A transient elastohydrodynamic lubrication solution for spur gear meshing cycles

This paper presents a full elastohydrodynamic lubrication (EHL) model for the solution of involute spur gear meshing cycles using a line contact transient approach. The resulting mathematical model utilises a simultaneous solution of the Reynolds equation and the elastic film equation, both of which are highly nonlinear due to their dual dependencies on pressure and film thickness. The contact between the teeth of the spur gears was represented by a set of time varying contact parameters. These included the radius of relative curvature, the relevant surface velocities, and the load variation over the meshing cycle. The model was solved numerically based on the central finite difference method under relaxation, and different operating conditions were examined to determine their effects on both pressure distribution and film thickness, though a difference of less than 5% was observed. The results were verified against available literature, and very good agreement was obtained, suggesting that this comprehensive transient solution represents a significant model for the assessment of the behaviour of the contact problem in heavily loaded spur gears. The results also showed that the time varying parameters have a significant influence on the pressure distribution and film thickness, particularly at the change points of the load.