A multibody simulation model for deep-groove ball bearings is presented. The model considers friction in both the raceway and cage contacts, resulting from radial and axial loads. The model is validated against experimental measurements for a 6319 bearing under oil-bath lubrication over a speed range of 500–3000 min⁻¹ and two load ratios ($C/P=10$ and 6.5). Predicted friction torques show good agreement with measurements, with deviations between 5.5% and 22% at moderate speeds. In addition, electrical contact capacitances are calculated for a 6208 bearing and compared with an analytical approach, showing deviations in the range of 10–14%. Beyond friction prediction, the fully dynamic approach enables time-resolved analysis of roller kinematics and the identification of instability limits under axial excitation. The developed tool therefore enables reliable bearing loss prediction, supports efficiency-oriented drivetrain design, and provides a basis for electro-tribological and stability investigations.

The electrical capacitance of rolling bearings is essential for understanding and predictingparasitic bearing currents in inverter-fed machines and could also be used to evaluate lubrication, film thickness, and mechanical load conditions. However, many existing models require large correction factors to represent regions outside the Hertzian contact, which constitutes a large knowledge gap. Analytical models are often far from measured values without correction; 3D simulation models come closer but introduce many degrees of freedom with the risk that better accuracy can be a consequence of model flexibility as well as overfitting, and require higher modeling effort and computational cost. This paper proposes a hybrid capacitance estimation method in which only the Hertziancontact region is calculated analytically using Hertzian contact theory and elastohydrodynamic film-thickness equations, whereas electrostatic finite-element analysis (ANSYS Q3D Extractor) evaluates the remaining non-Hertzian regions numerically. This method avoids empirical correction factors and replaces them with geometry-based electrostatic field calculations for regions outside the Hertzian contact zone. The proposed method is validated using experimental measurements from a dedicated test setup for a 51208 thrust ball bearing operated under various mechanical conditions. The results show reliable agreement with the measurements, with about 52% of the cases showing deviations below 10% and 86% below 20%.

In layered systems with porous substrates and a dense solid surface, stiffness and strength are inherently coupled through porosity-dependent relations, influencing their load-bearing behaviour. This work presents a systematic methodology for the assessment and design of such layer-substrate systems based on a criterion of balanced material utilization. A dimensionless parameter is defined to characterize the stress state in both components relative to their admissible limits, from which the optimal layer thickness is determined at equal stress levels in both constituents. Stress distributions are calculated using a numerical half-space model for layered contacts and evaluated through material-dependent equivalent stress criteria. The relationship between material utilization and load-carrying capacity is reduced to a scaling factor that combines the influence of porosity-dependent parameters. The approach establishes a direct link between the governing material parameters and structural design variables. Across the investigated parameter range, the utilization rate scales linearly with optimal layer thickness, whereas the load-carrying capacity follows a cubic relation. For a representative Ashby strength scaling coefficient of $C_{\sigma }=0.3$, for example, a substrate porosity of 90% leads to a scaling factor of 1.6, corresponding to a possible load amplification of 60% relative to the homogeneous reference.

IntroductionFast switching frequency inverters are a key component in modern electric drive trains. They provide high efficiency in a wide speed range, which is why they are frequently used in vari...

Ball bearings are essential components in modern inverter-driven electric drives, such as wind turbines, electric vehicles, and variable-speed industrial systems. However, power electronics lead to the formation of internal voltages and currents across bearings, which fundamentally depend on their electrical impedance characteristics. The electrical impedance of bearings depends on the tribological conditions of the contact as well as the electrical properties of the lubricant. Previous approaches for modeling bearing impedance, including correction factors, elastohydrodynamic simulations, electric field analysis, and statistical models, have provided valuable insights, each with specific advantages and limitations in terms of general applicability. This study presents a model for calculating the electrical impedance of ball bearings, which incorporates the resistive and capacitive components. A combined modeling approach is proposed, in which microscopic electrostatic modeling of the contact area is coupled with macroscopic finite element analysis (FEA) to evaluate bearing resistance and capacitance. The microscopic electrostatic model is based on an elastohydrodynamic lubrication (EHL) approach enhanced by electric effects. These account for material deformation and lubricant film distribution within the rolling contact, while the macroscopic model accounts for the regions outside the contact zone. Together, these models incorporate pressure and temperature-dependent variations in lubricant properties and their effects on the dynamic impedance. This combined approach provides a more precise understanding of the electrical interactions within bearings under diverse mechanical conditions. The results indicate deviations below 20%, compared to experimental measurements across all tested frequencies without relying on empirical correction factors.