Adaptive tool servo diamond turning for enhancing machining efficiency and surface quality of freeform optics

Zhiwei Zhu; Suet To

doi:10.1364/OE.23.020234

Adaptive tool servo diamond turning for enhancing machining efficiency and surface quality of freeform optics

Zhiwei Zhu and Suet To

Optics Express
Vol. 23,
Issue 16,
pp. 20234-20248
(2015)
•https://doi.org/10.1364/OE.23.020234

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Zhiwei Zhu and Suet To, "Adaptive tool servo diamond turning for enhancing machining efficiency and surface quality of freeform optics," Opt. Express 23, 20234-20248 (2015)

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Related Topics
Table of Contents Category
- Geometrical Optics
Optics & Photonics Topics
?

The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Diamond machining (220.1920)
- Microstructure fabrication (220.4000)

About this Article
History
- Original Manuscript: April 15, 2015
- Manuscript Accepted: June 15, 2015
- Published: July 27, 2015

Accessible

Open Access

Abstract

Fast tool servo/ slow tool servo (FTS/STS) diamond turning is a very promising technique for the generation of freeform optics. However, the currently adopted constant scheme for azimuth sampling and side-feeding motion possesses no adaptation to surface shape variation, leading to the non-uniform surface quality and low machining efficiency. To overcome this defect, this paper reports on a novel adaptive tool servo (ATS) diamond turning technique which is essentially based on the novel two-degree-of-freedom (2-DOF) FTS/STS. In the ATS, the sampling interval and the side-feeding motion are actively controlled at any cutting point to adapt the machining process to shape variation of the desired surface, making both the sampling induced interpolation error and the side-feeding induced residual tool mark be within the desired tolerances. Characteristic of the required cutting motion suggests that besides the conventional z-axis servo motion, another servo motion along the x-axis synthesizing by the c-axis is mandatory for implementing the ATS. Comparative studies of surface generation of typical micro-structured surfaces in FTS/STS and ATS are thoroughly conducted both theoretically and experimentally. The result demonstrates that the ATS outperforms the FTS/STS with improved surface quality while simultaneously enhanced machining efficiency.

