Abstract

Based on micro-indentation mechanics and kinematics of grinding processes, theoretical formulas are deduced to calculate surface roughness (SR) and subsurface damage (SSD) depth. The SRs and SSD depths of a series of fused silica samples, which are prepared under different grinding parameters, are measured. By experimental and theoretical analysis, the relationship between SR and SSD depth is discussed. The effect of grinding parameters on SR and SSD depth is investigated quantitatively. The results show that SR and SSD depth decrease with the increase of wheel speed or the decrease of feed speed as well as cutting depth. The interaction effect between wheel speed and feed speed should be emphasized greatly. Furthermore, a relationship model between SSD depth and grinding parameters is established, which could be employed to evaluate SSD depth efficiently.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2017 (5)

J. K. Quan, Q. H. Fang, J. B. Chen, C. Xie, Y. W. Liu, and P. H. Wen, “Investigation of subsurface damage considering the abrasive particle rotation in brittle material grinding,” Int. J. Adv. Des. Manuf. Technol. 90(9–12), 2461–2476 (2017).
[Crossref]

H. N. Li, T. B. Yu, L. D. Zhu, and W. S. Wang, “Analytical modeling of grinding-induced subsurface damage in monocrystalline silicon,” Mater. Des. 130, 250–262 (2017).
[Crossref]

K. Wasmer, P. M. Pochno, D. Sage, and J. H. Giovanola, “Parametric experimental study and design of experiment modelling of sapphire grinding,” J. Clean. Prod. 141, 323–335 (2017).
[Crossref]

D. R. Unune and H. S. Mali, “Parametric modeling and optimization for abrasive mixed surface electro discharge diamond grinding of Inconel 718 using response surface methodology,” Int. J. Adv. Des. Manuf. Technol. 93(9–12), 3859–3872 (2017).
[Crossref]

H. Xiao, H. Wang, G. Fu, and Z. Chen, “Surface roughness and morphology evolution of optical glass with micro-cracks during chemical etching,” Appl. Opt. 56(3), 702–711 (2017).
[Crossref] [PubMed]

2016 (6)

H. Y. Yu, J. Wang, and Y. S. Lu, “Modeling and analysis of dynamic cutting points density of the grinding wheel with an abrasive phyllotactic pattern,” Int. J. Adv. Des. Manuf. Technol. 86(5–8), 1933–1943 (2016).
[Crossref]

F. A. Viana, “A tutorial on Latin hypercube design of experiments,” Qual. Reliab. Eng. Int. 32(5), 1975–1985 (2016).
[Crossref]

H. N. Li, T. B. Yu, L. D. Zhu, and W. S. Wang, “Evaluation of grinding-induced subsurface damage in optical glass BK7,” J. Mater. Process. Technol. 229, 785–794 (2016).
[Crossref]

H. R. Wang, H. F. Chen, G. L. Fu, and H. P. Xiao, “Relationship between grinding process and the parameters of subsurface damage based on the image processing,” Int. J. Adv. Des. Manuf. Technol. 83(9-12), 1707–1715 (2016).
[Crossref]

Y. Li, H. Ye, Z. Yuan, Z. Liu, Y. Zheng, Z. Zhang, S. Zhao, J. Wang, and Q. Xu, “Generation of scratches and their effects on laser damage performance of silica glass,” Sci. Rep. 6(1), 34818 (2016).
[Crossref] [PubMed]

C. C. Wang, Q. H. Fang, J. B. Chen, Y. W. Liu, and J. Tan, “Subsurface damage in high-speed grinding of brittle materials considering kinematic characteristics of the grinding process,” Int. J. Adv. Des. Manuf. Technol. 83(5–8), 937–948 (2016).
[Crossref]

2015 (2)

P. Blaineau, D. André, R. Laheurte, P. Darnis, N. Darbois, O. Cahuc, and J. Neauport, “Subsurface mechanical damage during bound abrasive grinding of fused silica glass,” Appl. Surf. Sci. 353, 764–773 (2015).
[Crossref]

J. B. Chen, Q. H. Fang, and P. Li, “Effect of grinding wheel spindle vibration on surface roughness and subsurface damage in brittle material grinding,” Int. J. Mach. Tools Manuf. 91, 12–23 (2015).
[Crossref]

2013 (1)

D. X. Lv, Y. H. Huang, Y. J. Tang, and H. X. Wang, “Relationship between subsurface damage and surface roughness of glass BK7 in rotary ultrasonic machining and conventional grinding processes,” Int. J. Adv. Des. Manuf. Technol. 67(1–4), 613–622 (2013).
[Crossref]

2012 (1)

Z. Q. Yao, W. B. Gu, and K. M. Li, “Relationship between surface roughness and subsurface crack depth during grinding of optical glass BK7,” J. Mater. Process. Technol. 212(4), 969–976 (2012).
[Crossref]

2011 (3)

W. Gu, Z. Yao, and K. Li, “Evaluation of subsurface crack depth during scratch test for optical glass BK7,” Proc. Inst. Mech. Eng., C J. Mech. Eng. Sci. 225(12), 2767–2774 (2011).
[Crossref]

W. B. Gu, Z. Q. Yao, and H. L. Li, “Investigation of grinding modes in horizontal surface grinding of optical glass BK7,” J. Mater. Process. Technol. 211(10), 1629–1636 (2011).
[Crossref]

A. Brient, M. Brissot, T. Rouxel, and J. C. Sangleboeuf, “Influence of grinding parameters on glass workpieces surface finish using response surface methodology,” J. Manuf. Sci. Eng. 133(4), 044501 (2011).
[Crossref]

2009 (1)

2008 (1)

S. Y. Li, Z. Wang, and Y. L. Wu, “Relationship between subsurface damage and surface roughness of optical materials in grinding and lapping processes,” J. Mater. Process. Technol. 205(1–3), 34–41 (2008).
[Crossref]

2007 (1)

X. N. Jing, S. Maiti, and G. Subhash, “A new analytical model for estimation of scratch-induced damage in brittle solids,” J. Am. Ceram. Soc. 90(3), 885–892 (2007).
[Crossref]

2006 (1)

T. Suratwala, L. Wong, P. Miller, M. D. Feit, J. Menapace, R. Steele, P. Davis, and D. Walmer, “Sub-surface mechanical damage distributions during grinding of fused silica,” J. Non-Cryst. Solids 352(52–54), 5601–5617 (2006).
[Crossref]

2004 (1)

