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Nonlinear time heteronymous damping in nonlinear parametric planetary systems

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Abstract

The analysis of dynamics of time heteronymous weakly and strongly nonlinear planetary transmission systems with kinematic couplings–gears constitutes a study of complicated function of many parameters including the material of gears, damping properties and damping viscous properties of lubricating oil film in the gear mesh. The purpose of this theoretical preexperimental study is to educe the methodology that makes possible to analyse the influence of all parameter variants in the area of linear and nonlinear systems with constant and time variable damping on internal dynamics. More precise dynamic analysis of such systems leads to mathematical–physical models, whose motions are described by ordinary deterministic nonlinear time heteronymous differential equations at the application of mass discretization. Their solution leads to the method of transformation of the nonlinear boundary problem of differential equations into the equivalent problem of solving integro-differential systems of equations by the method of decomposition of solving kernels of Green’s type and by the method of successive approximations. The structures with lightening holes in cog wheel discs are characterized by time variable damping in gear meshes. In this paper, the examples of resonance bifurcation characteristics in the gear mesh give a comparison between two variants with lightening wheel discs and the variant with full wheel disc, i.e. two variants with time variable quadratic damping and the variant with the constant one.

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  1. Institute of Thermomechanics AS CR, Dolejškova 5, 182 00, Prague 8, Czech Republic

    Milan Hortel & Alena Škuderová

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  1. Milan Hortel
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  2. Alena Škuderová
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Correspondence to Milan Hortel.

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Hortel, M., Škuderová, A. Nonlinear time heteronymous damping in nonlinear parametric planetary systems. Acta Mech 225, 2059–2073 (2014). https://doi.org/10.1007/s00707-013-1041-9

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  • DOI: https://doi.org/10.1007/s00707-013-1041-9

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