Vibration transmission through rolling element bearings in geared rotor systems

A new mathematical model is proposed to examine the vibration transmission through rolling element bearings in geared rotor systems. Current bearing models, based on either ideal boundary conditions for the shaft or purely translational stiffness element descriptions, cannot explain how the vibratory motion may be transmitted from the rotating shaft to the casing. For example, a vibration model based upon the simple bearing formulations can only predict purely in-plane type motion on the flexible casing plate give only bending motion on the shaft. However, experimental results have shown that the casing plate motion is primarily flexural. This study clarifies this issue qualitatively and quantitatively by developing a comprehensive bearing stiffness matrix of dimension 6 model for the precision rolling element bearings from basic principles. The proposed bearing stiffness matrix is verified partially using available analytical and experimental data, and is completely characterized.; This study extends the proposed bearing formulation to analyze the overall geared rotor system dynamics including casing and mounts. The bearing stiffness matrix is included in discrete system models using lumped parameter and/or dynamic finite element techniques. Eigensolution and forced harmonic response due to rotating mass unbalance or kinematic transmission error excitation for the following examples are computed: (I) single-stage rotor system with flexible shaft supported by two bearings on rigid casing and flexible mounts, (II) spur gear pair system with motor and load inertias attached to two flexible shafts supported by four bearings on flexibly mounted rigid casing, and (III) case II with flexible casing and rigid mounts. In several of these examples, analytical predictions match with measured data which validate the proposed formulation. Numerical predictions show that the proposed theory is capable of predicting bearing moment transmissibility in addition to force transmissibility.; A statistical energy analysis model combined with the bearing stiffness matrix is developed to predict the high frequency asymptotic dynamic behavior. The mean-square spatially averaged vibroacoustic responses are calculated for several example cases. A physical gearbox is also analyzed to demonstrate the salient features of the proposed technique. Good agreement is found between theory and experiment.