A Hydrodynamic Analysis of Fluid Flow Between Meshing Spur Gear Teeth

A hydrodynamic analysis of the pumping action resulting from the meshing of spur gear teeth was performed. Both compressible (for air) and incompressible (for oil) flow cases were considered. The computed results included the velocity of the fluid at the minimum flow area between the meshing teeth. The pressure and temperature in the mesh region were also computed for the compressible flow case. The velocities were computed as a function of the mesh angle with the pitch line velocity as the normalizing parameter. The calculations required a detailed analysis of the involute geometry to compute the proper mesh region volumes and exit flow areas. For the incompressible calculations with wide face gears, it was found the peak fluid velocity could greatly exceed the pitch line velocity. For the compressible calculations, it was found that sonic conditions could be reached at the minimum flow area leading to the possibility of shock formation downstream of this region. Parametric results for both sets of calculations, including backlash, diametral pitch, and other factors, are presented.