Czakó, A., Øehák, K., Prokop, A., Rekem, J., Láštic, D., and Trochta, M.: Static transmission error measurement of various gear-shaft systems by finite element analysis, Journal of Measurements in Engineering, 12, 183–198, https://doi.org/10.21595/jme.2023.23843, 2024.
Fernández-del-Rincón, A., Iglesias, M., de-Juan, A., Diez-Ibarbia, A., García, P., and Viadero, F.: Gear transmission dynamics: effects of index and run out errors, Appl. Acoust., 108, 63–83, https://doi.org/10.1016/j.apacoust.2015.11.012, 2016.
Gong, J., Liu, G., Liu, L., Yuan, B., Yang, L., and Ren, P.: Experimental study on vibration characteristics of double-helical gearbox with isolators, J. Mech. Sci. Technol., 36, 4379–4393, https://doi.org/10.1007/s12206-022-0803-5, 2022.
Guo, F. and Fang, Z.: The statistical analysis of the dynamic performance of a gear system considering random manufacturing errors under different levels of machining precision, Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, 234, 3–18, https://doi.org/10.1177/1464419319862165, 2020.
Han, B., Li, H., Zhang, Z., Song, L., Wang, J., Lv, X., and Wang, J.: A novel construction method of planetary gear dynamics model under indexing circle crack failure, J. Vib. Eng. Technol., 13, 251, https://doi.org/10.1007/s42417-025-01769-x, 2025.
Hong, J., Talbot, D., and Kahraman, A.: Effects of tooth indexing errors on load distribution and tooth load sharing of splines under combined loading conditions, J. Mech. Design, 137, 032601, https://doi.org/10.1115/1.4029282, 2015.
Hu, C., Yuan, T., Yang, S., Hu, Y., and Liang, X.: Dynamic load sharing behavior for the pitch drive in MW wind turbines, Processes, 11, 544, https://doi.org/10.3390/pr11020544, 2023.
Hu, Y. and Zhang, C.: A new semi-analytical slice model for elastic contact analysis of herringbone gears, J. Mech. Sci. Technol., 39, 757–765, https://doi.org/10.1007/s12206-025-0120-x, 2025.
Huang, W., Hu, H., and Ma, H.: Dynamic modeling and response analysis of cracked herringbone gear transmission systems with installation errors, Mech. Mach. Theory, 206, 105924, https://doi.org/10.1016/j.mechmachtheory.2025.105924, 2025.
Huo, G., Iglesias-Santamaria, M., Zhang, X., Sanchez-Espiga, J., Caso-Fernandez, E., Jiao, Y., and Viadero-Rueda, F.: Influence of eccentricity error on the orbit of a two-stage double-helical compound planetary gear train with different mesh phasing configurations, Mech. Mach. Theory, 196, 105634, https://doi.org/10.1016/j.mechmachtheory.2024.105634, 2024.
Inalpolat, M. and Kahraman, A.: A dynamic model to predict modulation sidebands of a planetary gear set having manufacturing errors, J. Sound Vib., 329, 371–393, https://doi.org/10.1016/j.jsv.2009.09.022, 2010.
Inalpolat, M., Handschuh, M., and Kahraman, A.: Influence of indexing errors on dynamic response of spur gear pairs, Mech. Syst. Signal Pr., 60–61, 391–405, https://doi.org/10.1016/j.ymssp.2014.11.017, 2015.
ISO: Cylindrical gears-ISO system of flank tolerance classification-Part 1: Definitions and allowable values of deviations relevant to flanks of gear teeth, International Organization for Standardization (ISO), ISO 1328-1:2013,
https://www.iso.org/obp/ui/en/#iso:std:iso:1328:-1:ed-2:v1:en (last access: 5 February 2026), 2013.
Li, M., Yang, Z., and Xie, L.: Effect of planet pin position errors on the fatigue reliability of large aviation planetary systems, Frontiers of Mechanical Engineering, 19, 29, https://doi.org/10.1007/s11465-024-0797-z, 2024.
Liu, J., Li, X., and Xia, M.: A dynamic model for the planetary bearings in a double planetary gear set, Mech. Syst. Signal Pr., 194, 110257, https://doi.org/10.1016/j.ymssp.2023.110257, 2023.
Pedrero, J. I., Sánchez, M. B., and Pleguezuelos, M.: Analytical model of meshing stiffness, load sharing, and transmission error for internal spur gears with profile modification, Mech. Mach. Theory, 197, 105650, https://doi.org/10.1016/j.mechmachtheory.2024.105650, 2024.
Sainsot, P., Velex, P., and Duverger, O.: Contribution of gear body to tooth deflections – a new bidimensional analytical formula, J. Mech. Design, 126, 748–752, https://doi.org/10.1115/1.1758252, 2004.