A. V. Gopal and P. V. Rao, “A new chip-thickness model for performance assessment of silicon carbide grinding,” Int. J. Adv. Manuf. Technol. 24(11–12), 816–820 (2004).
[Crossref]

2003 (1)

M. Nakamura, T. Sumomogi, and T. Endo, “Evaluation of surface and subsurface cracks on nano-scale machined brittle materials by scanning force microscope and scanning laser microscope,” Surf. Coat. Tech. 169–170, 743–747 (2003).
[Crossref]

1997 (1)

H. K. X. Hockin, S. Jahanmir, and L. K. Ives, “Effect of grinding on strength of tetragonal zirconia and zirconia-toughened alumina,” Mach. Sci. Technol. 1(1), 49–66 (1997).
[Crossref]

1994 (1)

J. E. Mayer, G. P. Fang, and R. L. Kegg, “Effect of grit depth of cut on strength of ground ceramics,” Ann. CIRP. 43(1), 309–312 (1994).
[Crossref]

1991 (1)

T. G. Bifano, T. A. Dow, and R. O. Scattergood, “Ductile-regime grinding: a new technology for machining brittle materials,” J. Manuf. Sci. Eng. 113(2), 184–189 (1991).

1982 (1)

D. B. Marshall, B. R. Lawn, and A. G. Evans, “Elastic/plastic indentation damage in ceramics: the lateral crack system,” J. Am. Ceram. Soc. 65(11), 561–566 (1982).
[Crossref]

1975 (1)

B. Lawn and R. Wilshaw, “Indentation fracture: principles and applications,” J. Mater. Sci. 10(6), 1049–1081 (1975).
[Crossref]

Ambard, C.

André, D.

P. Blaineau, D. André, R. Laheurte, P. Darnis, N. Darbois, O. Cahuc, and J. Neauport, “Subsurface mechanical damage during bound abrasive grinding of fused silica glass,” Appl. Surf. Sci. 353, 764–773 (2015).
[Crossref]

Bifano, T. G.

T. G. Bifano, T. A. Dow, and R. O. Scattergood, “Ductile-regime grinding: a new technology for machining brittle materials,” J. Manuf. Sci. Eng. 113(2), 184–189 (1991).

Blaineau, P.

P. Blaineau, D. André, R. Laheurte, P. Darnis, N. Darbois, O. Cahuc, and J. Neauport, “Subsurface mechanical damage during bound abrasive grinding of fused silica glass,” Appl. Surf. Sci. 353, 764–773 (2015).
[Crossref]

Brient, A.

A. Brient, M. Brissot, T. Rouxel, and J. C. Sangleboeuf, “Influence of grinding parameters on glass workpieces surface finish using response surface methodology,” J. Manuf. Sci. Eng. 133(4), 044501 (2011).
[Crossref]

Brissot, M.

A. Brient, M. Brissot, T. Rouxel, and J. C. Sangleboeuf, “Influence of grinding parameters on glass workpieces surface finish using response surface methodology,” J. Manuf. Sci. Eng. 133(4), 044501 (2011).
[Crossref]

Cahuc, O.

P. Blaineau, D. André, R. Laheurte, P. Darnis, N. Darbois, O. Cahuc, and J. Neauport, “Subsurface mechanical damage during bound abrasive grinding of fused silica glass,” Appl. Surf. Sci. 353, 764–773 (2015).
[Crossref]

Chen, H. F.

H. R. Wang, H. F. Chen, G. L. Fu, and H. P. Xiao, “Relationship between grinding process and the parameters of subsurface damage based on the image processing,” Int. J. Adv. Des. Manuf. Technol. 83(9-12), 1707–1715 (2016).
[Crossref]

Chen, J. B.

J. K. Quan, Q. H. Fang, J. B. Chen, C. Xie, Y. W. Liu, and P. H. Wen, “Investigation of subsurface damage considering the abrasive particle rotation in brittle material grinding,” Int. J. Adv. Des. Manuf. Technol. 90(9–12), 2461–2476 (2017).
[Crossref]

C. C. Wang, Q. H. Fang, J. B. Chen, Y. W. Liu, and J. Tan, “Subsurface damage in high-speed grinding of brittle materials considering kinematic characteristics of the grinding process,” Int. J. Adv. Des. Manuf. Technol. 83(5–8), 937–948 (2016).
[Crossref]

J. B. Chen, Q. H. Fang, and P. Li, “Effect of grinding wheel spindle vibration on surface roughness and subsurface damage in brittle material grinding,” Int. J. Mach. Tools Manuf. 91, 12–23 (2015).
[Crossref]

Chen, Z.

Cormont, P.

Darbois, N.

P. Blaineau, D. André, R. Laheurte, P. Darnis, N. Darbois, O. Cahuc, and J. Neauport, “Subsurface mechanical damage during bound abrasive grinding of fused silica glass,” Appl. Surf. Sci. 353, 764–773 (2015).
[Crossref]

J. Neauport, C. Ambard, P. Cormont, N. Darbois, J. Destribats, C. Luitot, and O. Rondeau, “Subsurface damage measurement of ground fused silica parts by HF etching techniques,” Opt. Express 17(22), 20448–20456 (2009).
[Crossref] [PubMed]

Darnis, P.

P. Blaineau, D. André, R. Laheurte, P. Darnis, N. Darbois, O. Cahuc, and J. Neauport, “Subsurface mechanical damage during bound abrasive grinding of fused silica glass,” Appl. Surf. Sci. 353, 764–773 (2015).
[Crossref]

Davis, P.

T. Suratwala, L. Wong, P. Miller, M. D. Feit, J. Menapace, R. Steele, P. Davis, and D. Walmer, “Sub-surface mechanical damage distributions during grinding of fused silica,” J. Non-Cryst. Solids 352(52–54), 5601–5617 (2006).
[Crossref]

Destribats, J.

Dow, T. A.

T. G. Bifano, T. A. Dow, and R. O. Scattergood, “Ductile-regime grinding: a new technology for machining brittle materials,” J. Manuf. Sci. Eng. 113(2), 184–189 (1991).

Endo, T.

M. Nakamura, T. Sumomogi, and T. Endo, “Evaluation of surface and subsurface cracks on nano-scale machined brittle materials by scanning force microscope and scanning laser microscope,” Surf. Coat. Tech. 169–170, 743–747 (2003).
[Crossref]

Evans, A. G.

D. B. Marshall, B. R. Lawn, and A. G. Evans, “Elastic/plastic indentation damage in ceramics: the lateral crack system,” J. Am. Ceram. Soc. 65(11), 561–566 (1982).
[Crossref]

Fang, G. P.

