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# Elastohydrodynamic lubrication and surface fatigue modelling of spur gears over the meshing cycle

 Khaustov, Sergey 2016. Elastohydrodynamic lubrication and surface fatigue modelling of spur gears over the meshing cycle. PhD Thesis, Cardiff University. Item availability restricted.

## Abstract

This thesis presents a modern method to evaluate spur gears based on the transient elastohydrodynamic lubrication (EHL) emulation of the full meshing cycle, evaluating elastic stresses in the gear flanks, collecting the stress history and applying stress and strain-life methods to calculate fatigue parameters and cumulative fatigue damage, i.e. predicting the fatigue life taking measured surface roughness into account. The EHL model is formulated as the coupled system of the hydrodynamic Reynolds equation and the elastic deflection equation. These are solved simultaneously including the transient effect by incorporating the squeeze film term of the Reynolds equation with a Crank-Nicolson discretization of time. The finite difference discretisation of the elastic deflection equation utilises the differential form first formulated at Cardiff to allow coupling of the equations. The Reynolds equation can be discretised either by a finite difference or by a finite element method. The coupled system is solved simultaneously either by a narrow bandwidth Gaussian elimination or a Gauss-Seidel iterative method. The elastic stresses due to the superimposed discrete values of the EHL pressure and shear stress at the EHL mesh nodes are evaluated by carrying out the necessary convolution of the stresses by a Fast Fourier Transform method. The weighting functions required have been calculated analytically. The stresses are obtained on the EHL solution mesh and are interpolated to meshes fixed in the pinion and the gear flanks. They are then sorted and stored efficiently to enable fatigue life prediction algorithms to be applied. A detailed description of the EHL and the stress evaluation models are provided as well as a brief description of some fatigue life theories and calculations. The results of the complete analysis are provided for test gears obtained from the NASA Glenn laboratory fatigue tests and the Newcastle University Design Unit micro-pitting investigation. The analyses were carried out for real operating conditions from gear testing under extreme conditions. The surface roughness profiles used were real measured profiles taken from the test gears after initial running-in. The simulations reported are therefore as realistic as can be achieved and represent the true mixed lubrication conditions occurring in heavily loaded gears. The research also shows the importance of precise alignment of the roughness profiles in these conditions.

Item Type: Thesis (PhD) Publication Unpublished Engineering T Technology > TJ Mechanical engineering and machinery Elastohydrodynamic lubrication; spur gears; fatigue life; contact stress analysis. 3 November 2016 20 Jul 2017 05:01 https://orca.cardiff.ac.uk/id/eprint/95787

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