Analytical determination of the end-winding portion of the winding-to-rotor capacitance for the prediction of bearing vo
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ORIGINAL PAPER
Analytical determination of the end‑winding portion of the winding‑to‑rotor capacitance for the prediction of bearing voltage in electrical machines Jan Ole Stockbrügger1 · Bernd Ponick1 Received: 30 March 2020 / Accepted: 15 June 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The number of inverter-fed motors is increasing due to the good controllability of the motor and the meanwhile low acquisition costs. As a result of the discrete switching states of the power transistors, the average of the three output voltages of a two-level inverter is a common mode voltage, which differs from zero. The common mode voltage is impressed into the motor winding by the inverter, and an image of the common mode voltage is produced across the bearings via the windingto-rotor capacitance. The voltage applied to the motor bearings can exceed the dielectric strength of the lubricating film of the bearings and lead to discharge currents resulting in damage to the motor bearings. The winding-to-rotor capacitance is composed of a slot and an end-winding portion. In this article, an analytical determination of the end-winding portion of the winding-to-rotor capacitance is presented, which, in addition to the rotor geometry, considers the influence of materials with different permittivities. The method is validated by means of FEM simulations for different geometries and materials. Keywords Winding-to-rotor capacitance · Bearing voltage · EDM currents · Traction motor
1 Introduction The inverter supply of electrical motors can lead to EDM bearing currents, which can result in matted raceway and rolling element surfaces, periodic raceway corrugation structures and chemical lubricant changes [1]. EDM currents occur in the area of liquid friction/full lubrication when the critical field strength of the lubricating film in the rolling bearing is exceeded and resulted from the discharge of the bearing capacitance [2]. The bearing voltage Ul is the image of the common mode voltage Ucm and can be calculated by means of the capacitive voltage divider [3] as
Ul =
Cwr ⋅ Ucm . Cwr + Csr + Cl1 + Cl2
(1)
The capacitive voltage divider is composed of the winding-to-rotor capacitance Cwr , the stator-to-rotor capacitance Csr and the capacitances of the two bearings Cl1 and Cl2 .
The winding-to-rotor capacitance, which is composed of the motor’s slot and end-winding portion, is decisive for the amount of bearing voltage applied [4, 5]. The end-winding portion of the winding-to-rotor capacitance can be estimated analytically or numerically. In [6], a complex 3D FEM simulation is performed to determine the capacitance. The current analytical determination of the end-winding portion of the winding-to-rotor capacitance is based on the calculation of a cylindrical capacitor [7–9]. The basic problem when applying the calculation rule for a cylindrical capacitor is the one-dimensional potential problem used for derivation. When using a cylindrical capacitor, the influenced charge on the front surface of the
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