J. E. Mayer, G. P. Fang, and R. L. Kegg, “Effect of grit depth of cut on strength of ground ceramics,” Ann. CIRP. 43(1), 309–312 (1994).
[Crossref]

Fang, Q. H.

J. K. Quan, Q. H. Fang, J. B. Chen, C. Xie, Y. W. Liu, and P. H. Wen, “Investigation of subsurface damage considering the abrasive particle rotation in brittle material grinding,” Int. J. Adv. Des. Manuf. Technol. 90(9–12), 2461–2476 (2017).
[Crossref]

C. C. Wang, Q. H. Fang, J. B. Chen, Y. W. Liu, and J. Tan, “Subsurface damage in high-speed grinding of brittle materials considering kinematic characteristics of the grinding process,” Int. J. Adv. Des. Manuf. Technol. 83(5–8), 937–948 (2016).
[Crossref]

J. B. Chen, Q. H. Fang, and P. Li, “Effect of grinding wheel spindle vibration on surface roughness and subsurface damage in brittle material grinding,” Int. J. Mach. Tools Manuf. 91, 12–23 (2015).
[Crossref]

Feit, M. D.

T. Suratwala, L. Wong, P. Miller, M. D. Feit, J. Menapace, R. Steele, P. Davis, and D. Walmer, “Sub-surface mechanical damage distributions during grinding of fused silica,” J. Non-Cryst. Solids 352(52–54), 5601–5617 (2006).
[Crossref]

Fu, G.

Fu, G. L.

H. R. Wang, H. F. Chen, G. L. Fu, and H. P. Xiao, “Relationship between grinding process and the parameters of subsurface damage based on the image processing,” Int. J. Adv. Des. Manuf. Technol. 83(9-12), 1707–1715 (2016).
[Crossref]

Giovanola, J. H.

K. Wasmer, P. M. Pochno, D. Sage, and J. H. Giovanola, “Parametric experimental study and design of experiment modelling of sapphire grinding,” J. Clean. Prod. 141, 323–335 (2017).
[Crossref]

Gopal, A. V.

A. V. Gopal and P. V. Rao, “A new chip-thickness model for performance assessment of silicon carbide grinding,” Int. J. Adv. Manuf. Technol. 24(11–12), 816–820 (2004).
[Crossref]

Gu, W.

W. Gu, Z. Yao, and K. Li, “Evaluation of subsurface crack depth during scratch test for optical glass BK7,” Proc. Inst. Mech. Eng., C J. Mech. Eng. Sci. 225(12), 2767–2774 (2011).
[Crossref]

Gu, W. B.

Z. Q. Yao, W. B. Gu, and K. M. Li, “Relationship between surface roughness and subsurface crack depth during grinding of optical glass BK7,” J. Mater. Process. Technol. 212(4), 969–976 (2012).
[Crossref]

W. B. Gu, Z. Q. Yao, and H. L. Li, “Investigation of grinding modes in horizontal surface grinding of optical glass BK7,” J. Mater. Process. Technol. 211(10), 1629–1636 (2011).
[Crossref]

Hockin, H. K. X.

H. K. X. Hockin, S. Jahanmir, and L. K. Ives, “Effect of grinding on strength of tetragonal zirconia and zirconia-toughened alumina,” Mach. Sci. Technol. 1(1), 49–66 (1997).
[Crossref]

Huang, Y. H.

D. X. Lv, Y. H. Huang, Y. J. Tang, and H. X. Wang, “Relationship between subsurface damage and surface roughness of glass BK7 in rotary ultrasonic machining and conventional grinding processes,” Int. J. Adv. Des. Manuf. Technol. 67(1–4), 613–622 (2013).
[Crossref]

Ives, L. K.

H. K. X. Hockin, S. Jahanmir, and L. K. Ives, “Effect of grinding on strength of tetragonal zirconia and zirconia-toughened alumina,” Mach. Sci. Technol. 1(1), 49–66 (1997).
[Crossref]

Jahanmir, S.

H. K. X. Hockin, S. Jahanmir, and L. K. Ives, “Effect of grinding on strength of tetragonal zirconia and zirconia-toughened alumina,” Mach. Sci. Technol. 1(1), 49–66 (1997).
[Crossref]

Jing, X. N.

X. N. Jing, S. Maiti, and G. Subhash, “A new analytical model for estimation of scratch-induced damage in brittle solids,” J. Am. Ceram. Soc. 90(3), 885–892 (2007).
[Crossref]

Kegg, R. L.

J. E. Mayer, G. P. Fang, and R. L. Kegg, “Effect of grit depth of cut on strength of ground ceramics,” Ann. CIRP. 43(1), 309–312 (1994).
[Crossref]

Laheurte, R.

P. Blaineau, D. André, R. Laheurte, P. Darnis, N. Darbois, O. Cahuc, and J. Neauport, “Subsurface mechanical damage during bound abrasive grinding of fused silica glass,” Appl. Surf. Sci. 353, 764–773 (2015).
[Crossref]

Lawn, B.

B. Lawn and R. Wilshaw, “Indentation fracture: principles and applications,” J. Mater. Sci. 10(6), 1049–1081 (1975).
[Crossref]

Lawn, B. R.

D. B. Marshall, B. R. Lawn, and A. G. Evans, “Elastic/plastic indentation damage in ceramics: the lateral crack system,” J. Am. Ceram. Soc. 65(11), 561–566 (1982).
[Crossref]

Li, H. L.

W. B. Gu, Z. Q. Yao, and H. L. Li, “Investigation of grinding modes in horizontal surface grinding of optical glass BK7,” J. Mater. Process. Technol. 211(10), 1629–1636 (2011).
[Crossref]

Li, H. N.

H. N. Li, T. B. Yu, L. D. Zhu, and W. S. Wang, “Analytical modeling of grinding-induced subsurface damage in monocrystalline silicon,” Mater. Des. 130, 250–262 (2017).
[Crossref]

H. N. Li, T. B. Yu, L. D. Zhu, and W. S. Wang, “Evaluation of grinding-induced subsurface damage in optical glass BK7,” J. Mater. Process. Technol. 229, 785–794 (2016).
[Crossref]

Li, K.

W. Gu, Z. Yao, and K. Li, “Evaluation of subsurface crack depth during scratch test for optical glass BK7,” Proc. Inst. Mech. Eng., C J. Mech. Eng. Sci. 225(12), 2767–2774 (2011).
[Crossref]

Li, K. M.

