Effects of boundary conditions on the natural modes of transmission ring gear structure

The natural modes of the ring gear structure commonly used in automotive transmissions are predicted using the finite element approach, and the sensitivities of these modes to boundary conditions between the housing and ring gear are analyzed. The specific boundary conditions of interest include free-free, simply-supports at equally spaced angular points, and discrete and distributed spring elements. For the free-free boundary condition, clear well-defined modes are observed that can be classified into four fundamental groups corresponding to radial inextensional, extensional, out-of-plane bending and pure torsional. However, when other boundary conditions are applied the mode shapes become more complex. For instance, in the simply-supported case the radial inextensional and torsional modes are seen to appear highly distorted. Also, the natural frequencies of these modes are higher than the free-free ones. The radial inextensional modes and the out-of-plane bending modes are seen to have substantial effect on vibration transmissibility. Torsional modes occur at relatively high frequency, and have less severe effects on vibration transmissibility as compared to the radial inextensional and out-of-plane bending modes. Extensional modes are quite insensitive to boundary conditions, and they occur at comparatively much higher frequency values that are practically out of the gear whine spectrum range.