| Citation: | Xia Yang, Song Zeyang, Feng Chuhan, et al. Equivalent vibration simulation model for aerospace bolted joints considering stepped contact stress distribution[J]. Journal of Aerospace Power, 2026, 41（X）：20250162 doi: 10.13224/j.cnki.jasp.20250162
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Bolted connections are widely used in aerospace equipment assembly due to their structural simplicity and high reliability. The dynamic characteristics of bolted connections significantly influence the dynamic behavior of assembled structures. While detailed finite element models can analyze vibration characteristics, their computational cost is often prohibitively high, making them unsuitable for analyzing complex bolted assemblies. To address this issue, this study proposes an equivalent bolted connection unit model, which simplifies the bolted connection into a stepped double-ring thin-layer unit to simulate the stress distribution at the bolted interface. The model consists of three parts: the upper joint, the double-ring thin-layer unit, and the lower joint. The size of the thin-layer unit model is determined based on the bolt stress distribution, and key parameters of the ring-shaped thin-layer unit—including thickness, elastic modulus, Poisson’s ratio, and density—are derived using Hertzian contact theory. The accuracy of the proposed model in simulating dynamic characteristics is validated through comparison with vibration experimental data from a typical aerospace tooling structure. The results demonstrate that, compared to the traditional virtual material method, the proposed model significantly improves simulation efficiency while maintaining vibration frequency simulation errors within 10%. This indicates that the model is effective for dynamic simulation analysis of bolted connection structures .
| [1] |
马奔奔. 基于多尺度粗糙接触力学的无垫圈螺栓连接密封性研究[D]. 大连: 大连理工大学, 2018. Ma Benben. Sealing analysis for bolted joint systems without gaskets based on multi-scale rough contact mechannics[D]. Dalian: Dalian University of Technology, 2018. (in Chinese
Ma Benben. Sealing analysis for bolted joint systems without gaskets based on multi-scale rough contact mechannics[D]. Dalian: Dalian University of Technology, 2018. (in Chinese)
|
| [2] |
李森浩. 盘鼓结构中螺栓扭矩—转角法拧紧工艺研究[D]. 大连: 大连理工大学, 2023. Li Senhao. Study of bolt torque-angle tightening process in disc and drum structure[D]. Dalian: Dalian University of Technology, 2023. (in Chinese
Li Senhao. Study of bolt torque-angle tightening process in disc and drum structure[D]. Dalian: Dalian University of Technology, 2023. (in Chinese)
|
| [3] |
栾宇, 刘松, 关振群, 等. 小变形下螺栓法兰连接结构的静刚度非线性特性[J]. 强度与环境, 2011, 38(3): 29-35. Luan Yu, Liu Song, Guan Zhenqun, et al. The nonlinear character of static stiffness in the structure with bolted flanged connection under small deformation[J]. Structure & Environment Engineering, 2011, 38(3): 29-35. (in Chinese doi: 10.3969/j.issn.1006-3919.2011.03.006
Luan Yu, Liu Song, Guan Zhenqun, et al. The nonlinear character of static stiffness in the structure with bolted flanged connection under small deformation[J]. Structure & Environment Engineering, 2011, 38(3): 29-35. (in Chinese) doi: 10.3969/j.issn.1006-3919.2011.03.006
|
| [4] |
何国军, 竺润祥, 尹云玉, 等. 考虑连接刚度的导弹固有特性分析[J]. 强度与环境, 2006, 33(1): 14-17. He Guojun, Zhu Runxiang, Yin Yunyu, et al. Analysis on inherent behavior considering the connecting rigidity of missiles[J]. Structure & Environment Engineering, 2006, 33(1): 14-17. (in Chinese doi: 10.3969/j.issn.1006-3919.2006.01.003
He Guojun, Zhu Runxiang, Yin Yunyu, et al. Analysis on inherent behavior considering the connecting rigidity of missiles[J]. Structure & Environment Engineering, 2006, 33(1): 14-17. (in Chinese) doi: 10.3969/j.issn.1006-3919.2006.01.003
