交替测量式掘进机定位系统误差建模与分析

李志海; 刘治翔; 谢苗; 李玉岐; 王帅

doi:10.13272/j.issn.1671-251x.2021060015

交替测量式掘进机定位系统误差建模与分析

doi: 10.13272/j.issn.1671-251x.2021060015

李志海^1,,
刘治翔^2, ,,
谢苗²,
李玉岐²,
王帅²

1.
山西西山晋兴能源有限责任公司, 山西吕梁　033600
2.
辽宁工程技术大学辽宁省高等学校矿产资源开发利用技术及装备研究院, 辽宁阜新　123000

基金项目: 国家自然科学基金资助项目(51904142, 51874158)；辽宁省自然科学基金计划指导项目(2019-ZD-0036)。

详细信息

作者简介:
李志海(1968—)，男，山西交城人，硕士，主要从事煤矿安全管理工作，E-mail: lzh20208@126.com

通讯作者:
刘治翔(1988—)，男，辽宁大连人，副教授，博士，研究方向为煤矿掘进装备智能化技术，E-mail: 380357369@qq.com

中图分类号: TD632
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出版历程
- 收稿日期: 2021-06-05
- 修回日期: 2022-01-10
- 刊出日期: 2022-01-20

Error modeling and analysis of alternating measurement mode roadheader positioning system

1.
Shanxi Xishan Jinxing Energy Co., Ltd., Lüliang 033600, China
2.
Liaoning Academy of Mineral Resources Development and Utilization Technology and Equipment Research Institute, Liaoning Technical University, Fuxin 123000, China

摘要

摘要: 交替测量式掘进机定位技术在多次交替测量过程中会产生累计测量误差，从而影响掘进机定位精度。目前主要围绕单次测量误差产生原因、误差分布规律及误差减小方法展开研究，未有针对多次交替测量误差分布规律的研究成果。通过分析交替测量式掘进机定位系统工作原理及定位过程，构建了掘进机定位误差模型。采用作图法验证误差模型的正确性，结果表明作图法与误差模型得到的定位误差基本一致，二者仅存在10⁻³数量级误差。通过误差模型研究了角度测量误差、测距误差、推移步长及掘进机与测量平台间距对掘进机定位误差的影响，结果表明：角度测量误差越大，定位误差曲线的曲率越大，即误差增大越快，且Y_T轴定位误差增大速度远大于X_T轴；测距误差对X_T轴定位误差影响较大，测距误差越小，初始X_T轴定位误差越小，但误差变化速度不受影响；随着推移步长增大，Y_T轴定位误差曲线曲率增大，即Y_T轴定位误差增大速度加快；掘进机与测量平台间距和推移步长对掘进机定位误差的影响基本是等效的。采用正交试验方法分析了各因素对掘进机定位误差的影响程度，结果表明：测距误差对X_T轴定位误差影响最大，其次为角度测量误差，推移步长和掘进机与测量平台间距影响最小且二者影响程度一致；角度测量误差对Y_T轴定位误差影响最大，其次为推移步长和掘进机与测量平台间距且二者影响程度一致，测距误差影响最小。通过极差分析方法得到了降低定位误差的最优参数组合。
- 煤矿智能掘进 /
- 掘进机定位 /
- 交替测量式定位 /
- 定位误差 /
- 角度测量误差 /
- 测距误差 /
- 正交分析
Abstract: The alternating measurement mode roadheader positioning technology will produce cumulative measurement error in the process of multiple alternating measurement, which will affect the positioning precision of roadheader. At present, the research mainly focuses on the causes of single measurement error, error distribution law and error reduction methods, but there is no research results on the error distribution law of multiple alternating measurement. By analyzing the working principle and positioning process of alternating measurement mode roadheader positioning system, the positioning error model of roadheader is established. The accuracy of the error model is verified by the graphic method, and the results show that the positioning errors obtained by the graphic method and the error model are basically the same, and and there are only 10⁻³ orders of magnitude errors between them. The impact of angle measurement error, distance measurement error, moving step length and distance between the roadheader and measuring platform on roadheader positioning error is studied by error model. The results show that the larger the angle measurement error, the larger the curvature of the positioning error curve, that is, the faster the error grows. And the Y_T axis positioning error grows faster than the X_T axis. The distance measurement error has a greater impact on the X_T axis positioning error, and the smaller the distance measurement error, the smaller the initial X_T axis positioning error. However, the error change speed is not affected. As the moving step length increases, the Y_T axis positioning error curvature increases, that is, the Y_T axis positioning error growing speed increases. The impacts of the distance between the roadheader and measuring platform and the moving step length on roadheader positioning error are basically equivalent. The orthogonal test method is used to analyze the impact degree of each factor on the positioning error of roadheader. The results show that the distance measurement error has the greatest impact on the positioning error of the X_T axis, followed by the angle measurement error. The moving step length and the distance between the roadheader and the measuring platform have the smallest impact and the two have the same degree of impact. The angle measurement error has the greatest impact on the positioning error of the Y_T axis, followed by the moving step length and the distance between the roadheader and the measuring platform, and the impacts of the two are the same. The impact of the distance measurement error is the smallest. The range analysis method is used to obtain the optimal parameter combination to reduce the positioning error.
- intelligent roadway heading of coal mine /
- roadheader positioning /
- alternating measurement mode positioning /
- positioning error /
- angle measurement error /
- distance measurement error /
- orthogonal analysis

