Abstract
A gear mesh dynamic model of spur gears is presented in this paper. Initially, the influence of variation in center distance due to geometric eccentricity, assembly error and bending deformation of shaft on gear mesh parameters such as pressure angle, backlash and time-varying mesh stiffness were determined. Then, the gear mesh dynamic model was formulated by replacing the constant backlash and time-varying mesh stiffness under quasi-static conditions of the previous model with continuously calculated time-varying backlash and time-varying mesh stiffness under dynamic conditions. A six-degree-of-freedom lateral-torsional coupled nonlinear dynamic model was established with the gear mesh dynamic model. A gear pair was analyzed to demonstrate and qualify the impact of shaft stiffness and operating conditions on the differences between the dynamic responses predicted by the nonlinear dynamic model established in this study and the previous nonlinear dynamic model. The results showed clear differences between the dynamic responses predicted by different models, especially for the gear rotor bearing system with high compliant shafts. A strong coupling effect between dynamic response and gear mesh parameters was found. The comparison between the gear mesh forces within a wide range of torque and speed also revealed differences, especially in the vicinity of the primary resonance speed and 1/3 of this speed. With increasing torque, the differences increased and the range of speeds corresponding to same difference also increased. The differences reached to a minimum near half of the resonance speed under different input torques.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ozgüven HN, Houser DR. Mathematical models used in gear dynamic-a review. J Sound Vib. 1988;121:383–411.
Kahraman A, Blankenship GW. Experiments on nonlinear dynamic behavior of an oscillator with clearance and periodically time-varying parameters. J Appl Mech. 1997;64:217–26.
Kang MR, Kahraman A. Measurement of vibratory motions of gears supported by compliant shafts. Mech Syst Signal Process. 2012;29:391–403.
Blankenship GW, Kahraman A. Steady state forced response of a mechanical oscillator with combined parametric excitation and clearance type non-linearity. J Sound Vib. 1995;185:743–65.
Li S, Kahraman A. A tribo-dynamic model of a spur gear pair. J Sound Vib. 2013;332:4963–78.
Ambarisha VK, Parker RG. Nonlinear dynamics of planetary gears using analytical andfinite element models. J Sound Vib. 2007;302:577–95.
Kim W, Yoo H, Chung J. Dynamic analysis for a pair of spur gears with transla-tional motion due to bearing deformation. J Sound Vib. 2010;329:4409–21.
Chen S, Tang J, Luo C, Wang Q. Nonlinear dynamic characteristics of geared rotor bearing systems with dynamic backlash and friction. Mech Mach Theory. 2011;46:466–78.
Fernandez del Rincon A, Iglesias M, de-Juan A, Garcia P, Sancibrian R, Viadero F. Gear transmission dynamic: effects of tooth profile deviationsand support flexibility. Appl Acoust. 2014;77:138–49.
Zhang H, Tian J, Zhou J, Zhao Y, Bindi Y, Dynamic and experimental investigation of gear-rotor system with multiple clearances coupled. Chin J Mech Eng. 2017;39:1–9.
Yua Wennian, Mechefskea Chris K, Timuskb Markus. Influence of the addendum modification on spur gear back-side mesh stiffness and dynamics. J Sound Vib. 2017;389:183–201.
He S, Gunda R, Singh R. Effect of sliding friction on the dynamics of spur gear pair with realistic time-varying stiffness. J Sound Vib. 2007;301:927–49.
Kim W, Yoo H, Chung J. Dynamic analysis for a pair of spur gears with translational motion due to bearing deformation. J Sound Vib. 2010;329:4409–21.
Chaari F, Fakhfakh T, Haddar M. Analytical modelling of spur gear tooth crack and influence on gearmesh stiffness. Eur J Mech A/Solids. 2009;28:461–8.
Sainsot P, Velex P, Duverger O. Contribution of gear body to tooth deflections—a new bi-dimensional analytical formula. J Mech Des. 2004;126:748–52.
Ozgüven HN, Houser DR. Dynamic analysis of high speed by using loaded static transmission error. J Sound Vib. 1988;125:71–83.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Wang, C., Liu, H., Du, M., Xiang, C. (2018). A Gear Mesh Dynamic Model for Analyzing the Nonlinear Vibrations of Spur Gears Supported by Compliant Shafts. In: Tan, J., Gao, F., Xiang, C. (eds) Advances in Mechanical Design. ICMD 2017. Mechanisms and Machine Science, vol 55. Springer, Singapore. https://doi.org/10.1007/978-981-10-6553-8_7
Download citation
DOI: https://doi.org/10.1007/978-981-10-6553-8_7
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-6552-1
Online ISBN: 978-981-10-6553-8
eBook Packages: EngineeringEngineering (R0)