Intelligent Early Warning Method for Interference Fit Quality Based on Twin Data

doi:10.3969/j.issn.1004-132X.2026.08.018

Abstract

Abstract:

Aiming at the problems of real-time state changes and difficult to control assembly quality in the overfill assembly processes， an intelligent early warning method of overfill assembly quality was proposed based on twin data， considering the relationship between press-fit force and displacement， which were the two key parameters reflecting the assembly quality. A comprehensive analysis of the actual assembly processes was carried out， and the framework of the overfill assembly quality intelligent warning system was constructed. A local outlier detection algorithm was designed based on the weighted fusion of area density and information entropy by combining twin data； the mathematical model of the overfill assembly processes between the press force and displacement was established by analyzing the changes of press force and the changes of displacement in the assembly processes as well as the relationship of the two by applying the method of linear fitting. The reasonable press-fit force corresponding to each displacement value x in the assembly processes was determined； and the mathematical model between press-fit force F and displacement was established by applying linear fitting method. The results show that the proposed method may determine a more accurate quality control range and improve the passing rate of the interference assembly quality. The method has important reference significance for the realization of abnormality monitoring and quality control in the interference assembly processes.

Key words: twinn data, interference fit, regional density, information entropy, Bollinger band

摘要：

针对过盈装配过程中状态实时变化、装配质量难以控制的问题，基于压装力与位移这两个反映装配质量的关键参量之间的关系，提出一种基于孪生数据的过盈装配质量智能预警方法。综合分析实际装配过程，构建了过盈装配质量智能预警系统框架；结合孪生数据，设计了一种基于区域密度和信息熵加权融合的局部异常值检测算法；通过分析装配过程中压装力、位移的变化及两者关系，运用线性拟合方法建立了过盈装配过程中压装力-位移的数学模型，确定装配过程中每个位移值x对应的合理压装力F；结合布林线方法，进一步确定了用于装配过程质量控制的合格压装力范围。以行星减速器过盈配合组件为例进行验证，结果表明，所提方法可以确定更精准的质量控制范围，使得过盈装配质量的合格率得到提高。所提方法在过盈装配过程中对异常监测与质量控制的实现具有重要参考意义。

关键词: 孪生数据, 过盈装配, 区域密度, 信息熵, 布林线

CLC Number:

U664.22

YANG Yanfang, YANG Yonglu, ZHANG Bo, SHENG Biwu, CHEN Dingfang, SHAO Wenjun, WU Junfeng. Intelligent Early Warning Method for Interference Fit Quality Based on Twin Data[J]. China Mechanical Engineering, 2026, 37(8): 1989-1998.

杨艳芳, 杨永禄, 张博, 盛毕武, 陈定方, 邵文军, 吴俊峰. 基于孪生数据的过盈装配质量智能预警方法[J]. 中国机械工程, 2026, 37(8): 1989-1998.

Figures/Tables 15

Fig.1 A Framework for intelligent early warning of interference fit quality based on twin data

Fig.2 Algorithm flowchart

Tab.1 Data characteristics of the ODDS dataset

数据集	总样本个数	异常样本个数	属性	异常样本比例/%
Iris	110	10	4	9.1
Glass	214	9	9	4.2
Ionosphere	351	126	32	35.9
Shuttle	1013	13	9	1.3
Page Blocks	5474	560	11	10.2

Fig.3 Comparison of accuracy and execution time for algorithms on the ODDS dataset

Fig.4 Schematic diagram of a planetary gearbox

Tab.2 Bollinger band parameters and thresholds at different confidence levels

置信度 $α$ /%	调整参数 $k$	上限值	下限值
95	2	$μ + 2 σ$	$μ - 2 σ$
99	3	$μ + 3 σ$	$μ - 3 σ$

Tab.2 Bollinger band parameters and thresholds at different confidence levels

置信度 $α$ /%	调整参数 $k$	上限值	下限值
95	2	$μ + 2 σ$	$μ - 2 σ$
99	3	$μ + 3 σ$	$μ - 3 σ$

Fig.5 Quality control flowchart

Fig.6 Physics assembly experiment platform and its components

Fig.7 Model of the interference fit assembly between the input shaft and the sun gear in a planetary gearbox

Tab.3 Composition and function of laboratory equipment

设备名称

详细组成及参数

功能

TSTY-3103

伺服压力机

移动工作台、导向柱、主油缸、液压系统、压头等

1）装配实验设备；2）装配过程实时监测对象

传感器数据

采集试验台

试验台由力、位移传感器、上位机及中间件组成

1）装配过程实时数据采集；2）数据预处理与上传

PC端

CPU：Intel（R） Core^TMi5-4210M CPU @ 3.2 GHz 2.6 GHz

显卡：NVIDIA GeForce 840 M

硬盘：250 GB 内存：8 GB

1）部署中间件数据采集流程；2）运行数字孪生质量监测系统

Tab.4 Raw press-fitting force–displacement data

位移 x/mm	压装力 F/N
位移 x/mm	F₁	F₂	F₃	…	F₉₉	F₁₀₀
0	0.0	0.0	0.0	…	0.0	0.0
1	1102.8	1180.0	1191.4	…	1803.0	1814.3
2	2947.1	3293.8	3684.0	…	3322.4	2501.9
3	3738.7	4992.0	5214.2	…	5125.5	4669.9
4	8572.8	7202.8	6690.4	…	5819.1	5934.0
5	10 285.3	9248.7	9462.9	…	7591.2	8430.6
$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$
11	17 736.9	15 059.2	18 029.9	…	19 765.5	18 514.1
12	16 842.7	16 300.7	18 813.5	…	17 511.7	17 844.3

