Mechanism and Machine Theory 122 (2018) 371–388 Contents lists available at ScienceDirect Mechanism and Machine Theory journal homepage: www.elsevier.com/locate/mechmachtheory Research paper Damping models identification of a spur gear pair Nourhaine Yousfi a,b , Bacem Zghal a , Ali Akrout a,b , Lassaad Walha a,∗ , Mohamed Haddar a a Mechanics, Modelling and Production research Laboratory (LA2MP), Engineering National School of Sfax, University of Sfax, Tunisia b Engineering National School of Tunis, University of Tunis El-Manar, Tunisia a r t i c l e i n f o Article history: Received 25 May 2017 Revised 19 November 2017 Accepted 2 January 2018 Keywords: Wavelet demodulation Model estimation Spur gear Damping a b s t r a c t In this research paper, estimation damping in spur gear pair system using Integral method and the continuous wavelet transform based approach (CWT) is proposed. In the first method, the motion equations of the model describing the system are reformulated in terms of integrals that give a set of linear equations solved by linear least squares method to allow a new methodology that starts with a constant piecewise model to bootstrap the most suitable model of damping. The constant model is validated using the wavelet demodulation approach that’s based on the envelope extraction procedure to obtain the damping ratio associated with structural modes. In order to show the ability to predict the response, damping estimation procedures are tested on a signal obtained from numerical simulation of the spur gear pair system. © 2018 Elsevier Ltd. All rights reserved. 1. Introduction Dynamic modeling of the gear pair system has been an active research field in engineering. A numerous dynamic mod- els have been proposed as it’s presented by Ozguven and Houser [1], Blankenship and Kahraman [2], Theodossiades and Natsiavas [3] and more recently by Wang et al. [4]. These models typically employed two rigid disks that are connected with each other through a gear mesh interface model along the line of action characterized by time-varying stiffness and mesh damping to account for the energy loss at the gear mesh interface. The dynamic behavior of the gear system is largely affected by damping. Gregory et al. [5] highlighted the importance of damping on dynamic loading and the need for fur- ther research into the mechanism of damping in mechanical transmissions. Almost all of the previous gear dynamic models employed a user-defined constant viscous damping coefficient, stating that it must be determined empirically. Therefore, the estimation of damping from an observed response data of the gear system appears to be an important task of dynamic analysis. Because of the dependence of damping on complex mechanisms in the structure, the damping is the most difficult quantity to evaluate in comparison to the identification of another parameter. Several damping models exist in the literature. Liu et al. [6] recently proposed an analytical method to characterize damping and stiffness in lightly loaded, lubricated gear pairs at different operating speeds and lubricant temperatures. A common practice is to consider the damping as a Rayleigh damping [7] obtained by combining the mass matrix and stiffness matrix. The limitations of the current viscous damping model are discussed [8] and an advanced formulation for viscous damping, which depends on frequency using the Rayleigh damping, is developed. ∗ Corresponding author. E-mail addresses: nouhaine.yousfi@enit.utm.tn (N. Yousfi), bacem.zghal@isgis.rnu.tn (B. Zghal), ali.akrout@enit.rnu.tn (A. Akrout), lassaad.walha@enis.tn (L. Walha), mohamed.haddar@enis.rnu.tn (M. Haddar). https://doi.org/10.1016/j.mechmachtheory.2018.01.002 0094-114X/© 2018 Elsevier Ltd. All rights reserved.