Z. Q. Yao, W. B. Gu, and K. M. Li, “Relationship between surface roughness and subsurface crack depth during grinding of optical glass BK7,” J. Mater. Process. Technol. 212(4), 969–976 (2012).
[Crossref]

Li, P.

J. B. Chen, Q. H. Fang, and P. Li, “Effect of grinding wheel spindle vibration on surface roughness and subsurface damage in brittle material grinding,” Int. J. Mach. Tools Manuf. 91, 12–23 (2015).
[Crossref]

Li, S. Y.

S. Y. Li, Z. Wang, and Y. L. Wu, “Relationship between subsurface damage and surface roughness of optical materials in grinding and lapping processes,” J. Mater. Process. Technol. 205(1–3), 34–41 (2008).
[Crossref]

Li, Y.

Y. Li, H. Ye, Z. Yuan, Z. Liu, Y. Zheng, Z. Zhang, S. Zhao, J. Wang, and Q. Xu, “Generation of scratches and their effects on laser damage performance of silica glass,” Sci. Rep. 6(1), 34818 (2016).
[Crossref] [PubMed]

Liu, Y. W.

J. K. Quan, Q. H. Fang, J. B. Chen, C. Xie, Y. W. Liu, and P. H. Wen, “Investigation of subsurface damage considering the abrasive particle rotation in brittle material grinding,” Int. J. Adv. Des. Manuf. Technol. 90(9–12), 2461–2476 (2017).
[Crossref]

C. C. Wang, Q. H. Fang, J. B. Chen, Y. W. Liu, and J. Tan, “Subsurface damage in high-speed grinding of brittle materials considering kinematic characteristics of the grinding process,” Int. J. Adv. Des. Manuf. Technol. 83(5–8), 937–948 (2016).
[Crossref]

Liu, Z.

Y. Li, H. Ye, Z. Yuan, Z. Liu, Y. Zheng, Z. Zhang, S. Zhao, J. Wang, and Q. Xu, “Generation of scratches and their effects on laser damage performance of silica glass,” Sci. Rep. 6(1), 34818 (2016).
[Crossref] [PubMed]

Lu, Y. S.

H. Y. Yu, J. Wang, and Y. S. Lu, “Modeling and analysis of dynamic cutting points density of the grinding wheel with an abrasive phyllotactic pattern,” Int. J. Adv. Des. Manuf. Technol. 86(5–8), 1933–1943 (2016).
[Crossref]

Luitot, C.

Lv, D. X.

D. X. Lv, Y. H. Huang, Y. J. Tang, and H. X. Wang, “Relationship between subsurface damage and surface roughness of glass BK7 in rotary ultrasonic machining and conventional grinding processes,” Int. J. Adv. Des. Manuf. Technol. 67(1–4), 613–622 (2013).
[Crossref]

Maiti, S.

X. N. Jing, S. Maiti, and G. Subhash, “A new analytical model for estimation of scratch-induced damage in brittle solids,” J. Am. Ceram. Soc. 90(3), 885–892 (2007).
[Crossref]

Mali, H. S.

D. R. Unune and H. S. Mali, “Parametric modeling and optimization for abrasive mixed surface electro discharge diamond grinding of Inconel 718 using response surface methodology,” Int. J. Adv. Des. Manuf. Technol. 93(9–12), 3859–3872 (2017).
[Crossref]

Marshall, D. B.

D. B. Marshall, B. R. Lawn, and A. G. Evans, “Elastic/plastic indentation damage in ceramics: the lateral crack system,” J. Am. Ceram. Soc. 65(11), 561–566 (1982).
[Crossref]

Mayer, J. E.

J. E. Mayer, G. P. Fang, and R. L. Kegg, “Effect of grit depth of cut on strength of ground ceramics,” Ann. CIRP. 43(1), 309–312 (1994).
[Crossref]

Menapace, J.

T. Suratwala, L. Wong, P. Miller, M. D. Feit, J. Menapace, R. Steele, P. Davis, and D. Walmer, “Sub-surface mechanical damage distributions during grinding of fused silica,” J. Non-Cryst. Solids 352(52–54), 5601–5617 (2006).
[Crossref]

Miller, P.

T. Suratwala, L. Wong, P. Miller, M. D. Feit, J. Menapace, R. Steele, P. Davis, and D. Walmer, “Sub-surface mechanical damage distributions during grinding of fused silica,” J. Non-Cryst. Solids 352(52–54), 5601–5617 (2006).
[Crossref]

Nakamura, M.

M. Nakamura, T. Sumomogi, and T. Endo, “Evaluation of surface and subsurface cracks on nano-scale machined brittle materials by scanning force microscope and scanning laser microscope,” Surf. Coat. Tech. 169–170, 743–747 (2003).
[Crossref]

Neauport, J.

P. Blaineau, D. André, R. Laheurte, P. Darnis, N. Darbois, O. Cahuc, and J. Neauport, “Subsurface mechanical damage during bound abrasive grinding of fused silica glass,” Appl. Surf. Sci. 353, 764–773 (2015).
[Crossref]

J. Neauport, C. Ambard, P. Cormont, N. Darbois, J. Destribats, C. Luitot, and O. Rondeau, “Subsurface damage measurement of ground fused silica parts by HF etching techniques,” Opt. Express 17(22), 20448–20456 (2009).
[Crossref] [PubMed]

Pochno, P. M.

K. Wasmer, P. M. Pochno, D. Sage, and J. H. Giovanola, “Parametric experimental study and design of experiment modelling of sapphire grinding,” J. Clean. Prod. 141, 323–335 (2017).
[Crossref]

Quan, J. K.

J. K. Quan, Q. H. Fang, J. B. Chen, C. Xie, Y. W. Liu, and P. H. Wen, “Investigation of subsurface damage considering the abrasive particle rotation in brittle material grinding,” Int. J. Adv. Des. Manuf. Technol. 90(9–12), 2461–2476 (2017).
[Crossref]

Rao, P. V.

A. V. Gopal and P. V. Rao, “A new chip-thickness model for performance assessment of silicon carbide grinding,” Int. J. Adv. Manuf. Technol. 24(11–12), 816–820 (2004).
[Crossref]

Rondeau, O.

Rouxel, T.

A. Brient, M. Brissot, T. Rouxel, and J. C. Sangleboeuf, “Influence of grinding parameters on glass workpieces surface finish using response surface methodology,” J. Manuf. Sci. Eng. 133(4), 044501 (2011).
[Crossref]

Sage, D.

