Analysis and design of a flexible tooth gear.

摘要

There has been little apparent interest in developing innovative gear teeth that possess "designed compliance"; that is, tooth flexure that is an integral part of the designed mechanical system. This, in part, may be due to the commonly held assumption 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. Additionally, a reduction of the cost of manufacturing of these gears could potentially be accomplished by modular construction of flexible gears. Such gears could simplify construction and reduce cost of maintenance in certain applications. They could also employ advanced materials for teeth without a requirement for them to be used in the main body of the gear. Allowing gear teeth to have a designed flexibility is a novel and as of yet unexplored 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. The curved beam model is based on the Castigliano's energy theory for displacement. This thesis will also examine large displacement mechanics of gears with flexible teeth by using the principle of minimum potential energy. The effects of various design parameters on gear properties such as the pressure line and the satisfaction of the law of gearing are studied.;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, in some instances it is shown how properties of flexible circular gears can be modified to improve their performance.