Abstract

We report a way to shape surfaces by optimizing the path instead of changing the removal function of a polishing tool for magnetorheological jet polishing (MJP). The M-shaped removal function of MJP generates a track with a W-shaped profile along one path. However, applying two parallel paths with appropriate line spacing can obtain a track with V-shaped profile, which has a removal distribution similar to that by using the Gaussian removal function along one path. Based on this, a multiplex path applying an M-shaped removal function is constructed in an actual process. A transformation model describing the relationship between the M-shaped removal function and the Gaussian removal function is established, which is crucial to determine the velocity function on the multiplex path. By using the M-shaped removal function, we have planned new processing steps by applying the multiplex path and the velocity function for full aperture polishing. Polishing performance is designed and demonstrated on two K9 work-pieces with different multiplex paths. The form error on 23 mm diameter is decreased from 0.256λ PV (λ=632.8nm) and 0.068λ RMS to 0.038λ PV and 0.005λ RMS with scanning multiplex path. Results indicate that this method of path optimization is suitable for optical manufacturing.

© 2014 Optical Society of America

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References

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  1. W. I. Kordonski, A. B. Shorey, and M. Tricard, “Magnetorheological jet (MR JetTM) finishing technology,” J. Fluids Eng. 128, 20–26 (2006).
    [CrossRef]
  2. M. Tricard, W. I. Kordonski, and A. B. Shorey, “Magnetorheological jet finishing of conformal, freeform and steep concave optics,” CIRP Annals 55, 309–312 (2006).
    [CrossRef]
  3. W. Kordonski and A. Shorey, “Magnetorheological (MR) jet finishing technology,” J. Intell. Mater. Syst. Struct. 18, 1127–1130 (2007).
    [CrossRef]
  4. T. Wang, H. B. Cheng, Y. Chen, Y. P. Feng, Z. C. Dong, and H. Y. Tam, “Correction of remounting errors by masking reference points in small footprint polishing process,” Appl. Opt. 52, 7851–7858 (2013).
    [CrossRef]
  5. S. M. Booij, H. V. Brug, J. J. M. Braat, and O. W. Fähnle, “Nanometer deep shaping with fluid jet polishing,” Opt. Eng. 41, 1926–1931 (2002).
    [CrossRef]
  6. H. Fang, P. J. Guo, and J. C. Yu, “Optimization of the material removal in fluid jet polishing,” Opt. Eng. 45, 053401 (2006).
    [CrossRef]
  7. T. Wang, H. B. Cheng, Z. C. Dong, and H. Y. Tam, “Removal character of vertical jet polishing with eccentric rotation motion using magnetorheological fluid,” J. Mater. Process. Technol. 213, 1532–1537 (2013).
    [CrossRef]
  8. C. Y. Shi, J. H. Yuan, F. Wu, X. Hou, and Y. J. Wan, “Material removal model of vertical impinging in fluid jet polishing,” Chin. Opt. Lett. 8, 323–325 (2010).
    [CrossRef]
  9. H. Y. Tam, H. B. Cheng, and Z. C. Dong, “Peano-like paths for subaperture polishing of optical aspherical surfaces,” Appl. Opt. 52, 3624–3636 (2013).
    [CrossRef]
  10. C. R. Dunn and D. D. Walker, “Pseudo-random tool paths for CNC sub-aperture polishing and other applications,” Opt. Express 16, 18942–18949 (2008).
    [CrossRef]
  11. H. Y. Tam and H. B. Cheng, “An investigation of the effects of the tool path on the removal of material in polishing,” J. Mater. Process. Technol. 210, 807–818 (2010).
    [CrossRef]
  12. D. D. Walker, G. Y. Yu, H. Y. Li, W. Messelink, R. Evans, and A. Beaucamp, “Edges in CNC polishing: from mirror-segments towards semiconductors, paper 1: edges on processing the global surface,” Opt. Express 20, 19787–19798 (2012).
    [CrossRef]

