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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.

Motivated by accurate representations in gear dynamics models, this work analyzes the force-deflection relationship between spur gear pairs when the gear teeth have tooth root cracks. A finite element/contact mechanics approach is used to accurately capture the elastic deformations of the gear mesh incorporating kinematic gear motion; elastic deflections of the teeth, root, and blank; and elastic contact between the mating gear teeth. Tooth root crack damage of fixed sizes are analyzed, and the resulting static transmission error and mesh stiffness are calculated. These FE/CM model outputs are relatively insensitive to important gear crack geometry, including the initial crack location, the path it follows, and its final location. Crack-induced changes in static transmission error and mesh stiffness are driven by the remaining amount of the tooth that is healthy. Calculations of average-slope and local-slope mesh stiffness are included because both are used in gear dynamic models.