24th International Colloquium Tribology - January 2024 193 Digital Twin Parametrization of a Roller Bearing based on Ultrasonic Film Thickness Measurement Fabio Tatzgern, Boris Gigov, Michal Kracalik, Georg Vorlaufer, Markus Varga * AC2T research GmbH, Wiener Neustadt, Austria * Corresponding author: E-mail (optional) 1. Introduction Lubricant film thickness is a crucial parameter in machine elements to ensure optimal and safe operation [1]. Measuring the film thickness in-situ allows the development of an accurate Digital Twin predicting the film thickness under real operational conditions and opens up new possibilities for efficiency optimization and extension of lifetime. In this work, the Digital Twin is based on the empirical Hamrock & Dowson (H&D) model [2], which has long been used to estimate the film thickness to a reasonable degree of accuracy, but relies on a complex set of empirical parameters, which cannot be determined by direct measurements. Therefore, in this work we base a Digital Twin on the H&D model and setup a test rig with novel ultrasonic sensors to measure the film thickness. With this input we can parametrize the used lubricant for further use in Digital Twins. 2. Experimental The work was carried out on a test rig applying industrial rolling element bearings following the DIN51350-6 standard. It comprises a pair of SKF32008X rolling element bearings from SKF that are loaded axially (Fig. 1). The bearings were lubricated with two greases, namely one with mineral base (NLGI 2) and one with synthetic base (NLGI 2.5). Lithium soap as main additive was used in both. Figure 1: Test setup and control units. A parameter range from 2.3-6.9-kN load and 1000-2000-rpm rotational frequency were investigated in a full matrix approach. Additional to load and torque and temperature sensors, the test rig is equipped with a sensor based on ultrasound reflectometry for in-situ lubricant film thickness measurement. A customized Lead Metanobiate transducer with 10 MHz central frequency bonded on the outside of the bearing outer raceway was used. 3. Model The goal of the Digital Twin is to predict the film thickness based on the dynamical loading of the bearings with the applied grease. In our test study the system dynamics is fully characterized by the rotational speed w 21 of a roller, F raceway - the force between outer raceway and the roller and the temperature T (Fig. 2). Figure 2: Loading of a single roller. In this work, only the basic form of the H&D model is retained (Eq. 1) and the model parameters are based on real-time data collected at the system level, such as load and speed. This allows the adaption of the H&D model to a wide range of operating conditions and types of lubricants for improved accuracy in prediction. (1) Equation 1: Hamrock & Dowson formula for film thickness [2]. In the next step, the exponential values in the model Eq. 1 are chosen to be variables and then fit to the film thickness measurements as: (2) Equation 2: where a, b and c are the parameters of interest and r serves as a parameter for the offset. 194 24th International Colloquium Tribology - January 2024 Digital Twin Parametrization of a Roller Bearing based on Ultrasonic Film Thickness Measurement 4. Results The data from this sensor are used to characterize a given lubricant by determining its specific H&D parameters, which can then be used to calculate film thickness under real load conditions in machinery. This also allows the prediction and simulation of other parameters, such as slip, torque, viscosity of the lubricant, and many more, to further improve the tribological efficiency of the machine element. Fig. 3 shows exemplarily the measured values during the run parameter set of the mineral base grease. The film thickness results show increasing film thickness with increasing velocity, and contrary, decreasing film thickness with increasing load level. Naturally, the measured torque increases with increasing load, while the temperature overall increases with increasing test time. Figure 3: Results of the mineral based grease. Several regression models were applied to the obtained measurements, to identify the parameters a, b, c of Eq. 2 and so parametrize the Digital Twin for the film thickness of the rolling element bearing with the given lubricant. Fig. 4 shows the results of linear regression of the parameters for the mineral base grease. It is clearly visible, the mean film thickness can be predicted accurately based on the loading conditions applied to the bearing. Hence, the H&D Digital Twin model for the film thickness is fully defined by the parameters a, b, c and those parameters are potentially unique and fully define the grease under different operating conditions. Figure 4: Linear regression (red) of the measured film thickness (black) of the mineral base grease. 5. Conclusions Digital Twins of tribosystems are a useful tool to understand the influence of load and system parameters onto critical tribological conditions, such as the minimum film thickness of a lubricated contact. Therefore, in this work, we have established a Digital Twin of the film thickness of a rolling element bearing with grease lubrication. Ultrasonic film thickness measurements based on reflectometry allowed us for the determination of the real film thickness in-situ. These results were applied to a Hamrock & Dowson prediction of the film thickness. Regression models allowed us to describe the system with three parameters, which abled us to uniquely and fully define the grease behaviour under the different operating conditions. References [1] M. Schirru, M. Varga: A Review of Ultrasonic Reflectometry for the Physical Characterization of Lubricated Tribological Contacts: History, Methods, Devices, and Technological Trends, Tribology Letters 70 (2022), 129. [2] Engineering Tribology. In Engineering Tribology (Fourth Edition); Stachowiak, G.W., Batchelor, A.W., Eds.; Butterworth-Heinemann: Boston, 2013; ISBN 978-0-12-397047-3.