Nonlinear Dyn DOI 10.1007/s11071-016-3037-1 ORIGINAL PAPER A new model for spall-rolling-element interaction G. Kogan · J. Bortman · R. Klein Received: 2 May 2016 / Accepted: 17 August 2016 © Springer Science+Business Media Dordrecht 2016 Abstract Evaluation of the spall size of a radially loaded rolling-element bearing is required for the assessment of the bearing damage severity and esti- mation of its remaining useful life. A new multi-body, nonlinear dynamic model of the interaction between the rolling-element and a spalled outer race is presented. The study focuses on the physics of rolling-element contact in a broader range of spall sizes than has been investigated to date, with intermittent contact between rolling-element and the outer race, which is a relevant defect size for diagnostics and prognosticsquery. The analysis is performed in several time intervals accord- ing to periods of rolling-element/race contact and peri- ods when the rolling-element is not connected with the outer race. An explicit expression of the spall size as function of the time-to-impact has been developed by considering radial load, shaft speed, and gravity. The We gratefully acknowledge the invaluable support of the Pearlstone Foundation. G. Kogan · J. Bortman (B ) Pearlstone Center for Aeronautical Engineering Studies and Laboratory for Mechanical Health Monitoring, Department of Mechanical Engineering, Ben-Gurion University of the Negev, P.O. Box 653, 8410501 Beer Sheva, Israel e-mail: jacbort@gmail.com G. Kogan e-mail: ggkogan@gmail.com R. Klein R.K. Diagnostics, P.O. Box 101, 20103 Gilon, D.N. Misgav, Israel e-mail: renata.klein@rkdiagnostics.co.il expression of the spall size was used in a sensitivity study of the effect of parameters such as geometry and radial load. The results obtained from the new model are in good agreement with a well-established general bearing model. The acceleration of the outer ring dur- ing the rolling-element/spall interaction with intermit- tent rolling-element race connection is a novel con- tribution, which allows verification of the model from direct observations using vibration sensors mounted on the structure Keywords Vibration response · Rolling-element bearing · Nonlinear dynamics · Contact model · Spall size · Localized surface defect List of symbols a r Radial acceleration C d RE bearing clearance diameter c Damping coefficient of each of the RE- raceways contact c B Damping coefficient of the bearing c RE Damping coefficient of each RE c 0 Speed of sound in a solid material D p Bearing pitch diameter d Spall depth E Elasticity modulus E Trailing edge relative to the outer ring centre F Force applied to the RE by the raceway 123