• Journal of Applied Optics
  • Vol. 43, Issue 3, 518 (2022)
Yu ZHANG, Feng ZHANG, Rui GUO, Ying SU..., Yunlong ZHANG, Zengqi XU and Fuchao WANG|Show fewer author(s)
Author Affiliations
  • Xi'an Institute of Applied Optics, Xi'an 710065, China
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    DOI: 10.5768/JAO202243.0305002 Cite this Article
    Yu ZHANG, Feng ZHANG, Rui GUO, Ying SU, Yunlong ZHANG, Zengqi XU, Fuchao WANG. Tooling calibration of secondary aspheric workpiece position in magneto-rheological polishing[J]. Journal of Applied Optics, 2022, 43(3): 518 Copy Citation Text show less

    Abstract

    In recent years, the magneto-rheological polishing as a deterministic processing method has become an essential way to obtain the high-precision aspheric surfaces. Take the rotationally symmetric secondary paraboloid as an example, the theoretical method of using the polishing wheel to calibrate the workpiece position in magneto-rheological polishing was analyzed, and the experimental verification was carried out on a Φ 230 mm fused quartz workpiece. The workpiece position was calibrated with less than 3 times of adjustment in the X direction and Y direction, respectively, and the offset in both X direction and Y direction was lower than 0.009 mm, respectively. The surface polishing experiment was conducted by magneto-rheological polishing technology on the workpiece, and the root-mean-square (RMS) of surface shape was converged from λ/7 to λ/40 after processing. The experimental results show that the proposed tooling calibration method of aspheric workpiece position is simple and reliable, which can accurately locate the workpiece and conducive to magneto-rheological polishing processing for high-precision aspheric surface.
    $ Z = \frac{{c{X^2}}}{{1 + \sqrt {1 - (1 + K){c^2}{X^2}} }} $(1)

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    $ Z = \frac{{c{X^2}}}{2} $(2)

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    $ Z = \frac{c}{2}({X^2} + {Y^2}) + h $(3)

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    $ Z = \frac{c}{2}[{(X - a)^2} + {(Y - b)^2}] + h $(4)

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    $ \left\{ Z=c2[(Xa)2+b2]+hy=0 \right. $(5)

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    $ Z = \frac{c}{2}[{(X - a + {d_1})^2} + {b^2}] + h $(6)

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    $ {\text{d}}{\textit{z}} = c(X - a + {d_1}){\text{d}}x $(7)

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    $ \Delta Z_2 = c({X_1} - a + {d_1})\Delta {X_2} $(8)

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    $ {(X - m)^2} + {(Z + n)^2} = {r^2} $(9)

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    $ {(X - m)^2} + {(Z + n + p)^2} = {r^2} $(10)

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    $ 2(X - m){\text{d}}x + 2(Z + n + p){\text{d}}{\textit{z}} = 0 $(11)

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    $ Z_3 + n + p = \frac{{m - X_3}}{{c(X_3 - a + d_1)}} $(12)

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    $ c2(X3m)2(X3a+d1)2+(X3m)2c2r2(X3a+d1)2=0 $(13)

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    $ {Z_3} = \frac{c}{2}\left\{ [(L + r)\sin {\beta _1} + \Delta {X_2} - a + {d_1}{]^2} + {b^2} \right\} + h\;\;\;\;\;\;\;\; $(14)

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    $ Z = \frac{c}{2}[{(X - a - {d_2})^2} + {b^2}] + h $(15)

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    $ c2(X3+m)2(X3ad2)2+(X3+m)2c2r2(X3ad2)2=0 $(16)

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    $ {Z_{3'}} = \frac{c}{2}\left\{ {{{[ - (L + r)\sin {\beta _2} + \Delta {X_{2'}} - a - {d_2}]}^2} + {b^2}} \right\} + h \;\;\;\;\;\;$(17)

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    $ \Delta {X_2} = \kappa a $(18)

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    $ {d_1} = {d_2} $(19)

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    $ {\beta _1} = {\beta _2} $(20)

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    $ (1{\text{ - }}\kappa )a = \frac{{{Z_{3'}} - {Z_3}}}{{2c[(L + r)\sin {\beta _1} + {d_1}]}} $(21)

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    $ (1 - \varepsilon )b = \frac{{Z_3' - Z_3}}{{2c[(M + r)\sin {\alpha _1} + {f_1}]}} $(22)

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    Yu ZHANG, Feng ZHANG, Rui GUO, Ying SU, Yunlong ZHANG, Zengqi XU, Fuchao WANG. Tooling calibration of secondary aspheric workpiece position in magneto-rheological polishing[J]. Journal of Applied Optics, 2022, 43(3): 518
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