# Bearing impedance measurement

### Basics of measuring the impedance of rolling bearings with the E-Lub Tester

Each lubricant has a specific electrical conductivity and a permittivity, also known as the relative permittivity.

Both quantities can be determined by determining the complex impedance of the medium; this is composed of the real part on the one hand and the imaginary part on the other. In the equivalent circuit, an ohmic resistance and a capacitance are obtained, which are connected in parallel.

Figure: Equivalent circuit diagram of a radial bearing (PhD thesis D. Bechev, TU Kaiserslautern 2020)

Independent of the bearing type (axial/radial), the following formula results for the capacitive behavior of the bearing:

The electrical resistance is also calculated by the following formula:

The complex impedance is measured by applying an AC voltage. The current is measured according to magnitude and phase.

For the measurement of the dielectric constant, the imaginary part is decisive. Therefore, it is favorable to select a high frequency for the measurement of the dielectric constant. For the measurement of the specific conductivity, on the other hand, a low frequency is favorable, since the imaginary part becomes small and thus the decisive real part predominates.

This applies to a defined operating condition or to a fixed geometry. In the bearing, these can vary greatly due to the wide range of applications.

The VKA adapter (rolling bearing carrier) of the E-Lub Tester was therefore designed in such a way that the real operating range can be simulated by varying the temperature, force and speed. All parameters change the lubricant film. This in turn influences the ohmic and capacitive behavior, which can be seen on the following graph by means of displacements.

Therefore, the impedance measurements are recorded over a defined frequency range (100 Hz to 10 MHz) to allow a qualified evaluation.

The temperature dependence of the dielectric properties of fluids under laboratory conditions can be determined using the EPSILON+ laboratory device.

Temperature control of the VKA adapter or the bearing inside it with lubricant is possible through cooling channels inside the adapter. The temperature measurement is realized with an integrated PT100.

An automated temperature control bath is used to realize precise temperature control of the lubricant. The control is carried out via the Windows software flucon E-Lub Tester.

A thermal equilibrium is set before each measurement to ensure the highest possible measurement accuracy.

Isotherms of the impedance curve in the desired frequency spectrum can be recorded via standardized measurement campaigns.