|
| [5] |
Zhang Ouqi, Poirier J A. New analytical model of bolted joints[J]. Journal of Mechanical Design, 2004, 126(4): 721-728. doi: 10.1115/1.1760777
|
| [6] |
邹元杰. Bush有限单元原理及其在航天器结构建模中的应用[J]. 航天器工程, 2010, 19(1): 99-105. Zou Yuanjie. Bush finite element principle and its application in building structural models for spacecraft[J]. Spacecraft Engineering, 2010, 19(1): 99-105. (in Chinese doi: 10.3969/j.issn.1673-8748.2010.01.018
Zou Yuanjie. Bush finite element principle and its application in building structural models for spacecraft[J]. Spacecraft Engineering, 2010, 19(1): 99-105. (in Chinese) doi: 10.3969/j.issn.1673-8748.2010.01.018
|
| [7] |
石川千, 周徐斌, 张永涛, 等. 点式连接航天器等效刚度模态分析方法[J]. 航天器工程, 2016, 25(1): 31-39. Shi Chuanqian, Zhou Xubin, Zhang Yongtao, et al. Modal analysis of spacecraft with dotted joints based on equivalent stiffness[J]. Spacecraft Engineering, 2016, 25(1): 31-39. (in Chinese doi: 10.3969/j.issn.1673-8748.2016.01.005
Shi Chuanqian, Zhou Xubin, Zhang Yongtao, et al. Modal analysis of spacecraft with dotted joints based on equivalent stiffness[J]. Spacecraft Engineering, 2016, 25(1): 31-39. (in Chinese) doi: 10.3969/j.issn.1673-8748.2016.01.005
|
| [8] |
程来, 宋言明, 李贺, 等. 基于等效接触区域的螺栓连接结构模态分析[J]. 机械设计与研究, 2012, 28(2): 44-47. Cheng Lai, Song Yanming, Li He, et al. Modal analysis based on the equivalent contact area of the structure with bolt connections[J]. Machine Design & Research, 2012, 28(2): 44-47. (in Chinese doi: 10.3969/j.issn.1006-2343.2012.02.012
Cheng Lai, Song Yanming, Li He, et al. Modal analysis based on the equivalent contact area of the structure with bolt connections[J]. Machine Design & Research, 2012, 28(2): 44-47. (in Chinese) doi: 10.3969/j.issn.1006-2343.2012.02.012
|
| [9] |
Liu S G, Wang J, Hong J, et al. Dynamics design of the aero-engine rotor joint structures based on experimental and numerical study: GT2013-95029[R]. Glasgow: ASME Turbo Expo 2013.
|
| [10] |
樊宁. 航空发动机连接结构刚度非线性及其对转子动力学影响[D]. 北京: 北京航空航天大学, 2013. Fan Ning. Nonlinear stiffness of aero-engine joint structures and its influence on rotor dynamics[D]. Beijing: Beijing University of Aeronautics and Astronautics, 2013. (in Chinese
Fan Ning. Nonlinear stiffness of aero-engine joint structures and its influence on rotor dynamics[D]. Beijing: Beijing University of Aeronautics and Astronautics, 2013. (in Chinese)
|
| [11] |
Kim J, Yoon J C, Kang B S. Finite element analysis and modeling of structure with bolted joints[J]. Applied Mathematical Modelling, 2007, 31(5): 895-911. doi: 10.1016/j.apm.2006.03.020
|
| [12] |
赵广, 金鑫, 崔颖, 等. 基于模态应变能的接触刚度识别方法[J]. 机械工程学报, 2020, 56(9): 147-153. Zhao Guang, Jin Xin, Cui Ying, et al. Contact stiffness identification method based on modal strain energy[J]. Journal of Mechanical Engineering, 2020, 56(9): 147-153. (in Chinese doi: 10.3901/JME.2020.09.147
Zhao Guang, Jin Xin, Cui Ying, et al. Contact stiffness identification method based on modal strain energy[J]. Journal of Mechanical Engineering, 2020, 56(9): 147-153. (in Chinese) doi: 10.3901/JME.2020.09.147
|
| [13] |
黄开放, 金建新. 基于虚拟材料方法的螺栓预紧力模拟的研究[J]. 机械设计与制造, 2012(8): 148-150. Huang Kaifang, Jin Jianxin. Research on bolt preload simulation based on virtual material method[J]. Machinery Design & Manufacture, 2012(8): 148-150. (in Chinese doi: 10.3969/j.issn.1001-3997.2012.08.054
Huang Kaifang, Jin Jianxin. Research on bolt preload simulation based on virtual material method[J]. Machinery Design & Manufacture, 2012(8): 148-150. (in Chinese) doi: 10.3969/j.issn.1001-3997.2012.08.054
|
| [14] |
Greenwood J A, Williamson J B P. Contact of nominally flat surfaces[J]. Proceedings of the Royal Society of London Series A: Mathematical and Physical Sciences, 1966, 295(1442): 300-319.
