Phenomenological Modeling and Analysis of Planetary Gear Train under Corner Contact and Fault-Induced Impact Coupled Excitations

doi:10.3901/JME.260477

Abstract

Abstract: During the meshing process, the gear pairs often deviate from the theoretical meshing line, leading to corner contact mesh impacts. Under fault conditions, corner contact impacts increase significantly and form coupled excitation with fault impacts, influencing the vibration response of the planetary gear train. However, existing phenomenological models are found difficult to characterize this coupled impact excitation. For this reason, corner contact forces and stiffness variations in gear pairs under both healthy and faulty conditions are analyzed through the corner contact force and stiffness models, respectively. A meshing impact function is derived based on the meshing phase relationship, establishing a key link that characterizes the time-sequence correlation between corner contact forces, fault impact forces, and the meshing cycle. Based on this meshing impact function, a phenomenological model under the coupled excitation of corner contact mesh - fault impacts is developed. The matching synchrosqueezing transform method is employed to analyze the response characteristics under the impact excitation. Simulation and experimental signal analysis results under different fault sizes show that sideband amplitude and time-frequency energy increase with growing fault size. Capitalizing on this phenomenon, the fault evolution patterns is quantitatively characterized using FM0 and MSET energy spectra. The concordant variation patterns observed in simulation and experimental results validate the effectiveness of the proposed model in characterizing coupled impact excitation.

Key words: corner contact meshing, mesh impact function, coupled excitation, sun gear crack fault, planetary gear train

CLC Number:

TG165

JING Hongxiang, ZHEN Dong, FENG Guojin, ZANG Libin, GU Fengshou. Phenomenological Modeling and Analysis of Planetary Gear Train under Corner Contact and Fault-Induced Impact Coupled Excitations[J]. Journal of Mechanical Engineering, 2026, 62(12): 47-59.

