Towards predicting removal rate and surface roughness during grinding of optical materials

Tayyab Suratwala; Rusty Steele; Lana Wong; Phil Miller; Eyal Feigenbaum; Nan Shen; Nathan Ray; Michael Feit

doi:10.1364/AO.58.002490

Applied Optics
Vol. 58,
Issue 10,
pp. 2490-2499
(2019)
•https://doi.org/10.1364/AO.58.002490

Towards predicting removal rate and surface roughness during grinding of optical materials

Tayyab Suratwala, Rusty Steele, Lana Wong, Phil Miller, Eyal Feigenbaum, Nan Shen, Nathan Ray, and Michael Feit

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Tayyab Suratwala, Rusty Steele, Lana Wong, Phil Miller, Eyal Feigenbaum, Nan Shen, Nathan Ray, and Michael Feit, "Towards predicting removal rate and surface roughness during grinding of optical materials," Appl. Opt. 58, 2490-2499 (2019)

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- Optical Design and Fabrication
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About this Article
History
- Original Manuscript: November 19, 2018
- Revised Manuscript: February 20, 2019
- Manuscript Accepted: February 22, 2019
- Published: March 27, 2019

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Abstract

A series of controlled grinding experiments, utilizing loose or fixed abrasives of either alumina or diamond at various particle sizes, were performed on a wide range of optical workpiece materials [single crystals of ${Al}_{2} O_{3}$ (sapphire), SiC, $Y_{3} {Al}_{5} O_{12}$ (YAG), ${CaF}_{2}$ , and ${LiB}_{3} O_{5}$ (LBO); a ${SiO}_{2} - {Al}_{2} O_{3} - P_{2} O_{5} - {Li}_{2} O$ glass ceramic (Zerodur); and glasses of ${SiO}_{2} : {TiO}_{2}$ (ULE), ${SiO}_{2}$ (fused silica), and $P_{2} O_{5} - {Al}_{2} O_{3} - K_{2} O - BaO$ (phosphate)]. The material removal rate, surface roughness, and morphology of surface fractures were measured. Separately, Vickers indentation was performed on the workpieces, and the depths of various crack types as a function of applied load was measured. Single pass grinding experiments showed distinct differences in the spatial pattern of surface fracturing between the loose alumina abrasive (isolated indent-type lateral cracking) and the loose or fixed diamond abrasive (scratch-type elongated lateral cracking). Each of the grinding methods had a removal rate and roughness that scaled with the lateral crack slope, $s_{ℓ}$ (i.e., the rate of increase in lateral crack depth with the applied load) of the workpiece material. A grinding model (based on the volumetric removal of lateral cracks accounting for neighboring lateral crack removal efficiency and the fraction of abrasive particles leading to fracture initiation) and a roughness model (based on the depth of lateral cracks or the interface gap between the workpiece and lap) are shown to quantitatively describe the material removal rate and roughness as a function of workpiece material, abrasive size, applied pressure, and relative velocity. This broad, multiprocess variable grinding model can serve as a predictive tool for estimating grinding rates and surface roughness for various grinding processes on different workpiece materials.

