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Different solution methods, using finite element method in continuous and discrete frequency domain, are compared with each other in order to find the most appropriate method for the estimation of steady state vibrations in linear structural and mechanical problems. The purpose of this paper is to describe the procedures.

The continuous and some relevant discrete frequency domain solution methods are compared by an analytical investigation as well as by the numerical examination of a simple model. Finally, results for a more relevant example using finite elements are presented.

It is shown that the steady state computation using the continuous frequency domain system description delivers the exact solution for a given system.

Based on the presented results, the use of continuous frequency domain system description is recommendable in most cases.

The purpose of this paper is to analyse the eigenforms and eigenfrequencies of stator core stack by experimental and numerical investigation. The influence of material parameters on the structural vibrations is carried out in order to describe the laminated structure of stator core stack with a homogeneous material model.

The finite element method is applied for a numerical modal analysis. Therefore, a homogeneous transversally isotropic material model is introduced and the influence of each material parameter on the dynamical behavior is investigated. These material parameters are stepwise adjusted to the results from the experimental modal analysis. The investigation includes results from different stator core stacks.

The influence of material on the modal parameters is shown. Furthermore, material parameters are carried out for stator core stacks, which describe the measured dynamical behaviour.

The presented investigations show a useable material model and corresponding parameters to the description of the laminated structure of stator core stacks.

The purpose of this paper is to set up a comprehensive numerical approach to estimate the 3D structural vibration and noise radiation of an induction machine.

The rotating force waves, acting in the air gap of an induction machine and obtained by an electromagnetic finite element multi‐slice simulation, are applied to the 3D structural finite element model and a structural harmonic simulation is performed. The sound emission due to the vibration of the surface of the machine is computed with a 3D boundary element model.

The paper outlays problematic issues when setting up the numerical models, i.e. the structural finite element model. The material properties strongly affect the structural behaviour and therefore the radiated noise.

The 3D force distribution in the air gap and the resulting vibrations are computed. The structural behaviour, i.e. the different vibrational behaviour of stator and surface is discussed. The correlation of the structural vibrations and the noise radiation is investigated.

The purpose of this paper is to analyse the surface vibrations of an induction machine due to force waves acting on the stator and rotor core. The focus lies on the investigation of the influence of force waves with axial variation and with higher spatial ordinal numbers on the surface vibration of an induction machine and thus its emitted noise.

Unit force waves with different spatial ordinal numbers and varying in axial direction are set up and applied on the stator and rotor teeth of a structural finite element model of an induction machine. Structural harmonic analyses with different frequencies are performed and the deformation of the machine is determined. After that, the root mean square of the normal component of the velocity on the surface of the machine's housing is determined and compared for the different force waves.

The influence of force waves with spatial ordinal numbers of higher order can have a significant influence on the structural vibration, especially if the spatial ordinal number is near the number of teeth. Furthermore, it is shown that the structure may react sensitively to axial variations of the forces, particularly near distinct structural resonances.

The presented investigations show relevant issues influencing the noise behaviour of electrical machines.

Synchronous Reluctance (SynRel) motors are known to suffer from excessive torque ripples. The classical way to avoid this drawback of the motor is skewing the slots. This paper aims to provide an analytic estimation of the best skew angle to minimize the ripples in such SynRel motors with tooth windings. The approach used in this paper consists of the minimization of the spectral components of the magnetic energy that cause these oscillation torques. The method was validated by means of a multi-slice finite element model (FEM).

An analytic model, based on permeance theory, is derived to analyse the electromagnetic phenomena taking place inside of the motor. This model allows the identification of the causes underlying the torque ripple production. Based on this understanding, the most suitable skew angle can be determined. The analytic method, together with the best skew angle, is validated by means of an FEM of a SynRel machine.

A method to determine the optimum skew angle for a SynRel machine is presented. It depends on the wave-number of the magnetic waves producing the torque ripple. It is twice the one typically chosen for induction machines.

The proposed approach allows improving on the design methodology for the production of smoothly running SynRel machines.

The methodology utilized in this paper is based on the relationship between the mechanical torque and the magnetic energy stored in the motor (virtual work law). From this, the best skew angle to eliminate the magnetic energy causing torque ripple can be determined. It, therefore, proposes an effective alternative to the common use of inductance models to determine such angles.

The purpose of this paper is to define a time‐efficient numerical procedure for the extraction of load‐dependent equivalent circuit (EC) parameters of induction machines. The parameters are determined for every operating point, thus their variation due to skin effect and material saturation under arbitrary load condition is taken into consideration.

Two methods are presented and compared. The first one is based on the numerical simulation of the standard measurement process, yielding an EC with constant parameters. A time‐harmonic finite element analysis is applied in the second method to calculate the load‐dependent EC parameters. Material linearization and the superposition principle for the magnetic flux are employed to define the leakage inductances.

