DETERMINATION OF POWER LOSSES DUE TO PERIODIC COMPRESSION-EXPANSION OF THE OIL-AIR MIXTURE BETWEEN THE TEETH OF GEARS. PART 1. MATHEMATICAL MODEL

The simultaneous contact of two pairs of teeth between their active profiles creates a closed volume of the oil-air mixture. Reducing this volume leads to the occurrence of such a negative phenomenon as periodic compression and expansion of the oil-air mixture in volume. At high gear rotation speeds, a significant increase in the pressure of the oil-air mixture is observed and, as a result, additional vibration of the gearing occurs. The oil-air mixture outflow rate can reach the speed of sound, which causes additional noise during gear operation, and at high rotational speeds, a hydraulic shock occurs in the space closed between the pinion and gear teeth, resulting in cavitation. By representing the helical gear as a set of spur gears displaced relative to each other in the tangential direction, it simplified the mathematical model to describe thermodynamic processes in a series of isolated cavities. The following variants are considered: a) the first cavity in the direction of engagement is connected to the environment on one side and to the next second cavity on the other side; b) some i-th cavity is connected to the cavities i - 1 and i + 1, respectively; c) the edge cavity N is connected to the previous cavity N - 1 and the environment. Thus, a mathematical model of the periodic compression-expansion of the oil-air mixture in the space closed between the teeth is presented, which considers the cross-sectional areas of the axial and radial flows of the oil-air mixture, the ambient pressure of the space closed between the teeth, the velocity of the radial flow of the oil-air mixture, the instantaneous volume of the elementary cavity closed between the teeth, and the current pressure in the cavity. Keywords: power losses, oil-air mixture, periodic compression-expansion, toothed gears, mathematical model, hydrodynamic model