Date of Award


Document Type

Dissertation - Restricted

Degree Name

Doctor of Philosophy (PhD)


Mechanical Engineering

First Advisor

Stango, Robert J.

Second Advisor

Nigro, Nicholas J.

Third Advisor

Heinrich, Stephen


This paper explores ways in which gear teeth that possess "designed compliance"; that is, tooth flexure that is an integral part of the designed mechanical system, affect transmission of angular motion and torque. It is commonly assumed that deformation of engineered components is counterproductive to the function and performance of machinery and, hence, must be minimized. However, none of the current gear designs alone can address problems such as absorption of shock loads, vibration ("chatter") attenuation, and reduction of the overall mass and inertia. Allowing gear teeth to have a designed flexibility is another way of approaching the above problems in gear system design.

In this study, the deformation of flexible gear teeth is treated as a classical curved beam deformation problem. A quasi-static, mechanics based model is used for computing displacements of slender tooth profiles subjected to contact forces that arise during the tooth engagement process. The teeth are analyzed as slender cantilever circular beams with a constant curvature and the curved beam model is based on the Castigliano's energy theory for displacement. Non-dimensional parameters are created to study the effects of various design parameters on gear properties such as the pressure line and the satisfaction of the law of gearing.

It is observed from conducted studies that the engagement process involving teeth with circular profiles has properties which differ from those of rigid gears with involute profile teeth. The pressure line for gears with circular teeth is not linear and the law of gearing is not satisfied with this profile. These differences increase further when compliance is introduced into gear teeth. However, effects of tooth compliance on the engagement process are expected to equally apply to gears whose teeth have other profiles as well.



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