Mechanics & Industry
Volume 19, Number 3, 2018
|Number of page(s)||16|
|Published online||11 October 2018|
An implicit algorithm for the dynamic study of nonlinear vibration of spur gear system with backlash
Laboratoire d’Ingénierie et Matériaux LIMAT, Faculté des Sciences Ben M’Sik, Université Hassan II de Casablanca,
* e-mail: firstname.lastname@example.org
Accepted: 17 January 2017
In this work, we propose some regularization techniques to adapt the implicit high order algorithm based on the coupling of the asymptotic numerical methods (ANM) (Cochelin et al., Méthode Asymptotique Numérique, Hermès-Lavoisier, Paris, 2007; Mottaqui et al., Comput. Methods Appl. Mech. Eng. 199 (2010) 1701–1709; Mottaqui et al., Math. Model. Nat. Phenom. 5 (2010) 16–22) and the implicit Newmark scheme for solving the non-linear problem of dynamic model of a two-stage spur gear system with backlash. The regularization technique is used to overcome the numerical difficulties of singularities existing in the considered problem as in the contact problems (Abichou et al., Comput. Methods Appl. Mech. Eng. 191 (2002) 5795–5810; Aggoune et al., J. Comput. Appl. Math. 168 (2004) 1–9). This algorithm combines a time discretization technique, a homotopy method, Taylor series expansions technique and a continuation method. The performance and effectiveness of this algorithm will be illustrated on two examples of one-stage and two-stage gears with spur teeth. The obtained results are compared with those obtained by the Newton–Raphson method coupled with the implicit Newmark scheme.
Key words: spur gear system / high order algorithm / homotopy / vibration / backlash
© AFM, EDP Sciences 2018
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