Citation: Kirchner, E.; Bienefeld, C.;
Schirra, T.; Moltschanov, A.
Predicting the Electrical Impedance
of Rolling Bearings Using Machine
Learning Methods. Machines 2022, 10,
156. https://doi.org/10.3390/
machines10020156
Academic Editor: Davide Astolfi
Received: 11 January 2022
Accepted: 15 February 2022
Published: 18 February 2022
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Article
Predicting the Electrical Impedance of Rolling Bearings Using
Machine Learning Methods
Eckhard Kirchner
1,
* , Christoph Bienefeld
1,2
, Tobias Schirra
1
and Alexander Moltschanov
1
1
Institute for Product Development and Machine Elements, Technische Universität Darmstadt,
Otto Berndt Straße 2, 64287 Darmstadt, Germany; christoph.bienefeld@gast.tu-darmstadt.de (C.B.);
schirra@pmd.tu-darmstadt.de (T.S.); a.moltschanov@outlook.com (A.M.)
2
Corporate Research, Robert Bosch GmbH, Robert-Bosch-Campus 1, 71272 Renningen, Germany
* Correspondence: kirchner@pmd.tu-darmstadt.de
Abstract:
The present paper describes a measurement setup and a related prediction of the electrical
impedance of rolling bearings using machine learning algorithms. The impedance of the rolling
bearing is expected to be key in determining the state of health of the bearing, which is an essential
component in almost all machines. In previous publications, the determination of the impedance of
rolling bearings has already been advanced using analytical methods. Despite the improvements
in accuracy achieved within the calculations, there are still discrepancies between the calculated
and the measured impedance, leading to an approximately constant off-set value. This discrepancy
motivates the machine learning approach introduced in this paper. It is shown that with the help of
the data-driven methods the difference between analytical prediction and measurement is reduced
to the order of up to 2% across the operational range analyzed so far. To introduce the context of
the research shown, first the underlying physics of bearing impedance is presented. Subsequently
different machine learning approaches are highlighted and compared with each other in terms of
their prediction quality in the results part of this paper. As a further aspect, in addition to the
prediction of the bearing impedance, it is investigated whether the rotational speed present at
the bearing can be predicted from the frequency spectrum of the impedance using order analysis
methods which is independent from the force prediction accuracy. The background to this is that, if
the prediction quality is sufficiently high, the additional use of speed sensors could be omitted in
future investigations.
Keywords: rolling bearings; impedance; force sensor; machine learning
1. Introduction
The increasing digitalization in mechanical engineering leads to a demand for new,
integrated sensor solutions. Martin et al. [
1
] have presented a sensor concept, shown in
Figure 1, in which the electrical impedance of rolling bearings is measured to estimate
the bearing load. With the use of the sensing bearing concept it is possible to implement
predictive maintenance and process monitoring more easily in new and existing machines
based on load data. The technology is based on the relationship that elasto-hydrodynamic
lubricated contacts have a capacitive behavior, which leads to a measurable electrical
impedance in an alternating current circuit [
2
]. The voltage levels of the sensor concept are
below harmful values as mentioned in [
3
]. The literature gives analytical models to describe
this effect, but they have an accuracy that is not sufficient to use the models as sensors. For
this reason, the models available in the literature were extended in
Schirra et al. [3]
so that
a much more accurate analytical calculation of the bearing impedance is possible. Despite
the improvements in the models achieved, there is still a discrepancy between calculated
and measured values.
Machines 2022, 10, 156. https://doi.org/10.3390/machines10020156 https://www.mdpi.com/journal/machines
