Established formulas for trapped-oil area and relief-load area of external spur-gear pump

In order to study quantitatively the trapped-oil phenomenon, with distance between meshing point and nodal point as a variable, a formula for calculating trapped-oil area and a fit formula for calculating relief-load area were derived from the geometrical relationship of gear transmission and positional relationship of relief groove. The calculated results were compared with the measured results from an accurate 3-D model. The results indicated that trapped-oil area and relief-load area could be expressed by a parabola with different index; simplified transition curve is feasible for calculating the two areas; fitting constant derived could be directly used aimed at different tooth number and module for calculating relief-load area. Finally, the two area-formulas were proved feasible to be used for forecasting the trapped oil pressure.