Multi-Time Scale Modeling strategy for bearing life prognosis
Prediction of a bearing service life is traditionally based on empirical or physical models. In an effort of combining the strengths of these modeling approaches and minimizing their respective limitations, this research establishes a unified framework that couples the empirical and physical models, based on the concept of Multi-Time Scale Modeling (MTSM). Specifically, a MTSM strategy for bearing life prognosis is developed by correlating experimentally acquired bearing vibration data, which reflect upon the global defective condition in a bearing, with the microscopic growth in the crack size. The focus of study is on the coupling mechanism between the process that can be characterized by a fast-changing scale, e.g. vibration level (that is determined experimentally) and the process that evolves on a slow-changing scale, e.g., crack propagation.
A model for the fast-changing process is developed by means of a polynomial regression analysis. Various curve fitting methods have been evaluated using data obtained from a finite element model of a ball bearing that contains a seeded defect in the outer ring. The slow-changing process is modeled based on the concept of the Paris Law, which describes crack propagation as a result of stress concentration. The coupling between the two time scales is established by relating the observed (or predicted) vibration feature to the crack size, based on the concept of dynamic mass. The validity of the proposed MTSM strategy is evaluated using data from bearing life cycle experiments. Comparison with results obtained from traditional single-time scale techniques indicates that the MTSM approach is capable of achieving longer term and more accurate remaining service life prognosis of the test bearing.
While this study addresses bearings as the application domain, the concept of MTSM is applicable to a broad range of research, where understanding and exploration of phenomena and mechanisms characterized by different time scales may significantly improve the accuracy and reliability in machine service life prognosis.