A distinct load dependence of all EC parameters has been proven as well as the clear disparity between stator and rotor leakage inductances. These effects can only be taken accurately into account by the EC obtained by the second numerical procedure proposed.

The presented method successfully overcomes typical problems of the measurement process and of the standard numerical procedure for EC parameter estimation, thus the obtained EC parameters are load‐dependent while the physical interpretation of the variables and parameters remains straightforward. Hence, the paper of the internal machine variables is enabled.

The purpose of this paper is to study the effects of inverter supply on the iron loss characteristics of slip-ring induction machines. Pulse width modulated (PWM) voltage supply on the stator side, as well as a doubly fed operation mode with rotor-sided inverter, are investigated.

An inverter fed machine model is coupled to previously developed eddy current and hysteresis loss models. The eddy current model is based on a finite element method and considers the three-dimensional (3D) eddy current distribution in the steel sheets. The hysteresis losses are computed by a static Preisach vector model.

It is found that under stator-sided inverter supply the eddy current losses do significantly increase when compared to sinusoidal feeding, contributing to a total loss increase of 10-15 percent. In doubly fed operation, the additional losses are generally lower owing to the winding topology of the studied machine.

The analyses presented are restricted to single PWM pattern only. The influences of different PWM parameters remain to be investigated in future.

Regarding practical applications, the reduced additional losses in doubly fed configurations can be considered as a further advantage when competing against other topologies available.

The 3D eddy current model is applied for the first time to quantify the effects of inverter supply. Furthermore, the presented studies on the iron losses in doubly fed operation are original and of practical value for designers and researches.

The purpose of this paper is to get a more consistent finite element description for three-dimensional (3D) Timoshenko beam elements. It extends the common description of beam elements by modifying the shape functions and considers the warping of the cross-section due to torsion.

The paper builds mainly on a finite element description of 3D Timoshenko beam elements. The implementation of high-order shape functions for torsion is done by adding a seventh degree of freedom to the system.

The results reveal that for some beams, depending on their physical dimensions, the warping of the cross-section has large influence. In comparison to a conventional FE program, the extended finite element description considers the warping and yields more accurate results.

An application of the extended finite element description is done with an implementation of the code in MATLAB. The static and dynamic behavior of a rotor in an electrical machine is investigated.

This paper presents a more consistent finite element description of 3D Timoshenko beam elements considering the warping. A comparison to conventional finite element descriptions is given.

The purpose of this paper is to develop an effective, yet simple analytical framework for optimization of permanent-magnet synchronous machines. Also, single/multi-objective optimizations are performed for a case-study machine with surface-mounted permanent magnets.

First, an accurate magnetic equivalent circuit is developed which takes all the material such as iron saturation and PM parameters into account. Then, through a Fourier analysis, it is combined with the d-q model of PM synchronous machines to achieve an optimization framework including the developed torque, back-EMF and a number of design considerations. Finally, a genetic algorithm (GA) is employed in the single/multi-objective design optimizations, which offers several design characteristics upon different desired outcomes.

An analytical design framework for the optimization of permanent-magnet synchronous machines is developed in this paper that can effectively account for all material properties such as iron saturation and PM characteristics, and take into account the design considerations, all of which are shown as superiorities of the proposed approach over the existing method. In addition, the proposed framework is relatively simpler in terms of implementing. The model is verified by employing finite element method. Moreover, sensitivity analysis is carried out to investigate the influence of the design parameters on the machine performance, which provides valuable information for the designer of such devices. Finally, a GA is utilized to perform single/multi-objective optimization schemes whose objectives are minimizing the torque ripples, back-EMF total harmonic distortion and PM volume.

The proposed framework is new approach that could be employed in the design optimization of PM synchronous machines. Contrary to existing method, it is simpler and more effective in taking the material properties such as iron saturation and PM characteristics into account.

The purpose of this paper is to compare different types of electric motor drives for high-efficiency applications: an induction motor (IM) drive, a synchronous reluctance motor drive and a permanent magnet-assisted synchronous reluctance motor drive. An innovative field-oriented analysis technique is applied to estimate the performance of the IM drive. This method of analysis is particularly advantageous in comparing the IM performance to those of synchronous machines.

The comparison among the capabilities of the three electric drives is carried out combining both analytical and finite element methods.

From the analysis, it results that the REL motor exhibits higher torque density than IM, but lower losses since there are no Joule losses in the rotor. On the contrary, the REL motor exhibits a very power factor, which corresponds to a high-volt-ampere ratings of the inverter that supplies the motor itself.

A new analysis technique is adopted to investigate and compare the energy efficiency performance of different machines.