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

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

1.
陕西科技大学电气与控制工程学院, 西安 710021
2.
西安拓尔微电子有限责任公司, 西安 710000

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
计量
- 文章访问数: 302
- HTML全文浏览量: 108
- PDF下载量: 41
- 被引次数: 0
出版历程
- 收稿日期: 2021-02-17
- 刊出日期: 2022-02-25

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

1.
School of Electrical and Control Engineering, Shaanxi University of Science & Technology, Xi′an 710021, China
2.
Xi′an Toll Microelectronics Co., Ltd., Xi′an 710000, China

摘要

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。
- 插补法 /
- OC近似法 /
- 弓高误差 /
- 双向Hausdorff距离 /
- NURBS曲线
Abstract: In numerical control system, interpolation is often used to realize complex curve machining, which will introduce some chord errors. The commonly used Osculating Circle(OC) method and single-direction Hausdorff distance method can obtain estimated chord errors, then make subsequent compensations, but they both introduce other errors in the estimation process. For this problem, based on the both-direction Hausdorff distance definition of the chord error, an iterative evaluation algorithm is proposed in this paper. This algorithm can improve the estimation precision of chord error without considering the flexibility of curves, and obtain the maximum interpolation step length that satisfies the error limitation, thereby further generating the accurate feed rate constraints to prevent the reduction of both machining accuracy and efficiency due to the introduction of other errors. Finally, it is simulated by '∞'-shaped and petal-shaped NURBS curves, the simulation results verify the performance and the effectiveness of the proposed algorithm.
- interpolation /
- OC method /
- chord error /
- both-direction Hausdorff distance /
- NURBS curve

HTML全文

图 1 弓高误差的OC近似法示意图

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图 2 弓高误差的双向Hausdorff距离定义示意图

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图 3 迭代算法流程图

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图 4 弧弦Hausdorff距离迭代示意图

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图 5 弦弧Hausdorff距离迭代示意图

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图 6 ‘∞’形NURBS曲线

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图 7 两种算法评估的弓高误差结果(‘∞’形)

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图 8 花瓣形NURBS曲线

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图 9 两种算法评估的弓高误差结果(花瓣形)

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图 10 花瓣形NURBS曲线加工路径

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图 11 改进后的进给速度约束曲线

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图 12 七段式S型进给速度曲线

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图 13 刀具路径的实际弓高误差曲线

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表 1 仿真系统参数表

参数名称	数值
插补周期T_s	1 ms
最大允许弓高误差δ_max	0.001 mm
最大允许进给速度v_max	100 mm/s
最大允许加速度a_max	3 000 mm/s²
最大允许加加速度j_max	60 000 mm/s³
最大允许轴向速度v_xmax, v_ymax	100 mm/s
最大允许轴向加速度a_xmax, a_ymax	3 000 mm/s²
最大允许轴向加加速度j_xmax, j_ymax	60 000 mm/s³
向心加速度系数M	0.2

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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

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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

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