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References

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Publication

X. Jiang, P. Scott, and D. Whitehouse, “Freeform surface characterisation-A fresh strategy,” CIRP Annals-Manufacturing Technology 56(1), 553–556 (2007).
[Crossref]
A. Bauer and J. P. Rolland, “Visual space assessment of two all-reflective, freeform, optical see-through head-worn displays,” Opt. Express 22(11), 13155–13163 (2014).
[Crossref] [PubMed]
E. Brinksmeier, R. Gläbe, and L. Schönemann, “Diamond Micro Chiseling of large-scale retroreflective arrays,” Precis. Eng. 36(4), 650–657 (2012).
[Crossref]
F. Fang, X. Zhang, A. Weckenmann, G. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Annals-Manufacturing Technology 62(2), 823–846 (2013).
[Crossref]
H.-S. Kim, K.-I. Lee, K.-M. Lee, and Y.-B. Bang, “Fabrication of free-form surfaces using a long-stroke fast tool servo and corrective figuring with on-machine measurement,” Int. J. Mach. Tools Manuf. 49(12-13), 991–997 (2009).
[Crossref]
H. Zhang, L. Li, D. L. McCray, S. Scheiding, N. J. Naples, A. Gebhardt, S. Risse, R. Eberhardt, A. Tünnermann, and A. Y. Yi, “Development of a low cost high precision three-layer 3D artificial compound eye,” Opt. Express 21(19), 22232–22245 (2013).
[Crossref] [PubMed]
J. Zhou, L. Li, N. Naples, T. Sun, and A. Y. Yi, “Fabrication of continuous diffractive optical elements using a fast tool servo diamond turning process,” J. Micromech. Microeng. 23(7), 075010 (2013).
[Crossref]
G. L. Wang, Y. F. Dai, Z. W. Zheng, and D. C. Zhu, “Machining characteristics of complex surfaces using fast tool servo system,” Min. Sci. Technol. 15, 324–337 (2011).
F. Z. Fang, X. D. Zhang, and X. T. Hu, “Cylindrical coordinate machining of optical freeform surfaces,” Opt. Express 16(10), 7323–7329 (2008).
[Crossref] [PubMed]
X. Zhang, F. Fang, H. Wang, G. Wei, and X. Hu, “Ultra-precision machining of sinusoidal surfaces using the cylindrical coordinate method,” J. Micromech. Microeng. 19(5), 054004 (2009).
[Crossref]
D. P. Yu, Y. Wong, and G. S. Hong, “Optimal selection of machining parameters for fast tool servo diamond turning,” Int. J. Adv. Manuf. Technol. 57(1-4), 85–99 (2011).
[Crossref]
S. Scheiding, A. Y. Yi, A. Gebhardt, L. Li, S. Risse, R. Eberhardt, and A. Tünnermann, “Freeform manufacturing of a microoptical lens array on a steep curved substrate by use of a voice coil fast tool servo,” Opt. Express 19(24), 23938–23951 (2011).
[Crossref] [PubMed]
D. P. Yu, G. S. Hong, and Y. S. Wong, “Profile error compensation in fast tool servo diamond turning of micro-structured surfaces,” Int. J. Mach. Tools Manuf. 52(1), 13–23 (2012).
[Crossref]
X. Lu and D. L. Trumper, “Spindle rotary position estimation for fast tool servo trajectory generation,” Int. J. Mach. Tools Manuf. 47(9), 1362–1367 (2007).
[Crossref]
D. Yu, Y. Wong, and G. Hong, “Ultraprecision machining of micro-structured functional surfaces on brittle materials,” J. Micromech. Microeng. 21(9), 095011 (2011).
[Crossref]
Z. Zhu, X. Zhou, Q. Liu, J. Lin, and S. Zhao, “Fabrication of micro-structured surfaces on bulk metallic glasses based on fast tool servo assisted diamond turning,” Science of Advanced Materials 4(9), 906–911 (2012).
[Crossref]
D. W. K. Neo, A. S. Kumar, and M. Rahman, “A novel surface analytical model for cutting linearization error in fast tool/slow slide servo diamond turning,” Precis. Eng. 38(4), 849–860 (2014).
[Crossref]
L. Dick, S. Risse, and A. Tünnermann, “Injection molded high precision freeform optics for high volume applications,” Adv. Opt. Technol. 1, 39–50 (2012).
W. Gao, T. Araki, S. Kiyono, Y. Okazaki, and M. Yamanaka, “Precision nano-fabrication and evaluation of a large area sinusoidal grid surface for a surface encoder,” Precis. Eng. 27(3), 289–298 (2003).
[Crossref]
M. Zhou, H. Zhang, and S. Chen, “Study on diamond cutting of nonrationally symmetric microstructured surfaces with fast tool servo,” Mater. Manuf. Process. 25(6), 488–494 (2010).
[Crossref]
H. Gong, Y. Wang, L. Song, and F. Fang, “Spiral tool path generation for diamond turning optical freeform surfaces of quasi-revolution,” Comput. Aided Des. 59, 15–22 (2015).
[Crossref]
Q. Liu, X. Zhou, and P. Xu, “A new tool path for optical freeform surface fast tool servo diamond turning,” Proc. Inst. Mech. Eng., B J. Eng. Manuf. 228(12), 1721–1726 (2014).
[Crossref]
E. Brinksmeier and W. Preuss, “How to diamond turn an elliptic half-shell?” Precis. Eng. 37(4), 944–947 (2013).
[Crossref]
Z. Zhu, X. Zhou, Z. Liu, R. Wang, and L. Zhu, “Development of a piezoelectrically actuated two-degree-of-freedom fast tool servo with decoupled motions for micro-/nanomachining,” Precis. Eng. 38(4), 809–820 (2014).
[Crossref]
T. Wada, M. Takahashi, T. Moriwaki, and K. Nakamoto, “Development of a Three Axis controlled Fast Tool Servo for Ultra Precision Machining (1st Report),” Journal of the Japan Society for Precision Engineering 73(12), 1345–1349 (2007).
[Crossref]
Z. Zhu, X. Zhou, D. Luo, and Q. Liu, “Development of pseudo-random diamond turning method for fabricating freeform optics with scattering homogenization,” Opt. Express 21(23), 28469–28482 (2013).
[Crossref] [PubMed]
Z. Lin, J. Fu, H. Shen, and W. Gan, “A generic uniform scallop tool path generation method for five-axis machining of freeform surface,” Comput. Aided Des. 56, 120–132 (2014).
[Crossref]
A. Lasemi, D. Xue, and P. Gu, “Recent development in CNC machining of freeform surfaces: A state-of-the-art review,” Comput. Aided Des. 42(7), 641–654 (2010).
[Crossref]
X. Liu, Y. Li, S. Ma, and C.- Lee, “A tool path generation method for freeform surface machining by introducing the tensor property of machining strip width,” Comput. Aided Des. 66, 1–13 (2015).
[Crossref]
S. Ding, M. Mannan, A. N. Poo, D. Yang, and Z. Han, “Adaptive iso-planar tool path generation for machining of free-form surfaces,” Comput. Aided Des. 35(2), 141–153 (2003).
[Crossref]
Z. Zhu, S. To, and S. Zhang, “Theoretical and experimental investigation on the novel end-fly-cutting-servo diamond machining of hierarchical micro-nanostructures,” Int. J. Mach. Tools Manuf. 94, 15–25 (2015).
[Crossref]
Website of DiffSys software, http://www.diffsys.com/ .
R.-S. Lin and Y. Koren, “Efficient tool-path planning for machining free-form surfaces,” J. Manuf. Sci. Eng. 118, 20–28 (1996).
C. De Boor, “A practical guide to splines,” Math. Comput. (1978).
R. Goldman, “Curvature formulas for implicit curves and surfaces,” Comput. Aided Geom. Des. 22(7), 632–658 (2005).
[Crossref]

