Nanofinishing of BK7 glass using a magnetorheological solid rotating core tool

Sumit Kumar; Anant Kumar Singh

doi:10.1364/AO.57.000942

Applied Optics
Vol. 57,
Issue 4,
pp. 942-951
(2018)
•https://doi.org/10.1364/AO.57.000942

Nanofinishing of BK7 glass using a magnetorheological solid rotating core tool

Sumit Kumar and Anant Kumar Singh

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Sumit Kumar and Anant Kumar Singh, "Nanofinishing of BK7 glass using a magnetorheological solid rotating core tool," Appl. Opt. 57, 942-951 (2018)

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Abstract

Surface finishing is a promising method to improve the optical characteristics of crown glass. BK7 finds its applications in transmissive optics, i.e., lenses of binoculars, lenses of microscopes, lenses of telescopes, and light-emitting diodes. The magnetorheological (MR) nanofinishing of optical glasses using a solid rotating core tool is found more advantageous than the other advanced finishing processes in aspects such as precision and accuracy. In the present research, the MR nanofinishing with a solid rotating core tool is carried out on the BK7 glass of size $10 \times 10 \times 3 mm$ . Response surface methodology is conducted in order to find the optimum process parameters. The effects of process parameters on the percentage change in surface roughness are analyzed. The best surface roughness $R_{a}$ and $R_{q}$ values are achieved at 22 nm and 32 nm from the initial of 41 nm and 57 nm in 30 min of the finishing time cycle. To study the surface morphology of nanofinished BK7 glass, scanning electron microscopy is performed with sputter coating of gold on a glass specimen.

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Parameter	Units	Low Actual	High Actual
${CeO}_{2}$ abrasives (P)	Vol. %	5.00	15.00
Magnetizing current (M)	Amp	1.00	3.00
Rotational speed of solid rotating core tool (S)	rpm	300.00	500.00
Working gap (R)	mm	0.60	1.00

Std. Order	Factors				Initial Average Roughness Value (μm) $R_{a i}$	After Finishing Average Roughness Value (μm) $R_{a f}$	% Change in Roughness Values ( $% Δ R_{a}$ )
Std. Order	P	M	S	R	Initial Average Roughness Value (μm) $R_{a i}$	After Finishing Average Roughness Value (μm) $R_{a f}$	% Change in Roughness Values ( $% Δ R_{a}$ )
1	5	1	500	0.6	0.041	0.028	30.151
2	5	1	300	0.6	0.041	0.027	32.221
3	15	3	500	0.6	0.041	0.023	43.191
4	5	3	500	0.6	0.041	0.027	33.526
5	15	3	300	0.6	0.041	0.022	46.062
6	10	2	400	0.6	0.041	0.026	34.887
7	5	1	300	1	0.041	0.028	29.706
8	10	1	400	0.8	0.041	0.028	30.001
9	15	1	500	0.6	0.041	0.027	33.101
10	10	2	400	0.8	0.041	0.027	32.682
11	10	2	500	0.8	0.041	0.027	33.599
12	10	2	400	0.8	0.041	0.027	32.382
13	15	1	500	1	0.041	0.030	26.332
14	5	3	300	1	0.041	0.027	32.371
15	10	3	400	0.8	0.041	0.026	35.497
16	5	3	500	1	0.041	0.033	18.541
17	10	2	300	0.8	0.041	0.025	36.805
18	15	3	300	1	0.041	0.025	36.763
19	15	1	300	0.6	0.041	0.026	35.004
20	15	3	500	1	0.041	0.030	25.188
21	10	2	400	0.8	0.041	0.027	32.112
22	10	2	400	0.8	0.041	0.027	32.782
23	5	1	500	1	0.041	0.031	22.886
24	10	2	400	0.8	0.041	0.027	32.882
25	10	2	400	1	0.041	0.031	22.054
26	15	2	400	0.8	0.041	0.026	34.885
27	5	3	300	0.6	0.041	0.022	46.069
28	10	2	400	0.8	0.041	0.026	34.899
29	5	2	400	0.8	0.041	0.028	30.536
30	15	1	300	1	0.041	0.028	30.184

Source		Sum of Squares	DOF^a	Mean Square	F-value	$Prob > F$	Remark
Model		1030.93	10	103.09	48.76	$< 0.0001$	Significant
	P	66.91	1	66.91	31.64	$< 0.0001$
	M	125.99	1	125.99	59.59	$< 0.0001$
	S	191.23	1	191.23	90.44	$< 0.0001$
	R	451.87	1	451.87	213.71	$< 0.0001$
	$S^{2}$	36.43	1	36.43	17.23	0.0005
	$R^{2}$	41.70	1	41.70	19.72	0.0003
	PS	14.18	1	14.18	6.71	0.0180
	MS	42.82	1	42.82	20.25	0.0002
	MR	74.89	1	74.89	35.42	$< 0.0001$
	SR	17.41	1	17.41	8.233	0.0098
Residual		40.17	19	2.11			Not significant
Lack of fit		35.25	14	2.52	2.55	0.1535
Pure error		4.93	5	0.99

Std. Dev.	1.45	$R^{2}$	0.9625
Mean	32.58	Adj $R^{2}$	0.9428
C.V.	4.46	Pred $R^{2}$	0.8709
PRESS	138.27	Adeq precision	31.739

Source	Sum of Squares	Percentage Contribution
P	66.91	6.26
M	125.99	11.79
S	191.23	17.89
R	451.87	42.29
$S^{2}$	36.43	3.40
$R^{2}$	41.70	3.90
PS	14.18	1.32
MS	42.82	4.01
MR	74.89	7.01
SR	17.41	1.63
Pure error	4.93	0.46

S. no.	Experimental Conditions				Experimental Values of $% Δ R_{a}$	Predicted Values of $% Δ R_{a}$	% Error
S. no.	P	M	S	R	Experimental Values of $% Δ R_{a}$	Predicted Values of $% Δ R_{a}$	% Error
1	10	2	400	0.8	32.5	32.71	+0.21
2	15	2	500	0.6	38.8	38.15	−0.65
3	10	3	400	0.8	35.9	35.36	−0.54
4	5	1	300	1	30	28.67	−1.33
5	15	3	500	1	24	24.89	+0.89

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Applied Optics