Nano-finishing of BK7 optical glass using magnetic abrasive finishing process

Farzad Pashmforoush; Abdolreza Rahimi

doi:10.1364/AO.54.002199

Applied Optics
Vol. 54,
Issue 9,
pp. 2199-2207
(2015)
•https://doi.org/10.1364/AO.54.002199

Nano-finishing of BK7 optical glass using magnetic abrasive finishing process

Farzad Pashmforoush and Abdolreza Rahimi

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Farzad Pashmforoush and Abdolreza Rahimi, "Nano-finishing of BK7 optical glass using magnetic abrasive finishing process," Appl. Opt. 54, 2199-2207 (2015)

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Abstract

BK7 is an optical glass extensively used in lens manufacturing. In this work, magnetic abrasive finishing (MAF) method was utilized for finishing of this hard-to-machine material and the effect of various process parameters on surface roughness was investigated using response surface methodology. The best surface roughness value achieved was 23 nm. Among various finishing parameters, the abrasive size was found to be the most significant parameter followed by machining gap, magnetic particles size, rotational speed, and percentage weight of binding agent. Also, the mechanisms of material removal were studied by using atomic force microscopy (AFM). The AFM observations revealed that both microcutting and microfracture mechanisms might exist during MAF of brittle materials depending on the finishing conditions.

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Process Parameters	Levels
Process Parameters	Low	Medium	High
Machining gap (mm)	1	1.5	2
Rotational speed (rpm)	800	1000	1250
Abrasive size (μm)	1	5	10
MAP size (μm)	50	75	100
Percentage by weight of glass binder	25	30	35

Standard Order	Machining Gap (mm)	Rotational Speed (rpm)	Abrasive Size (μm)	MAP Size (μm)	Percentage by Weight of Binder	Initial Roughness (nm)	Final Roughness (nm)	% $Δ Ra$	% $Δ \dot{R} a$ ( $\min^{- 1}$ )
1	1	800	1	50	25	205	87	57.561	2.878
2	2	800	1	50	25	196	112	42.857	2.143
3	1	1250	1	50	25	183	76	58.469	2.923
4	2	1250	1	50	25	162	101	37.654	1.883
5	1	800	10	50	25	218	116	46.789	2.339
6	2	800	10	50	25	144	118	18.055	0.903
7	1	1250	10	50	25	155	96	38.064	1.903
8	2	1250	10	50	25	220	133	39.545	1.977
9	1	800	1	100	25	225	104	53.778	2.688
10	2	800	1	100	25	193	159	17.616	0.880
11	1	1250	1	100	25	181	140	22.652	1.132
12	2	1250	1	100	25	178	77	56.741	2.837
13	1	800	10	100	25	221	161	27.149	1.357
14	2	800	10	100	25	201	194	3.482	0.174
15	1	1250	10	100	25	211	148	29.858	1.493
16	2	1250	10	100	25	208	188	9.615	0.480
17	1	800	1	50	35	201	109	45.771	2.288
18	2	800	1	50	35	134	110	17.910	0.895
19	1	1250	1	50	35	122	96	21.311	1.065
20	2	1250	1	50	35	121	73	39.669	1.983
21	1	800	10	50	35	166	150	9.638	0.482
22	2	800	10	50	35	180	156	13.333	0.666
23	1	1250	10	50	35	243	122	49.794	2.489
24	2	1250	10	50	35	179	110	38.547	1.927
25	1	800	1	100	35	209	128	38.756	1.938
26	2	800	1	100	35	192	142	26.042	1.302
27	1	1250	1	100	35	203	128	36.946	1.847
28	2	1250	1	100	35	187	94	49.733	2.486
29	1	800	10	100	35	233	188	19.313	0.965
30	2	800	10	100	35	197	187	5.076	0.254
31	1	1250	10	100	35	229	176	23.144	1.157
32	2	1250	10	100	35	231	192	16.883	0.844
33	1	1000	5	75	30	183	79	56.831	2.841
34	2	1000	5	75	30	133	87	34.586	1.729
35	1.5	800	5	75	30	176	36	79.545	3.977
36	1.5	1250	5	75	30	162	23	85.802	4.290
37	1.5	1000	1	75	30	224	92	58.928	2.946
38	1.5	1000	10	75	30	144	101	29.861	1.493
39	1.5	1000	5	50	30	173	41	76.300	3.815
40	1.5	1000	5	100	30	164	72	56.097	2.805
41	1.5	1000	5	75	25	198	42	78.788	3.939
42	1.5	1000	5	75	35	155	53	65.806	3.290
43	1.5	1000	5	75	30	191	32	83.246	4.162
44	1.5	1000	5	75	30	190	36	81.053	4.052
45	1.5	1000	5	75	30	201	40	80.099	4.005
46	1.5	1000	5	75	30	192	38	80.208	4.010
47	1.5	1000	5	75	30	178	32	82.022	4.101
48	1.5	1000	5	75	30	169	30	82.248	4.112
49	1.5	1000	5	75	30	191	36	81.152	4.057
50	1.5	1000	5	75	30	206	39	81.068	4.053