2015 (3)

H. Gong, Y. Wang, L. Song, and F. Fang, “Spiral tool path generation for diamond turning optical freeform surfaces of quasi-revolution,” Comput. Aided Des. 59, 15–22 (2015).
[Crossref]

X. Liu, Y. Li, S. Ma, and C.- Lee, “A tool path generation method for freeform surface machining by introducing the tensor property of machining strip width,” Comput. Aided Des. 66, 1–13 (2015).
[Crossref]

Z. Zhu, S. To, and S. Zhang, “Theoretical and experimental investigation on the novel end-fly-cutting-servo diamond machining of hierarchical micro-nanostructures,” Int. J. Mach. Tools Manuf. 94, 15–25 (2015).
[Crossref]

2014 (5)

Z. Lin, J. Fu, H. Shen, and W. Gan, “A generic uniform scallop tool path generation method for five-axis machining of freeform surface,” Comput. Aided Des. 56, 120–132 (2014).
[Crossref]

Q. Liu, X. Zhou, and P. Xu, “A new tool path for optical freeform surface fast tool servo diamond turning,” Proc. Inst. Mech. Eng., B J. Eng. Manuf. 228(12), 1721–1726 (2014).
[Crossref]

D. W. K. Neo, A. S. Kumar, and M. Rahman, “A novel surface analytical model for cutting linearization error in fast tool/slow slide servo diamond turning,” Precis. Eng. 38(4), 849–860 (2014).
[Crossref]

Z. Zhu, X. Zhou, Z. Liu, R. Wang, and L. Zhu, “Development of a piezoelectrically actuated two-degree-of-freedom fast tool servo with decoupled motions for micro-/nanomachining,” Precis. Eng. 38(4), 809–820 (2014).
[Crossref]

A. Bauer and J. P. Rolland, “Visual space assessment of two all-reflective, freeform, optical see-through head-worn displays,” Opt. Express 22(11), 13155–13163 (2014).
[Crossref] [PubMed]

2013 (5)

F. Fang, X. Zhang, A. Weckenmann, G. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Annals-Manufacturing Technology 62(2), 823–846 (2013).
[Crossref]

H. Zhang, L. Li, D. L. McCray, S. Scheiding, N. J. Naples, A. Gebhardt, S. Risse, R. Eberhardt, A. Tünnermann, and A. Y. Yi, “Development of a low cost high precision three-layer 3D artificial compound eye,” Opt. Express 21(19), 22232–22245 (2013).
[Crossref] [PubMed]

J. Zhou, L. Li, N. Naples, T. Sun, and A. Y. Yi, “Fabrication of continuous diffractive optical elements using a fast tool servo diamond turning process,” J. Micromech. Microeng. 23(7), 075010 (2013).
[Crossref]

Z. Zhu, X. Zhou, D. Luo, and Q. Liu, “Development of pseudo-random diamond turning method for fabricating freeform optics with scattering homogenization,” Opt. Express 21(23), 28469–28482 (2013).
[Crossref] [PubMed]

E. Brinksmeier and W. Preuss, “How to diamond turn an elliptic half-shell?” Precis. Eng. 37(4), 944–947 (2013).
[Crossref]

2012 (4)

L. Dick, S. Risse, and A. Tünnermann, “Injection molded high precision freeform optics for high volume applications,” Adv. Opt. Technol. 1, 39–50 (2012).

