Dynamic Design and Experimental Study of Combined Spring System under High-magnitude Vibration

YAO Mingge; LIU Hao; SUN Liming; WANG Canhui

doi:10.7643/ issn.1672-9242.2026.05.010

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Equipment Environmental Engineering ›› 2026, Vol. 23 ›› Issue (5) : 85-91. DOI: 10.7643/ issn.1672-9242.2026.05.010

Aviation and Aerospace Equipment

Dynamic Design and Experimental Study of Combined Spring System under High-magnitude Vibration

YAO Mingge^1,2, LIU Hao^1,2, SUN Liming^1,2, WANG Canhui¹

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Abstract

The work aims to address the technical bottlenecks of limited output of existing vibration tables and poor adaptability of traditional amplification structures, improve the dynamic design theory of combined spring systems in the field of high-magnitude vibration, and develop parallel spring amplification tooling applicable to engineering for different frequencies to meet the high-magnitude vibration test requirement of over 110g for bearing joint components of aerospace and other equipment. Based on the spring resonance principle, a refined dynamic model of the parallel spring system was established to analyze the internal correlation between resonance frequency, damping ratio and amplitude amplification factor. Combined spring amplification tooling for different frequencies was designed, and the natural frequency of the system was optimized by adjusting the spring combination mode. An experimental test system was built, and resonance amplification performance verification tests were carried out with the basic excitation of 1 g-2 g acceleration. The results showed that the dynamic design of the combined spring system and the tooling development were completed. The system resonance frequency could be flexibly adjusted and accurately matched with the excitation frequency. Experimental verification indicated that under the resonance frequency of 26.5 Hz and a load mass of 43 kg, the acceleration amplification of more than 50 times was realized under different basic excitations, with the output acceleration exceeding 110 g. The error between theoretical calculation and experimental results was small, and the test stability was excellent. It is concluded that the proposed dynamic design method of the combined spring system is feasible and effective. The developed tooling can break through the limit of existing vibration equipment and realize high-magnitude vibration testing above 110 g in the laboratory environment. This research perfects the resonance amplification theory of combined spring systems, providing a feasible technical approach and experimental reference for the fatigue, wear and reliability testing of key components in aerospace and other fields.

Key words

spring oscillator / vibration amplification / high-magnitude vibration test / tooling design / experimental verification / fatigue and wear

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YAO Mingge, LIU Hao, SUN Liming, WANG Canhui. Dynamic Design and Experimental Study of Combined Spring System under High-magnitude Vibration[J]. Equipment Environmental Engineering. 2026, 23(5): 85-91 https://doi.org/10.7643/ issn.1672-9242.2026.05.010