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图 1 交替测量式掘进机定位系统工作原理

Figure 1. Working principle of alternating measurement mode roadheader positioning system

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图 2 坐标系定义

Figure 2. Coordinate systems definition

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图 3 掘进机定位过程

Figure 3. Positioning process of roadheader

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图 4 不同测距误差下掘进机和测量平台的真实位置和测量位置

Figure 4. Real position and measuring position of roadheader and measuring platform under different ranging errors

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图 5 作图法确定掘进机定位误差原理

Figure 5. Principle of roadheader positioning error determined by drawing method

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图 6 恒定角度测量误差下掘进机定位误差

Figure 6. Positioning errors of roadheader under constant angle measurement errors

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图 7 变角度测量误差下掘进机定位误差

Figure 7. Positioning errors of roadheader under variable angle measurement errors

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图 8 不同测距误差下掘进机定位误差

Figure 8. Positioning errors of roadheader under different ranging errors

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图 9 不同推移步长下掘进机定位误差

Figure 9. Positioning errors of roadheader under different moving step length

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图 10 不同掘进机与测量平台间距下掘进机定位误差

Figure 10. Positioning errors of roadheader under different distances between roadheader and measuring platform

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表 1 掘进机定位误差对比

Table 1. Comparison of positioning errors of roadheader

掘进机迈步次数	作图法确定的掘进机定位误差/mm		式(7)计算的掘进机定位误差/mm
掘进机迈步次数	X_T轴	Y_T轴	X_T轴	Y_T轴
1	49.96	20.42	49.964 4	20.420 3
2	49.77	46.42	49.766 7	46.424 9
3	49.37	78.01	49.367 9	78.012 5
4	48.64	115.18	48.642 3	115.181 5
5	47.72	157.93	47.721 1	157.930 1

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表 2 正交试验参数

Table 2. Orthogonal test parameters

试验水平	A/(°)	B /mm	C/mm	D/mm
水平1	0.1	20	500	5 000
水平2	0.2	40	600	6 000
水平3	0.3	60	700	7 000
水平4	0.4	80	800	8 000

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表 3 正交试验结果

Table 3. Results of orthogonal test

序号	A/(°)	B/mm	C/mm	D/mm	定位误差/mm
序号	A/(°)	B/mm	C/mm	D/mm	X_T轴	Y_T轴
1	0.1	20	500	6 000	17.24	192.32
2	0.1	40	600	7 000	36.75	227.55
3	0.1	60	700	8 000	56.25	262.81
4	0.1	80	800	5 000	76.91	228.25
5	0.2	20	600	7 000	67.02	454.21
6	0.2	40	700	8 000	25.03	524.69
7	0.2	60	800	5 000	47.66	455.63
8	0.2	80	500	6 000	68.91	386.53
9	0.3	20	700	8 000	13.62	785.41
10	0.3	40	800	5 000	12.31	681.92
11	0.3	60	500	6 000	35.12	578.21
12	0.3	80	600	7 000	50.64	683.95
13	0.4	20	800	5 000	29.12	907.02
14	0.4	40	500	6 000	64.11	768.92
15	0.4	60	600	7 000	67.90	909.61
16	0.4	80	700	8 000	19.97	1 050.25

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表 4 X_T轴定位误差极差分析结果

Table 4. Range analysis results of X_T-axis positioning errors

指标	A	B	C	D
K₁/mm	187.2	67.0	125.4	166.0
K₂/mm	148.6	78.2	102.3	125.4
K₃/mm	111.7	146.9	114.9	102.3
K₄/mm	61.1	216.4	166.0	114.9
k₁/mm	46.8	16.8	31.3	41.5
k₂/mm	37.2	19.6	25.6	31.3
k₃/mm	27.9	36.7	28.7	25.6
k₄/mm	15.3	54.1	41.5	28.7
极差/mm	31.5	37.4	15.9	15.9

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表 5 Y_T轴定位误差极差分析结果

Table 5. Range analysis results of Y_T-axis positioning errors

指标	A	B	C	D
K₁/mm	910.9	2 339.0	1 926.0	2 272.8
K₂/mm	1 821.1	2 203.1	2 275.3	1 926.0
K₃/mm	2 729.5	2 206.3	2 623.2	2 275.3
K₄/mm	3 635.8	2 349.0	2 272.8	2 623.2
k₁/mm	227.7	584.7	481.5	568.2
k₂/mm	455.3	550.8	568.8	481.5
k₃/mm	682.4	551.6	655.8	568.8
k₄/mm	909.0	587.2	568.2	655.8
极差/mm	681.2	36.5	174.3	174.3

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