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Workpiece Material	Material Type	Material Properties ^a			Crack Properties
		Young’s Modulus, $E_{1}$	Knoop Hardness, $H_{1}$	Fracture Toughness, $K_{I c}$	Lateral Crack Depth Slope, $s_{ℓ}$	Radial Crack Depth Slope, $s_{r}$
		GPa	GPa	$MPa \cdot m^{0.5}$	${μm / N}^{1 / 2}$	${μm / N}^{2 / 3}$
Sapphire ( ${Al}_{2} O_{3}$ )	Single crystal	345	17.2	3.45	$2.7 \pm 0.6$	$6.1 \pm 3.5$
Silicon Carbide (SiC)	Single crystal	410	27.5	4.6	$1.3 \pm 0.2$	$3.0 \pm 0.2$
YAG ( $Y_{3} {Al}_{5} O_{12}$ )	Single crystal	300	11.9	2	$3.0 \pm 0.8$	$9.1 \pm 2.2$
Calcium Fluoride ( ${CaF}_{2}$ )	Single crystal	76	1.5	0.55	$84.0 \pm 11.8$	$39.6 \pm 6.6$
LBO ( ${LiB}_{3} O_{5}$ )	Single crystal	140	6.0	0.54	$7.0 \pm 1.4$	$19.7 \pm 3.0$
Zerodur ( ${SiO}_{2} : {Al}_{2} O_{3} : P_{2} O_{5} : {Li}_{2} O$ )	Glass-ceramic	90.3	6.1	0.9	$8.8 \pm 1.5$	$11.9 \pm 0.8$
ULE ( ${SiO}_{2} : {TiO}_{2}$ )	Glass	68	4.3	1.43	$15.9 \pm 1.8$	$4.2 \pm 1.0$
Fused Silica ( ${SiO}_{2}$ )	Glass	72.7	5.9	0.75	$17.1 \pm 1.9$	$9.5 \pm 1.0$
Phosphate ( $P_{2} O_{5} - {Al}_{2} O_{3} - K_{2} O - BaO$ )	Glass	50	3.2	0.51	$40.3 \pm 6.0$	$29.8 \pm 4.5$

Parameter	9 μm Loose Abrasive	30 μm Loose Abrasive
Average lateral crack length ( $b_{ℓ}$ )	5.0 μm	11.4 μm
Calculated load per particle using Eq. (3c) ( $P$ )	0.0038 N	0.014 N
Calculated load per particle ( $P$ ) assuming $f_{L} = 5 \times 10^{- 4}$ using Eqs. (7) and (8)	0.0032 N	0.036 N

Workpiece Material	Material Type	Material Properties ^a			Crack Properties
		Young’s Modulus, $E_{1}$	Knoop Hardness, $H_{1}$	Fracture Toughness, $K_{I c}$	Lateral Crack Depth Slope, $s_{ℓ}$	Radial Crack Depth Slope, $s_{r}$
		GPa	GPa	$MPa \cdot m^{0.5}$	${μm / N}^{1 / 2}$	${μm / N}^{2 / 3}$
Sapphire ( ${Al}_{2} O_{3}$ )	Single crystal	345	17.2	3.45	$2.7 \pm 0.6$	$6.1 \pm 3.5$
Silicon Carbide (SiC)	Single crystal	410	27.5	4.6	$1.3 \pm 0.2$	$3.0 \pm 0.2$
YAG ( $Y_{3} {Al}_{5} O_{12}$ )	Single crystal	300	11.9	2	$3.0 \pm 0.8$	$9.1 \pm 2.2$
Calcium Fluoride ( ${CaF}_{2}$ )	Single crystal	76	1.5	0.55	$84.0 \pm 11.8$	$39.6 \pm 6.6$
LBO ( ${LiB}_{3} O_{5}$ )	Single crystal	140	6.0	0.54	$7.0 \pm 1.4$	$19.7 \pm 3.0$
Zerodur ( ${SiO}_{2} : {Al}_{2} O_{3} : P_{2} O_{5} : {Li}_{2} O$ )	Glass-ceramic	90.3	6.1	0.9	$8.8 \pm 1.5$	$11.9 \pm 0.8$
ULE ( ${SiO}_{2} : {TiO}_{2}$ )	Glass	68	4.3	1.43	$15.9 \pm 1.8$	$4.2 \pm 1.0$
Fused Silica ( ${SiO}_{2}$ )	Glass	72.7	5.9	0.75	$17.1 \pm 1.9$	$9.5 \pm 1.0$
Phosphate ( $P_{2} O_{5} - {Al}_{2} O_{3} - K_{2} O - BaO$ )	Glass	50	3.2	0.51	$40.3 \pm 6.0$	$29.8 \pm 4.5$

Parameter	9 μm Loose Abrasive	30 μm Loose Abrasive
Average lateral crack length ( $b_{ℓ}$ )	5.0 μm	11.4 μm
Calculated load per particle using Eq. (3c) ( $P$ )	0.0038 N	0.014 N
Calculated load per particle ( $P$ ) assuming $f_{L} = 5 \times 10^{- 4}$ using Eqs. (7) and (8)	0.0032 N	0.036 N

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Applied Optics