References

[1] 乔驿珺, 朱顺杰, 冯元清. 航空航天材料疲劳特性的测试[J]. 上海计量测试, 2025, 52(2): 84-86.
QIAO Y J, ZHU S J, FENG Y Q.Testing of Fatigue Characteristics of Aerospace Materials[J]. Shanghai Measurement and Testing, 2025, 52(2): 84-86.
[2] LORENZ S J, SADEGHI F, TRIVEDI H K, et al.Investigation into Rolling Contact Fatigue Performance of Aerospace Bearing Steels[J]. International Journal of Fatigue, 2023, 172: 107646.
[3] HONG Y S, HU Y P, ZHAO A G.Effects of Loading Frequency on Fatigue Behavior of Metallic Materials—A Literature Review[J]. Fatigue & Fracture of Engineering Materials & Structures, 2023, 46(8): 3077-3098.
[4] 范真, 宦海祥, 李平, 等. 振动环境试验设备与技术的现状及进展[J]. 机械设计与制造, 2006(10): 164-165.
FAN Z, HUAN H X, LI P, et al.Development of Technology and Equipment of Vibration Environment Testing[J]. Machinery Design & Manufacture, 2006(10): 164-165.
[5] 郑艳伟, 刘公平, 赵滨海, 等. 高温高速混合陶瓷球轴承性能分析与试验研究[J]. 航空动力学报, 2024, 39(8): 20210402.
ZHENG Y W, LIU G P, ZHAO B H, et al.Performance Analysis and Test Research of High Temperature and High Speed Hybrid Ceramic Ball Bearings[J]. Journal of Aerospace Power, 2024, 39(8): 20210402.
[6] 姜震, 瞿飞, 袁钦. 移动式通用振动工装的设计及试验验证[J]. 航空电子技术, 2023, 54(1): 47-52.
JIANG Z, QU F, YUAN Q.Design and Test Verification of a Mobile General-Purpose Vibration Tool[J]. Avionics Technology, 2023, 54(1): 47-52.
[7] 高俊超, 牟浩文, 林淡, 等. 基于有限元仿真的大量级振动放大夹具设计[J]. 环境技术, 2024, 42(2): 154-161.
GAO J C, MOU H W, LIN D, et al.Design of Large Scale Vibration Amplification Fixture Based on Workbench Simulation[J]. Environmental Technology, 2024, 42(2): 154-161.
[8] 杨永宝, 张博, 张立昌, 等. 基于弹簧振幅放大的电磁式振动发电设计[J]. 发电技术, 2023, 44(2): 244-252.
YANG Y B, ZHANG B, ZHANG L C, et al.Design of Electromagnetic Vibration Power Generation Based on Spring Amplitude Amplification[J]. Power Generation Technology, 2023, 44(2): 244-252.
[9] WANG L, ZHANG Y X, WANG S P.Design and Performance Research of Multimodal Composite Piezoelectric Energy Harvester Based on Spring Oscillator[J]. Journal of Alloys and Compounds, 2025, 1039: 182936.
[10] 秦承武, 刘景阳, 孙德华, 等. 弹性振幅放大器对参数激励压电俘能器的影响[J]. 压电与声光, 2022, 44(1): 53.
QIN C W, LIU J Y, SUN D H, et al.Influence of Elastic Magnifier on Characteristics of Piezoelectric Energy Harvester under Parametric Excitation[J]. Piezoelectrics & Acoustooptics, 2022, 44(1): 53.
[11] 钟继根, 王东升. 振动试验夹具设计技术发展[J]. 振动与冲击, 2006, 25(S1): 1062-1064.
ZHONG J G, WANG D S.Development of Vibration Test Fixture Design Technology[J]. Journal of Vibration and Shock, 2006, 25(S1): 1062-1064.
[12] 张晓红. 弹簧振子振动图像演示装置[J]. 物理实验, 2017, 37(8): 58-59.
ZHANG X H.Visual Demonstration Instrument of Spring Vibration[J]. Physics Experimentation, 2017, 37(8): 58-59.
[13] 姜先策, 孙双双. 基于弹簧振子的简谐振动图像演示实验的改进设计与制作[J]. 科技视界, 2019, 9(32): 23.
JIANG X C, SUN S S.The Application of Polaroid Light in Engineering[J]. Science&Technology Vision, 2019, 9(32): 23.
[14] 娄仁志, 刘金生, 芮泽皓, 等. 基于弹簧振子原理的失重条件下体重测量装置研制[J]. 航天医学与医学工程, 2019, 30(6): 503-507.
LOU R Z, LIU J S, RUI Z H, et al.Development of Body Mass Measuring Device under Weightless Condition Based on Spring Oscillator Principle[J]. Space Medicine & Medical Engineering, 2019, 30(6): 503-507.
[15] 王光庆, 岳玉秋, 展永政, 等. 宽频压电振动能量采集器的实验研究[J]. 振动测试与诊断, 2017, 37(2): 261-265.
WANG G Q, YUE Y Q, ZHAN Y Z, et al.Experimental Researches for Broadband Piezoelectric Vibration Energy Harvester[J]. Journal of Vibration, Measurement & Diagnosis, 2017, 37(2): 261-265.
