Analytical Solution to the Heat Transfer in Fling-Off Cooling of Spur Gears

In this research paper, the cooling process of an impingement cooled spur gear is examined by means of an analytical model. The process is modeled as a coolant film, which is flung off a rotating gear tooth flank by centrifugal forces. During the process, heat is transferred from the isothermal gear tooth flank to the coolant film. With a numerical solution to the analytical model, a formulation for the transient local Nusselt number is derived. The evaluation of the numerical solution revealed that the heat transfer is dominated by heat conduction in the coolant film. The heat transfer process ends when the thermal capacity of the coolant film is reached. The transient Nusselt number is used to derive a time-averaged and a global heat transfer coefficient. Furthermore, the influence of the initial coolant film height is examined by using a modified version of the analytical model. The global heat transfer coefficient decreases toward smaller initial cooling film heights. The analytical model is then extended to include the temperature dependency of the viscosity of the coolant. A viscosity that decreases with increasing temperature yields a moderate decrease in heat transfer. A discussion is presented regarding the applicability of the analytical model toward impingement cooled spur gears. The effect of the simplifications made in the derivation of the analytical model is outlined and assessed with regard to the heat transfer mechanism.