E. Brinksmeier, R. Gläbe, and L. Schönemann, “Diamond Micro Chiseling of large-scale retroreflective arrays,” Precis. Eng. 36(4), 650–657 (2012).
[Crossref]

D. P. Yu, G. S. Hong, and Y. S. Wong, “Profile error compensation in fast tool servo diamond turning of micro-structured surfaces,” Int. J. Mach. Tools Manuf. 52(1), 13–23 (2012).
[Crossref]

Z. Zhu, X. Zhou, Q. Liu, J. Lin, and S. Zhao, “Fabrication of micro-structured surfaces on bulk metallic glasses based on fast tool servo assisted diamond turning,” Science of Advanced Materials 4(9), 906–911 (2012).
[Crossref]

2011 (4)

D. Yu, Y. Wong, and G. Hong, “Ultraprecision machining of micro-structured functional surfaces on brittle materials,” J. Micromech. Microeng. 21(9), 095011 (2011).
[Crossref]

D. P. Yu, Y. Wong, and G. S. Hong, “Optimal selection of machining parameters for fast tool servo diamond turning,” Int. J. Adv. Manuf. Technol. 57(1-4), 85–99 (2011).
[Crossref]

S. Scheiding, A. Y. Yi, A. Gebhardt, L. Li, S. Risse, R. Eberhardt, and A. Tünnermann, “Freeform manufacturing of a microoptical lens array on a steep curved substrate by use of a voice coil fast tool servo,” Opt. Express 19(24), 23938–23951 (2011).
[Crossref] [PubMed]

G. L. Wang, Y. F. Dai, Z. W. Zheng, and D. C. Zhu, “Machining characteristics of complex surfaces using fast tool servo system,” Min. Sci. Technol. 15, 324–337 (2011).

2010 (2)

M. Zhou, H. Zhang, and S. Chen, “Study on diamond cutting of nonrationally symmetric microstructured surfaces with fast tool servo,” Mater. Manuf. Process. 25(6), 488–494 (2010).
[Crossref]

A. Lasemi, D. Xue, and P. Gu, “Recent development in CNC machining of freeform surfaces: A state-of-the-art review,” Comput. Aided Des. 42(7), 641–654 (2010).
[Crossref]

2009 (2)

H.-S. Kim, K.-I. Lee, K.-M. Lee, and Y.-B. Bang, “Fabrication of free-form surfaces using a long-stroke fast tool servo and corrective figuring with on-machine measurement,” Int. J. Mach. Tools Manuf. 49(12-13), 991–997 (2009).
[Crossref]

X. Zhang, F. Fang, H. Wang, G. Wei, and X. Hu, “Ultra-precision machining of sinusoidal surfaces using the cylindrical coordinate method,” J. Micromech. Microeng. 19(5), 054004 (2009).
[Crossref]

2008 (1)

F. Z. Fang, X. D. Zhang, and X. T. Hu, “Cylindrical coordinate machining of optical freeform surfaces,” Opt. Express 16(10), 7323–7329 (2008).
[Crossref] [PubMed]

2007 (3)

X. Jiang, P. Scott, and D. Whitehouse, “Freeform surface characterisation-A fresh strategy,” CIRP Annals-Manufacturing Technology 56(1), 553–556 (2007).
[Crossref]

X. Lu and D. L. Trumper, “Spindle rotary position estimation for fast tool servo trajectory generation,” Int. J. Mach. Tools Manuf. 47(9), 1362–1367 (2007).
[Crossref]

T. Wada, M. Takahashi, T. Moriwaki, and K. Nakamoto, “Development of a Three Axis controlled Fast Tool Servo for Ultra Precision Machining (1st Report),” Journal of the Japan Society for Precision Engineering 73(12), 1345–1349 (2007).
[Crossref]

2005 (1)

R. Goldman, “Curvature formulas for implicit curves and surfaces,” Comput. Aided Geom. Des. 22(7), 632–658 (2005).
[Crossref]

2003 (2)

S. Ding, M. Mannan, A. N. Poo, D. Yang, and Z. Han, “Adaptive iso-planar tool path generation for machining of free-form surfaces,” Comput. Aided Des. 35(2), 141–153 (2003).
[Crossref]

W. Gao, T. Araki, S. Kiyono, Y. Okazaki, and M. Yamanaka, “Precision nano-fabrication and evaluation of a large area sinusoidal grid surface for a surface encoder,” Precis. Eng. 27(3), 289–298 (2003).
[Crossref]

1996 (1)

R.-S. Lin and Y. Koren, “Efficient tool-path planning for machining free-form surfaces,” J. Manuf. Sci. Eng. 118, 20–28 (1996).

