^{- 3} t + 9.15 \times 10^{- 7} t^{2}$	0.9974
	5	0.50	1.054	4.35	$d (t) = 4.41 - 1.12 \times 10^{- 2} t + 8.31 \times 10^{- 6} t^{2}$	0.9947
	6	0.56	1.247	4.24	$d (t) = 4.31 - 1.39 \times 10^{- 2} t + 1.77 \times 10^{- 5} t^{2}$	0.9939

	CASE A	CASE B	CASE C
Contact situation
Pressure distribution

Preston model	Simple in form, but those various parameters involved in the bonnet polishing cannot be captured, thus not detailed enough. Does not take the pad wear effect with the cumulative polishing time into consideration, thus overestimates the material removal.
Previous analysis model	Various parameters involved in the bonnet polishing are considered, thus detailed. Non-Prestonian behavior can also be interpreted, but only effective when the polishing time is relatively short or the pad effect wear is almost neglected.
Improved analysis model	On the basis of the previous analysis model, and the pad wear effect with the cumulative polishing time is taken into consideration, thus, in addition to the detailed form, it is also much more general than the other two models. Moreover, the material removal decay can be modeled.

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Applied Optics