Vibration transmission through rolling element bearings, part IV: statistical energy analysis

A theoretical coupling loss factor for the vibration transmission through a rolling element bearing problem has been developed for the statistical energy analysis (SEA) technique. This scheme includes the bearing stiffness matrix developed earlier in the companion paper Part I. The same problem has been analyzed previously by using deterministic vibration models in Parts II and III. In this paper, a new analytical procedure is developed to obtain the coupling loss factor between the shaft and casing which is based on the solution of the boundary value problem at the plate-bearing interface. Several example cases are chosen to demonstrate the salient features of this method: I, a plate-cantilevered beam problem; II, case I with circular shaft-bearing replacing the cantilevered beam; III, a shaft-bearing-plate system. Example case I is a revised version of the problem analyzed earlier by Lyon and Eichler (reference [6] of this paper). Our proposed calculation indicates an improvement in the coupling loss factor prediction for a thin plate-cantilevered beam system. Example case II deals with the development of a theoretical scheme to compute coupling loss factor for a bearing system. This development is extended further to predict mean-square vibratory response of a rectangular plate for example case III. Results of the statistical energy analysis compare well with the predictions yielded by deterministic model of Part II. Predictions for example cases I and III are found to be in good agreement with measurements.