Tab.4 Raw press-fitting force–displacement data

位移 x/mm	压装力 F/N
位移 x/mm	F₁	F₂	F₃	…	F₉₉	F₁₀₀
0	0.0	0.0	0.0	…	0.0	0.0
1	1102.8	1180.0	1191.4	…	1803.0	1814.3
2	2947.1	3293.8	3684.0	…	3322.4	2501.9
3	3738.7	4992.0	5214.2	…	5125.5	4669.9
4	8572.8	7202.8	6690.4	…	5819.1	5934.0
5	10 285.3	9248.7	9462.9	…	7591.2	8430.6
$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$
11	17 736.9	15 059.2	18 029.9	…	19 765.5	18 514.1
12	16 842.7	16 300.7	18 813.5	…	17 511.7	17 844.3

Tab.5 Data before outliers were removed

位移x/mm	压装力均值μ_F	标准差 σ	μ_F +2σ	μ_F －2σ	μ_F +3σ	μ_F －3σ
0	0.0	0.0	0.0	0.0	0.0	0.0
1	1487.9	148.1	1784.1	1191.8	1932.2	1043.7
2	3010.9	389.8	3790.6	2231.3	4180.4	1841.5
3	4531.6	487.9	5507.4	3555.8	5995.3	3067.9
4	5951.2	681.4	7313.9	4588.4	7995.3	3907.1
5	7506.4	982.7	9471.8	5541.0	10454.5	4558.3
$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$
11	16 431.7	1999.8	20 431.2	12 432.1	22 431.0	10 432.3
12	18 022.1	2047.8	22 117.8	13 926.5	24 165.6	11 878.7

Tab.5 Data before outliers were removed

位移x/mm	压装力均值μ_F	标准差 σ	μ_F +2σ	μ_F －2σ	μ_F +3σ	μ_F －3σ
0	0.0	0.0	0.0	0.0	0.0	0.0
1	1487.9	148.1	1784.1	1191.8	1932.2	1043.7
2	3010.9	389.8	3790.6	2231.3	4180.4	1841.5
3	4531.6	487.9	5507.4	3555.8	5995.3	3067.9
4	5951.2	681.4	7313.9	4588.4	7995.3	3907.1
5	7506.4	982.7	9471.8	5541.0	10454.5	4558.3
$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$
11	16 431.7	1999.8	20 431.2	12 432.1	22 431.0	10 432.3
12	18 022.1	2047.8	22 117.8	13 926.5	24 165.6	11 878.7

Tab.6 Data after outliers have been removed

位移x/mm	压装力均值 μ	标准差 σ	上限值		下限值
位移x/mm	压装力均值 μ	标准差 σ	μ+2σ	μ+3σ	μ－2σ	μ+3σ
0	0.0	0.0	0.0	0.0	0.0	0.0
1	1473.5	143.7	1760.8	1904.5	1186.2	1042.5
2	2998.3	370.8	3740.0	4110.8	2256.6	1885.8
3	4484.5	457.7	5400.0	5857.5	3569.2	3111.5
4	5911.8	615. 3	7142.3	7757.6	4681.2	4065.9
5	7470.4	925.9	9322.2	10248.1	5618.5	4692.6
$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$
11	16 197.2	19 53.0	20 103.1	22 056.1	12 291.2	10 338.3
12	17 914.3	17 70.0	21 454.4	23 224.4	14 374.2	12 604.1

Tab.6 Data after outliers have been removed

位移x/mm	压装力均值 μ	标准差 σ	上限值		下限值
位移x/mm	压装力均值 μ	标准差 σ	μ+2σ	μ+3σ	μ－2σ	μ+3σ
0	0.0	0.0	0.0	0.0	0.0	0.0
1	1473.5	143.7	1760.8	1904.5	1186.2	1042.5
2	2998.3	370.8	3740.0	4110.8	2256.6	1885.8
3	4484.5	457.7	5400.0	5857.5	3569.2	3111.5
4	5911.8	615. 3	7142.3	7757.6	4681.2	4065.9
5	7470.4	925.9	9322.2	10248.1	5618.5	4692.6
$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$
11	16 197.2	19 53.0	20 103.1	22 056.1	12 291.2	10 338.3
12	17 914.3	17 70.0	21 454.4	23 224.4	14 374.2	12 604.1

Fig.8 Comparison of press-fitting force–displacement curves before and after outlier removal

Fig.9 Comparison of traditional quality control methods and the Bollinger bands method

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