Parametric analysis of ring gear structure vibration modes

A comprehensive parametric analysis to quantify the sensitivity of planetary ring gear structural modes to variations in its geometrical parameters is performed by applying the dynamic finite element method. Specifically, the effects of the rim thickness to radius ratio, rim thickness to width ratio, helix angle, number of teeth, number of splines, and spline height and angular width are examined. The eigen-solutions reveal four classes of commonly occurring radial inextensional, extensional, out-of-plane bending and torsional ring modes. Of these four groups of modes, the radial inextensional and out-of-plane bending, frequencies are generally lower and fall more within the undesirable gear whine spectrum caused by the transmission error excitation. The predicted natural frequency sensitivities to the ring gear design parameters of interest are compiled graphically. The resulting trends are useful in identifying more robust designs with a lesser tendency towards the generation and transmissibility of excessive gear noise levels.