K. Wasmer, P. M. Pochno, D. Sage, and J. H. Giovanola, “Parametric experimental study and design of experiment modelling of sapphire grinding,” J. Clean. Prod. 141, 323–335 (2017).
[Crossref]

Sangleboeuf, J. C.

A. Brient, M. Brissot, T. Rouxel, and J. C. Sangleboeuf, “Influence of grinding parameters on glass workpieces surface finish using response surface methodology,” J. Manuf. Sci. Eng. 133(4), 044501 (2011).
[Crossref]

Scattergood, R. O.

T. G. Bifano, T. A. Dow, and R. O. Scattergood, “Ductile-regime grinding: a new technology for machining brittle materials,” J. Manuf. Sci. Eng. 113(2), 184–189 (1991).

Steele, R.

T. Suratwala, L. Wong, P. Miller, M. D. Feit, J. Menapace, R. Steele, P. Davis, and D. Walmer, “Sub-surface mechanical damage distributions during grinding of fused silica,” J. Non-Cryst. Solids 352(52–54), 5601–5617 (2006).
[Crossref]

Subhash, G.

X. N. Jing, S. Maiti, and G. Subhash, “A new analytical model for estimation of scratch-induced damage in brittle solids,” J. Am. Ceram. Soc. 90(3), 885–892 (2007).
[Crossref]

Sumomogi, T.

M. Nakamura, T. Sumomogi, and T. Endo, “Evaluation of surface and subsurface cracks on nano-scale machined brittle materials by scanning force microscope and scanning laser microscope,” Surf. Coat. Tech. 169–170, 743–747 (2003).
[Crossref]

Suratwala, T.

T. Suratwala, L. Wong, P. Miller, M. D. Feit, J. Menapace, R. Steele, P. Davis, and D. Walmer, “Sub-surface mechanical damage distributions during grinding of fused silica,” J. Non-Cryst. Solids 352(52–54), 5601–5617 (2006).
[Crossref]

Tan, J.

C. C. Wang, Q. H. Fang, J. B. Chen, Y. W. Liu, and J. Tan, “Subsurface damage in high-speed grinding of brittle materials considering kinematic characteristics of the grinding process,” Int. J. Adv. Des. Manuf. Technol. 83(5–8), 937–948 (2016).
[Crossref]

Tang, Y. J.

D. X. Lv, Y. H. Huang, Y. J. Tang, and H. X. Wang, “Relationship between subsurface damage and surface roughness of glass BK7 in rotary ultrasonic machining and conventional grinding processes,” Int. J. Adv. Des. Manuf. Technol. 67(1–4), 613–622 (2013).
[Crossref]

Unune, D. R.

D. R. Unune and H. S. Mali, “Parametric modeling and optimization for abrasive mixed surface electro discharge diamond grinding of Inconel 718 using response surface methodology,” Int. J. Adv. Des. Manuf. Technol. 93(9–12), 3859–3872 (2017).
[Crossref]

Viana, F. A.

F. A. Viana, “A tutorial on Latin hypercube design of experiments,” Qual. Reliab. Eng. Int. 32(5), 1975–1985 (2016).
[Crossref]

Walmer, D.

T. Suratwala, L. Wong, P. Miller, M. D. Feit, J. Menapace, R. Steele, P. Davis, and D. Walmer, “Sub-surface mechanical damage distributions during grinding of fused silica,” J. Non-Cryst. Solids 352(52–54), 5601–5617 (2006).
[Crossref]

Wang, C. C.

C. C. Wang, Q. H. Fang, J. B. Chen, Y. W. Liu, and J. Tan, “Subsurface damage in high-speed grinding of brittle materials considering kinematic characteristics of the grinding process,” Int. J. Adv. Des. Manuf. Technol. 83(5–8), 937–948 (2016).
[Crossref]

Wang, H.

Wang, H. R.

H. R. Wang, H. F. Chen, G. L. Fu, and H. P. Xiao, “Relationship between grinding process and the parameters of subsurface damage based on the image processing,” Int. J. Adv. Des. Manuf. Technol. 83(9-12), 1707–1715 (2016).
[Crossref]

Wang, H. X.

D. X. Lv, Y. H. Huang, Y. J. Tang, and H. X. Wang, “Relationship between subsurface damage and surface roughness of glass BK7 in rotary ultrasonic machining and conventional grinding processes,” Int. J. Adv. Des. Manuf. Technol. 67(1–4), 613–622 (2013).
[Crossref]

Wang, J.

H. Y. Yu, J. Wang, and Y. S. Lu, “Modeling and analysis of dynamic cutting points density of the grinding wheel with an abrasive phyllotactic pattern,” Int. J. Adv. Des. Manuf. Technol. 86(5–8), 1933–1943 (2016).
[Crossref]

Y. Li, H. Ye, Z. Yuan, Z. Liu, Y. Zheng, Z. Zhang, S. Zhao, J. Wang, and Q. Xu, “Generation of scratches and their effects on laser damage performance of silica glass,” Sci. Rep. 6(1), 34818 (2016).
[Crossref] [PubMed]

Wang, W. S.

H. N. Li, T. B. Yu, L. D. Zhu, and W. S. Wang, “Analytical modeling of grinding-induced subsurface damage in monocrystalline silicon,” Mater. Des. 130, 250–262 (2017).
[Crossref]

H. N. Li, T. B. Yu, L. D. Zhu, and W. S. Wang, “Evaluation of grinding-induced subsurface damage in optical glass BK7,” J. Mater. Process. Technol. 229, 785–794 (2016).
[Crossref]

Wang, Z.

S. Y. Li, Z. Wang, and Y. L. Wu, “Relationship between subsurface damage and surface roughness of optical materials in grinding and lapping processes,” J. Mater. Process. Technol. 205(1–3), 34–41 (2008).
[Crossref]

Wasmer, K.

K. Wasmer, P. M. Pochno, D. Sage, and J. H. Giovanola, “Parametric experimental study and design of experiment modelling of sapphire grinding,” J. Clean. Prod. 141, 323–335 (2017).
[Crossref]

Wen, P. H.

J. K. Quan, Q. H. Fang, J. B. Chen, C. Xie, Y. W. Liu, and P. H. Wen, “Investigation of subsurface damage considering the abrasive particle rotation in brittle material grinding,” Int. J. Adv. Des. Manuf. Technol. 90(9–12), 2461–2476 (2017).
[Crossref]

Wilshaw, R.

B. Lawn and R. Wilshaw, “Indentation fracture: principles and applications,” J. Mater. Sci. 10(6), 1049–1081 (1975).
[Crossref]

Wong, L.