[16] 喻琴, 聂国柱, 赵玉杰, 等. 放大工装及响应谱控制在振动试验中的应用[J]. 机械研究与应用, 2024, 37(4): 184-186.
YU Q, NIE G Z, ZHAO Y J, et al.Application of Amplifying Tool and Response Spectrum Control in Vibration Test[J]. Mechanical Research & Application, 2024, 37(4): 184-186.
[17] 杨晶然, 赵丽明, 周云松, 等. 弹簧质量对振动及波动特性的影响[J]. 首都师范大学学报(自然科学版), 2021, 42(5): 32-36.
YANG J R, ZHAO L M, ZHOU Y S, et al.Influence of Spring Mass on Vibration and Wave Characteristics[J]. Journal of Capital Normal University (Natural Science Edition), 2021, 42(5): 32-36.
[18] 朱亮, 周涛, 吴乙万, 等. 正负刚度并联隔振系统建模与性能分析[J]. 噪声与振动控制, 2022, 42(5): 268-273.
ZHU L, ZHOU T, WU Y W, et al.Modeling and Performance Analysis of Vibration Isolation Systems with Parallel Connection of Positive and Negative Stiffness[J]. Noise and Vibration Control, 2022, 42(5): 268-273.
[19] 薛聪聪, 张万福, 田海洋, 等. 一种质量可调准零刚度隔振系统设计及动力学特性研究[J]. 机械工程学报, 2025, 61(1): 209-219.
XUE C C, ZHANG W F, TIAN H Y, et al.Design and Dynamic Characteristics of a Quasi-Zero Stiffness Vibration Isolation System with Adjustable Mass[J]. Journal of Mechanical Engineering, 2025, 61(1): 209-219.
[20] 卢华喜, 罗青峰, 周瑜健, 等. 地铁引起装配式结构振动的组合碟形弹簧隔振研究[J]. 噪声与振动控制, 2022, 42(3): 196-202.
LU H X, LUO Q F, ZHOU Y J, et al.Study on the Effect of Combined Disc Spring Isolation on Assembled Structure Vibration in Subways[J]. Noise and Vibration Control, 2022, 42(3): 196-202.
[21] 张青鹏, 张童玉, 单莹, 等. 振动工装的实践与分析[J]. 制造业自动化, 2024, 46(9): 215-220.
ZHANG Q P, ZHANG T Y, SHAN Y, et al.Practice and Analysis of Vibration Fixtures[J]. Manufacturing Automation, 2024, 46(9): 215-220.
[22] 陈家焱, 王海东, 周建川, 等. 多点激励振动试验控制技术进展[J]. 振动与冲击, 2011, 30(3): 69-73.
CHEN J Y, WANG H D, ZHOU J C, et al.Progress in Multi-Exciter Vibration Testing Control Technology[J]. Journal of Vibration and Shock, 2011, 30(3): 69-73.
[23] 许煜, 刘景元, 程礼, 等. 一种共振频率可调的振动放大器设计[J]. 实验力学, 2018, 33(4): 599-609.
XU Y, LIU J Y, CHENG L, et al.On the Design of a Vibration Amplifier with Adjustable Resonance Frequency[J]. Journal of Experimental Mechanics, 2018, 33(4): 599-609.
[24] BRANCATI R, DE FALCO D, DI MASSA G, et al.An Air Spring Resonant Vibration Exciter for Large Structures[J]. Machines, 2024, 12(2): 131.
[25] ADHIKARI S, CHOWDHURY S.Advanced Vibration Mitigation with Novel Stiffened Inertial Amplifier Designs[J]. Journal of Earthquake Engineering, 2025, 29(13): 2768-2803.
[26] SMITH M C.Synthesis of Mechanical Networks: The Inerter[J]. IEEE Transactions on Automatic Control, 2002, 47(10): 1648-1662.
[27] 马爱军, 石蒙, 刘洪英, 等. 应用谐振装置在电动振动台上实现高量级冲击响应谱的仿真研究[J]. 航天器环境工程, 2011, 28(5): 427-430.
MA A J, SHI M, LIU H Y, et al.Simulations of High Level Shock Response Spectrum Test Using Resonant Fixture on an Electrodynamics Shaker[J]. Spacecraft Environment Engineering, 2011, 28(5): 427-430.
[28] 王小强, 李斌, 邓传锦, 等. 航空航天用CQFP封装复杂集成电路振动夹具优化设计[J]. 航天器环境工程, 2021, 38(6): 662-669.
WANG X Q, LI B, DENG C J, et al.Optimized Design of Vibration Fixture for CQFP Packaged Complex Integrated Circuit Used in Aerospace[J]. Spacecraft Environment Engineering, 2021, 38(6): 662-669.
[29] 邵敏强, 利云云, 周徐斌, 等. 一类双层高静低动刚度隔振系统试验研究[J]. 振动工程学报, 2025, 38(1): 47-53.
SHAO M Q, LI Y Y, ZHOU X B, et al.Experimental Investigation on a Two-Stage High-Static-Low-Dynamic Stiffness Vibration Isolation System[J]. Journal of Vibration Engineering, 2025, 38(1): 47-53.