Analytical model for meshing stiffness, load sharing, and transmission error for spur gears with profile modification under non-nominal load conditions

Abstract

The loaded tooth deflections, manufacturing deviations, and assembly errors on spur gears induce a delay on the driven gear respect to the driving gear, which is called loaded transmission error. This delay causes an earlier start of contact outside the pressure line, resulting in a mesh-in impact, which is an important source of noise and vibrations. To avoid or mitigate this mesh-in impact, profile modifications on the driven tooth tip are frequently used. The additional gap due to the profile relief delays the effective start of contact, and a suitable amount of relief sets the mesh-in point back to the theoretical inner point of contact, which prevents the mesh-in impact and ensures a smooth contact. However, as the loaded transmission error depends on the transmitted load, a specific amount of relief will be suitable only for a specific input torque. For higher transmitted load mesh-in impact will occur again, while for lower transmitted load the effective contact ratio will be reduced due to an excessive delay of the start of contact. Therefore, under variable load conditions it is not possible to adjust the start of contact to the theoretical inner point of contact, so mesh-in impact, smooth contact and reduction of contact ratio may alternatively occur. In this paper, a simple analytical model for the meshing stiffness, load sharing ratio and transmission error is presented for spur gears with profile modification under non nominal -or variable- load conditions.