Analytical Model for the Heat Transfer in Impingement Cooled Spur Gears

Abstract The geared turbofan is a promising concept for civil aircraft jet engines. With the introduction of a gearbox between the low-pressure turbine and the fan, both components can rotate at their respective optimum speed. The geared turbofan enables a lower specific fuel consumption as well as jet engine noise reductions. A planetary gear train is usually chosen for the transmission with the sun gear connected to the low-pressure turbine. This high-speed reduction gear train needs to transmit high loads with a high efficiency in limited installation space. To ensure a safe operation of the gear train, the thermal behavior of the gears needs to be understood. The heat generated by the meshing processes is dissipated by oil impingement cooling. While the field of Elastohydrodynamic lubrication yields good results for the heat generation, no validated model for the impingement cooling process is available in literature. In this study, an analytical model is developed and validated against experimental data. First, the surface area of the oil film on the gear tooth flank formed by the impinging oil jet is calculated. Second, the heat transfer from the gear tooth flank to the oil film is determined. The fluid motion is modeled as an oil film that is flung off the gear tooth flank by centrifugal forces. In addition to the film flow, the presented model takes into account the temperature dependence of the viscosity of the oil and the initial oil film height. The effect of a lubrication oil film on the gear tooth flank before the oil jet impinges is included and its effect on the heat transfer is assessed. The analytical model agrees well with experimental results over the entire range of investigated operating conditions. Finally, a discussion on the effect of several assumptions in the derivation of the analytical model is presented. The validated analytical model can be used as an efficient tool for the design of gear trains with impingement cooled spur gears.