• High Power Laser and Particle Beams
  • Vol. 36, Issue 9, 091001 (2024)
Zhikai Mi1, Fengming Nie1,*, Siling Huang1, and Feng Xue2
Author Affiliations
  • 1Ningbo Branch of Chinese Academy of Ordnance Science, Ningbo 315103, China
  • 2School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China
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    DOI: 10.11884/HPLPB202436.240068 Cite this Article
    Zhikai Mi, Fengming Nie, Siling Huang, Feng Xue. Predictive modeling of the surface pattern of double-sided polishing process of optical components[J]. High Power Laser and Particle Beams, 2024, 36(9): 091001 Copy Citation Text show less

    Abstract

    To address the challenge of establishing a stable removal function for double-sided polishing to predict the finished surface profile, we use the coordinate transformation method to derive the relative velocity distribution equations for the upper and lower surfaces of the component. Subsequently, static pressure distributions on both surfaces are simulated using ANSYS software. The simulation data is then imported into Matlab and fitted with a polynomial method to determine the time-varying pressure distribution formulas for the component's surfaces. Based on the Preston equation, an expression for the correction coefficient K is derived. The value of the correction coefficient K is calculated to be 2.588×10-15 from four sets of polishing experimental data, enabling the construction of a predictive model for the surface pattern in double-sided polishing processes. The predictive model is ultimately validated through machining experiments. The experimental results indicate that the error in predicting the PV (Peak-to-Valley) value accounts for 1.07% to 7.4% of the actual PV value after processing, demonstrating good agreement between the predicted model and the actual post-processing surface pattern.
    $ \mathrm{d}{\textit{z}}/\mathrm{d}t=Kpv $(1)

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    $ \left\{ {xp=rpcosαyp=rpsinα} \right. $(2)

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    $ \left[ {xpyp1} \right] = \left[ {cosω1tsinω1t0sinω1tcosω1t0001} \right]\left[ {xpyp1} \right] $(3)

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    $ \left\{ {xp=rpcos(α+ω1t)yp=rpsin(α+ω1t)} \right. $(4)

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    $ \left[ {xpyp1} \right] = \left[ {cosω2tsinω2t0sinω2tcosω2t0001} \right]\left[ {10e010001} \right]\left[ {xpyp1} \right] $(5)

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    $ \left\{ {xp=rpcos(α+ω1tω2t)ecos(ω2t)yp=rpsin(α+ω1tω2t)+esin(ω2t)} \right. $(6)

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    $ \left\{ {vx=(ω1ω2)rpsin(α+ω1tω2t)+eω2sin(ω2t)vy=(ω1ω2)rpcos(α+ω1tω2t)+eω2cos(ω2t)} \right. $(7)

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    $ v = \sqrt {{{{r}}_{p}}^2{{({\omega_{\text{1}}} - {\omega_2})}^2} + {e^2}{\omega_{\text{2}}}^2 + 2e{{{r}}_{p}}{\omega_2}({\omega_1} - {\omega_2})\cos (\alpha + {\omega_1}t)} $(8)

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    $ \left[ {xpyp1} \right] = \left[ {cosω2tsinω2t0sinω2tcosω2t0001} \right]\left[ {10e010001} \right]\left[ {cosω3tsinω3t0sinω3tcosω3t0001} \right]\left[ {xpyp1} \right] $(9)

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    $ \left\{ {xp=rpcos(αω2t+ω3t)+ecos(ω2t)yp=rpsin(αω2t+ω3t)esin(ω2t)} \right. $(10)

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    $ v=\sqrt{r_{p}^2(\omega_3-\omega_2)^2+e^2\omega_2^2-2er_{p}\omega_2(\omega_3-\omega_2)\cos(\alpha+\omega_3t)} $(11)

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    $ e = {{\text{e}}_{\text{0}}} + 0.5{{L}} + 0.5L{\text{Sawtooth}}({\text{π }}{v_{\mathrm{s}}}t/{{L}},0.5) $(12)

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    $ p(x,y)=p00+p10x+p01y+p20x2+p11xy+p02y2+p30x3+p21x2y+p12xy2+p03y3+p40x4+p31x3y+p22x2y2+p13xy3+p04y4 $(13)

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    $ \left\{ {x=xbcos(ω2tω3t)+ybsin(ω2tω3t)+ecos(ω2t)+215y=xbsin(ω3tω2t)+ybcos(ω3tω2t)esin(ω2t)+215} \right. $(14)

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    $ \displaystyle\int_0^th(x,y)\mathrm{d}t=K\displaystyle\int_0^tp(x,y)v(x,y)\mathrm{d}t $(15)

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    $ {{K}} = \displaystyle\int_0^t {h(x,y){\mathrm{d}}t/\displaystyle\int_0^t {p(x,y)v(x,y){\mathrm{d}}t} } $(16)

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    Zhikai Mi, Fengming Nie, Siling Huang, Feng Xue. Predictive modeling of the surface pattern of double-sided polishing process of optical components[J]. High Power Laser and Particle Beams, 2024, 36(9): 091001
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