Sharma, S. K., Kumar, N., Avesh, M., Sharma, R. C., Siddiqui, M. I. H., and Lee, J.: Navigating tranquillity with H8 controller to mitigate ship propeller shaft vibration, J. Vib. Eng. Technol., 12, 7969–7979, https://doi.org/10.1007/s42417-024-01340-0, 2024a.
Sharma, S. K., Sharma, R. C., Mohapatra, S., Fouly, A., Hossain, I., and Lee, J.: Technological advancements in oscillation reduction for propulsion shaft systems, J. Vib. Eng. Technol., 12, 1779–1797, https://doi.org/10.1007/s42417-024-01503-z, 2024b.
Sharma, S. K., Sharma, R. C., and Lee, J.: Propelling precision of longitudinal vibration mitigation in ship propeller shafts through advanced nonlinear intelligent semi-active control leveraging adaptive neuro-fuzzy inference system with linear quadratic regulator, J. Vib. Control, 31, 1472–1484, https://doi.org/10.1177/10775463241244836, 2025.
Shehata, A., Adnan, M. A., and Mohammed, O. D.: Modeling the effect of misalignment and tooth microgeometry on helical gear pair in mesh, Eng. Fail. Anal., 106, 104190, https://doi.org/10.1016/j.engfailanal.2019.104190, 2019.
Talbot, D., Sun, A., and Kahraman, A.: Impact of tooth indexing errors on dynamic factors of spur gears: experiments and model simulations, J. Mech. Design, 138, 093302, https://doi.org/10.1115/1.4034175, 2016.
Wang, F., Xu, X., Fang, Z., and Chen, L.: Study of the influence mechanism of pitch deviation on cylindrical helical gear meshing stiffness and vibration noise, Adv. Mech. Eng., 9, 168781401772058, https://doi.org/10.1177/1687814017720586, 2017.
Wang, S. and Zhu, R.: An improved mesh stiffness model for double-helical gear pair with spalling defects considering time-varying friction coefficient under mixed EHL, Eng. Fail. Anal., 121, 105174, https://doi.org/10.1016/j.engfailanal.2020.105174, 2021.
Wang, S. and Zhu, R.: An improved mesh stiffness model of helical gear pair considering axial mesh force and friction force influenced by surface roughness under EHL condition, Appl. Math. Model., 102, 453–471, https://doi.org/10.1016/j.apm.2021.10.007, 2022.
Wang, S. and Zhu, R.: Research on dynamics and failure mechanism of herringbone planetary gearbox in wind turbine under gear surface pitting, Eng. Fail. Anal., 146, 107130, https://doi.org/10.1016/j.engfailanal.2023.107130, 2023.
Xu, X., Ge, H., Wu, H., and Jia, H.: Research on nonlinear characteristics of herringbone planetary gear transmission system considering double-sided meshing impact, Nonlinear Dynam., 112, 3195–3215, https://doi.org/10.1007/s11071-023-09201-3, 2024.
Yang, H., Shi, W., Chen, Z., and Guo, N.: An improved analytical method for mesh stiffness calculation of helical gear pair considering time-varying backlash, Mech. Syst. Signal Pr., 170, 108882, https://doi.org/10.1016/j.ymssp.2022.108882, 2022a.
Yang, J., Lin, T., He, Z., and Chen, M.: Novel calculation method for dynamic excitation of modified double-helical gear transmission, Mech. Mach. Theory, 167, 104467, https://doi.org/10.1016/j.mechmachtheory.2021.104467, 2022b.
Yang, J., Zhu, R., Lee, H., Li, M., and Yin, X.: Experimental and numerical dynamic analysis of marine herringbone planetary gearbox supported by journal bearings, J. Sound Vib., 545, https://doi.org/10.1016/j.jsv.2022.117426, 2023.
Yang, L., Chen, Q., Yin, L., Wang, L., and Shao, Y.: Dynamic characteristic of spur gear system with spalling fault considering tooth pitch error, Qual. Reliab. Eng. Int., 38, 2921–2938, https://doi.org/10.1002/qre.2869, 2022c.
Yuan, B., Chang, S., Liu, G., and Wu, L.-Y.: Quasi-static and dynamic behaviors of helical gear system with manufacturing errors, Chin. J. Mech. Eng., 31, 30, https://doi.org/10.1186/s10033-018-0238-1, 2018.
Zhang, T., Lin, T., and Fu, L.: Analytical and experimental study on acoustic-vibration characteristics of double-helical planetary gear transmission systems with multi-field coupling effect, Mech. Syst. Signal Pr., 224, 112143, https://doi.org/10.1016/j.ymssp.2024.112143, 2025.