2013

2012

2010

H. Y. Tam and H. B. Cheng, “An investigation of the effects of the tool path on the removal of material in polishing,” J. Mater. Process. Technol. 210, 807–818 (2010).
[CrossRef]

C. Y. Shi, J. H. Yuan, F. Wu, X. Hou, and Y. J. Wan, “Material removal model of vertical impinging in fluid jet polishing,” Chin. Opt. Lett. 8, 323–325 (2010).
[CrossRef]

2008

2007

W. Kordonski and A. Shorey, “Magnetorheological (MR) jet finishing technology,” J. Intell. Mater. Syst. Struct. 18, 1127–1130 (2007).
[CrossRef]

2006

H. Fang, P. J. Guo, and J. C. Yu, “Optimization of the material removal in fluid jet polishing,” Opt. Eng. 45, 053401 (2006).
[CrossRef]

W. I. Kordonski, A. B. Shorey, and M. Tricard, “Magnetorheological jet (MR JetTM) finishing technology,” J. Fluids Eng. 128, 20–26 (2006).
[CrossRef]

M. Tricard, W. I. Kordonski, and A. B. Shorey, “Magnetorheological jet finishing of conformal, freeform and steep concave optics,” CIRP Annals 55, 309–312 (2006).
[CrossRef]

2002

S. M. Booij, H. V. Brug, J. J. M. Braat, and O. W. Fähnle, “Nanometer deep shaping with fluid jet polishing,” Opt. Eng. 41, 1926–1931 (2002).
[CrossRef]

Beaucamp, A.

Booij, S. M.

S. M. Booij, H. V. Brug, J. J. M. Braat, and O. W. Fähnle, “Nanometer deep shaping with fluid jet polishing,” Opt. Eng. 41, 1926–1931 (2002).
[CrossRef]

Braat, J. J. M.

S. M. Booij, H. V. Brug, J. J. M. Braat, and O. W. Fähnle, “Nanometer deep shaping with fluid jet polishing,” Opt. Eng. 41, 1926–1931 (2002).
[CrossRef]

Brug, H. V.

S. M. Booij, H. V. Brug, J. J. M. Braat, and O. W. Fähnle, “Nanometer deep shaping with fluid jet polishing,” Opt. Eng. 41, 1926–1931 (2002).
[CrossRef]

Chen, Y.

Cheng, H. B.

T. Wang, H. B. Cheng, Y. Chen, Y. P. Feng, Z. C. Dong, and H. Y. Tam, “Correction of remounting errors by masking reference points in small footprint polishing process,” Appl. Opt. 52, 7851–7858 (2013).
[CrossRef]

T. Wang, H. B. Cheng, Z. C. Dong, and H. Y. Tam, “Removal character of vertical jet polishing with eccentric rotation motion using magnetorheological fluid,” J. Mater. Process. Technol. 213, 1532–1537 (2013).
[CrossRef]

H. Y. Tam, H. B. Cheng, and Z. C. Dong, “Peano-like paths for subaperture polishing of optical aspherical surfaces,” Appl. Opt. 52, 3624–3636 (2013).
[CrossRef]

H. Y. Tam and H. B. Cheng, “An investigation of the effects of the tool path on the removal of material in polishing,” J. Mater. Process. Technol. 210, 807–818 (2010).
[CrossRef]

Dong, Z. C.

Dunn, C. R.

Evans, R.

Fähnle, O. W.

S. M. Booij, H. V. Brug, J. J. M. Braat, and O. W. Fähnle, “Nanometer deep shaping with fluid jet polishing,” Opt. Eng. 41, 1926–1931 (2002).
[CrossRef]

Fang, H.

H. Fang, P. J. Guo, and J. C. Yu, “Optimization of the material removal in fluid jet polishing,” Opt. Eng. 45, 053401 (2006).
[CrossRef]

Feng, Y. P.

Guo, P. J.

H. Fang, P. J. Guo, and J. C. Yu, “Optimization of the material removal in fluid jet polishing,” Opt. Eng. 45, 053401 (2006).
[CrossRef]

Hou, X.

Kordonski, W.

