This paper extends the proposed bearing matrix formulation of Parts I and II to analyze the overall dynamics of a geared rotor system which includes a spur gear pair, shafts, rolling element bearing, a prime mover and a load (attached to the geared rotor system through flexible torsional couplings), a rigid or flexible casing, and compliant or massive mounts. Linear time-invariant, discrete dynamic models of a generic geared rotor system with proportional viscous damping are developed, by using lumped parameter and dynamic finite element techniques, which are then used to predict the vibration transmissibility through bearings and mounts, casing vibration motion, and dynamic response of the internal rotating system. Each rotating shaft is modeled as an Euler beam in the lumped parameter model and as a Timoshenko beam in the dynamic finite element model, but the gyroscopic moment is not included. Eigensolution and forced harmonic response studies due to rotating mass unbalance or kinematic transmission error excitation for the following example cases are obtained by using the formulation, and the results are compared with those of simple models currently available in the literature and/or experiment: case I, a single-stage rotor system with flexibly mounted rigid casing consisting of two bearings as a special case of the geared rotor system; case II, a spur gear pair drive supported by four bearings installed in a flexibly mounted rigid casing; and case III, an experimental set-up consisting of a high-precision gear and pinion, and four identical rolling element bearings contained in a flexible casing mounted rigidly on a massive foundation. Analytical predictions show that the theory is indeed capable of predicting bearing and mount moment transmissibilities in addition to the force transmissibilities. Also, flexural vibrations of the casing plate are predicted well as the theory is in good agreement with measurements made on case III; such predictions are not provided by simple models due to inadequate bearing formulation.
All Science Journal Classification (ASJC) codes
- Condensed Matter Physics
- Mechanics of Materials
- Acoustics and Ultrasonics
- Mechanical Engineering