Book Description

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 description, 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 given 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 is partially verified 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 casting 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 transmissions 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 inertials attached to two flexible shafts and 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 compare well with measured data, validating the purposed formulation.