圆度误差不确定度的PDF优化估计评定

张珂; 成果; 阎卫增

doi:10.13433/j.cnki.1003-8728.20190116

圆度误差不确定度的PDF优化估计评定

doi: 10.13433/j.cnki.1003-8728.20190116

张珂^1,2,,
成果^1,2,
阎卫增³

1.
上海应用技术大学机械工程学院, 上海 201418
2.
上海应用技术大学上海物理气相沉积(PVD)超硬涂层及装备工程技术研究中心, 上海 201418
3.
上海人本集团有限公司, 上海 201411

基金项目:

上海市联盟计划项目 LM2018-5

上海应用技术大学协同创新基金 XTCX2018-13

详细信息

作者简介:
张珂(1968-), 教授, 博士, 研究方向为机械精密测量、机械设计, zkwy2004@126.com

中图分类号: TG801;TG83
计量
- 文章访问数: 158
- HTML全文浏览量: 63
- PDF下载量: 19
- 被引次数: 0
出版历程
- 收稿日期: 2019-03-08
- 刊出日期: 2020-02-01

Evaluation of PDF Optimal Estimation of Roundness Error Uncertainty

Zhang Ke^{1,2
,},
Cheng Guo^1,2,
Yan Weizeng³

1.
School of Mechanical Engineering, Shanghai Institute of Technology, Shanghai 201418, China
2.
Shanghai Engineering Research Center of Physical Vapor Deposition Superhard Coating and Equipment, Shanghai Institute of Technology, Shanghai 201418, China
3.
Shanghai C&U GmbH, Shanghai 201411, China

摘要

摘要: 针对现有工件圆度误差的不确定度评定国标方法不能兼顾简化计算和避免分布假设的问题，对以圆度误差评定为基础的不确定度评定新方法进行研究。首先，基于最小二乘拟合圆法进行误差评定。然后，利用最大熵原理结合粒子群算法求解圆度误差概率密度函数（PDF）的优化估值。最后，利用数值积分对圆度误差不确定度进行评定，并与测量不确定度表示指南（GUM）和蒙特卡罗法（MCM）进行对比验证。结果表明，PDF估计法可实现小样本数据、无分布假设下的圆度误差不确定度评定，算法收敛性好、估值稳定。
- 圆度误差 /
- 不确定度评定 /
- 最大熵原理 /
- 粒子群算法 /
- PDF估计
Abstract: Aiming at the existing national standard method for uncertainty analysis of workpiece measurement error not to simplify calculation and avoid distribution hypothesis, a new method for evaluating uncertainty considering roundness error is studied. Firstly, the least squares fitting method is used to evaluate the error. Then, the optimal estimation of roundness error probability density function (PDF) is solved by using maximum entropy principle and particle swarm optimization (PSO). Finally, the roundness error uncertainty is evaluated by numerical integration and compared with the evaluation by GUM and Monte Carlo method (MCM). The results show that PDF estimation method can evaluate the roundness error uncertainty with small sample data and no distribution assumption, and the algorithm has good convergence and stable estimation.
- roundness error /
- uncertainty analysis /
- maximum entropy principle /
- PSO /
- PDF estimation

HTML全文

图 1 粒子群算法程序流程框图

下载: 全尺寸图片幻灯片

图 2 轴承外圈测量过程

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图 3 粒子迭代收敛过程

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图 4 圆度误差PDF对比图

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图 5 MCM概率分布图

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表 1 三坐标测量机实测数据

序号	X/mm	Y/mm
1	27.496 2	0.000 9
2	26.913 9	5.628 3
3	25.590 2	10.057 5
4	23.546 8	14.198 1
5	20.843 2	17.934 3
6	17.540 4	21.175 1
7	13.759 5	23.806 1
8	9.578 2	25.773 9
9	5.129 0	27.013 5
10	0.534 7	27.490 8
11	-4.073 5	27.192 7
12	-8.569 5	26.126 0
13	-12.820 6	24.323 8
14	-16.713 6	21.832 7
15	-20.123 3	18.735 6
16	-22.975 7	15.101 4
17	-25.182 1	11.038 6
18	-27.413 5	2.118 0
19	-27.381 5	-2.503 8
20	-26.575 0	-7.053 6
21	-25.018 9	-11.402 5
22	-22.754 0	-15.434 4
23	-19.854 7	-19.018 0
24	-16.388 7	-22.075 3
25	-12.459 8	-24.508 5
26	-8.178 3	-26.249 7
27	-3.675 0	-27.248 1
28	0.932 0	-27.479 2
29	5.529 0	-26.933 5
30	9.947 5	-25.633 3
31	14.099 7	-23.604 7
32	17.853 9	-20.911 5
33	21.099 3	-17.632 5
34	23.753 2	-13.850 6
35	25.734 7	-9.683 9
36	27.489 2	-0.640 4

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表 2 最小二乘圆度误差信息表

序号	δ/mm
1	0.002 19
2	0.002 02
3	0.001 98
4	0.001 68
5	0.002 13
6	0.002 19
7	0.002 59
8	0.002 14
9	0.002 32
10	0.002 24

下载: 导出CSV

表 3 PDF参数列表

序号	λ₀	λ₁	λ₂	λ₃
f₁	6.811 0	89.719 5	-171.341 4	-106.560 3
f₂	6.811 4	89.536 6	-157.023 0	-91.936 4
f₃	6.811 1	89.624 0	-147.488 4	-127.136 3
f₄	6.811 3	89.513 9	-125.967 7	-78.100 0
f₅	6.811 6	89.355 3	-127.882 5	-84.148 0
f₆	6.811 1	89.593 4	-134.553 1	-156.560 4
f₇	6.811 2	89.519 1	-121.131 7	-89.244 5
f₈	6.811 0	89.771 2	-189.204 1	-119.466 2
f₉	6.811 3	89.528 7	-133.726 3	-129.551 9
f₁₀	6.811 1	89.602 2	-141.558 4	-132.423 8

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表 4 GUM和MCM评定结果

序号	GUM法		MCM法
	δ/mm	u/μm	δ/mm	u/μm
1	0.002 191	0.294 4	0.002 185	0.418 3
2	0.002 026	0.294 2	0.002 023	0.424 4
3	0.001 975	0.319 1	0.001 976	0.412 4
4	0.001 684	0.283 5	0.001 675	0.401 8
5	0.002 129	0.294 8	0.002 127	0.423 1
6	0.002 193	0.294 5	0.002 187	0.418 9
7	0.002 591	0.291 3	0.002 523	0.412 7
8	0.002 136	0.294 1	0.002 133	0.422 3
9	0.002 315	0.293 9	0.002 311	0.410 6
10	0.002 241	0.294 3	0.002 238	0.417 4

下载: 导出CSV

表 5 GUM和MCM评定方法对比

名称	δ/mm	u/μm
PDF估计法	0.002 141	0.262 7
GUM法评定均值	0.002 148	0.295 4
MCM法评定均值	0.002 137	0.416 2

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