W. Kordonski and A. Shorey, “Magnetorheological (MR) jet finishing technology,” J. Intell. Mater. Syst. Struct. 18, 1127–1130 (2007).
[CrossRef]

Kordonski, W. I.

M. Tricard, W. I. Kordonski, and A. B. Shorey, “Magnetorheological jet finishing of conformal, freeform and steep concave optics,” CIRP Annals 55, 309–312 (2006).
[CrossRef]

W. I. Kordonski, A. B. Shorey, and M. Tricard, “Magnetorheological jet (MR JetTM) finishing technology,” J. Fluids Eng. 128, 20–26 (2006).
[CrossRef]

Li, H. Y.

Messelink, W.

Shi, C. Y.

Shorey, A.

W. Kordonski and A. Shorey, “Magnetorheological (MR) jet finishing technology,” J. Intell. Mater. Syst. Struct. 18, 1127–1130 (2007).
[CrossRef]

Shorey, A. B.

M. Tricard, W. I. Kordonski, and A. B. Shorey, “Magnetorheological jet finishing of conformal, freeform and steep concave optics,” CIRP Annals 55, 309–312 (2006).
[CrossRef]

W. I. Kordonski, A. B. Shorey, and M. Tricard, “Magnetorheological jet (MR JetTM) finishing technology,” J. Fluids Eng. 128, 20–26 (2006).
[CrossRef]

Tam, H. Y.

T. Wang, H. B. Cheng, Y. Chen, Y. P. Feng, Z. C. Dong, and H. Y. Tam, “Correction of remounting errors by masking reference points in small footprint polishing process,” Appl. Opt. 52, 7851–7858 (2013).
[CrossRef]

T. Wang, H. B. Cheng, Z. C. Dong, and H. Y. Tam, “Removal character of vertical jet polishing with eccentric rotation motion using magnetorheological fluid,” J. Mater. Process. Technol. 213, 1532–1537 (2013).
[CrossRef]

H. Y. Tam, H. B. Cheng, and Z. C. Dong, “Peano-like paths for subaperture polishing of optical aspherical surfaces,” Appl. Opt. 52, 3624–3636 (2013).
[CrossRef]

H. Y. Tam and H. B. Cheng, “An investigation of the effects of the tool path on the removal of material in polishing,” J. Mater. Process. Technol. 210, 807–818 (2010).
[CrossRef]

Tricard, M.

W. I. Kordonski, A. B. Shorey, and M. Tricard, “Magnetorheological jet (MR JetTM) finishing technology,” J. Fluids Eng. 128, 20–26 (2006).
[CrossRef]

M. Tricard, W. I. Kordonski, and A. B. Shorey, “Magnetorheological jet finishing of conformal, freeform and steep concave optics,” CIRP Annals 55, 309–312 (2006).
[CrossRef]

Walker, D. D.

Wan, Y. J.

Wang, T.

T. Wang, H. B. Cheng, Z. C. Dong, and H. Y. Tam, “Removal character of vertical jet polishing with eccentric rotation motion using magnetorheological fluid,” J. Mater. Process. Technol. 213, 1532–1537 (2013).
[CrossRef]

T. Wang, H. B. Cheng, Y. Chen, Y. P. Feng, Z. C. Dong, and H. Y. Tam, “Correction of remounting errors by masking reference points in small footprint polishing process,” Appl. Opt. 52, 7851–7858 (2013).
[CrossRef]

Wu, F.

Yu, G. Y.

Yu, J. C.

H. Fang, P. J. Guo, and J. C. Yu, “Optimization of the material removal in fluid jet polishing,” Opt. Eng. 45, 053401 (2006).
[CrossRef]

Yuan, J. H.

Appl. Opt.

Chin. Opt. Lett.