Sequential Model Sum of Squares
Source	Sum of Squares	Degrees of Freedom	Mean Square	$F$ -Value	$p$ -Value	Remark
Mean versus total	261.15	1	261.15
Linear versus mean	12.86	5	2.57	1.78	0.1374
2FI versus linear	5.36	10	0.54	0.31	0.9727
Quadratic versus 2FI	51.16	5	10.23	41.33	$< 0.0001$	Suggested
Cubic versus quadratic	3.40	15	0.23	0.84	0.6290
Residual	3.78	14	0.27
Total	337.71	50	6.75
Model Summary Statistics
Source	Standard Deviation	$R^{2}$	$R^{2}$		Remark
Linear	1.20	0.1680	0.0735
2FI	1.31	0.2380	$- 0.0982$
Quadratic	0.5	0.9062	0.8416		Suggested
Qubic	0.52	0.9507	0.8274

Source	Sum of Squares	Df	$F$ -Value	$p$ -Value
Model	69.38	20	14.01	$< 0.0001$
A, machining gap	2.07	1	8.35	0.0072
B, rotational speed	1.29	1	5.20	0.0301
C, abrasive size	5.11	1	20.65	$< 0.0001$
D, MAP size	1.86	1	7.53	0.0103
E, percentage weight	1.06	1	4.29	0.0473
AB	2.10	1	8.48	0.0069
AC	0.2	1	0.82	0.3731
AD	0.014	1	0.057	0.8132
AE	0.4	1	1.60	0.2155
BC	0.52	1	2.09	0.1586
BD	0.019	1	0.076	0.7851
BE	0.45	1	1.80	0.1904
CD	0.75	1	3.10	0.0890
CE	0.095	1	0.39	0.5396
DE	0.75	1	3.02	0.0922
$A^{2}$	4.04	1	16.31	0.0004
$B^{2}$	0.75	1	3.02	0.0927
$C^{2}$	4.17	1	16.84	0.0003
$D^{2}$	0.16	1	0.64	0.4298
$E^{2}$	0.006376	1	0.027	0.8717
$R^{2}$ , 0.9062; adjusted $R^{2}$ , 0.8416

Source	Sum of Squares	Df	$F$ Value	$p$ -value
Model	65.33	20	29.81	$< 0.0001$
A, machining gap	2.06	1	7.52	0.0090
B, rotational speed	1.34	1	4.89	0.0327
C, abrasive size	5.13	1	18.74	$< 0.0001$
D, MAP size	1.84	1	6.73	0.0131
E, percentage weight	1.08	1	3.93	0.0542
AB	2.10	1	7.65	0.0085
$A^{2}$	4.57	1	16.67	0.0002
$C^{2}$	4.74	1	17.32	0.0002
$R^{2}$ , 0.8533; adjusted $R^{2}$ , 0.8247

Abstract

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Applied Optics