Citation: Ohana, R.; Klein, R.; Shneck, R.; Bortman, J. New Damage Accumulation Model for Spall Propagation Mechanism in Bearing Raceways. Materials 2023, 16, 1750. https://doi.org/10.3390/ma16041750 Academic Editor: Enrique Casarejos Received: 24 December 2022 Revised: 9 February 2023 Accepted: 17 February 2023 Published: 20 February 2023 Copyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). materials Article New Damage Accumulation Model for Spall Propagation Mechanism in Bearing Raceways Ravit Ohana 1 , Renata Klein 2 , Roni Shneck 3 and Jacob Bortman 1, * 1 PHM Laboratory, Department of Mechanical Engineering, Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva 8410501, Israel 2 R. K. Diagnostics, Gilon, P.O. Box 101, D. N. Misgav 2010300, Israel 3 Department of Material Engineering, Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva 8410501, Israel * Correspondence: jacbort@bgu.ac.il Abstract: The aim of this study was to investigate the spall propagation mechanism in ball bearing raceways using physics-based models. Spalling is one of the most common types of bearing failures that can lead to catastrophic failure. This research takes a step forward toward developing a prognostic tool for ball bearings. It is first necessary to understand the spall progression process in order to formulate a constitutive law of spall deterioration and to estimate the amount of remaining useful life. Fragment formation in the vicinity of the spall edge was found to consist of surface and sub-surface cracks that eventually coalesce, and a fragment is released from the raceway, based on naturally- developed spalls. Here, we describe a physics-based model, integrating a dynamic model with a finite element one to simulate this process. A continuum damage mechanics (CDM) approach and fracture mechanics tools were embedded into the finite element model to simulate the damage propagation. The formation of cracks in the vicinity of the spall (surface and sub-surface cracks) were studied using this effective stress CDM model, and the propagation of the cracks was examined using two approaches: a fracture mechanics approach and an accumulated inelastic hysteresis energy CDM approach. The latter also predicts the overall process of a single fragment release. The simulation results of the spall propagation models are supported by experimental results of spalls from both laboratory experimental bearings and an in-service Sikorsky CH-53 helicopter swashplate bearing. The results obtained show that the impact of the ball on the spall edge affects the crack propagation and the appearance of the surface and sub-surface cracks. Both release the residual stresses and cause crack propagation until a fragment is released. Keywords: rolling element bearings; spall propagation; damage mechanics; fatigue crack growth; finite element 1. Introduction (Spall Initiation and Propagation) Understanding the driving mechanism of spall propagation is a step toward perform- ing physics-based bearing prognostics for condition-based maintenance (CBM). These prognostics intend to enable the prediction of remaining useful life (RUL), and thereby improve safety and reduce costs and the probability of fault development. Spall evolution in raceways can be divided into three stages: (i) spall initiation by a rolling contact fatigue (RCF) mechanism, (ii) steady spall propagation, and (iii) accelerated spall propagation until final failure. As the spall initiation process has been studied both empirically [1–3] and theoretically [4–9], the present research focused on the spall propagation process and factors that affect it. While several studies attempted to quantify the spall growth mecha- nism, such as those of Arakere et al. [10] and Branch et al. [11,12], none have addressed the progression of cracks and removal of material from the spall edge, which results in flake release and spall propagation. Morales-Espejal et al. [13,14] focused on the progression of the initial damage around an indentation. They introduced a physically-based surface Materials 2023, 16, 1750. https://doi.org/10.3390/ma16041750 https://www.mdpi.com/journal/materials