Time-varying Meshing Stiffness Calculation of Spur Gears with Asymmetric Spalling Defects

Wenqiang Han; Hanjun Jiang

doi:10.62051/ijmee.v3n3.03

Authors

Wenqiang Han
Hanjun Jiang

DOI:

https://doi.org/10.62051/ijmee.v3n3.03

Keywords:

Tooth Spalling, Asymmetric Rectangular Spalling, Torsional Stiffness

Abstract

Gear systems are subjected to repeated loads during long-term operation, and factors such as insufficient lubricant to increase friction between gears, resulting in elevated temperatures and wear, are highly susceptible to tooth spalling. Tooth spalling is a common form of failure in gear failure. In previous studies, the vibration response of a gear pair with spalling defects at the tooth center near the pitch circle has been investigated. However, the location of the spalling defects offset from the center of the tooth flank is rarely studied. Tooth spalling faults occur in the pitch circle, but not necessarily in the center of the tooth, often formed on both sides of the center of the tooth and torsion in the meshing process. the symmetric and asymmetric rectangular spalling defects are considered, the torsional deformation is introduced. “torsional stiffness” is introduced into the overall TVMS due to the spalling defect. Therefore, it is meaningful to grasp the reasons for the formation of tooth spalling.

References

[1] A. Haris, E. Motato, S. Theodossiades, et al., A study on torsional vibration attenuation in automotive drivetrains using absorbers with smooth and non-smooth nonlinearities, Appl. Math. Model, 46 ,674–690, 2017.

[2] B. Mashadi, M. Badrykoohi, Driveline oscillation control by using a dry clutch system, Appl. Math. Model,39 (21) 6471–6490, 2015.

[3] Li, S., Kahraman, A.: Influence of dynamic behaviour on elastohydrodynamic lubrication of spur gears. Inst. Mech.Eng. 225(8), 740–753 ,2011.

[4] Pizzolante, F., Battarra, M., D’Elia, G., et al.: A rattle index formulation for single and multiple branch geartrains.Mech. Mach. Theory 158, 104246 ,2021.

[5] Meng, Z., Shi, G., Wang, F.: Vibration response and fault characteristics analysis of gear based on time-varying mesh stiffness. Mech. Mach. Theory 148, 103786 ,2020.

[6] Liu, F., Jiang, H., Liu, S., et al.: Dynamic behavior analysis of spur gears with constant & variable excitations considering sliding friction influence. J. Mech. Sci. Technol.30(12), 5363–5370 ,2016.

[7] L. Wang, Y. Shao, Fault mode analysis and detection for gear tooth crack during its propagating process based on dynamic simulation method, Eng. Fail. Anal. 71,166–178, 2017.

[8] F. Chaari, T. Fakhfakh, M. Haddar, Analytical modelling of spur gear tooth crack and influence on gearmesh stiffness, Europ. J. Mech. - A/Solids 28 , 461–468,2009.

[9] D.C.H. Yang, J.Y. Lin, Hertzian damping, tooth friction and bending elasticity in gear impact dynamics, J. Mech. Transm. Autom. Des. 109 ,189–196,1987.

[10] X.H. Tian, Dynamic Simulation for System Response of Gearbox Including Localized Gear FaultsM.S. thesis University of Alberta, Edmonton, 2004.

[11] S. Wu, Gearbox Dynamic Simulation and Estimation of Fault GrowthM.S. thesis University of Alberta, Edmonton, 2007.

[12] S. Jia, I. Howard, Comparison of localised spalling and crack damage from dynamic modelling of spur gear vibrations, Mech. Syst. Signal Process. 20 , 332–349,2006.

[13] Yang L, Wang L, Shao Y et al A double-layer iterative analytical model for mesh stiffness and load distribution of early-stage cracked gear based on the slicing method[J]. Mech Syst Signal Process 198:110456,2023.

[14] Z. Meng, G. Shi, F. Wang, Vibration response and fault characteristics analysis of gear based on time-varying mesh stiffness, Mech. Mach. Theory 148 103786,2020.

[15] L. Yang, Y. Shao, W. Jiang, L. Zhang, L. Wang, J. Xu, Effects of tooth surface crack propagation on meshing stiffness and vibration characteristic of spur gear system, Appl. Sci. 11 (4) 1968,2021.

[16] F. Chaari, W. Baccar, M.S. Abbes, M. Haddar, Effect of spalling or tooth breakage on gearmesh stiffness and dynamic response of a one-stage spur gear transmission, Eur. J. Mech-A/Solid,27 691–705, 2008.

[17] Y.M. Shao, X.L. Wang, J. Liu, Z.G. Chen, Time-varying stiffness model and dynamic response characteristics of gears with tooth surface spalling and edge contact, J. Vib. Shock.,33 8–14, 2014.

[18] R. Ma, Y.S. Chen, Q.J. Cao, Research on dynamics and fault mechanism of spur gear pair with spalling defect, J. Sound Vib, 331 2097–2109,2012.

[19] R. Ma, Y.S. Chen, Research on the dynamic mechanism of the gear system with local crack and spalling failure, Eng. Fail. Anal.,26,12–20,2012.

[20] H.J. Jiang, Y.M. Shao, C.K. Mechefske, Dynamic characteristics of helical gears under sliding friction with spalling defect, Eng. Fail. Anal.,39 92–107,2014.

[21] A. Saxena, A. Parey, M. Chouksey, Time varying mesh stiffness calculation of spur gear pair considering sliding friction and spalling defects, Engineering Failure Analysis 70200–211,2016.

[22] Saxena A, Parey A and Chouksey M. Effect of shaft misalignment and friction force on time varying mesh stiffness of spur gear pair. Eng Fail Anal,49: 79–91,2015.

[23] L. Han, H. Qi, Influences of tooth spalling or local breakage on time–varying mesh stiffness of helical gears, Eng. Fail. Anal, 79 ,75–88,2017.

[24] Wang F, Dai P, Yan S, et al. Investigation on double shock in vibration response of the gear pair with spalling defects[J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 237(20): 4882-4894,2023.

[25] Xue, S., Howard, I., Wang, C., et al.: Dynamic modelling of the gear system under non-stationary conditions using the iterative convergence of the tooth mesh stiffness. Eng. Fail. Anal,131, 105908,2022.

[26] Guan, X., Tang, J., Hu, Z., et al.: A new dynamic model of light-weight spur gear transmission system considering the elasticity of the shaft and gear body. Mech. Mach. Theory 170, 104689, 2022.

[27] Ma R, Chen Y. Bifurcation of multi-freedom gear system with spalling defect[J]. Applied Mathematics and Mechanics, 34: 475-488,2013.

[28] Luo Y, Baddour N, Liang M. A shape-independent approach to modelling gear tooth spalls for time varying mesh stiffness evaluation of a spur gear pair[J]. Mechanical Systems and Signal Processing ,120: 836-852,2019.