Laser & Optoelectronics Progress, Volume. 59, Issue 19, 1912002(2022)

Recurrence of Laplace Deformation Surface Based on Optimized Control Point Monitoring

Xiaobo Cheng1,2, Yundong Zhu1,2、*, Xuezhu Lin1,2, Funing Liu1,2, and Linxin Yin1,2
Author Affiliations
  • 1School of Optoelectronic Engineering, Changchun University of Science and Technology,Changchun 130022, Jilin, China
  • 2National Demonstration Center for Experimental Opto-Electronic Engineering Education, School of Opto-Electronic Engineering, Changchun University of Science and Technology, Changchun 130022, Jilin, China
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    Figures & Tables(15)
    Flow chart of Laplace deformation
    Simplified models corresponding to different fixed ends. (a) Unilateral constraints; (b) adjacent constraint; (c) boundary constraints; (d) quadrilateral constraint; (e) trilateral constraints
    Deformation of standard components under random control points
    Distribution of deflection curve under simplified model
    Selecting control points according to deflection curve and different spacing. (a) Unilateral constraints; (b) adjacent constraint; (c) boundary constraints; (d) trilateral constraints; (e) quadrilateral constraint and unconstraint
    Mapping relationship diagram
    Diagram of proportional relation of y plane
    3D reconstruction based on control points
    Optimal selection of control points. (a) Set a control point at maximum deflection; (b) add a control point in reverse direction of flexure; (c) control points are added one by one in reverse direction of flexure
    Analysis route of surface deformation[15]
    Deformation coincidence diagram of experimental surface. (a) Adjacent constraint; (b) boundary constraints; (c) quadrilateral constraint; (d) unilateral constraints
    Test deformation and control points diagram of an aircraft wing
    Deformation coincidence degree analysis of an aircraft wing
    • Table 1. Deformation control point coincidence degree analysis of an aircraft wing

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      Table 1. Deformation control point coincidence degree analysis of an aircraft wing

      Point nameRealistic deformation modelLaplace deformation modelCoincidence test
      xyzxyzDxDyDzDMag
      Pt1179.625973.7721171.030179.627973.7721171.0140.0020.000-0.0160.016
      Pt2486.712592.8921177.927486.776592.9141178.0040.0650.0220.0770.103
      Pt31398.368474.006788.1481398.449474.030788.2140.0810.0250.0660.107
      Pt42046.715162.067141.9222046.815162.103141.9570.1000.0360.0350.112
      Pt51613.514796.529246.4221613.592796.557246.4490.0780.0280.0280.087
      Pt61220.5681275.179251.8411220.5881275.179251.8730.0200.0000.0320.038
      Pt7907.1341187.139727.732907.1361187.139727.7050.0020.000-0.0270.027
    • Table 2. Advantages and disadvantages comparison between traditional methods and proposed method

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      Table 2. Advantages and disadvantages comparison between traditional methods and proposed method

      MethodData acquisition modeSurface of repetition /minOperationPrecision /mmCharacteristic
      Traditional methodsScanning technique200Tedious0.10~0.15Large deformation has limitations
      Proposed methodMeasuring point80Simple0.12Accuracy control depends on human operation
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    Xiaobo Cheng, Yundong Zhu, Xuezhu Lin, Funing Liu, Linxin Yin. Recurrence of Laplace Deformation Surface Based on Optimized Control Point Monitoring[J]. Laser & Optoelectronics Progress, 2022, 59(19): 1912002

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    Paper Information

    Category: Instrumentation, Measurement and Metrology

    Received: Aug. 27, 2021

    Accepted: Oct. 11, 2021

    Published Online: Oct. 11, 2022

    The Author Email: Zhu Yundong (865040845@qq.com)

    DOI:10.3788/LOP202259.1912002

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