Journal of Jilin University(Engineering and Technology Edition) ›› 2026, Vol. 56 ›› Issue (3): 653-661.doi: 10.13229/j.cnki.jdxbgxb.20240747

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High precision deformation condition and reliability analysis of bolt group connection

Zhi-qun ZHENG1(),Xian-zhen HUANG1,2(),Yu-ping WANG1,Zhi-yuan LU1   

  1. 1.School of Mechanical Engineering and Automation，Northeastern University，Shenyang 110819，China
    2.Key Laboratory of Vibration and Control of Aero?Propulsion Systems Ministry of Education of China，Northeastern University，Shenyang 110819，China
  • Received:2024-06-24 Online:2026-03-01 Published:2026-03-31
  • Contact: Xian-zhen HUANG E-mail:807874475@qq.com;xzhhuang@mail.neu.edu.cn

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Abstract:

A finite element model of the bolt group was established， and its accuracy was verified through bolt group tightening experiments. The effects of arrangement pattern， preload， and tightening sequence on the deformation at the center of the connected parts were analyzed using the finite element method. Considering the uncertainty of bolt group connection parameters due to errors， the deformation reliability of the connected parts was calculated using the Monte Carlo simulation （MCS） method. To improve computational efficiency， a surrogate model was constructed based on the finite element model presented in this study， and specific applications for calculating deformation reliability were provided. The results indicate that the deformation of the connected parts after tightening is reduced when the thickness of the connected parts is increased and the hole spacing is decreased； the tightening sequence affects the deformation process； the surrogate model constructed in this study demonstrates accuracy； and when the uncertain parameters follow a normal distribution， the deformation of the connected parts also approximately follows a normal distribution.

Key words: bolt connection, tightening deformation, surrogate model, reliability analysis

CLC Number: 

  • TH131.3

Fig.1

Schematic diagram of bolt connection"

Fig.2

Mesh of bolt connection"

Table 1

Material properties"

参数数值
35CrMo304不锈钢
密度/（kg·m-3）7 9007 930
弹性模量/MPa206 075204 000
泊松比0.2860.285
许用应力/MPa228137

Fig.3

Tightening process"

Fig.4

Mesh independent verification"

Fig.5

Fastening experimental device"

Table 2

Comparison of experimental results"

预紧力/kN有限元应变值/μm实验测试应变值/μm相对偏差/%
1234均值
2.51551841351741441592.5
42472632522262382441.2
53163433153243093221.8
107447757387597647592

Fig.6

Influence of bolt hole space on deformation"

Fig.7

Influence of connected part thickness ondeformation"

Fig.8

Influence of preload on deformation"

Fig.9

Influence of bolt hole space on deformation"

Table 3

Sampling parameter"

参 数抽样上限抽样下限
被连接件厚度l/mm3020
x方向孔间距a/mm7525
y方向孔间距b/mm7525
螺栓I预紧力F1/kN12k8k
螺栓Ⅱ预紧力F2/kN12k8k
螺栓Ⅲ预紧力F3/kN12k8k
螺栓Ⅳ预紧力F4/kN12k8k

Fig.10

Comparison of surrogate model results"

Table 4

Uncertainty parameter distribution"

变量分布均值标准差变异系数
l/mm正态251.8750.075
a/mm正态503.750.075
b/mm正态503.750.075
F1/kN正态10k7500.075
F2/kN正态10k7500.075
F3/kN正态10k7500.075
F4/kN正态10k7500.075

Fig.11

Probability and cumulative probability distribution of deformation failure"

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