Modular hybrid models to simulate the static and dynamic behaviour of high-speed thin-rimmed gears

Abstract Several modular hybrid gear dynamic models are presented which account for both the local phenomena associated with the instant contact conditions between the tooth flanks and the more global aspects related to shafts, bearings and particularly the contributions of light thin-rimmed/-webbed gear bodies. The proposed models combine sub-structures, lumped parameter and beam elements to simulate components with linear behaviour such as webs, rims, shafts, etc. while local mesh elasticity is simulated by time-varying, possibly non-linear Winkler foundations. A specific interface has been developed to connect discretised tooth contact lines with continuous finite element models and avoid singularities in tooth load distributions. A number of comparisons with numerical and experimental results show that the proposed modelling is sound and can capture most of the quasi-static and dynamic behaviour of single stage reduction units with thin-webbed gears and/or pinions. Finally, the modelling strategy is applied to the analysis of high–speed industrial gears and results are presented which illustrate the interest of the proposed methodology compared with the classic gear dynamic models.

[1]  Anette Andersson,et al.  A method to determine dynamic loads on spur gear teeth and on bearings , 2003 .

[2]  David Dureisseix,et al.  A mixed domain decomposition approach , 2007 .

[3]  S. Vijayakar.  A combined surface integral and finite element solution for a three‐dimensional contact problem , 1991 .

[4]  Robert G. Parker,et al.  Three-dimensional nonlinear vibration of gear pairs , 2012 .

[5]  Michel Lalanne,et al.  Rotordynamics prediction in engineering , 1998 .

[6]  Wim Desmet,et al.  Static modes switching for more efficient flexible multibody simulation , 2011 .

[7]  P. Velex,et al.  A MATHEMATICAL MODEL FOR ANALYZING THE INFLUENCE OF SHAPE DEVIATIONS AND MOUNTING ERRORS ON GEAR DYNAMIC BEHAVIOUR , 1996 .

[8]  D. N. Herting,et al.  A general purpose, multi-stage, component modal synthesis method , 1985 .

[9]  P. Velex,et al.  Optimum profile relief in thin-rimmed spur and helical gear , 2016 .

[10]  C. Colette,et al.  Non-intrusive measurement of gear dynamic response , 2014 .

[11]  Robert G. Parker,et al.  NON-LINEAR DYNAMIC RESPONSE OF A SPUR GEAR PAIR: MODELLING AND EXPERIMENTAL COMPARISONS , 2000 .

[12]  David Dureisseix,et al.  A Mortar-Based Mesh Interface for Hybrid Finite-Element/Lumped-Parameter Gear Dynamic Models - Applications to Thin-Rimmed Geared Systems , 2016 .

[13]  Shuting Li,et al.  Deformation and Bending Stress Analysis of a Three-dimensional, Thin-rimmed Gear , 2002 .

[14]  Ahmet Kahraman,et al.  A deformable body dynamic analysis of planetary gears with thin rims , 2003 .

[15]  C. Bernardi,et al.  A New Nonconforming Approach to Domain Decomposition : The Mortar Element Method , 1994 .

[16]  Donald R. Houser,et al.  Mathematical models used in gear dynamics—A review , 1988 .

[17]  Robert G. Parker,et al.  Vibration of high-speed rotating rings coupled to space-fixed stiffnesses , 2014 .

[18]  M. Ajmi,et al.  A Static and Dynamic Model of Geared Transmissions by Combining Substructures and Elastic Foundations—Applications to Thin-Rimmed Gears , 2007 .

[19]  Rajendra Singh,et al.  Non-linear dynamics of a spur gear pair , 1990 .

[20]  P. Velex,et al.  A hybrid 3D finite element/lumped parameter model for quasi-static and dynamic analyses of planetary/epicyclic gear sets , 2006 .

[21]  M. Kubur,et al.  Dynamic Analysis of a Multi-Shaft Helical Gear Transmission by Finite Elements: Model and Experiment , 2004 .

[22]  Wim Desmet,et al.  A nonlinear parametric model reduction method for efficient gear contact simulations , 2015 .

[23]  Shuting Li,et al.  Effects of misalignment error, tooth modifications and transmitted torque on tooth engagements of a pair of spur gears , 2015 .

[24]  M. Géradin,et al.  A new approach to finite element modelling of flexible rotors , 1984 .

[25]  P. Velex,et al.  Static and Dynamic Tooth Loading in Spur and Helical Geared Systems-Experiments and Model Validation , 2002 .

[26]  Y. Maday,et al.  Two different approaches for matching nonconforming grids: The Mortar Element method and the Feti Method , 1997 .

[27]  P. Velex,et al.  A model for simulating the quasi-static and dynamic behaviour of solid wide-faced spur and helical gears , 2005 .

[28]  Philippe Velex,et al.  Contribution of Gear Body to Tooth Deflections—A New Bidimensional Analytical Formula , 2004 .

[29]  Shuting Li,et al.  Effects of centrifugal load on tooth contact stresses and bending stresses of thin-rimmed spur gears with inclined webs , 2013 .