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.

© 2015 Optical Society of America

Full Article  |  PDF Article
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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  27. 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]
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    [Crossref]
  29. 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]
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    [Crossref]
  31. 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]
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    [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)

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.

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]

Bang, Y.-B.

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]

Bauer, A.

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.

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.

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]

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.

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.

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]

Kiyono, S.

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]

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.

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]

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.-

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]

Lee, K.-I.

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]

Lee, K.-M.

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]

Li, L.

Li, Y.

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]

Lin, J.

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]

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]

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. 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]

Liu, X.

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]

Liu, Z.

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]

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.

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]

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.

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]

Nakamoto, K.

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]

Naples, N.

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]

Naples, N. J.

Neo, D. W. K.

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]

Okazaki, Y.

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]

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.

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]

Risse, S.

Rolland, J. P.

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.

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]

Takahashi, M.

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]

To, S.

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]

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.

Wada, T.

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]

Wang, G. L.

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).

Wang, H.

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]

Wang, R.

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]

Wang, Y.

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]

Weckenmann, A.

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]

Wei, G.

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]

Whitehouse, D.

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

Wong, Y.

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]

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]

Wong, Y. 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]

Xu, P.

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]

Xue, D.

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]

Yamanaka, M.

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]

Yang, D.

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]

Yi, A. Y.

Yu, D.

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]

Yu, D. P.

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]

Zhang, G.

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]

Zhang, H.

Zhang, S.

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]

Zhang, X.

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]

Zhang, X. D.

Zhao, S.

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]

Zheng, Z. W.

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).

Zhou, J.

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]

Zhou, M.

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]

Zhou, X.

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]

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]

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. 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]

Zhu, D. C.

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).

Zhu, L.

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]

Zhu, Z.

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]

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]

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. 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]

Adv. Opt. Technol. (1)

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

CIRP Annals-Manufacturing Technology (2)

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

Comput. Aided Des. (5)

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]

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]

Comput. Aided Geom. Des. (1)

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

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

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]

Int. J. Mach. Tools Manuf. (4)

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]

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]

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]

J. Manuf. Sci. Eng. (1)

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

J. Micromech. Microeng. (3)

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]

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]

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]

Journal of the Japan Society for Precision Engineering (1)

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]

Mater. Manuf. Process. (1)

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]

Min. Sci. Technol. (1)

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).

Opt. Express (5)

Precis. Eng. (5)

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]

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

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]

Proc. Inst. Mech. Eng., B J. Eng. Manuf. (1)

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]

Science of Advanced Materials (1)

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]

Other (2)

Website of DiffSys software, http://www.diffsys.com/ .

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

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Figures (8)

Fig. 1
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.
Fig. 2
Fig. 2 Schematic of the adaptive strategy of (a) the sampling and (b) the side-feeding motion.
Fig. 3
Fig. 3 Relationship between the CCP and the CLP.
Fig. 4
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.
Fig. 5
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.
Fig. 6
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.
Fig. 7
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.
Fig. 8
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.

Tables (1)

Tables Icon

Table 1 Results of the turned surfaces

Equations (16)

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θ w ( k , l ) = 2 π ( k 1 ) + 2 π l N s
k s ( k , l ) = 2 g w θ w 2 [ 1 + g w θ w ] 3 2 | θ w = θ w ( k , l )
L s ( k , l ) = 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 ) + 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
{ 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 ) )
{ θ w ( 1 , l ) = 2 π l / N s ρ w ( 1 , l ) = θ w ( 1 , l ) ρ w ( 2 , 1 ) / 2 π
θ w ( k , g ) = arg : min { | θ w ( k , l ) φ w ( k , j ) | , 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
Tan ( F w , G ) = F w × G = ( F w x w , F w y w , 1 ) × ( G x w , G y w , 0 )
R f = | 1 k f | = | [ Tan ( F w , G ) · ( Tan ( F w , G ) ) ] × Tan ( F w , G ) | | Tan ( F w , G ) | 3 | x w = r w ( k , j ) cos φ w ( k , j ) y w = r w ( k , j ) sin φ w ( k , j )
[ 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 ) ) ] = L f
n w ( k , j ) = ( f w x w , f w y w , 1 ) ( f w x w , f w y w , 1 ) | x w = r w ( k , j ) cos φ w ( k , j ) y w = r w ( k , j ) sin φ w ( k , j )
[ x CLP ( k , j ) y CLP ( k , j ) z CLP ( k , j ) ] = [ x CCP ( k , j ) y CCP ( k , j ) z CCP ( k , j ) ] + n w ( k , j ) ( n w ( k , j ) n t ( k , j ) ) n t ( k , j ) n w ( k , j ) ( n w ( k , j ) 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 )

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