VIBRATION OF HIGH-SPEED SPUR GEAR WEBS

High cycle fatigue loading of gear webs due to in-plane stresses, caus ed by forced excitation resulting from centrifugal loading and dynamic tooth loads, has been known to cause radial fatigue cracks. This is e specially prevalent in high-speed gears used in aerospace applications , with small web thickness, for weight reduction. Radial machined in g ear webs for weight reduction. This paper presents an analytical crack s have also, been observed to originate at the outer edge of lightenin g holes treatment of the in-plane vibration of high-speed gear webs re sulting from rotational effects and periodic excitation from dynamic t ooth loading. Dynamic tooth loads result from the combined effect of i nertia forces of gear wheels which are significant at high speeds, the periodic variation of gear mesh stiffness, and involute tooth profile errors. The gear web is modeled as a thin rotating disc and the gover ning differential equations of motion and the associated boundary cond itions are derived from first principles. The equations are then nondi mensionalized which leads to some essential nondimensional parameters. A comprehensive tooth stiffness model for spur gears is used that acc ounts for periodic variation of mesh stiffness. The dynamic tooth load s ale obtained by solving the pertinent equations of motion, using a c ollocation method, that yields a closed-form expression for the period ic excitation, that is used as an input for the in-plane vibration pro blem. The in-plane vibration equations are solved by an approximate me thod of weighted residuals. It is found that the displacement fields a nd the resulting stresses can be significant under certain speeds and loading conditions. The interaction between the forcing frequencies du e to gear teeth dynamics and the in-plane vibration natural frequencie s can result in resonances that induce high fatigue stresses in the ge ar web. The in-plane stresses leading to high cycle fatigue loading, a nd frequency components of the resulting response are discussed in det ail.