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    Journals >Infrared and Laser Engineering >Volume 50 >Issue 5 >Page 20200316 > Article
    • Infrared and Laser Engineering
    • Vol. 50, Issue 5, 20200316 (2021)
    Research on angle setting error of diameter measurement based on laser displacement sensors
    Jinyu Ma1, Xin Chen1, Guoqing Ding1, and Jigang Chen2
    Author Affiliations
  • 1School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
  • 2Shanghai Precision Metrology and Test Research Institute, Shanghai 201109, China
    • show less
    DOI: 10.3788/IRLA20200316 Cite this Article
    Jinyu Ma, Xin Chen, Guoqing Ding, Jigang Chen. Research on angle setting error of diameter measurement based on laser displacement sensors[J]. Infrared and Laser Engineering, 2021, 50(5): 20200316 Copy Citation Text show less

    Abstract

    The diameter and roundness measurement of ring workpieces based on the laser displacement sensors is widely used in the measuring process of the product quality in the industrial site. The effect of angle setting errors of laser displacement sensors on the measurement of the workpiece’s diameter was studied, and the calibration method of them was proposed. Firstly, the relationship between angle setting errors of displacement sensors and calculated errors of the diameter was analyzed quantitatively. Secondly, a calibration method was proposed, which could calculate the angle setting errors of the sensors in accordance with the measurement data of three displacement sensors, and the diameter of the standard circle was unknown. The modeling process of the calibration method was illustrated and the effectiveness of the method through simulations was confirmed. Finally, the angle setting errors were calibrated by using coordinate measuring machine. The experiment result shows that the absolute errors of diameter are improved from 20 μm to 1.5 μm after calibration.

    Keywords

    $\left\{ \begin{array}{l} {A_x} = - \left( {{t_1} - {s_1} - {m_1}} \right),{A_y} = 0\\ {B_x} = \dfrac{1}{2}({t_2} - {s_2} - {m_2}),{B_y} = \dfrac{{\sqrt 3 }}{2}({t_2} - {s_2} - {m_2})\\ {C_x} = \dfrac{1}{2}({t_3} - {s_3} - {m_3}),{C_y} = - \dfrac{{\sqrt 3 }}{2}({t_3} - {s_3} - {m_3}) \end{array} \right.$(1)

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    $\left\{ \begin{array}{l} {({P_x} - {A_x})^2} + {({P_y} - {A_y})^2} = {r^2} \\ {({P_x} - {B_x})^2} + {({P_y} - {B_y})^2} = {r^2} \\ {({P_x} - {C_x})^2} + {({P_y} - {C_y})^2} = {r^2} \\ \end{array} \right.$(2)

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    $\left\{ \begin{array}{l} {A_x} = - [{t_1} - \left( {{s_1} + {m_1}} \right)]\cos {\gamma _1},{A_y} = (s_1 + m_1)\sin {\gamma _1}\\ {B_x} = [{t_2} - ({s_2} + {m_2})]\cos {\gamma _2},{B_y} = ({t_2} - {s_2} - {m_2})\sin {\gamma _2}\\ {C_x} = [{t_3} - ({s_3} + {m_3})]\cos {\gamma _3},{C_y} = - [{t_3} - ({s_3} + {m_3})]\sin {\gamma _3} \end{array} \right.$(3)

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    $ {{P}} = F({{M}},{ S})$(4)

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    $ {{S}} = \mathop {\left[ {s_1\;s_2\;s_3\;\alpha _1\;\alpha _2\;\alpha _3} \right]}\nolimits^{\rm T} $(5)

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    ${{{R}}} = {\rm{ }}\left\{ {\begin{array}{*{20}{c}} {C\left[ {F({{{{M}_1}},{{S}}})} \right]} \\ \vdots \\ {C\left[ {F({ {{{M}}_j},{{S}}})} \right]} \\ \vdots \\ {C\left[ {F({ {{{M}}_m},{{S}}})} \right]} \end{array}} \right\}$(6)

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    ${{{S}}_{\rm new}} = {\rm{ }}{ {{S}}_{\rm old}} + {({{{J}}^{\rm T}}{{{W}}^{ - 1}}{{J}})^{ - 1}}{{{J}}^{\rm T}}{{{W}}^{ - 1}}{ {{R}}}$(7)

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    ${{J}}{\rm{ }} = {\rm{ }}\left[ {\begin{array}{*{20}{c}} {\dfrac{{\partial {{R}}_1}}{{\partial s_1}}}&{\dfrac{{\partial {{R}}_1}}{{\partial s_2}}}&{\dfrac{{\partial {{R}}_1}}{{\partial s_3}}}&{\dfrac{{\partial {{R}}_1}}{{\partial \alpha _1}}}&{\dfrac{{\partial {{R}}_1}}{{\partial \alpha _2}}}&{\dfrac{{\partial {{R}}_1}}{{\partial \alpha _3}}} \\ \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\ {\dfrac{{\partial {{R}}_m}}{{\partial s_1}}}&{\dfrac{{\partial {{R}}_m}}{{\partial s_2}}}&{\dfrac{{\partial {{R}}_m}}{{\partial s_3}}}&{\dfrac{{\partial {{R}}_m}}{{\partial \alpha _1}}}&{\dfrac{{\partial {{R}}_m}}{{\partial \alpha _2}}}&{\dfrac{{\partial {{R}}_m}}{{\partial \alpha _3}}} \end{array}} \right]$(8)

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    ${{W}_{{ij}}}{\rm{ = }}\left\{ \begin{array}{l} \sigma _{{R}}^2 + \sigma _M^2\displaystyle\sum_{k = 1}^m {{{\left(\dfrac{{\partial {{{{R}}}_i}}}{{\partial {{{M}}_k}}}\right)}^2},\;\;\;\;\;i = j} \\ 0,\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;i \ne j \\ \end{array} \right.$(9)

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    Jinyu Ma, Xin Chen, Guoqing Ding, Jigang Chen. Research on angle setting error of diameter measurement based on laser displacement sensors[J]. Infrared and Laser Engineering, 2021, 50(5): 20200316
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