Honors Theses

Document Type

Thesis

Date of Completion

5-2024

Academic Year

2023-2024

Department

Engineering & Physics

Academic Major

Mechanical Engineering

Faculty Advisor

Brad Miller, Ph.D.

Abstract

This thesis considers the novel angular contact rolling-element bearings proposed by NASA’s Glenn Research Center, which are coated with a thin solid lubricant that exhibits viscoelastic behavior. Current analytical models for the dynamic stiffness matrix of angular contact bearings, critical for vibration analysis, lack the ability to model the effects of a solid coating, as well as the time dependencies inherent in viscoelastic theory. The author first presents an overview of the stiffness matrix derivation, followed by a treatment of the underlying Hertzian contact theory. An analytical extension of this theory is proposed which accounts for a thin elastic layer within the contact model, used to formulate a stiffness matrix for angular contact bearings with a thin elastic coating. Finally, the elastic-viscoelastic correspondence principle is applied to yield the proposed model for the dynamic stiffness matrix in the Laplace or frequency domain for angular contact bearings with a thin viscoelastic coating. The analytical model captures the general case and allows the input of custom bearing parameters and coating relaxation function determined by Dynamic Mechanical Analysis (DMA) techniques. The Prony Series relaxation model is briefly discussed as one such function. Predictions of the proposed model can be compared to vibration spectra of physical bearings to assess the model’s validity and potential for commercial application, particularly in aerospace contexts.

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