Date of Award

8-2018

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mechanical Engineering

Committee Chair

Farshid Sadeghi

Committee Member 1

Arun Prakash

Committee Member 2

Carl Wassgren

Committee Member 3

Jeffrey F. Rhoads

Abstract

The objective of this investigation was to develop a 3D dynamic model to study the rotorbearing- housing system. To achieve the objective, an existing dynamic bearing model (DBM) was combined with a flexible bearing housing model and a flexible rotor model. The DBM is based on the discrete element method (DEM), in which all bearing components are assumed to be rigid and have six degrees of freedom. The 3D explicit finite element method (EFEM) was used to develop the flexible housing and rotor models. To couple the bearing outer race (OR) with housing, a novel algorithm was developed to detect contact conditions between the housing support and OR and then calculate contact forces based on the penalty method. A study of housing support geometry demonstrates that bearing support plays a large role on the dynamic performance of the bearing. Motion of bearing outer race is closely related to the geometry and deformation of the housing.

The effect of elastomeric bushing support on bearing dynamics was also studied and then compared to the bearing housings made with linear-elastic material. The EFEM was used to model a cylindrical elastomeric bushing, which was then coupled with DBM. Constitutive relationship for the elastomeric material is based on the Arruda-Boyce model combined which uses a generalized Maxwell-element model to capture both hyperelastic and viscoelastic behaviors of the material. Comparison between the two types of housings illustrated that elastomeric materials as expected have large damping to reduce vibration and absorb energy which leads to a reduction in ball-race contact forces and friction. It was also shown that a desired bushing support performance can be achieved by varying bushing geometry. Simulations using the combined EFEM bushing and DBM model demonstrated that the elastomeric bushing provides better compliance to bearing misalignment as compared to a commonly used rigid support model. Modeling with a bearing surface dent showed that vibrations due to surface abnormalities can be significantly reduced using elastomeric bushing support. It has also been shown that choosing a proper bushing is an efficient way to tuning bushing vibration frequencies.

The model was further developed to study the effects of rotor and support flexibilities on the performance of rotor-bearing-housing system. The system is composed of a flexible rotor and two supporting deep-groove ball bearings mounted in flexible bearing housings. In order to combine the dynamic bearing model with finite element rotor and support system, new contact algorithms were developed for the interactions between the various components in the system. The Total Lagrangian formulation approach was applied to decrease the computational effort needed for modeling the rotor-bearing-housing system. The combined model was then used to investigate the effects of bearing clearances and housing clearances. It was found that as the rotor is deformed due to external loading, the clearances have a significant impact on the bearing varying compliance motion and reaction moments. Results also show that the deformation of the flexible housing depends on the total force and moment generated within the bearing due to rotor deformation. The first critical speed of rotor was simulated to investigate the unbalance response of the rotor-bearing system. It was demonstrated that rotor critical speed has a significant effect on inner race displacement and reaction moment generated at bearing location.

The dynamic behavior of the cage in a ball bearing was studied using experimental and analytical investigations. For the experimental investigation, a wireless sensor telemeter system was designed and developed to monitor the cage motions. The sensor, which was integrated on the bearing cage, is comprised of a commercially-available capacitor-inductor (LC) circuit. The LC circuit on the rotating cage was coupled to a transceiver which was stationary and positioned in close proximity to the cage. In order to achieve the objective of the analytical investigation, the explicit finite element method (EFEM) was used to simulate the bearing cage. The EFEM cage model was then combined with the dynamic bearing model to simulate the cage motion during operation. The results from the experimental measurement using the telemeter were then compared with the analytical modeling. The developed telemeter demonstrated the capability of the cage telemeter in detecting various bearing frequencies. These include: the cage frequency, shaft frequency, and ball pass frequency on outer race (BPFO) which was introduced by creating a spall on bearing outer race. Compared to standard accelerometers which are commonly used to measure vibrations on the bearing housing, the cage telemeter has shown advantage in sensing cage motions and detecting bearing defect regardless of the location of the damage. Analytical simulation using the EFEM cage model correlated well with the experimental results and provided more insight into the bearing cage dynamics.

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