CIRP Annals

M. Tricard, W. I. Kordonski, and A. B. Shorey, “Magnetorheological jet finishing of conformal, freeform and steep concave optics,” CIRP Annals 55, 309–312 (2006).
[CrossRef]

J. Fluids Eng.

W. I. Kordonski, A. B. Shorey, and M. Tricard, “Magnetorheological jet (MR JetTM) finishing technology,” J. Fluids Eng. 128, 20–26 (2006).
[CrossRef]

J. Intell. Mater. Syst. Struct.

W. Kordonski and A. Shorey, “Magnetorheological (MR) jet finishing technology,” J. Intell. Mater. Syst. Struct. 18, 1127–1130 (2007).
[CrossRef]

J. Mater. Process. Technol.

T. Wang, H. B. Cheng, Z. C. Dong, and H. Y. Tam, “Removal character of vertical jet polishing with eccentric rotation motion using magnetorheological fluid,” J. Mater. Process. Technol. 213, 1532–1537 (2013).
[CrossRef]

H. Y. Tam and H. B. Cheng, “An investigation of the effects of the tool path on the removal of material in polishing,” J. Mater. Process. Technol. 210, 807–818 (2010).
[CrossRef]

Opt. Eng.

S. M. Booij, H. V. Brug, J. J. M. Braat, and O. W. Fähnle, “Nanometer deep shaping with fluid jet polishing,” Opt. Eng. 41, 1926–1931 (2002).
[CrossRef]

H. Fang, P. J. Guo, and J. C. Yu, “Optimization of the material removal in fluid jet polishing,” Opt. Eng. 45, 053401 (2006).
[CrossRef]

Opt. Express

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Figures (9)

Fig. 1.
Fig. 1.

Effect of Gaussian removal function after translation in the x direction. (a) Schematic view of the movement of the footprint. (b) Cross section of the track along the y direction.

Fig. 2.
Fig. 2.

Regular removal function of MJP.

Fig. 3.
Fig. 3.

Methods to create V-shaped profile track by regular removal function of MJP. (a) Optimizing removal function. (b) Using multiplex path.

Fig. 4.
Fig. 4.

Effect of the M-shaped removal function after translation in the x direction along the multipex path. (a) Cross sections of the tracks with different dl along y. (b) Track profile for dl=0.8mm. (c) Depth of the tracks with different dl.

Fig. 5.
Fig. 5.

Processing steps with multiplex path. (a) Diagram of the simple simulation steps. (b) Scanning path as an example.

Fig. 6.
Fig. 6.

Footprint of a nozzle on K9 optical glass.

Fig. 7.
Fig. 7.

Dependence on the dl of polishing shape. (a) Profile curves of tracks. (b) Depths of tracks with different dl. (c) V-shaped profile curves of tracks for dl=0.8mm.

Fig. 8.
Fig. 8.

Experiment on the 23 mm diameter work-piece with grid multiplex path. (a) Form error of original work-piece: 0.256λ PV, 0.068λ RMS. (b) Multiplex path.

Fig. 9.
Fig. 9.

Polishing results. (a) Final surface: 0.038λ PV, 0.005λ RMS. (b) Average PSD curves along x direction. (c) Average PSD curves along y direction.

Tables (1)

Tables Icon

Table 1. Parameters of Polishing Processing

Equations (14)

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R=KPV=KFμSV=KDrμ,
E(x,y)=R(x,y)**D(x,y)=pathR(xx,yy)·D(x,y)dxdy.
RG(x,y)=Bexp[u·(x2+y2)],
{HGm=HMmSG=SM,
HM(xA,y)=RP1Rw(xAx1,yy1)Dw1(x1,y1)dx1+RP2Rw(xAx2,yy2)Dw2(x2,y2)dx2,
HMm=max[HM(xA,y)],
SM=HM(xA,y)dy,
HG(xA,y)=PathRG(xAx,yy)DG(x,y)dx,
DG(xA,yA)=Dw1(xA1,yA1)+Dw2(xA2,yA2),
HGm=max[HG(xA,y)],
SG=HG(xA,y)dy.
{HGm=max{B·exp[u(x2+y2)]·Tdx}=TB(πu)1/2SG=B·exp[u(x2+y2)]·Tdxdy=TBπu.
{B=HMm2SMTu=HMm2πSM2.
R(x,y)=7.83×103×exp[0.665×(x2+y2)].

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