Elastic waves in bearing raceways: the forward and inverse problem

TL;DR

This paper models elastic waves in bearing raceways to improve defect detection and vibration analysis, offering a simplified mathematical approach for both forward and inverse problems with fewer sensors.

Contribution

It introduces a new quantitative model of elastic waves in bearing raceways using 4x4 systems, enabling efficient defect detection and contact traction recovery.

Findings

Successful full recovery of contact traction

Effective detection of elastic emissions

Reduced sensor requirements using prior knowledge

Abstract

Turbines are crucial to our energy infrastructure, and ensuring their bearings function with minimal friction while often supporting heavy loads is vital. Vibrations within a bearing can signal the presence of defects, friction, or misalignment. However, current detection methods are neither robust nor easy to automate. We propose a more quantitative approach by modelling the elastic waves within bearing raceways. By approximating the raceway as a hollow cylinder, we derive straightforward 4x4 systems for its vibrational modes, enabling both forward and inverse problem-solving. We also demonstrate how to significantly reduce the number of required sensors by using a simple prior: the known number of rollers and their angular speed. We present numerical examples showcasing the full recovery of contact traction between bearings and the raceway, as well as the detection of elastic emissions.