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The 3D magnetic field in the region with ventilation duct of electrical machine has been analyzed. The method of reduced scalar magnetic potential in connection with the FE method has been used to solve the problem. On the basis of field distribution, the slot leakage permeance has been calculated. The problem has also been solved analytically. It has been assumed that the radial component of magnetic field density in ventilation ducts is equal to zero. The comparison of results leads to the conclusion that, in practice, the analytical calculations are satisfactory accurate.

For the electromagnetic simulation of electrical machines, models with different ranges of values, levels of detail and accuracies are used. In this paper, numerical and two analytical models of an induction machine (IM) are analysed with respect to these aspects. The purpose of the paper is to use these analyses to discuss the suitability of the models for the simulation of various physical quantities of an IM.

An exemplary IM is simulated using the two-dimensional numerical finite element method, an analytical harmonic wave model (HWM) and an extended HWM. The simulation results are analyzed among themselves in terms of their level of detail and accuracy. Furthermore, the results of operating map simulations are compared with measured operating maps of the exemplary machine, and the accuracy of the simulation approaches is discussed in the context of measurement deviations and uncertainties.

The difference in the accuracy of the machine models depends on the physical quantity of interest. Therefore, the choice of the simulation method depends on the nature of the problem and the expected range of results. For modeling global machine quantities, such as mean torque or losses, analytical methods such as the HWM s are sufficient in many applications because the simulation results are within the range of measurement accuracy of current measurement systems. Analytical methods are also suitable for local flux density curves under certain conditions. However, for the simulation of the influence of local physical effects on the machine behavior and of temporally highly resolved quantities in saturated operating points, the accuracy of the analytical models decreases and the use of the finite element method becomes necessary.

In this paper, an extension of the HWM is used to calculate the IM, which, in contrast to the HWM, models the saturation. Furthermore, the simulation results of the different electromagnetic IM models are put into the context of the uncertainty of a measurement of several identical IMs.

The electromagnetic torque oscillations caused by saturation harmonics in a squirrel cage machine are analysed. Special attention is paid to the most important saturation harmonic of alternating field that has three times as many poles as fundamental harmonic and three times its frequency. The operations of the machine as a motor and as a self‐excited generator have been investigated. The 2D finite element time‐stepping method has been applied to the analysis of a particular machine performance. The finite element equations are coupled with circuits equations which describe the winding connections. The skew of the rotor slots is taken into account.

Based on Fourier series theory, for almost periodic functions, the general as well as the specific harmonic‐balance model of induction machines is presented together with a brief derivation. Whereas the general model refers to both symmetrical and asymmetrical machines, the specific one is valid for only the former ones, with windings without parallel branches. The specific model permits classification of all symmetrical machines into three categories. The classification preserves its usefulness for machines not strictly fulfilling assumptions for the validity of the specific model. Expressions for the asynchronous and synchronous torque components are derived. Categories as well as frequencies of both the slot harmonics and the synchronous torques are listed in four tables referring to machines with one to four pole pairs.

Presents a method for the finite element (FE) analysis of saturation effects in a squirrel‐ cage electrical machine. The proposed mathematical model includes the FE equations of the electromagnetic field, the equations which define the connection of windings, and the mechanical equation. Applies an approach based on a simultaneous solution of these equations, paying special attention to the movement simulation. Applies the time‐stepping method with a fixed grid, independent of the rotar position. In the method the motional effects are simulated by trigonometric interpolation of the results for the previous time step.

The purpose of this paper is to validate dynamic analytic force modeling techniques with experimental results. The performance of previously presented 2-D and 3-D eddy current models will be assessed when the steady-state models are coupled to a dynamic mechanical model.

The previously presented 2-D analytic model was formulated in terms of the magnetic vector potential in conductive region and magnetic scalar potential in non-conductive region whereas the 3-D model was formulated in terms of the magnetic vector potential in both the conductive and non-conductive regions.

This paper experimentally confirms that incorporating the heave velocity term is important for accurately predicting the forces under dynamic mechanical motion while using a steady-state eddy current solution. A close agreement between the experimental and the dynamic analytic-based eddy current solution was achieved.

The force results presented from the previously developed 3-D analytic model assume that the width of the guideway is larger than that of the magnetic source and the magnetic source is placed at the center of the guideway along the z-axis.

The rotational and translational motion of a permanent magnet rotor above a conductive plate create lift and thrust force that are suitable for magnetic levitated (maglev) transportation. The previously developed 2-D and 3-D analytic models are fundamental to such maglev research as the models can quickly compute the electromagnetic forces acting on the maglev vehicle. This paper is of immense importance as the paper experimentally validates the analytic models.

The quasi-static analytic eddy current force models that are validated in this paper are different to analogous models developed by prior authors in that the heave velocity as well as the translational velocity of a magnetic source is incorporated into the eddy current force equation.

The purpose of this paper is to focus on the mechanical bearing load caused by the unbalanced magnetic pull (UMP), which is studied in detail. The applied approach is based on an analysis of static and dynamic eccentricities at different positions and different amplitudes. The influence of the operating points is calculated to show the effective bearing load for machines operating at different speeds. The decreasing lifetime of the applied bearings is examined and evaluated in detail.

To evaluate the proposed methodology a permanent magnet synchronous machine (PMSM) with buried magnets is used. To consider effects of slotting and saturation, a finite element (FE) model is employed. The Monte Carlo method is used to determine the most likely amplitudes of the eccentricities. Calculating the UMP for all possible operating points using a control strategy for the machine and coupling this results with a drive cycle, determines the effective force acting on the bearing.

It has been shown that the position of the eccentricity has a not significant influence on the behavior of the UMP and may therefore be neglected. The amplitude of the eccentricity vector influences the amplitude of the UMP including all harmonic force components. For technical relevant eccentricities, the influence is approximately linear for the average and the dominant harmonics of the UMP. In most cases, it is sufficient to displace the rotor at an arbitrary position and amplitude. It is sufficient to simulate one type of eccentricity (static or dynamic) with an arbitrary value of displacement (rotor or stator) to evaluate all possible airgap unbalances. Using stochastic simulations of the eccentricity amplitudes enables an a priori design and lifetime estimation of bearings.

This paper gives a close insight on the effect of mechanical bearing load caused by rotor eccentricities. The effect of the position of the eccentricity vector, the operational range and a drive cycle are considered. A stochastic simulation and an empirical lifetime model of one bearing gives an example of using this methodological approach.

The current distribution within multi strand windings is investigated for transient current and voltage supplies. The difference in losses between transient and sinusoidal waveforms is elaborated. Therefore, a wide range of frequencies as well as different kinds of transient waveforms has been investigated. The definition of the skin depth is no longer sufficient. A new parameter is required for transients, which is related to time. This parameter will be defined and called “skin time”. A numerical method is developed based upon a finite element transient calculation. The method is applied to the winding as well as to the core. A comparison with measurements verifies the approach described.