Operating condition-dependent model for describing the electrical impedance of rolling bearings for sensorial use
The premature failure of rolling bearings generally leads quickly to the breakdown of machines and plants and in some cases entails enormous economic but also ecological risks. Predictive maintenance approaches therefore aim to use sensor data to derive information about the maintenance and repair requirements of systems. In rotating machines, rolling bearings are a central machine element, which can be used to gain measurement data on speed and bearing load. The approach of acquiring data in so-called in-situ positions has led to the concept of a load-measuring rolling bearing, which can lead to an increased determinacy of the measured data as a prerequisite of the rapidly advancing digitalization. The approach is based on measuring the impedance of a rolling bearing as part of an electrical circuit. The bearing's operating conditions can be inferred via the bearing rings, which determine the electrical characteristics of the rolling bearing via the elasto-hydrodynamic (EHD) rolling contact of the rolling partners. With the help of this data, knowledge of the acting stress can enable near-real-time calculation of the service life consumption of highly stressed structural elements. However, initial experiments show that the existing model for describing the electrical impedance of rolling bearings as part of a measurement section, which was originally developed for calculating damaging inverter-induced currents at constant bearing loads, is not able to reproduce the measured impedance behavior of the rolling bearing with sufficient accuracy. The approaches from the state of research do not yet provide a generally satisfactory solution for the inference from the impedance as a measured variable to the acting bearing load as a variable of interest.
The current state of research shows that relevant influencing factors of the electrical capacitance of a rolling bearing, which depends on the operating condition, are neglected in the existing model. Recent investigations confirm that, in the case of pure radial loads, the rolling contacts outside the load zone (Figure 1) have an influence on the impedance of the rolling bearing and make a significant contribution to improve the model correlation between the acting load and measurable impedance. By calculating the impedance of unloaded rolling elements, taking into account the operating condition-dependent distribution of the radial clearance, and including this in the impedance model of the rolling bearing, this influence is to be represented. For this purpose, the model of a generally curved capacitor with operating condition-dependent geometry corresponding to the point contact between ball and inner or outer ring is used. In addition to radial deep groove ball bearings, angular contact and shoulder ball bearings are considered at varying load angles. The calculated impedance contributions of all rolling elements are aggregated in an overall electrical model of the bearing and results are validated with tests on the institute's own Athene rolling bearing test rig.
In a first step, the position and kinematics of unloaded rolling elements outside the load zone are investigated and their influence on the impedance model is determined (Figure 2, left). The knowledge gained will be extended to the boundary regions outside the Hertzian area of loaded rolling elements (Figure 2, right). Thus, the working hypothesis will be investigated that a correction factor, which is widely used in the literature and which includes the edge influence, can be replaced with the help of a complete description of all impedance contributions. For the subsequent test execution, the range of the bearing life must first be identified in which a constant electrical behavior of the bearing can be expected, because a change in bearing impedance can be observed both in the running-in phase and towards the end of the service life. This is followed by a detailed and statistically validated experimental design in which bearing type, speed, equivalent bearing load, load angle, measurement frequency and oil temperature are varied. Finally, the previously developed impedance model is to be validated based on the experimental results, thus enriching the scientific community with new knowledge of electrical bearing properties. In addition to its application in sensing rolling bearings, it can also help, e.g., in the prediction of the electrical behavior of electrical machines during operation in order to avoid failures caused by damaging bearing currents.