T. Suratwala, L. Wong, P. Miller, M. D. Feit, J. Menapace, R. Steele, P. Davis, and D. Walmer, “Sub-surface mechanical damage distributions during grinding of fused silica,” J. Non-Cryst. Solids 352(52–54), 5601–5617 (2006).
[Crossref]

Wu, Y. L.

S. Y. Li, Z. Wang, and Y. L. Wu, “Relationship between subsurface damage and surface roughness of optical materials in grinding and lapping processes,” J. Mater. Process. Technol. 205(1–3), 34–41 (2008).
[Crossref]

Xiao, H.

Xiao, H. P.

H. R. Wang, H. F. Chen, G. L. Fu, and H. P. Xiao, “Relationship between grinding process and the parameters of subsurface damage based on the image processing,” Int. J. Adv. Des. Manuf. Technol. 83(9-12), 1707–1715 (2016).
[Crossref]

Xie, C.

J. K. Quan, Q. H. Fang, J. B. Chen, C. Xie, Y. W. Liu, and P. H. Wen, “Investigation of subsurface damage considering the abrasive particle rotation in brittle material grinding,” Int. J. Adv. Des. Manuf. Technol. 90(9–12), 2461–2476 (2017).
[Crossref]

Xu, Q.

Y. Li, H. Ye, Z. Yuan, Z. Liu, Y. Zheng, Z. Zhang, S. Zhao, J. Wang, and Q. Xu, “Generation of scratches and their effects on laser damage performance of silica glass,” Sci. Rep. 6(1), 34818 (2016).
[Crossref] [PubMed]

Yao, Z.

W. Gu, Z. Yao, and K. Li, “Evaluation of subsurface crack depth during scratch test for optical glass BK7,” Proc. Inst. Mech. Eng., C J. Mech. Eng. Sci. 225(12), 2767–2774 (2011).
[Crossref]

Yao, Z. Q.

Z. Q. Yao, W. B. Gu, and K. M. Li, “Relationship between surface roughness and subsurface crack depth during grinding of optical glass BK7,” J. Mater. Process. Technol. 212(4), 969–976 (2012).
[Crossref]

W. B. Gu, Z. Q. Yao, and H. L. Li, “Investigation of grinding modes in horizontal surface grinding of optical glass BK7,” J. Mater. Process. Technol. 211(10), 1629–1636 (2011).
[Crossref]

Ye, H.

Y. Li, H. Ye, Z. Yuan, Z. Liu, Y. Zheng, Z. Zhang, S. Zhao, J. Wang, and Q. Xu, “Generation of scratches and their effects on laser damage performance of silica glass,” Sci. Rep. 6(1), 34818 (2016).
[Crossref] [PubMed]

Yu, H. Y.

H. Y. Yu, J. Wang, and Y. S. Lu, “Modeling and analysis of dynamic cutting points density of the grinding wheel with an abrasive phyllotactic pattern,” Int. J. Adv. Des. Manuf. Technol. 86(5–8), 1933–1943 (2016).
[Crossref]

Yu, T. B.

H. N. Li, T. B. Yu, L. D. Zhu, and W. S. Wang, “Analytical modeling of grinding-induced subsurface damage in monocrystalline silicon,” Mater. Des. 130, 250–262 (2017).
[Crossref]

H. N. Li, T. B. Yu, L. D. Zhu, and W. S. Wang, “Evaluation of grinding-induced subsurface damage in optical glass BK7,” J. Mater. Process. Technol. 229, 785–794 (2016).
[Crossref]

Yuan, Z.

Y. Li, H. Ye, Z. Yuan, Z. Liu, Y. Zheng, Z. Zhang, S. Zhao, J. Wang, and Q. Xu, “Generation of scratches and their effects on laser damage performance of silica glass,” Sci. Rep. 6(1), 34818 (2016).
[Crossref] [PubMed]

Zhang, Z.

Y. Li, H. Ye, Z. Yuan, Z. Liu, Y. Zheng, Z. Zhang, S. Zhao, J. Wang, and Q. Xu, “Generation of scratches and their effects on laser damage performance of silica glass,” Sci. Rep. 6(1), 34818 (2016).
[Crossref] [PubMed]

Zhao, S.

Y. Li, H. Ye, Z. Yuan, Z. Liu, Y. Zheng, Z. Zhang, S. Zhao, J. Wang, and Q. Xu, “Generation of scratches and their effects on laser damage performance of silica glass,” Sci. Rep. 6(1), 34818 (2016).
[Crossref] [PubMed]

Zheng, Y.

Y. Li, H. Ye, Z. Yuan, Z. Liu, Y. Zheng, Z. Zhang, S. Zhao, J. Wang, and Q. Xu, “Generation of scratches and their effects on laser damage performance of silica glass,” Sci. Rep. 6(1), 34818 (2016).
[Crossref] [PubMed]

Zhu, L. D.

H. N. Li, T. B. Yu, L. D. Zhu, and W. S. Wang, “Analytical modeling of grinding-induced subsurface damage in monocrystalline silicon,” Mater. Des. 130, 250–262 (2017).
[Crossref]

H. N. Li, T. B. Yu, L. D. Zhu, and W. S. Wang, “Evaluation of grinding-induced subsurface damage in optical glass BK7,” J. Mater. Process. Technol. 229, 785–794 (2016).
[Crossref]

Ann. CIRP. (1)

J. E. Mayer, G. P. Fang, and R. L. Kegg, “Effect of grit depth of cut on strength of ground ceramics,” Ann. CIRP. 43(1), 309–312 (1994).
[Crossref]

Appl. Opt. (1)

Appl. Surf. Sci. (1)

P. Blaineau, D. André, R. Laheurte, P. Darnis, N. Darbois, O. Cahuc, and J. Neauport, “Subsurface mechanical damage during bound abrasive grinding of fused silica glass,” Appl. Surf. Sci. 353, 764–773 (2015).
[Crossref]

Int. J. Adv. Des. Manuf. Technol. (6)

H. R. Wang, H. F. Chen, G. L. Fu, and H. P. Xiao, “Relationship between grinding process and the parameters of subsurface damage based on the image processing,” Int. J. Adv. Des. Manuf. Technol. 83(9-12), 1707–1715 (2016).
[Crossref]

C. C. Wang, Q. H. Fang, J. B. Chen, Y. W. Liu, and J. Tan, “Subsurface damage in high-speed grinding of brittle materials considering kinematic characteristics of the grinding process,” Int. J. Adv. Des. Manuf. Technol. 83(5–8), 937–948 (2016).
[Crossref]

