Abstract
In this paper, we propose a new approach for taking into account uncertainties based on the projection on polynomial chaos method. The new approach is used to determine the dynamic response of a one-stage spur gear system modeled by eight degrees of freedom in the presence of friction coefficient between teeth that admits some dispersion. Therefore, it becomes necessary to take this uncertainty into account in the stability analysis of gear system to ensure robust predictions of stable and instable behaviors. The simulation results are obtained by the polynomial chaos approach for the dynamic analysis of a one-stage spur gear system with the uncertainty associated with friction coefficient on the teeth contact. The proposed approach is an efficient probabilistic tool for uncertainty propagation. The polynomial chaos results are compared with Monte Carlo simulations. The main results of the present study show that the polynomial chaos may be an efficient tool to take into account the dispersions of the friction coefficient of a one-stage spur gear system.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Beyaoui M, Guerine A, Walha L, El Hami A, Fakhfakh T, Haddar M (2016) Dynamic behavior of the one-stage gear system with uncertainties. Struct Eng Mech 58(3):443–458
Blanchard E, Sandu A, Sandu C (2009) Parameter estimation for mechanical systems via an explicit representation of uncertainty. Int J Comput Aided Eng Comput 26:541–569
Blanchard E, Sandu A, Sandu C (2010) Polynomial chaos-based parameter estimation methods applied to vehicle system. Proc. Inst Mech Eng Part K J Multi-Body Dyn 224:59–81
Fishman GS (1996) Monte carlo, concepts, algorithms and applications, 1st edn. Springer
Guerine A, Driss Y, Beyaoui M, Walha L, Fakhfakh T, Haddar M (2014) A polynomial chaos method for the analysis of uncertain spur gear system. In: Mechatronic systems: theory and applications, pp 89–97
Guerine A, El Hami A, Walha L, Fakhfakh T, Haddar M (2015a) A perturbation approach for the dynamic analysis of one stage gear system with uncertain parameters. Mech Mach Theory 92:113–126
Guerine A, El Hami A, Fakhfakh T, Haddar M (2015b) A polynomial chaos method to the analysis of the dynamic behavior of spur gear system. Struct Eng Mech Int J 53:819–831
Guerine A, El Hami A, Walha L, Fakhfakh T, Haddar M (2016a) A polynomial chaos method for the analysis of the dynamic behavior of uncertain gear friction system. Eur J Mech A/Solids 59:76–84
Guerine A, El Hami A, Walha L, Fakhfakh T, Haddar M (2016b) Dynamic response of a spur gear system with uncertain parameters. J Theor Appl Mech 54(3):1039–1049
Guerine A, El Hami A, Walha L, Fakhfakh T, Haddar M (2016c) Dynamic response of a Spur gear system with uncertain friction coefficient. Adv Eng Softw. https://doi.org/10.1016/j.advengsoft.2016.05.009
Guerine A, El Hami A (2016) Uncertainty analysis of one stage gear system using interval analysis method. In: 2016 4th IEEE international colloquium on information science and technology (CiSt), pp 670–674
Guerine A, El Hami A, Walha L, Fakhfakh T, Haddar M (2017) Dynamic response of wind turbine gear system with uncertain-but-bounded parameters using interval analysis method. Renew Energ 113:679–687
Lindsley NJ, Beran PS (2005) Increased efficiency in the stochastic interrogation of an uncertain nonlinear aeroelastic system. In: International forum on aeroelasticity and structural dynamics, Munich, Germany, June
Papadrakakis M, Papadopoulos V (1999) Parallel solution methods for stochastic finite element analysis using Monte Carlo simulation. Comput Methods Appl Mech Eng 168:305–320
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this paper
Cite this paper
Guerine, A., El Hami, A. (2018). A Polynomial Chaos Method for the Analysis of the Dynamic Response of a Gear Friction System. In: Haddar, M., Chaari, F., Benamara, A., Chouchane, M., Karra, C., Aifaoui, N. (eds) Design and Modeling of Mechanical Systems—III. CMSM 2017. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-66697-6_87
Download citation
DOI: https://doi.org/10.1007/978-3-319-66697-6_87
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-66696-9
Online ISBN: 978-3-319-66697-6
eBook Packages: EngineeringEngineering (R0)