Araki, T.

Bang, Y.-B.

Bauer, A.

A. Bauer and J. P. Rolland, “Visual space assessment of two all-reflective, freeform, optical see-through head-worn displays,” Opt. Express 22(11), 13155–13163 (2014).
[Crossref] [PubMed]

Brinksmeier, E.

E. Brinksmeier and W. Preuss, “How to diamond turn an elliptic half-shell?” Precis. Eng. 37(4), 944–947 (2013).
[Crossref]

E. Brinksmeier, R. Gläbe, and L. Schönemann, “Diamond Micro Chiseling of large-scale retroreflective arrays,” Precis. Eng. 36(4), 650–657 (2012).
[Crossref]

Chen, S.

M. Zhou, H. Zhang, and S. Chen, “Study on diamond cutting of nonrationally symmetric microstructured surfaces with fast tool servo,” Mater. Manuf. Process. 25(6), 488–494 (2010).
[Crossref]

Dai, Y. F.

G. L. Wang, Y. F. Dai, Z. W. Zheng, and D. C. Zhu, “Machining characteristics of complex surfaces using fast tool servo system,” Min. Sci. Technol. 15, 324–337 (2011).

De Boor, C.

C. De Boor, “A practical guide to splines,” Math. Comput. (1978).

Dick, L.

L. Dick, S. Risse, and A. Tünnermann, “Injection molded high precision freeform optics for high volume applications,” Adv. Opt. Technol. 1, 39–50 (2012).

Ding, S.

S. Ding, M. Mannan, A. N. Poo, D. Yang, and Z. Han, “Adaptive iso-planar tool path generation for machining of free-form surfaces,” Comput. Aided Des. 35(2), 141–153 (2003).
[Crossref]

Eberhardt, R.

Evans, C.

F. Fang, X. Zhang, A. Weckenmann, G. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Annals-Manufacturing Technology 62(2), 823–846 (2013).
[Crossref]

Fang, F.

H. Gong, Y. Wang, L. Song, and F. Fang, “Spiral tool path generation for diamond turning optical freeform surfaces of quasi-revolution,” Comput. Aided Des. 59, 15–22 (2015).
[Crossref]

F. Fang, X. Zhang, A. Weckenmann, G. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Annals-Manufacturing Technology 62(2), 823–846 (2013).
[Crossref]

X. Zhang, F. Fang, H. Wang, G. Wei, and X. Hu, “Ultra-precision machining of sinusoidal surfaces using the cylindrical coordinate method,” J. Micromech. Microeng. 19(5), 054004 (2009).
[Crossref]

Fang, F. Z.

F. Z. Fang, X. D. Zhang, and X. T. Hu, “Cylindrical coordinate machining of optical freeform surfaces,” Opt. Express 16(10), 7323–7329 (2008).
[Crossref] [PubMed]

Fu, J.

Z. Lin, J. Fu, H. Shen, and W. Gan, “A generic uniform scallop tool path generation method for five-axis machining of freeform surface,” Comput. Aided Des. 56, 120–132 (2014).
[Crossref]

Gan, W.

Z. Lin, J. Fu, H. Shen, and W. Gan, “A generic uniform scallop tool path generation method for five-axis machining of freeform surface,” Comput. Aided Des. 56, 120–132 (2014).
[Crossref]

Gao, W.

Gebhardt, A.

Gläbe, R.

E. Brinksmeier, R. Gläbe, and L. Schönemann, “Diamond Micro Chiseling of large-scale retroreflective arrays,” Precis. Eng. 36(4), 650–657 (2012).
[Crossref]

Goldman, R.

R. Goldman, “Curvature formulas for implicit curves and surfaces,” Comput. Aided Geom. Des. 22(7), 632–658 (2005).
[Crossref]

Gong, H.

H. Gong, Y. Wang, L. Song, and F. Fang, “Spiral tool path generation for diamond turning optical freeform surfaces of quasi-revolution,” Comput. Aided Des. 59, 15–22 (2015).
[Crossref]

Gu, P.

A. Lasemi, D. Xue, and P. Gu, “Recent development in CNC machining of freeform surfaces: A state-of-the-art review,” Comput. Aided Des. 42(7), 641–654 (2010).
[Crossref]

Han, Z.

