Model based detection and diagnosis of bearing defects
Authors: Mol Henk , Gabelli Antonio 
Published: March 2024

In this paper we present the Amplitude Spectral Density of Spectrogram [1] (ASDS) and how its output is post processed for determining the size of defects in bearings using acceleration signals. Fatigue modeling of the bearing is then used to define the moment to stop the operation and replace the bearing.
Initially, small defects in the order of a 0.1 to 1 millimeter may arise in the running surface of the bearing. This is the moment when vibrations start to be excited by the rolling contact forces and can be observed by accelerometers on the structure of the machine. At this stage most machines are still operating well. The rolling bearing modeling work shows that characteristic bandwidth of the force impulse for defects smaller than the Hertzian length approximates the speed rolling divided by the sum of the length of the defect and length of the Hertzian contact. This simple result has been proven experimentally by running a bearing with a small defect and varying the running speed, and by varying the size of the Hertzian contact by changing the load [1].
When the small defect grows, the amplitude of the acceleration is growing with defect size but it’s bandwidth is hardly changing until the Hertzian contact is completely disrupted. At that point the force impulse’s bandwidth starts going down as the defect length becomes the dominant factor. This property is used to calculate the actual size of the defect in order to avoid operational disruption and the decision to stop is based on fatigue modeling. Eventually when the defect is about 20 percent of the roller spacing in the bearing, the bandwidth starts to become similar to the repetition frequency and the ASDS transform will no longer be able to estimate it. Experimental work with artificial defects proves the size quantification.
The diagnosis with defect size quantification makes future prognosis possible. For small defects, we have proof that the defect’s rate of growth is slow [2], [3]. When the defect passes a certain size stage which depends on the load, the erosion process will exponentially increase the area damaged in the bearing . Using rolling contact fatigue modeling, under the condition of defects in a rolling bearings, it is possible to predict the likely defect growth rate [2],[4]. By fitting the estimated defect size to the exponential growth rate curve, the decision to replace the defective bearing can be deferred to the right moment without much risk of immediate failure.

[1] Mol, H.A., van Nijen, G.C., “Method for Analysing Regularly Recurring Mechanical Vibrations”, Patent US5698788. Published December 16, 1997.
[2] Morales-Espejel G.E., Gabelli A., “The progression of surface rolling contact fatigue damage of rolling bearings with artificial dents”. Tribology Trans. (2015); 58: pp. 418–31.
[3] Rycerz et al: Propagation of surface initiated rolling contact fatigue cracks in bearing steel, International Journal of Fatigue 97 (2017) 29-38.
[4] Gabelli A., Morales-Espejel G.E., “Improved Fatigue Life Analysis of Pre-Dented Raceways Used in Bearing Material Testing”, Bearing Steel Technologies 11th Volume, “Progress in Steel Technologies and Bearing Steel Quality Assurance”, ASTM STP1600, 2017, pp. 167–191
[5] A.V. Oppenheim and R.W. Schafer, "Digital Signal Processing", Englewood Cliffs, NJ: Prentice Hall, 1975, pp 358 ff.
[6] D.A. Rice, V. Venkatachalam, M.J. Wegmann: "A simple envelope detector". IEEE transactions on instrumentation and measurement, vol 37, no. 2, June 1988, pp 223-226.