平面内直线度最小包容区域包络模型与算法实现

干江红; 张新宝

doi:10.12338/j.issn.2096-9015.2020.0361

平面内直线度最小包容区域包络模型与算法实现

doi: 10.12338/j.issn.2096-9015.2020.0361

干江红^1,,
张新宝²

1.
武汉铁路职业技术学院武汉 430205
2.
华中科技大学机械科学与工程学院武汉 430074

详细信息

作者简介:
干江红(1981-)，武汉铁路职业技术学院讲师，研究方向：精密测量，邮箱：35415341@qq.com

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- PDF下载量: 45
- 被引次数: 0
出版历程
- 网络出版日期: 2021-11-01
- 刊出日期: 2021-12-01

An Enveloping Model of the Minimum Tolerance Zone Method for Evaluating Straightness in a Plane and the Associated Algorithm

GAN Jianghong^1
,,
ZHANG Xinbao²

1.
Wuhan Railway Vocational College of Technology, Wuhan 430205, China
2.
School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China

摘要

摘要: 根据国家标准GB/T 11336-2004中给出的平面内直线度误差的几何描述，提出了一种基于评估点集中包络点的平面内直线度最小包容区域模型，并给出了评估点集中包络点的判定原则。根据包络点的判定原则，提出了基于单向搜索构建包络向量的评估点集中包络点搜寻的高效算法，同时利用对比分析的方法说明了所提模型和算法的准确性与完备性。借助仿真数据对万级点集到百万级点集的最小包容区域进行求取，并统计了算法消耗的时间，结果显示算法的时间复杂度为O(N)级别，验证了算法的高效性。
- 包络点 /
- 包络直线 /
- 最小包容区域 /
- 包络模型 /
- 大数据点集
Abstract: According to the geometrical description of straightness error presented in the national standard GB/T 11336-2004, a new enveloping model of the minimum tolerance zone method for evaluating straightness in a plain and a principle for judging envelop points are proposed in this paper. Based on the principle, a highly efficient algorithm is proposed to search for the envelope points. The proposed algorithm is suitable for searching for the envelope points of a mass points set. A comparison with a traditional method shows that the proposed algorithm had good completeness and produced reliable results. By means of simulation, sets of a million points were calculated using the algorithm and the costs of the algorithm were recorded. The result showed that the time complexity of the algorithm was O(N). The enveloping model proposed in this paper is simple and accurate.
- envelope points /
- envelope straight line /
- minimum tolerance zone /
- enveloping model /
- big data points set

HTML全文

图 1 基于包络点的最小区域包络模型

Figure 1. Minimum enveloping zone model based on enveloping points

下载: 全尺寸图片幻灯片

图 2 最小包容区域算法输出结果示意图

Figure 2. Output of the minimum enveloping zone agorithm

下载: 全尺寸图片幻灯片

图 3 利用本文的模型和算法对文献[10]数据的处理结果

Figure 3. Results of the proposed algorithm applied to the data in reference[10]

下载: 全尺寸图片幻灯片

图 4 评估点集大小（1万到500万）与算法耗时及包络点个数关系图

Figure 4. Plots of number of points vs computing costs and vs number of enveloping points

下载: 全尺寸图片幻灯片

表 1 精密直线导轨的直线度测量数据

Table 1. Measured straightness of a precision linear rail

No.	X(mm)	Y₁ (μm)	Y₂ (μm)	Y₃ (μm)
1	0.0	0.0	0.0	0.0
2	40.0	−1.92	−0.29	−2.01
3	80.0	−5.67	−1.42	1.36
4	120.0	−6.64	−0.75	−6.36
5	160.0	−7.41	−4.36	−7.92
6	200.0	−8.72	−4.24	−8.26
7	240.0	−8.14	−6.11	−8.12
8	280.0	−6.08	−14.94	−6.00
9	320.0	−3.38	−9.87	−0.36
10	360.0	−0.24	−10.01	0.36
11	400.0	2.57	−13.62	2.78
12	440.0	4.37	−15.75	4.09
13	480.0	5.70	−18.53	5.73
14	520.0	5.03	−21.86	6.39
15	560.0	5.59	−24.32	5.01
16	600.0	3.67	−29.17	3.21
17	640.0	1.66	−33.01	1.96
18	680.0	−1.64	−37.42	−3.15
19	720.0	−6.67	−41.51	−5.89
20	760.0	−10.94	−45.51	−10.64
21	800.0	−14.57	−48.18	−15.98
22	840.0	−24.22	−49.32	−20.03
23	880.0	−29.78	−50.46	−27.86
24	920.0	−33.94	−49.32	−32.07
25	960.0	−32.04	−46.25	−36.92
26	1000.0	−36.99	−44.39	−46.20

下载: 导出CSV

参考文献(12)

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