J. K. Quan, Q. H. Fang, J. B. Chen, C. Xie, Y. W. Liu, and P. H. Wen, “Investigation of subsurface damage considering the abrasive particle rotation in brittle material grinding,” Int. J. Adv. Des. Manuf. Technol. 90(9–12), 2461–2476 (2017).
[Crossref]

D. R. Unune and H. S. Mali, “Parametric modeling and optimization for abrasive mixed surface electro discharge diamond grinding of Inconel 718 using response surface methodology,” Int. J. Adv. Des. Manuf. Technol. 93(9–12), 3859–3872 (2017).
[Crossref]

D. X. Lv, Y. H. Huang, Y. J. Tang, and H. X. Wang, “Relationship between subsurface damage and surface roughness of glass BK7 in rotary ultrasonic machining and conventional grinding processes,” Int. J. Adv. Des. Manuf. Technol. 67(1–4), 613–622 (2013).
[Crossref]

H. Y. Yu, J. Wang, and Y. S. Lu, “Modeling and analysis of dynamic cutting points density of the grinding wheel with an abrasive phyllotactic pattern,” Int. J. Adv. Des. Manuf. Technol. 86(5–8), 1933–1943 (2016).
[Crossref]

Int. J. Adv. Manuf. Technol. (1)

A. V. Gopal and P. V. Rao, “A new chip-thickness model for performance assessment of silicon carbide grinding,” Int. J. Adv. Manuf. Technol. 24(11–12), 816–820 (2004).
[Crossref]

Int. J. Mach. Tools Manuf. (1)

J. B. Chen, Q. H. Fang, and P. Li, “Effect of grinding wheel spindle vibration on surface roughness and subsurface damage in brittle material grinding,” Int. J. Mach. Tools Manuf. 91, 12–23 (2015).
[Crossref]

J. Am. Ceram. Soc. (2)

D. B. Marshall, B. R. Lawn, and A. G. Evans, “Elastic/plastic indentation damage in ceramics: the lateral crack system,” J. Am. Ceram. Soc. 65(11), 561–566 (1982).
[Crossref]

X. N. Jing, S. Maiti, and G. Subhash, “A new analytical model for estimation of scratch-induced damage in brittle solids,” J. Am. Ceram. Soc. 90(3), 885–892 (2007).
[Crossref]

J. Clean. Prod. (1)

K. Wasmer, P. M. Pochno, D. Sage, and J. H. Giovanola, “Parametric experimental study and design of experiment modelling of sapphire grinding,” J. Clean. Prod. 141, 323–335 (2017).
[Crossref]

J. Manuf. Sci. Eng. (2)

A. Brient, M. Brissot, T. Rouxel, and J. C. Sangleboeuf, “Influence of grinding parameters on glass workpieces surface finish using response surface methodology,” J. Manuf. Sci. Eng. 133(4), 044501 (2011).
[Crossref]

T. G. Bifano, T. A. Dow, and R. O. Scattergood, “Ductile-regime grinding: a new technology for machining brittle materials,” J. Manuf. Sci. Eng. 113(2), 184–189 (1991).

J. Mater. Process. Technol. (4)

W. B. Gu, Z. Q. Yao, and H. L. Li, “Investigation of grinding modes in horizontal surface grinding of optical glass BK7,” J. Mater. Process. Technol. 211(10), 1629–1636 (2011).
[Crossref]

Z. Q. Yao, W. B. Gu, and K. M. Li, “Relationship between surface roughness and subsurface crack depth during grinding of optical glass BK7,” J. Mater. Process. Technol. 212(4), 969–976 (2012).
[Crossref]

H. N. Li, T. B. Yu, L. D. Zhu, and W. S. Wang, “Evaluation of grinding-induced subsurface damage in optical glass BK7,” J. Mater. Process. Technol. 229, 785–794 (2016).
[Crossref]

S. Y. Li, Z. Wang, and Y. L. Wu, “Relationship between subsurface damage and surface roughness of optical materials in grinding and lapping processes,” J. Mater. Process. Technol. 205(1–3), 34–41 (2008).
[Crossref]

J. Mater. Sci. (1)

B. Lawn and R. Wilshaw, “Indentation fracture: principles and applications,” J. Mater. Sci. 10(6), 1049–1081 (1975).
[Crossref]

J. Non-Cryst. Solids (1)

T. Suratwala, L. Wong, P. Miller, M. D. Feit, J. Menapace, R. Steele, P. Davis, and D. Walmer, “Sub-surface mechanical damage distributions during grinding of fused silica,” J. Non-Cryst. Solids 352(52–54), 5601–5617 (2006).
[Crossref]

Mach. Sci. Technol. (1)

H. K. X. Hockin, S. Jahanmir, and L. K. Ives, “Effect of grinding on strength of tetragonal zirconia and zirconia-toughened alumina,” Mach. Sci. Technol. 1(1), 49–66 (1997).
[Crossref]

Mater. Des. (1)

H. N. Li, T. B. Yu, L. D. Zhu, and W. S. Wang, “Analytical modeling of grinding-induced subsurface damage in monocrystalline silicon,” Mater. Des. 130, 250–262 (2017).
[Crossref]

Opt. Express (1)

Proc. Inst. Mech. Eng., C J. Mech. Eng. Sci. (1)

W. Gu, Z. Yao, and K. Li, “Evaluation of subsurface crack depth during scratch test for optical glass BK7,” Proc. Inst. Mech. Eng., C J. Mech. Eng. Sci. 225(12), 2767–2774 (2011).
[Crossref]

Qual. Reliab. Eng. Int. (1)

F. A. Viana, “A tutorial on Latin hypercube design of experiments,” Qual. Reliab. Eng. Int. 32(5), 1975–1985 (2016).
[Crossref]

Sci. Rep. (1)

Y. Li, H. Ye, Z. Yuan, Z. Liu, Y. Zheng, Z. Zhang, S. Zhao, J. Wang, and Q. Xu, “Generation of scratches and their effects on laser damage performance of silica glass,” Sci. Rep. 6(1), 34818 (2016).
[Crossref] [PubMed]

Surf. Coat. Tech. (1)

M. Nakamura, T. Sumomogi, and T. Endo, “Evaluation of surface and subsurface cracks on nano-scale machined brittle materials by scanning force microscope and scanning laser microscope,” Surf. Coat. Tech. 169–170, 743–747 (2003).
[Crossref]

Other (4)

I. D. Marinescu, W. B. Rowe, B. Dimitrov, and I. Inasaki, Tribology of Abrasive Machining Processes (William Andrew, 2004).