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References

[1] LIU Zongyao，MA Haibin，MAO Shixiang，et al. Phenomenological modeling and experimental validation of time-varying transfer paths for condition monitoring of planetary gearboxes[J]. Mechanical Systems and Signal Processing，2025，230:112594.
[2] 宋泽树，黄伟国，石娟娟，等. 广义平滑对数正则化稀疏分解方法研究及其在齿轮箱复合故障诊断中的应用[J]. 机械工程学报，2022，58(23):123-137. SONG Zeshu，HUANG Weiguo，SHI Juanjuan，et al. Research on generalized smooth logarithm regularization sparse decomposition method and its application in compound fault diagnosis of gearbox[J]. Journal of Mechanical Engineering，2022，58(23):123-137.
[3] QIAO Zijian，CHEN Shuai，LAI Zhihui，et al. Harmonic-Gaussian double-well potential stochastic resonance with its application to enhance weak fault characteristics of machinery[J]. Nonlinear Dynamics，2023，111:7293-7307.
[4] 姚俊，章翔峰，周建星，等. 考虑信号传递路径的行星齿轮传动太阳轮裂纹故障响应分析[J]. 振动工程学报，2023，36(6):1714-1722. YAO Jun，ZHANG Xiangfeng，ZHOU Jianxing，et al. Crack fault response analysis of sun wheel in planetary gear drive considering signal transmission path[J]. Journal of Vibration Engineering，2023，36(6):1714-1722.
[5] MCFADDEN P D，SMIT J D. An explanation for the asymmetry of the modulation sidebands about the tooth meshing frequency in epicyclic gear vibration[J]. Proceedings of the Institution of Mechanical Engineers，Part C:Journal of Mechanical Engineering Science，1985，199:65-70.
[6] FENG Zhipeng，LIANG Ming，ZHANG Yi，et al. Fault diagnosis for wind turbine planetary gearboxes via demodulation analysis based on ensemble empirical mode decomposition and energy separation[J]. Renewable Energy，2012，47:112-126.
[7] 雷亚国，罗希，刘宗尧，等. 行星轮系动力学新模型及其故障响应特性研究[J]. 机械工程学报，2016，52(13):111-122. LEI Yaguo，LUO Xi，LIU Zongyao，et al. A new dynamic model of planetary gear train and its fault response characteristics[J]. Journal of Mechanical Engineering，2016，52(13):111-122.
[8] LI Yangzhuo，DING Kang，HE Guolin，et al. Vibration modulation sidebands mechanisms of equally-spaced planetary gear train with a floating sun gear[J]. Mechanical Systems and Signal Processing，2019，129:70-90.
[9] 沈子钰，张砦，王友仁，等. 行星轮齿轮箱太阳轮齿根裂纹传递特性分析[J]. 中国机械工程，2023，34(18):2177-2185. SHEN Ziyu，ZHANG Zhai，WANG Youren，et al. Analysis of transmission characteristics of sun wheel root cracks in planetary wheel gearboxes[J]. China Mechanical Engineering，2023，34(18):2177-2185.
[10] LUO Yingchao，CUI Linli，MA Jianfeng，et al. An improved phenomenological model of the planetary gearbox based on meshing vibration characteristics[J]. IEEE Access，2020，8:103462-103475.
[11] LUO Yingchao，CUI Lingli，ZHANG Jianyu，et al. Vibration mechanism and improved phenomenological model of planetary gearbox with broken sun gear fault[J]. Measurement，2021，178:109356.
[12] YU Wennian，MECHEFSKE CHRIS K. Analytical modeling of spur gear corner contact effects[J]. Mechanism and Machine Theory，2016，96:146-164.
[13] HAN Hongzheng，YUAN Kaigang，MA Huima，et al. Mesh characteristic analysis and dynamic simulation of spur gear pair considering corner contact and tooth broken fault[J]. Engineering Failure Analysis，2023，143:106883.
[14] 何泽银，易锋，杨震，等. 计入冲击与受载齿轮副时变啮合刚度解析算法[J]. 湖南大学学报(自然科学版)，2024，51(12):38-46. HE Zeyin，YI Feng，YANG Zhen，et al. Analytical algorithm for time varying mesh stiffness of gear pairs considering impact and loading[J]. Journal of Hunan University (Natural Sciences)，2024，51(12):38-46.
[15] ZHU Lingyun，YANG Wenju，GOU Xiangfeng，et al. Dynamic characteristics of spur gear pair consideringmeshing impact and multi-state meshing[J]. Meccanica，2023，68:619-642.
[16] LIU Zongyao，WANG Yadong，WANG Yutong，et al. A phenomenological model of vibration signals of epicyclic gearboxes under meshing impact excitations[J]. Mechanical Systems and Signal Processing，2023，187:109904.
[17] ZHOU Peng，CHEN Shiqian，HE Qingbo，et al. Rotating machinery fault-induced vibration signal modulation effects:A review with mechanisms，extraction methods and applications for diagnosis[J]. Mechanical Systems and Signal Processing，2023，200:110489.
[18] ZHANG Dong，FENG Zhipeng. Wind turbine planetary gearbox fault diagnosis via proportion-extracting synchrosqueezing chirplet transform[J]. Journal of Dynamics，Monitoring and Diagnostics，2023，2(3):177-182.
[19] LIN Rongye，LIU Zhiwen，JIN Yulin. Instantaneous frequency estimation for wheelset bearings weak fault signals using second-order synchrosqueezing S-transform with optimally weighted sliding window[J]. ISA transactions，2021，115:218-233.
[20] YANG Laihao，CHEN Xuefeng，WANG Shibin，et al. Rub-impact detection of rotor systems using time-frequency techniques[C]//ASME International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers，2016，50558:V04BT05A011.
[21] CHEN Shiqian，YANG Yang，PENG Zhike，et al. Detection of rub-impact fault for rotor-stator systems:A novel method based on adaptive chirp mode decomposition[J]. Journal of Sound and Vibration，2019，440:83-99.
[22] 雷震，姜宏，章翔峰，等. 行星齿轮系统齿裂纹演化分析[J]. 机械工程学报，2024，60(19):101-115. LEI Zhen，JIANG Hong，ZHANG Xiangfeng，et al. Evolutionary analysis of tooth cracks in planetary gear systems[J]. Journal of Mechanical Engineering，2024，60(19):101-115.
[23] NIU Hang，CHEN Haibin，HU Aijun，et al. Investigation of mesh force features under different planet tooth faults in planetary gearboxes[J]. Engineering Failure Analysis，2024，159:108122.
[24] 易园园，轩亮，孟丽君，等. 计入线外啮合的风电齿轮动力学行为分析[J]. 太阳能学报，2023，44(12):200-206. YI Yuanyuan，XUAN Liang，MENG Lijun，et al. Dynamic behavior of wind turbine gears considering corner contact[J]. Acta Energiae Solaris Sinica，2023，44(12):200-206.
[25] NIE Yanyan，LI Fangyi，WANG Liming，et al. Phenomenological vibration models of planetary gearboxes for gear local fault diagnosis[J]. Mechanism and Machine Theory，2022，120:104698
[26] JING Hongxiang，ZHEN Dong，FENG Guojin，et al. Phenomenological modeling of planetary gear trains considering corner contact meshing impact with different fault size[J]. Nonlinear Dynamics，2025，113:16277-16299
[27] YU Gang，YU Mingjin，XU Chuanyan. synchroextracting transform[J]. IEEE Transactions on Industrial Electronics，2017，64(10):8042-8054.
[28] MA Yubo，LÜ Yong，YUAN Rui，et al. Matching synchroextracting transform for mechanical fault diagnosis under variable-speed conditions[J]. IEEE Transactions on Instrumentation and Measurement，2022，71:1-12.
[29] YANG Yi，TANG Jinyuan，HU Niaoqing，et al. Research on the time-varying mesh stiffness method and dynamic analysis of cracked spur gear system considering the crack position[J]. Journal of Sound and Vibration，2023，548:117505.