S. Ding, M. Mannan, A. N. Poo, D. Yang, and Z. Han, “Adaptive iso-planar tool path generation for machining of free-form surfaces,” Comput. Aided Des. 35(2), 141–153 (2003).
[Crossref]

Hong, G.

D. Yu, Y. Wong, and G. Hong, “Ultraprecision machining of micro-structured functional surfaces on brittle materials,” J. Micromech. Microeng. 21(9), 095011 (2011).
[Crossref]

Hong, G. S.

D. P. Yu, G. S. Hong, and Y. S. Wong, “Profile error compensation in fast tool servo diamond turning of micro-structured surfaces,” Int. J. Mach. Tools Manuf. 52(1), 13–23 (2012).
[Crossref]

D. P. Yu, Y. Wong, and G. S. Hong, “Optimal selection of machining parameters for fast tool servo diamond turning,” Int. J. Adv. Manuf. Technol. 57(1-4), 85–99 (2011).
[Crossref]

Hu, X.

X. Zhang, F. Fang, H. Wang, G. Wei, and X. Hu, “Ultra-precision machining of sinusoidal surfaces using the cylindrical coordinate method,” J. Micromech. Microeng. 19(5), 054004 (2009).
[Crossref]

Hu, X. T.

F. Z. Fang, X. D. Zhang, and X. T. Hu, “Cylindrical coordinate machining of optical freeform surfaces,” Opt. Express 16(10), 7323–7329 (2008).
[Crossref] [PubMed]

Jiang, X.

X. Jiang, P. Scott, and D. Whitehouse, “Freeform surface characterisation-A fresh strategy,” CIRP Annals-Manufacturing Technology 56(1), 553–556 (2007).
[Crossref]

Kim, H.-S.

Kiyono, S.

Koren, Y.

R.-S. Lin and Y. Koren, “Efficient tool-path planning for machining free-form surfaces,” J. Manuf. Sci. Eng. 118, 20–28 (1996).

Kumar, A. S.

Lasemi, A.

A. Lasemi, D. Xue, and P. Gu, “Recent development in CNC machining of freeform surfaces: A state-of-the-art review,” Comput. Aided Des. 42(7), 641–654 (2010).
[Crossref]

Lee, C.-

Lee, K.-I.

Lee, K.-M.

Li, L.

Li, Y.

Lin, J.

Lin, R.-S.

R.-S. Lin and Y. Koren, “Efficient tool-path planning for machining free-form surfaces,” J. Manuf. Sci. Eng. 118, 20–28 (1996).

Lin, Z.

Z. Lin, J. Fu, H. Shen, and W. Gan, “A generic uniform scallop tool path generation method for five-axis machining of freeform surface,” Comput. Aided Des. 56, 120–132 (2014).
[Crossref]

Liu, Q.

Q. Liu, X. Zhou, and P. Xu, “A new tool path for optical freeform surface fast tool servo diamond turning,” Proc. Inst. Mech. Eng., B J. Eng. Manuf. 228(12), 1721–1726 (2014).
[Crossref]

Liu, X.

Liu, Z.

Lu, X.

X. Lu and D. L. Trumper, “Spindle rotary position estimation for fast tool servo trajectory generation,” Int. J. Mach. Tools Manuf. 47(9), 1362–1367 (2007).
[Crossref]

Luo, D.

Ma, S.

Mannan, M.

S. Ding, M. Mannan, A. N. Poo, D. Yang, and Z. Han, “Adaptive iso-planar tool path generation for machining of free-form surfaces,” Comput. Aided Des. 35(2), 141–153 (2003).
[Crossref]

McCray, D. L.

Moriwaki, T.

Nakamoto, K.

Naples, N.

Naples, N. J.

Neo, D. W. K.

Okazaki, Y.

Poo, A. N.

S. Ding, M. Mannan, A. N. Poo, D. Yang, and Z. Han, “Adaptive iso-planar tool path generation for machining of free-form surfaces,” Comput. Aided Des. 35(2), 141–153 (2003).
[Crossref]

Preuss, W.

E. Brinksmeier and W. Preuss, “How to diamond turn an elliptic half-shell?” Precis. Eng. 37(4), 944–947 (2013).
[Crossref]

Rahman, M.

Risse, S.

L. Dick, S. Risse, and A. Tünnermann, “Injection molded high precision freeform optics for high volume applications,” Adv. Opt. Technol. 1, 39–50 (2012).

