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NURBS曲线插补弓高误差的双向Hausdorff距离评估方法

鲁毛毛 刘宝泉 徐梦杰 方建平

鲁毛毛, 刘宝泉, 徐梦杰, 方建平. NURBS曲线插补弓高误差的双向Hausdorff距离评估方法[J]. 机械科学与技术, 2022, 41(2): 253-262. doi: 10.13433/j.cnki.1003-8728.20200577
引用本文: 鲁毛毛, 刘宝泉, 徐梦杰, 方建平. NURBS曲线插补弓高误差的双向Hausdorff距离评估方法[J]. 机械科学与技术, 2022, 41(2): 253-262. doi: 10.13433/j.cnki.1003-8728.20200577
LU Maomao, LIU Baoquan, XU Mengjie, FANG Jianping. A Two-way Hausdorff Distance Evaluation Method of Chord Error using NURBS Curve Interpolation[J]. Mechanical Science and Technology for Aerospace Engineering, 2022, 41(2): 253-262. doi: 10.13433/j.cnki.1003-8728.20200577
Citation: LU Maomao, LIU Baoquan, XU Mengjie, FANG Jianping. A Two-way Hausdorff Distance Evaluation Method of Chord Error using NURBS Curve Interpolation[J]. Mechanical Science and Technology for Aerospace Engineering, 2022, 41(2): 253-262. doi: 10.13433/j.cnki.1003-8728.20200577

NURBS曲线插补弓高误差的双向Hausdorff距离评估方法

doi: 10.13433/j.cnki.1003-8728.20200577
基金项目: 

陕西省2020年重点研发计划项目 2020GY-042

详细信息
    作者简介:

    鲁毛毛(1993-), 硕士研究生, 研究方向为运动控制系统, lumaomao0203@163.com

    通讯作者:

    刘宝泉, 副教授, 硕士生导师, comeliu299@163.com

  • 中图分类号: TG65

A Two-way Hausdorff Distance Evaluation Method of Chord Error using NURBS Curve Interpolation

  • 摘要: 数控系统中采用插补方法进行复杂曲线加工会引入弓高误差。利用密切圆(Osculating circle,OC)近似法和单向Hausdorff距离近似法可以获取弓高误差并对其进行后续补偿,但弓高误差求解与补偿精度较低。基于弓高误差的双向Hausdorff距离定义,提出了一种弓高误差的迭代评估算法。该算法能在不考虑曲线复杂度的情况下提升弓高误差的求解精度,并获取满足误差限制要求的最大插补步长,从而进一步生成精确的进给速度限制,防止加工精度及效率因引入其它误差而下降。最后利用该算法对‘∞’形和花瓣形NURBS曲线进行仿真,仿真结果验证了算法的性能及其有效性。
  • 图  1  弓高误差的OC近似法示意图

    图  2  弓高误差的双向Hausdorff距离定义示意图

    图  3  迭代算法流程图

    图  4  弧弦Hausdorff距离迭代示意图

    图  5  弦弧Hausdorff距离迭代示意图

    图  6  ‘∞’形NURBS曲线

    图  7  两种算法评估的弓高误差结果(‘∞’形)

    图  8  花瓣形NURBS曲线

    图  9  两种算法评估的弓高误差结果(花瓣形)

    图  10  花瓣形NURBS曲线加工路径

    图  11  改进后的进给速度约束曲线

    图  12  七段式S型进给速度曲线

    图  13  刀具路径的实际弓高误差曲线

    表  1  仿真系统参数表

    参数名称 数值
    插补周期Ts 1 ms
    最大允许弓高误差δmax 0.001 mm
    最大允许进给速度vmax 100 mm/s
    最大允许加速度amax 3 000 mm/s2
    最大允许加加速度jmax 60 000 mm/s3
    最大允许轴向速度vxmax, vymax 100 mm/s
    最大允许轴向加速度axmax, aymax 3 000 mm/s2
    最大允许轴向加加速度jxmax, jymax 60 000 mm/s3
    向心加速度系数M 0.2
    下载: 导出CSV

    表  2  弓高误差评估超限测试点的分析统计表(‘∞’形)

    弓高误差评估方法 超限测试点数量 超限测试点占比/% 最大弓高误差/mm
    OC法 504 50.4 0.194 884
    本迭代算法 49 4.9 0.001 013
    下载: 导出CSV

    表  3  弓高误差评估超限测试点的分析统计表(花瓣形)

    弓高误差评估方法 超限测试点数量 超限测试点占比/% 最大弓高误差/mm
    OC法 519 51.9 0.469 542
    本迭代算法 67 6.7 0.001 019
    下载: 导出CSV
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  • 收稿日期:  2021-02-17
  • 刊出日期:  2022-02-25

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