|
| [15] |
刘勇, 夏天, 陈志英, 等. 粗糙表面统计接触模型的提出与发展[J]. 摩擦学学报, 2020, 40(3): 395-406. Liu Yong, Xia Tian, Chen Zhiying, et al. The development of statistical contact model for rough surface[J]. Tribology, 2020, 40(3): 395-406. (in Chinese doi: 10.16078/j.tribology.2019191
Liu Yong, Xia Tian, Chen Zhiying, et al. The development of statistical contact model for rough surface[J]. Tribology, 2020, 40(3): 395-406. (in Chinese) doi: 10.16078/j.tribology.2019191
|
| [16] |
田红亮, 方子帆, 赵春华, 等. 依据修正GW理论的结合部法向接触研究[J]. 华中科技大学学报(自然科学版), 2014, 42(6): 38-42, 47. Tian Hongliang, Fang Zifan, Zhao Chunhua, et al. Normal contact of joint interface using revised GW theory[J]. Journal of Huazhong University of Science and Technology (Natural Science Edition), 2014, 42(6): 38-42, 47. (in Chinese doi: 10.13245/j.hust.140608
Tian Hongliang, Fang Zifan, Zhao Chunhua, et al. Normal contact of joint interface using revised GW theory[J]. Journal of Huazhong University of Science and Technology (Natural Science Edition), 2014, 42(6): 38-42, 47. (in Chinese) doi: 10.13245/j.hust.140608
|
| [17] |
Majumdar A, Bhushan B. Fractal model of elastic-plastic contact between rough surfaces[J]. Journal of Tribology, 1991, 113(1): 1-11. doi: 10.1115/1.2920588
|
| [18] |
Majumdar A, Bhushan B. Role of fractal geometry in roughness characterization and contact mechanics of surfaces[J]. Journal of Tribology, 1990, 112(2): 205-216. doi: 10.1115/1.2920243
|
| [19] |
Jiang Shuyun, Zheng Yunjian, Zhu Hua. A contact stiffness model of machined plane joint based on fractal theory[J]. Journal of Tribology, 2010, 132: 011401. doi: 10.1115/1.4000305
|
| [20] |
孙洪泉. 分形几何与分形插值[M]. 北京: 科学出版社, 2011. Sun Hongquan. Fractal geometry and fractal interpolation[M]. Beijing: Science Press, 2011. (in Chinese
Sun Hongquan. Fractal geometry and fractal interpolation[M]. Beijing: Science Press, 2011. (in Chinese)
|
| [21] |
Xu Longjun, Peng Tiefeng, Zhang Dingyue, et al. Fractal desulfurization kinetics of high-sulfur coal[J]. International Journal of Mining Science and Technology, 2012, 22(1): 111-114. doi: 10.1016/j.ijmst.2011.07.010
|
| [22] |
Gao Qifeng, Wu Xiongxi, Li Zesong. Failure analysis of rolling bearings based on explicit dynamic method and theories of hertzian contact[J]. Journal of Failure Analysis and Prevention, 2019, 19(6): 1645-1654. doi: 10.1007/s11668-019-00756-1
|
| [23] |
Yang Hongping, Che Xiaowei, Yang Cheng. Investigation of normal and tangential contact stiffness considering surface asperity interaction[J]. Industrial Lubrication and Tribology, 2019, 72(3): 379-388. doi: 10.1108/ILT-03-2019-0072
|
| [24] |
李鹏, 杨成, 刘秀宇, 等. 基于非线性虚拟材料法的栓接结合部动态特性分析[J]. 导航与控制, 2023, 22(3): 106-115. Li Peng, Yang Cheng, Liu Xiuyu, et al. Dynamic analysis of bolted joint based on nonlinear virtual material method[J]. Navigation and Control, 2023, 22(3): 106-115. (in Chinese doi: 10.3969/j.issn.1674-5558.2023.03.015