Rolland, J. P.

A. Bauer and J. P. Rolland, “Visual space assessment of two all-reflective, freeform, optical see-through head-worn displays,” Opt. Express 22(11), 13155–13163 (2014).
[Crossref] [PubMed]

Scheiding, S.

Schönemann, L.

E. Brinksmeier, R. Gläbe, and L. Schönemann, “Diamond Micro Chiseling of large-scale retroreflective arrays,” Precis. Eng. 36(4), 650–657 (2012).
[Crossref]

Scott, P.

X. Jiang, P. Scott, and D. Whitehouse, “Freeform surface characterisation-A fresh strategy,” CIRP Annals-Manufacturing Technology 56(1), 553–556 (2007).
[Crossref]

Shen, H.

Z. Lin, J. Fu, H. Shen, and W. Gan, “A generic uniform scallop tool path generation method for five-axis machining of freeform surface,” Comput. Aided Des. 56, 120–132 (2014).
[Crossref]

Song, L.

H. Gong, Y. Wang, L. Song, and F. Fang, “Spiral tool path generation for diamond turning optical freeform surfaces of quasi-revolution,” Comput. Aided Des. 59, 15–22 (2015).
[Crossref]

Sun, T.

Takahashi, M.

To, S.

Trumper, D. L.

X. Lu and D. L. Trumper, “Spindle rotary position estimation for fast tool servo trajectory generation,” Int. J. Mach. Tools Manuf. 47(9), 1362–1367 (2007).
[Crossref]

Tünnermann, A.

L. Dick, S. Risse, and A. Tünnermann, “Injection molded high precision freeform optics for high volume applications,” Adv. Opt. Technol. 1, 39–50 (2012).

Wada, T.

Wang, G. L.

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Fig. 1 Schematic of cutting motions and error generations in FTS/STS, (a) the relative motions, (b) behavior in the forward cutting direction and (c) behavior in the side-feeding direction.

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Fig. 2 Schematic of the adaptive strategy of (a) the sampling and (b) the side-feeding motion.

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Fig. 3 Relationship between the CCP and the CLP.

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Fig. 4 Features of the adaptive toolpath, (a) the desired surface and the corresponding CCP, (b) the CLPs, (c) and (d) the projected toolpath for the FTS/STS and the ATS.

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Fig. 5 Features of the motion components in the ATS, (a) the sampling variations, (b) the translational servo motions along the z-axis, (c) side-feeding motions of the slide along the x-axis, and (d) the fluctuations of the motions along the x-axis.

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Fig. 6 Characteristics of the generated surface error maps in (a) the ATS turning, (b) the conventional FTS/STS turning, and the projected errors obtained in (c) the ATS turning, (d) the FTS/STS turning.

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Fig. 7 Hardware configuration of the ATS system, where (1) lubrication nozzle; (2) workpiece; (3) fixture; (4) vacuum chuck; (5) diamond tool, and o-xyz denotes the coordinate system of the machine tool.

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Fig. 8 The practical surface obtained by (a) ATS, (b) STS; and the error maps of the turned surfaces obtained by (c) ATS, (d) STS.

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Tables (1)

Table 1 Results of the turned surfaces

View Table

Equations (16)

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θ_{w}^{(k, l)} = 2 π (k - 1) + \frac{2 π l}{N_{s}}

{k_{s}^{(k, l)} = \frac{\frac{\partial^{2} g_{w}}{\partial θ_{w}^{2}}}{{[1 + \frac{\partial g_{w}}{\partial θ_{w}}]}^{\frac{3}{2}}} |}_{θ_{w} = θ_{w}^{(k, l)}}

L_{s}^{(k, l)} = \sqrt{\frac{8 R_{t} ε_{s}}{1 - R_{t} k_{s}^{(k, l)}}}

‖ P^{(k, l)} - P^{(k + 1, l)} ‖ = L_{s}^{(k, l)}

ρ_{w}^{(k + 1, l)} = ρ_{w}^{(k, l)} + \sqrt{\frac{8 R_{t} ε_{s}}{1 - R_{t} k_{s}^{(k, l)}} - {[g_{w} (ρ_{w}^{(k + 1, l)}, θ_{w}^{(k, l)} + 2 π) - g_{w} (ρ_{w}^{(k, l)}, θ_{w}^{(k, l)})]}^{2}}

