Numerical Investigation of the Influence of Rim and Web Thickness on Vibration Modes of Thin-Rimmed Cylindrical Gears

摘要

In certain domains such as aeronautics, mass restrictions often lead to thin-rimmed spur and helical gears. A thin rim modifies the load distribution and stress state, but also the wheel's rigidity and mass, and consequently its transmission error and vibrational response. Today, most of the published multi-body dynamic models are not adapted to industrial practice and they are time-consuming. Currently, a common practical method involves tuning individual component natural frequencies far from the gear mesh frequencies. Although tuning individual components is an adequate approach, to reach the optimum configuration demands a very experienced gear designer. This study establishes and discusses the effects of variations in rim and web thickness on the resonances of thin-rimmed spur gears. The paper presents a comprehensive generic dynamic analysis, useful for industrial engineers. The work concentrates on axial, tilting and rotational modes. The study is based on finite element modal analyses and a factorial design, which includes four factors, each at three levels to account for nonlinear influences: tooth number, face width, rim thickness and web thickness. Even though the module (m) is not explicitly included in the factors, its influence is established - when the natural frequencies of a thin-rimmed spur wheel are normalized to the natural frequencies of the corresponding full body gear, m has no influence. In most cases, the investigation also indicates that for a given rim thickness, increasing the web depth augments the natural frequencies.