M. C. Shaw, Principles of Abrasive Processing (Oxford University, 1996).

S. Malkin, Grinding Technology: Theory and Application of Machining with Abrasives (Ellis Horwood, 1989).

A. E. Taylor, General Theory of Functions and Integration (Dover Publications, 2012).

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Figures (9)

Fig. 1
Fig. 1 Typical crack systems in scratching brittle materials.
Fig. 2
Fig. 2 Kinetic characteristic of horizontal surface grinding.
Fig. 3
Fig. 3 Micrographs of a selected fused silica’s surface after etching for (a) 0 min, (b) 6 min and (c) 36 min; (d) SR evolution of each fused silica sample with the etching time.
Fig. 4
Fig. 4 The relationship between SR and SSD depth. (a) experimental results; (b) model (1): SSD = 6.00 × SR; (c) model (2): SSD = 2.95 × SR4/3; (d) model (3): SSD = 4.06 × SR4/3 − 2.32 × SR; (e) model (4): SSD = 0.14 × SR2 + 6.15 × SR − 11.13.
Fig. 5
Fig. 5 Relative effects of grinding parameters on (a) SR and (b) SSD depth by experiment. Re–relative effect; ap–cutting depth; vs–wheel speed; vw–feed speed.
Fig. 6
Fig. 6 Values of SR1, SR2, SSDm-1, SSDl-1, SSDm-2, SSDl-2 at (a) 10 μm ≤ ap ≤ 80 μm, vs/vw = 2050, α = 67.5°; (b) ap = 45 μm, 100 ≤ vs/vw ≤ 4000, α = 67.5°; (c) 0.1 μm ≤ ap ≤ 1 μm, vs/vw = 2050, α = 67.5°; (d) ap = 0.64 μm, 100 ≤ vs/vw ≤ 4000, α = 67.5°.
Fig. 7
Fig. 7 Relationships between SR and SSD depth at (a) 10 μm ≤ ap ≤ 80 μm, vs/vw = 2050, α = 67.5°; (b) ap = 45 μm, 100 ≤ vs/vw ≤ 4000, α = 67.5°; (c) 0.1 μm ≤ ap ≤ 1 μm, vs/vw = 2050, α = 67.5°; (d) ap = 0.64 μm, 100 ≤ vs/vw ≤ 4000, α = 67.5°.
Fig. 8
Fig. 8 Relative effects of grinding parameters on (a) SR and (b) SSD depth by theoretical calculation. Re– relative effect; ap–cutting depth; vs–wheel speed; vw–feed speed.
Fig. 9
Fig. 9 (a) Comparison among experimental SR and the calculated SR by Eq. (22) and Eq. (37); (b) Comparison among experimental SSD depth and the calculated SSD depth by Eqs. (24), (36) and (38).

Tables (3)

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Table 1 Material properties of fused silica

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Table 2 Grinding parameters by LHD method and SR and SSD depth for each fused silica sample

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Table 3 Coefficients of the quadratic model for SR and SSD depth. The data in second and third columns is used for Section 4.3; the data in fourth and fifth columns is used for Section 5.3.

Equations (38)

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C lhi =k (cotα) 1/3 E 1/2 H s F ni 1/2
C lwi =k (cotα) 5/12 ( E 3/4 H s K c (1 ν 2 ) 1/2 ) 1/2 F ni 5/8
C lwi = K 1 C lhi 5/4
C lhi = K 0 h i
C lwi = K 1 K 0 5/4 h i 5/4
C mi =λ h i 4/3
h c =0.15 E H s ( K c H s ) 2
h i = h m 2 ( d e a p ) 1/2 θ i
θ c = 2 h c h m ( a p d e ) 1/2
h m = [ 4 Cr v w v s ( a p d e ) 1/2 ] 1/2
h i =A θ i
h m =2B
C= 4f d g 2 (4π/3υ) 2/3
θ m =arcsin[ 2 ( a p / d e ) 1/2 ]
y i =0.25 d e θ i 2
SSD m =max( SSD mi ) =max(( C mi h i )cos θ i y i )
SSD l =max( SSD li ) =max(( C lhi h i )cos θ i + C lwi sin θ i y i )
SR=max( SR i ) =max(( C lhi h i )cos θ i y i )
SR i-1 =( K 0 1)A θ i cos θ i
cos θ i =1 1 2! θ i 2 + 1 4! θ i 4 ...+ (1) m 2m! θ i 2m
SR i-1 =( K 0 1)A θ i
SR 1 =2B( K 0 1)
SSD mi-1 =λ A 4/3 θ i 4/3 A θ i
SSD m-1 =λ (2B) 4/3 2B
SSD li-1 =( K 0 1)A θ i + K 1 K 0 5/4 A 5/4 θ i 9/4
SSD l-1 =2B( K 0 1)+2 K 1 K 0 5/4 (2B) 5/4 ( a p / d e ) 1/2
SSD 1 ={ λ ( SR 1 K 0 1 ) 4/3 SR 1 K 0 1 SSD m 1 SSD l 1 SR 1 + K 1 K 0 5/4 A ( SR 1 K 0 1 ) 9/4 SSD m 1 < SSD l 1
SR i-2 =( K 0 1)A θ i 0.25 d e θ i 2
SR 2 ={ 2B( K 0 1) a p θ m 2A( K 0 1 )/ d e A 2 ( K 0 1) 2 / d e θ m >2A( K 0 1 )/ d e
SSD mi-2 =λ A 4/3 θ i 4/3 A θ i 0.25 d e θ i 2
SSD li-2 =( K 0 1)A θ i + K 1 K 0 5/4 A 5/4 θ i 9/4 0.25 d e θ i 2
y=F( x 1 , x 2 , x 3 , ... x n )+ε
F= a 0 + i=1 n a i x i + i=1 n a ii x i 2 + i<j n a ij x i x j
Re i = β i i=1 N | β i | ×100%
SR or SSD= a 0 + a 1 a p + a 2 v s + a 3 v w + a 11 a p 2 + a 22 v s 2 + a 33 v w 2 + a 12 a p v s + a 13 a p v w + a 23 v s v w
SSD=λ (2B) 4/3 2B+ l 0
SR=2 l 2 B( l 1 K 0 1)
SSD= l 3 λ (2 l 2 B) 4/3 2 l 2 B

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