{\begin{cases} x_{CCP}^{(k + 1, l)} = ρ_{w}^{(k + 1, l)} \cos (θ_{w}^{(k, l)} + 2 π) = ρ_{w}^{(k + 1, l)} \cos θ_{w}^{(k, l)} \\ y_{CCP}^{(k + 1, l)} = ρ_{w}^{(k + 1, l)} \sin (θ_{w}^{(k, l)} + 2 π) = ρ_{w}^{(k + 1, l)} \sin θ_{w}^{(k, l)} \\ z_{CCP}^{(k + 1, l)} = g_{w} (ρ_{w}^{(k + 1, l)}, θ_{w}^{(k, l)} + 2 π) = f_{w} (x_{CCP}^{(k + 1, l)}, y_{CCP}^{(k + 1, l)}) \end{cases}

{\begin{cases} θ_{w}^{(1, l)} = 2 π l / N_{s} \\ ρ_{w}^{(1, l)} = θ_{w}^{(1, l)} ρ_{w}^{(2, 1)} / 2 π \end{cases}

θ_{w}^{(k, g)} = \arg : \min {| θ_{w}^{(k, l)} - φ_{w}^{(k, j)} |, \forall l}

r_{w}^{(k, j)} = S [(θ_{g}, ρ_{g}) | φ_{w}^{(k, j)}]

G (x_{w}, y_{w}, z_{w}) = x_{w}^{2} + y_{w}^{2} - r^{2}_{w}^{(k, j)} = 0

\begin{array}{l} Tan (F_{w}, G) = \nabla F_{w} \times \nabla G \\ = (\frac{\partial F_{w}}{\partial x_{w}}, \frac{\partial F_{w}}{\partial y_{w}}, - 1) \times (\frac{\partial G}{\partial x_{w}}, \frac{\partial G}{\partial y_{w}}, 0) \end{array}

R_{f} = | \frac{1}{k_{f}} | = {\frac{| [Tan (F_{w}, G) \cdot \nabla (Tan (F_{w}, G))] \times Tan (F_{w}, G) |}{{| Tan (F_{w}, G) |}^{3}} |}_{\begin{array}{l} x_{w} = r_{w}^{(k, j)} \cos φ_{w}^{(k, j)} \\ y_{w} = r_{w}^{(k, j)} \sin φ_{w}^{(k, j)} \end{array}}

‖ \begin{array}{l} [r_{w}^{(k, j + 1)} \cos φ_{w}^{(k, j + 1)}, r_{w}^{(k, j + 1)} \sin φ_{w}^{(k, j + 1)}, g_{w} (r_{w}^{(k, j + 1)}, φ_{w}^{(k, j + 1)})] \\ - [r_{w}^{(k, j)} \cos φ_{w}^{(k, j)}, r_{w}^{(k, j)} \sin φ_{w}^{(k, j)}, g_{w} (r_{w}^{(k, j)}, φ_{w}^{(k, j)})] \end{array} ‖ = L_{f}

n_{w}^{(k, j)} = {\frac{(- \frac{\partial f_{w}}{\partial x_{w}}, - \frac{\partial f_{w}}{\partial y_{w}}, 1)}{‖ (- \frac{\partial f_{w}}{\partial x_{w}}, - \frac{\partial f_{w}}{\partial y_{w}}, 1) ‖} |}_{\begin{array}{l} x_{w} = r_{w}^{(k, j)} \cos φ_{w}^{(k, j)} \\ y_{w} = r_{w}^{(k, j)} \sin φ_{w}^{(k, j)} \end{array}}

[\begin{array}{l} x_{CLP}^{(k, j)} \\ y_{CLP}^{(k, j)} \\ z_{CLP}^{(k, j)} \end{array}] = [\begin{array}{l} x_{CCP}^{(k, j)} \\ y_{CCP}^{(k, j)} \\ z_{CCP}^{(k, j)} \end{array}] + \frac{n_{w}^{(k, j)} - (n_{w}^{(k, j)} \cdot n_{t}^{(k, j)}) n_{t}^{(k, j)}}{‖ n_{w}^{(k, j)} - (n_{w}^{(k, j)} \cdot n_{t}^{(k, j)}) n_{t}^{(k, j)} ‖} R_{t}

n_{t}^{(k, j)} = (- \sin φ_{w}^{(k, j)}, \cos φ_{w}^{(k, j)}, 0)

	ATS	STS
Number of control points	38,3000	60,0000
Cutting time	23min32s	35min5s
PV error / nm	138.6	143.0
RMS error / nm	20.555	22.155
Roughness Ra / nm	7.063	7.212