Statistical studies show that in industrial applications more than 50% of malfunctions of rotating machineries are caused by shaft misalignment [1]. The usual monitoring technics based on the regular measurement of the vibrations are today very effective to provide a diagnosis of the machine when the wear is initiated in order to schedule a maintenance intervention. Unfortunately, this diagnosis is often quite late because the abnormal vibrations reflect an upcoming failure if nothing is done. Since 2008, several studies carried out in the Laboratory of Innovative Technologies (LTI EA-3899) have clearly established the relevance of electrical measurements located on dynamic interfaces and can be considered as an alternative to the exiting diagnosis technics. The electrical measurement can therefore be used as a predictive maintenance tool in the context of ball bearings monitoring, by using standard statistical indicators extracted from the electrical signature [2, 3].

In the context of the factory 4.0, the present work deals with the development of a digital twin of ball bearing using the Discrete Element Method (MED). The developed 3D discrete model is enriched with the phenomenological contribution of lubrication, in order to develop a monitoring tool based on an electrical measurement. In this sense, the lubricant consideration must remain sufficiently adapted to the scale of the apparent contact, where the competition between the metal-metal contact with asperities (resistive) and the contact through the fluid (capacitive) plays an essential role in electromechanical coupling. We have therefore implemented in the digital twin an elastohydrodynamic [4] model at the contact scale between rolling elements and raceways to predict the lubrication regime under a given mechanical loading and a real operating conditions. Furthermore, we have considered the effect of the deformation of surface asperities in the elastohydrodynamic lubrication (EHL) model, specifically developed for elliptical contact [4]. The numerical predictions allowed us to assess that the deformation of asperities increases the minimum fluid film thickness, in comparison with the smooth surface. Starting from the EHL modelling, an electrical formulation taking into account Hertz/Greenwood & Williamson theory is then implemented in the twin digital to compute the overall resistance (or impedance) from the bearing over time. For a fixed angular speed, the lubrication regime still unchanged according to Stribeck theory. The resistive responses show a load sensitivity in accordance with experimental studies. Hence, the decrease in resistance as the load increases is explained essentially by taking into account Hertz theory. Inversely, an increasing of angular speed indicates a change in the operating regime of lubrication. For higher angular speeds, the mixed regime and the full-film regime can be observed simultaneously at the contact between the rolling elements and raceways (inner and outer). Therefore, the electrical response passes from a few ohms for low speeds, to tens ohms in the mixed regime. As a conclusion, the numerical simulations obtained with the digital twin corroborate with experimental results, in the sense that the electrical response is strongly correlated to the mechanical state and the lubrication regime.

References

[1] A. Sapietová and V. Dekýǎ. Dynamic analysis of rotating machines in MAC.ADMAS. Procedia Engineering, 136:143 – 149, 2016.

[2] C. Machado, M. Guessasma, and E. Bellenger. Electromechanical modeling by DEM for assessing internal ball bearing loading. Mechanism and Machine Theory, 92 :338–355, 2015.

[3] C. Machado, M. Guessasma, and V. Bourny. Electromechanical prediction of the regime of lubrication in ball bearings using Discrete Element Method. Tribology International, 127: 69 – 83, 2018.

[4] M. Masjedi and M. Khonsari. On the effect of surface roughness in point-contact EHL: Formulas for film thickness and asperity load. Tribology International., 82: 228–244, 2015.