Dynamic Loads on the Teeth of Spur Gears

In a theoretical analysis of a single pair of high-class gears three internal sources of vibration are considered: (1) Periodic variations in the velocity ratio due either to running the gears above or below the designed load, or to small manufacturing errors. (2) Period variation in the tooth stiffness. (3) Non-linearity in tooth stiffness. The amplitudes of vibrations caused by (1) depend on damping, while those caused by (2) or (3) will only occur if the damping is below a limit estimated at 0.07 of critical damping. Damping currently reported for tests on steel gears is about 0.1 of critical, but might well be less. Dynamic tooth forces and amplitudes of vibration were found from photo-elastic stress patterns of model gears with both small and large errors. The more accurate gears showed only vibration caused by (1), variation in the velocity ratio, because the damping was too great for the other modes. Information on damping is insufficient for satisfactory prediction of dynamic increments. If the damping in any gears fell to 0.07 of critical the increment, instead of having a small value, might equal the applied load, irrespective of any errors, and this might prove disastrous.