Coupled Vibration of Geared Systems

Abstract

In the design of geared rotating systems in engineering practice a variety of configurations are used, and their torsional vibration has been extensively studied. Detailed analyses of the modes and frequencies of vibration of these systems have been given by Ker Wilson and Nestorides. When the rotating system is rigidly supported, standard methods may be used to obtain the characteristics of free vibration and the response to impressed forces, from which the transmissibility of the gear-box may be calculated. However, there are many applications in which the gearbox is flexibly mounted. The simple example of a geared engine with a flexibly mounted crankcase has been considered by Den Hartog and Butterfield. In some epicyclic gear-box assemblies, elastic elements are introduced between the reactive element and the gear-case to increase the capacity for absorbing impulsive loads and as a means of varying the natural frequencies of vibration'. Harmonic forces acting on the rotors excite coupled vibration of the rotating system and the supporting frame, and Ker Wilson has shown how the natural frequencies and modes of the combined system may be determined by Holzer-type tabular methods. This involves a trial-and-error technique which may sometimes be tedious. Vibration of geared systems may also be excited by the motion of the frame supporting the gear-box, and an analysis of the response is necessary in the determination of dynamic loads.