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基于遗传算法的插值Coons曲面孔位修正方法

孙新月 田威 胡俊山 廖文和

孙新月, 田威, 胡俊山, 等 . 基于遗传算法的插值Coons曲面孔位修正方法[J]. 北京航空航天大学学报, 2021, 47(9): 1814-1822. doi: 10.13700/j.bh.1001-5965.2020.0324
引用本文: 孙新月, 田威, 胡俊山, 等 . 基于遗传算法的插值Coons曲面孔位修正方法[J]. 北京航空航天大学学报, 2021, 47(9): 1814-1822. doi: 10.13700/j.bh.1001-5965.2020.0324
SUN Xinyue, TIAN Wei, HU Junshan, et al. A hole position correction method of interpolation Coons surface based on genetic algorithm[J]. Journal of Beijing University of Aeronautics and Astronautics, 2021, 47(9): 1814-1822. doi: 10.13700/j.bh.1001-5965.2020.0324(in Chinese)
Citation: SUN Xinyue, TIAN Wei, HU Junshan, et al. A hole position correction method of interpolation Coons surface based on genetic algorithm[J]. Journal of Beijing University of Aeronautics and Astronautics, 2021, 47(9): 1814-1822. doi: 10.13700/j.bh.1001-5965.2020.0324(in Chinese)

基于遗传算法的插值Coons曲面孔位修正方法

doi: 10.13700/j.bh.1001-5965.2020.0324
基金项目: 

国家科技重大专项 2018ZX04006001

详细信息
    通讯作者:

    田威, E-mail: tw_nj@nuaa.edu.cn

  • 中图分类号: V262.4

A hole position correction method of interpolation Coons surface based on genetic algorithm

Funds: 

National Science and Technology Major Project of China 2018ZX04006001

More Information
  • 摘要:

    在机器人自动制孔过程中,制孔点位信息通常从待制孔工件工艺数模上获取,而待制孔工件安装过程中会出现位置偏移和变形,由工艺数模得到的点位信息无法直接满足孔位精度要求。为了保证自动制孔的孔位精度,提出了一种基于遗传算法的插值Coons曲面孔位修正方法。利用制孔区域边角基准孔建立双线性Coons误差曲面模型,通过模型计算出待制孔的误差补偿向量,并补偿至理论制孔位置。针对误差曲面切矢模长无法确定的情况,利用制孔区域内的基准孔构建遗传算法模型,计算出切矢模长最优值,使拟合的误差曲面更符合实际制孔区域曲面。通过试验对算法的有效性和精度进行验证,结果表明:采用基于遗传算法的插值Coons曲面孔位修正方法,可以使孔位误差得到有效的补偿。补偿后的平均孔位误差仅为0.195 6 mm,与传统的插值曲面方法相比,孔位误差降低了5%~10%。

     

  • 图 1  理论曲面和实际曲面偏差

    Figure 1.  Deviation of theoretical surface and actual surface

    图 2  双线性Coons曲面拟合过程

    Figure 2.  Process diagram of bilinear Coons surface fitting

    图 3  单位切矢计算示意图

    Figure 3.  Schematic diagram of unit tangent vector calculation

    图 4  切矢模长对曲线丰满程度的影响

    Figure 4.  Influence of tangent vector length on the fullness of curves

    图 5  遗传算法求解切矢模长流程

    Figure 5.  Genetic algorithm for computing the tangent vector modulus length

    图 6  试验平台

    Figure 6.  Experimental platform

    图 7  试验工件孔位分布

    Figure 7.  Distribution map of hole positions of test pieces

    图 8  孔位仿真

    Figure 8.  Hole position simulation

    图 9  3种孔位修正方法孔位精度对比图

    Figure 9.  Comparison of hole position accuracy of three hole position correction methods

    图 10  基准孔位置对孔位误差的影响

    Figure 10.  Effect of reference hole position on hole position error

    图 11  基准孔数量对孔位误差的影响

    Figure 11.  Effect of the number of reference holes on hole position error

    表  1  边角基准孔理论坐标及法矢

    Table  1.   Theoretical coordinate and normal vector of corner reference holes

    基准孔 (x, y, z) /mm 法矢
    A1 (44.721, 89.443, 20) (0.447 2, 0.894 4, 0)
    B1 (76.022, 64.967, 20) (0.760 2, 0.649 7, 0)
    C1 (76.022, 64.967, -20) (0.760 2, 0.649 7, 0)
    D1 (44.721, 89.443, -20) (0.447 2, 0.894 4, 0)
    下载: 导出CSV

    表  2  边角基准孔孔位偏差

    Table  2.   Position deviation of corner reference holes

    基准孔 Δx /mm Δy /mm Δz /mm
    A1 -1.702 0.517 -0.049
    B1 -0.691 0.858 -0.203
    C1 -0.624 0.809 -0.402
    D1 -1.82 0.712 -0.161
    下载: 导出CSV

    表  3  待制孔孔位偏差

    Table  3.   Position deviation of hole to be drilled

    孔号 Δx /mm Δy /mm Δz/mm
    1 -1.518 0.702 -0.098
    2 -1.509 0.694 -0.148
    3 -1.65 0.832 -0.259
    4 -1.528 0.796 -0.233
    5 -1.318 0.754 -0.133
    6 -1.207 0.716 -0.134
    7 -1.235 0.941 -0.056
    8 -1.365 1.021 -0.488
    9 -1.276 0.806 -0.282
    10 -1.151 0.948 -0.201
    11 -0.732 0.674 0.064
    12 -0.874 0.793 -0.152
    13 -0.87 0.757 -0.08
    14 -0.935 0.877 -0.303
    15 -0.833 0.871 -0.274
    下载: 导出CSV

    表  4  孔位修正后的孔位误差对比

    Table  4.   Comparison of hole position errors after hole position correction

    类型 孔位误差范围/mm 平均值/mm
    孔位修正前 [0.997, 1.866] 1.476 2
    双线性插值法 [0.0314, 0.703] 0.325
    插值Coons曲面法 [0.105, 0.608] 0.259 2
    基于遗传算法的插值Coons曲面法 [0.058 2, 0.487] 0.195 6
    下载: 导出CSV

    表  5  仿真数据孔位修正后结果对比

    Table  5.   Comparison of results after hole position correction of simulation data

    类型 孔位误差范围/mm 平均值/mm
    孔位修正前 [1.745, 2.655] 2.215
    双线性插值法 [0.129, 0.693] 0.324
    插值Coons曲面法 [0.205, 0.477] 0.35
    基于遗传算法的插值Coons曲面法 [0.132, 0.437] 0.281
    下载: 导出CSV
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出版历程
  • 收稿日期:  2020-07-07
  • 录用日期:  2020-08-07
  • 网络出版日期:  2021-09-20

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