Li Peng, Yang Cheng, Liu Xiuyu, et al. Dynamic analysis of bolted joint based on nonlinear virtual material method[J]. Navigation and Control, 2023, 22(3): 106-115. (in Chinese) doi: 10.3969/j.issn.1674-5558.2023.03.015
|
| [25] |
Chen Zhe, Zhao Qijun, Zhou Guochen. Research on the simulation method for equivalent stiffness of bolted connection thin plate structures[J]. International Journal of Aerospace Engineering, 2024, 2024: 8648996. doi: 10.1155/2024/8648996
|
| [26] |
Tian Yu, Qian Hui, Cao Zhifu, et al. Identification of pre-tightening torque dependent parameters for empirical modeling of bolted joints[J]. Applied Sciences, 2021, 11(19): 9134. doi: 10.3390/app11199134
|
| [27] |
崔方圆. 螺栓结合部动态特性等效建模与参数识别方法研究[D]. 西安: 西安理工大学, 2020. Cui Fangyuan. Investigation on equivalent modeling and parameter identification method of dynamic characteristics of bolted joint[D]. Xi’an: Xi’an University of Technology, 2020. (in Chinese
Cui Fangyuan. Investigation on equivalent modeling and parameter identification method of dynamic characteristics of bolted joint[D]. Xi’an: Xi’an University of Technology, 2020. (in Chinese)
|
| [28] |
Xu Z H, Liu D, Hong Z Y, et al. An improved modeling method for thin layer elements of aeroengine bolted connections[J]. Computer Simulation, 2020, 37(7): 100-106.
|
| [29] |
Nassar S A, El-khiamy H, Barber G C, et al. An experimental study of bearing and thread friction in fasteners[J]. Journal of Tribology, 2005, 127(2): 263-272. doi: 10.1115/1.1843167
|
| [30] |
Nassar S A, Matin P H, Barber G C. Thread friction torque in bolted joints[J]. Journal of Pressure Vessel Technology, 2005, 127(4): 387-393. doi: 10.1115/1.2042474
|
| [31] |
马雅丽, 刘国超, 危家勇, 等. 基于有限元法改进螺栓连接刚度模型[J]. 组合机床与自动化加工技术, 2021(3): 45-48. Ma Yali, Liu Guochao, Wei Jiayong, et al. Improvement of bolt connection stiffness model based on finite element method[J]. Modular Machine Tool & Automatic Manufacturing Technique, 2021(3): 45-48. (in Chinese doi: 10.13462/j.cnki.mmtamt.2021.03.010
Ma Yali, Liu Guochao, Wei Jiayong, et al. Improvement of bolt connection stiffness model based on finite element method[J]. Modular Machine Tool & Automatic Manufacturing Technique, 2021(3): 45-48. (in Chinese) doi: 10.13462/j.cnki.mmtamt.2021.03.010
|
| [32] |
贾文锋, 张学良, 温淑花, 等. 基于虚拟材料的结合面建模与参数获取方法[J]. 太原科技大学学报, 2013, 34(5): 347-351. Jia Wenfeng, Zhang Xueliang, Wen Shuhua, et al. A method for modeling and parameter acquisitions of joints based on virtual materials[J]. Journal of Taiyuan University of Science and Technology, 2013, 34(5): 347-351. (in Chinese doi: 10.3969/j.issn.1673-2057.2013.05.006
Jia Wenfeng, Zhang Xueliang, Wen Shuhua, et al. A method for modeling and parameter acquisitions of joints based on virtual materials[J]. Journal of Taiyuan University of Science and Technology, 2013, 34(5): 347-351. (in Chinese) doi: 10.3969/j.issn.1673-2057.2013.05.006
|
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