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A finite element/contact mechanics formulation is used to analyze the dynamic tooth forces that arise from damage-induced vibrations in spur gear pairs. Tooth root crack damage of varying sizes are analyzed for a wide range of speeds that include resonant gear speeds. The added localized compliance from tooth root crack damage leads to a re-distribution of the forces on the individual gear teeth in mesh. At speeds away from resonance, smaller dynamic forces occur on the damaged tooth and larger dynamic forces occur on the tooth that engages immediately after it. These dynamic tooth contact forces cause additional transient dynamic response in the gear pair. For certain speeds and sufficiently large tooth root cracks, the damage-induced dynamic response causes large enough vibration that tooth contact loss nonlinearity occurs. For some speeds near resonance, the damage-induced vibrations cause teeth that normally lose contact to remain in contact due to vibration.

This work analyzes a cantilevered piezoelectric beam device for harvesting energy from the simultaneous rotation and translational vibration of vehicle wheels. The device attaches to the wheel rim so that it displaces tangentially during operation. A lumped-parameter analytical model for the coupled electromechanical system is derived. The device has one natural frequency that is speed-dependent because of centripetal acceleration affecting the total stiffness of the device. Even though the device has one natural frequency, it experiences three resonances as the rotation speed varies. One resonance occurs when the rotation speed coincides with the speed-dependent natural frequency of the device. The other two resonances are associated with excitations from the vibration of the vehicle wheel. The device’s parameters are chosen so that these three resonances occur when the wheel travels near 30 mph, 55 mph, and 70 mph.