24th International Colloquium Tribology - January 2024 179 Simulative and Experimental Characterization of the Tribo-Electrical Contact of Roller Bearings Stefan Paulus 1* , Simon Graf 1 , Oliver Koch 1 , Stefan Götz 2 1 RPTU Kaiserslautern-Landau, Chair of Machine Elements, Gears and Tribology (MEGT), 67663 Kaiserslautern, Germany 2 RPTU Kaiserslautern-Landau, Division of Mechatronics and Electrical Drives (MEAS), 67663 Kaiserslautern, Germany * Corresponding author: stefan.paulus@rptu.de 1. Introduction The usage of fast switching frequency inverters provides high performance operation of electric drive trains. Therefore, they are commonly used in modern drive systems, especially in electromobility. Beside their advantages, these inverters also induce parasitic voltages in the drive system that also affect the bearings. When the breakdown voltage of a lubricated contact is exceeded, discharge currents occur with a high energy density [1]. These currents can cause different kind of damages such as grey frosting [2], flutings [3] and white etching cracks [4]. All these can lead to premature failure of the bearing [5]. To predict the behavior of a bearing under electrical load, it has to be described as an electrical component. This is usually done by regarding the rolling contact between a rolling element and the raceway as a parallel connection of three capacitances, the capacitance of the Hertzian contact area C Hertz , the capacitance of the inlet zone of the contact C Inlet and the capacitance of the outlet zone C Outlet . The Hertzian contact area is thereby regarded as a parallel plate capacitor, due to the deformation of rolling element and the raceway und mechanical load. The capacitance of a parallel plate capacitor can be calculated by equation 1 (1) where 𝜖 0 is the permittivity of vacuum and 𝜖 r is the relative permittivity of the dielectric between the plates, here the lubricant. Inserting the Hertzian contact area h 0 , and the central lubrication gap height the Hertzian capacitance can be calculated. The relation between the total contact capacitance C Contact and C Hertz is commonly estimated with help of correction factors. In this work an electrically extended EHL-simulation model was used to investigate the contact capacitance, including the inlet and the outlet zone. The results are compared with experimental data. 2. Methods and Material In this work the capacitance of a thrust bearing of type-51208 is investigated using two different oils, mineral oil and polyglycol. The axial load was varied in the steps 700-N, 800-N, 1000-N, 1100-N, 1300-N, 2000-N, the rotational speed in the steps 1500-rpm, 2750-rpm, 4000-rpm and the temperature in the steps 40-°C and-60-°C. 2.1 Simulation Model To calculate the deformation of the lubrication gap the Reynolds-equation is solved iteratively. The dimensions of the calculation area in rolling direction x and perpendicular to the rolling direction y are defined by -4a < x < 4a and -3b < y < 3b where a and b are the half axes of the Hertzian contact ellipse. In this way the inlet zone and the outlet zone are part of the calculation area. The finite volume method is used for discretization. The Fischer-Burmeister-Newton-Schur-(FBNS) algorithm is used to solve the Reynolds-equation. This algorithm provides the lubrication gap height and the distribution of pressure and cavitation degree in the calculation area after converging. The oil density and viscosity are calculated in dependency of the pressure distribution and the inlet temperature with help of a set of Bode-equations. When the calculation of the lubrication gap has finished, the contact capacitance is calculated. For this purpose, every single control volume in the calculation area is assumed to be a parallel plate capacitor and the capacitance of each control volume is calculated with help of equation 2. The permittivity of oil is calculated in dependency of pressure and temperature with help of another Bode-equation. In the outlet region, cavitation occurs. Therefore, the capacitance of each control volume in the outlet region is calculated as a series connection of the permittivity of oil and air. The ratio between both phases is given by the cavity fraction, that was calculated in the EHL-simulation. The overall contact capacitance is calculated by summation of all control volume capacitances. 2.2 Experimental setup The experimental investigation of the capacitance of a thrust bearing type 51208 is carried out at the test bench called GESA (ger.: „Gerät zur erweiterten Schmierstoffanalyse“, eng.: „device for extended lubricant analysis“). At this test bench, thrust bearings can be loaded both, mechanically and electrically. 3. Results The simulative and experimental results for mineral oil are given in figure-1, the results for polyglycol are given in figure-2. 180 24th International Colloquium Tribology - January 2024 Simulative and Experimental Characterization of the Tribo-Electrical Contact of Roller Bearings Figure 1: Capacitance of bearing type 51208 with mineral oil determined by simulation (left) and testing (right) Figure 2: Capacitance of bearing type 51208 with polyglycol determined by simulation (left) and testing (right) The capacitance of the polyglycol is basically higher compared to the capacitance using mineral oil. This is due to the different permittivities of the oils. The permittivity of the mineral under normal conditions is about 2.2, the permittivity of the polyglycol is about 5.5. Both oils show a similar dependency of the bearing capacitance on the operating conditions. The capacitance increases with higher axial loads, due to the stronger deformation of the rolling elements which results in a larger Hertzian contact area, i.e. larger capacitor plates. At the same time, decreasing rotational speed and increasing temperature leads to an increase of the capacitance. Both parameters affect the gap height and thereby the distance between the capacitor plates. Lower gap heights lead to higher capacitances. This effect can be seen in both, the simulative and the experimental results but is slightly stronger developed in the simulative results. Furthermore, the experimental determined capacitance is overall a bit higher compared to the simulation results. Both observations can be attributed to the fact, that a bearing capacitance does not only consists of the capacitance values of the rolling contacts. Moreover, the bearing components outside the contact zone also contribute to the total capacitance of the bearing. These influences are not covered by the EHL contact simulation. Nevertheless, the main capacitance source is the contact capacitance and therefore the simulative results in general show good agreement to the experimental determined values. 4. Conclusions In this work an electrically extended EHL simulation model was used to determine the contact capacitance of a thrust bearing of type 51208. Overall, the results of the electrically extended simulation show good agreement with experimental determined values. The influence of varying axial load, speed and oil temperature on the capacitance can be captured, although the total bearing capacitance determined by simulation is in general lower than the experimental determined capacitance. For a more accurate determination of the bearing capacitance, the simulation is being expanded to include the capacitance sources outside the roller contacts. Furthermore, the calculation of the temperature inside the roller contact is to be implemented in the EHL model. 5. Acknowledgment The authors thank the Deutsche Forschungsgemeinschaft (DFG) for funding „Determination of ball bearing impedances under steady-state operating conditions by means of a further developed rolling contact model at full film lubrication“ (SA898/ 32-1/ 470273159). References [1] A. Jagenbrein: Investigations of bearing failures due to electric current passage, Technische Universität Wien Dissertation. Wien 2005. [2] S. Graf, B. Sauer: Surface mutation of the bearing raceway during electrical current passage in mixed friction operation. Bearing World Journal 2020 (2020) 5, S.-137-147. [3] T. Zika: Electric discharge damaging in lubricated rolling contacts, Technische Universität Wien Dissertation. Wien 2010. [4] J. Loos, I. Bergmann, M. Goss: Influence of High Electrical Currents on WEC Formation in Rolling Bearings. Tribology Transactions 64 (2021) 4, S.-708-720. [5] V. Schneider, J. O. Stockbrügger, G. Poll, B. Ponick: Stromdurchgang am Wälzlager - Verhalten stromführender Wälzlager. Abschlussbericht FVA 863 I Nr.-1501 (2022).