scholarly journals An implicit algorithm for the dynamic study of nonlinear vibration of spur gear system with backlash

2018 ◽  
Vol 19 (3) ◽  
pp. 310 ◽  
Author(s):  
Youssef Hilali ◽  
Bouazza Braikat ◽  
Hassane Lahmam ◽  
Noureddine Damil
Keyword(s):  
Continuation Method ◽  
Time Discretization ◽  
Contact Problems ◽  
Spur Gear ◽  
Gear System ◽  
Two Stage ◽  
Math Model ◽  
Newmark Scheme ◽  
Regularization Techniques ◽  
Taylor Series Expansions

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.

scholarly journals Transmission Error Analysis and Disturbance Optimization of Two-Stage Spur Gear Space Driven Mechanism with Large Inertia Load

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Jianfeng Ma ◽  
Chao Li ◽  
Lingli Cui
Keyword(s):  
Dynamic Model ◽  
Model Space ◽  
Transmission Error ◽  
Spur Gear ◽  
Gear System ◽  
Variable Load ◽  
Driving Mechanism ◽  
Nonlinear Dynamic Model ◽  
Profile Error ◽  
Two Stage

For the nonlinear disturbance actual issues of the model space drive mechanism two-stage spur gear system, a nonlinear dynamic model of 14-DOF (degree of freedom) two-stage spur gear with time-varying stiffness and damping was established. This model has been developed previously by the authors to access the large inertia on the dynamic response of spur gear space driving mechanism, and its effectiveness was proved by a motion simulation experiment. In this paper, the profile error (PE) and the index error (IE) were enhanced in the dynamic model. The effects of profile error, index error, and variable load torque on transmission error (TE) were analyzed, while the optimization was proposed according to the analyzed result. The peak-to-peak value of the optimized load transmission error (LTE) was reduced by 60.7%, which improved the transmission accuracy and reduced the phenomenon of disturbance. The research of nonlinear dynamical model of two-stage spur gear and the TE of the large inertia load were enriched, which provided an important reference for the actual design of the gear system.

Backlash Effect on Dynamic Analysis of a Two-Stage Spur Gear System

2006 ◽  
Vol 6 (3) ◽  
pp. 60-68
Author(s):  
L. Walha ◽  
T. Fakhfakh ◽  
M. Haddar
Keyword(s):  
Dynamic Analysis ◽  
Spur Gear ◽  
Gear System ◽  
Two Stage

Backlash effect on dynamic analysis of a two-stage spur gear system

2006 ◽  
Vol 6 (3) ◽  
pp. 60-68 ◽  
Author(s):  
L. Walha ◽  
T. Fakhfakh ◽  
M. Haddar
Keyword(s):  
Dynamic Analysis ◽  
Spur Gear ◽  
Gear System ◽  
Two Stage

scholarly journals Procedure for Optimum Design of a Two-Stage Spur Gear System

2003 ◽  
Vol 46 (4) ◽  
pp. 1582-1590 ◽  
Author(s):  
Bader Ahmed ABUID ◽  
Yahya Muhammed AMEEN
Keyword(s):  
Optimum Design ◽  
Spur Gear ◽  
Gear System ◽  
Two Stage

Dynamic analysis of nonlinear time-varying spur gear system subjected to multi-frequency excitation

2018 ◽  
Vol 25 (6) ◽  
pp. 1210-1226 ◽  
Author(s):  
Yi Yang ◽  
Mengjuan Xu ◽  
Yang Du ◽  
Pan Zhao ◽  
Yiping Dai
Keyword(s):  
Spur Gear ◽  
Numerical Results ◽  
Gear System ◽  
Working Environment ◽  
Single Frequency ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Time Varying ◽  
Harmonic Excitations ◽  
Frequency Excitation

Due to the complex working environment, gear systems always suffer from multiple excitations in actual engineering. This paper concerns the frequency response characteristics of a nonlinear time-varying spur gear system subjected to multi-frequency excitation. Firstly, a single degree-of-freedom gear pair model is established with consideration of the gear backlash, time-varying mesh stiffness and multiple harmonic excitations. Then, using the multiple time scales method, a comprehensive theoretical study is conducted to analyze various resonant cases including primary, parametric and combination resonances. Besides, parametric studies are accomplished to reveal the effects of the multi-frequency excitation on gear dynamics and to provide some useful references for reducing the vibration level. With the help of the fifth-order Runge–Kutta method, the numerical results are obtained to verify the validity of the analytical solutions and to emphasize the significances of the multi-frequency excitation. In addition, a comparison is performed between the numerical results and the published experimental results to validate the proposed gear model. Results show that the presence of the multi-frequency excitation will introduce the interaction between different harmonic excitations, which significantly affects the nonlinear vibration characteristics of a spur gear system. The proposed gear model with multi-frequency excitation could be more reliable and universal than that with single-frequency excitation. In addition, the results of parametric study could provide some suggestions to designers and researchers attempting to obtain desirable dynamic behaviors of a gear system subjected to multi-frequency excitation.

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