Establishment of an Analytical Model for Determining Leakage Surfaces in an External Tooth Spur Gear
In gear power transmission systems, the lubricant helps reduce friction, wear of parts in contact, cooling of surfaces, reduction of operating noise, protection of components against corrosion, etc. In spite of that, the lubricant entrapment in the gears inter-tooth space generates substantial energy losses at very high rotational speeds. The best optimization of these energy losses requires the preliminary knowledge of the behavior of leakage surfaces of trapped lubricant during the gears rotation. The aim of this work is to develop a purely analytical model enabling to calculate the exact values of the axial and radial leakage surfaces of the lubricant in the inter-tooth space of external spur gears as well as the volumes of the pockets. From the modeling of the tooth profile and the parametric equations relating to external spur gears, we have developed a purely analytical model of the lubricant leakage surfaces in the inter-tooth space as a function of the angle of rotation. Validation of the model was carried out via a comparative study between our results and those resulting from the work of Abdelilah LASRI and al and Diab Y. and al. Curves from our model and those of the reference articles merge after superposition and the relative differences are less than 10-2. This work is therefore the first step in the calculation of the power lost by the lubricant trapping in the gears inter-tooth. It will be of great importance in minimizing power losses.
