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The purpose of this paper is to present a method for analyzing higher magnetic force harmonics in electrical machines based on electromagnetic finite element simulation.

Sampling of air gap field solution data allows for a Fourier decomposition of magnetic forces and flux densities. A two‐dimensional convolution gives insight into the spectral decomposition of forces responsible for acoustic noise, vibration and higher torque harmonics.

The proposed approach seems especially suitable for synchronous machine models. The influence of magnetic circuit design parameters that are difficult to calculate analytically on the harmonic air gap content can be analyzed and the spectral force decomposition illustrated by means of space vectors.

The approach is generalized to the convolution and analysis of arbitrarily sampled two‐dimensional data in this paper.

Nowadays, the determination of the acoustic radiation of electric machines is of particular interest, because legal regulations restrict the maximum audible noise radiated by technical devices such as electrical machinery. The purpose of this paper is to analyze the electromagnetic excited structure‐borne sound and air‐borne noise of an AC servo drive.

This paper presents the required steps for the multiphysics acoustic simulation of electrical machines to evaluate its noise behaviour. This numerical approach starts with the electromagnetic force‐wave simulation. The computation by a structure dynamic model determines the deformation of the mechanical structure due to the force‐waves. The final step of the simulation approach consists of the computation of the acoustic radiation.

For the electromagnetic simulation analytical and numerical methods are combined to gain some acceleration of the entire multiphysics simulation approach. This combination offers additionally a detailed understanding of the noise generation mechanism in electrical machines.

Particular attention is paid to the structural‐dynamic model. Modelling of microstructures, such as the laminated iron core or insulated coils, is memory and computational expensive. A systematic material homogenisation technique, based on experimental‐ and numerical modal analyses, yields a higher accuracy at lower computational costs when compared to standard numerical approaches. The presented multiphysics simulation is validated by measurements. The methods are presented by means of a case study.

The electromagnetic excited audible noise of electrical machines can be mostly attributed to radial forces on stator tooth‐heads. The methodology proposed in this paper uses numerical field simulation to obtain the magnetic air gap field of electrical machines and an analytical‐based post‐processing approach to reveal the relationship between air gap field harmonics and the resulting force wave.

The simulated air gap field is sampled in space and time and a two‐dimensional Fourier transform is performed. The convolution of the Fourier transformed air gap field by itself represents a multiplication in space time domain. During the convolution process, all relevant combinations of field waves are stored and displayed using space vectors.

The effectiveness of the proposed approach is shown on an example machine. Particular examples of individual force waves demonstrate how the approach can be used for practical application in analysis of noise and vibration problems in electrical machines. The proposed method is compared to the result of a Maxwell stress tensor calculation. It shows that the deviation is small enough to justify the approach for analysis purposes.

The combination of analytically understood force waves and the use of numerical simulation by means of air gap field convolution has not been proposed before.

Disturbing vibrations and noise of electrical machines are gaining impact. The paper aims to focus on the necessity of estimating the electromagnetic, structure‐dynamical, and acoustic behaviour of the machine during designing and before proto‐typing.

An adequate tool is numerical simulation applying the finite‐element method (FEM) and the boundary‐element method (BEM) allowing for the structured analysis and evaluation of audible noise also caused by manufacturing tolerances.

The simulated results show good accordance to measurement results. The methods and simulation tools allow the analysis and evaluation of every type of energy converter with respect to its electromagnetic, structure‐dynamical and acoustic behaviour.

The methods developed and proved can be applied to any electromagnetic device in general.

It is essential to understand the structural dynamic behavior of electrical machines to predict their acoustic and vibrational behavior. Stacking technology, which is used to manufacture soft magnetic cores, has a strong influence on the material properties. The purpose of this paper is therefore to research the influence of the stacking technologies welding and bonding with bake varnish on the modal properties of iron cores.

A finite element simulation model is developed based on homogenization of the stator core. Eigenfrequencies, modeshapes and modal damping ratios are extracted from measurements and are used to validate the simulation model.

Modal characteristics depend on the participation of certain material layers at a certain mode. Higher amount of shear deformation results in higher modal damping. Bonded stacks exhibit lower shear stiffness and higher damping ratios.

This research paper provides insights to the modal characteristics of iron cores used in electric machine and compares the influence of stacking technologies.

The purpose of this paper is to present an experimental setup for the verification of coupled electromagnetic field‐circuit simulation, called TESTCASE. By means of simple and well‐defined geometries, the comparison of different coupling approaches among each other and with measurements should be possible.

The physical setup consists of a C‐core in conjunction with a reluctance rotor. The TESTCASE is designed to work in static operation and with motion induced voltage.

Simulation results using different approaches as well as measurement results are presented. Practical issues in measurement and simulation are discussed. It was found that particular care has to be taken concerning the modeling of the air around the TESTCASE structure.

With the proposed approach, it is possible to evaluate the coupled field circuit problem on a defined and well‐known geometry. Simulation results can be compared to measurements.

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.

The purpose of this paper is to propose a multi-objective particle swarm optimization (MOPSO) algorithm based design optimization of Brushless DC (BLDC) motor with a view to mitigate cogging torque and enhance the efficiency.

The suitability of MOPSO algorithm is tested on a 120 W BLDC motor considering magnet axial length, stator slot opening and air gap length as the design variables. It avails the use of MagNet 7.5.1, a Finite Element Analysis tool, to account for the geometry and the non-linearity of material for assuaging an improved design framework and operates through the boundaries of generalized regression neural network (GRNN) to advocate the optimum design. The results of MOPSO are compared with Multi-Objective Genetic Algorithm and Non-dominated Sorting Genetic Algorithm-II based formulations for claiming its place in real world applications.

A MOPSO design optimization procedure has been enlivened to escalate the performance of the BLDC motor. The optimality in design has been out reached through minimizing the cogging torque, maximizing the average torque and reducing the total losses to claim an increase in the efficiency. The results have been fortified in well-distributed Pareto-optimal planes to arrive at trade-off solutions between different objectives.

The rhetoric theory of multi objective formulations has been reinforced to provide a decisive solution with regard to the choice of the design obtained from Pareto-optimal planes.

The incorporation of a larger number of design variables together with an orientation to thermal and vibration analysis will still go a long way in bringing on board new dimensions to the fold of optimality in the design of BLDC motors.

The proposal offers a new perspective to the design of BLDC motor in the sense it be-hives the facility of a swarm based approach to optimize the parameters in order that it serves to improve its performance. The results of a 120 W motor in terms of lowering the losses, minimizing the cogging torque and maximizing the average torque emphasize the benefits of the GRNN based multi-objective formulation and establish its viability for use in practical applications.

The purpose of this paper is to calculate the electromagnetic torque at a radius of an integration contour for which an optimal value is determined.

To analyze electrical machine dynamics, the electromagnetic torque should be precisely determined. This paper presents a method for calculating the torque, where the radius of the integration contour is variable and estimated from the field distribution.

The electromagnetic torque of the three‐phase AC motor model proposed in TEAM Problem No. 30 is estimated using the proposed method. The obtained results are compared to solutions obtained analytically.

This paper examines the application of the presented method to determine the electromagnetic torque in three‐phase AC motors.

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.