Hassan Ebrahimi

Effects of Stress and Magnetostriction on Loss and Vibration Characteristics of Motor

A method of 3-D finite element magnetomechanical analysis is developed to investigate the effect of magnetostriction (MS) and stress on the core loss and vibration of motors. Shrink-fit stress calculation is carried out using static structural analysis and equivalent thermal force calculated by a novel method using the thermal stress tensor. A method of core loss calculation is proposed to take account of the 3-D stress in the core loss calculation. The methods are applied to the core loss and the vibration analysis of a permanent magnet motor. Numerical results show that the stator core loss increases significantly due to the shrink-fit stress. However, the radial velocity of the housing surface slightly decreases due to the MS and further decreases due to the shrink-fit stress because the MS increases under compressive stress.

Coupled Magneto-Mechanical Analysis Considering Permeability Variation by Stress Due to Both Magnetostriction and Electromagnetism

A general model for the coupled analysis of magneto-mechanical systems is developed by minimizing the continuum energy functional of the system using the calculus of variation. This approach, which is in contrast with the traditional approach of minimizing after discretization, allows the use of strain and stress tensors, vector identities and the divergence theorem, and results in coupled governing equations of the system with three coupling terms; the magnetic stress tensor, the magnetostriction stress tensor, and the magnetostriction reluctivity. The model uses the information contained in the set of experimental magnetostriction curves dependent on stress to calculate the permeability variation due to stress. The governing equations are then discretized using the Galerkin method resulting in methods for the calculation of nodal magnetic and magnetostriction forces including the coupling effects. Finally the model is applied to a simple 2D problem and the flux density distributions using the proposed method and the traditional method of using experimental magnetization curves are compared.

Coupled Magneto-Mechanical Analysis in Isotropic Materials Under Multiaxial Stress

In this paper, a model for the coupled analysis of magneto-mechanical problems with isotropic materials is proposed in which the effect of stress in transverse direction with respect to the flux density is also considered. To take into account the Villari effect in this case, magnetization data under zero stress and magnetostriction (MS) data under various levels of stress are required. The model uses stress-free magnetization curve and a set of MS curves together with the stress tensor to calculate the permeability variation due to the stress, including the stress-induced anisotropy. Unlike available methods in which an equivalent scalar stress is defined and used for the evaluation of permeability, the proposed method uses the full stress tensor. The model is then applied to a simple 2-D problem and the flux distribution in three cases of uncoupled, coupled without, and coupled with considering the transverse stress are compared.

Comparison of Time Integration Methods in Magnetomechanical Problems

This paper makes a survey of several popular time integration methods, including the backward Euler, central difference, Crank-Nicolson, Newmark, weighted residual finite element, and time-discontinuous Galerkin methods, and comparisons are made by applying some of the methods to the vibration analysis of a stator-housing structure as well as to the transient response analysis of an electromagnet. The comparison of vibration analysis shows that with an acceptably small step-size, the Newmark method gives result as accurate as the Euler method does, with half the cost. In the transient analysis of the electromagnet, however, it was observed that applying the Euler method to the magnetic equation performs much better compared with the Crank-Nicolson method even though the theoretical accuracy of the latter is higher.

New Type of Second-Order Tetrahedral Edge Elements by Reducing Edge Variables for Quasi-Static Field Analysis

Second-order tetrahedral edge elements afford much better accuracy in magnetic field analysis compared with first-order elements. However, they often entail higher computational cost due to the higher number of unknowns, many of them being redundant. The partial tree-gauging approach eliminates only a portion of the redundant edge variables, often reducing the overall computational cost. In this paper, we propose a new partial tree-gauging approach in second-order tetrahedral edge elements by unifying the two edges on the sides of elements into one, resulting in a new type of second-order tetrahedral edge element. Using the proposed elements in the analysis of two linear quasi-static magnetic field problems reveal the superiority of the edge unification over the conventional partial tree gauging in term of computational load.

Fast Nonlinear Magnetic Field Analysis of Inverter-Driven Machines by Applying POD on Linearized Coefficient Matrices

This paper proposes a model order reduction (MOR) technique based on the proper orthogonal decomposition method, to speed up nonlinear magnetostatic analysis of inverter-driven electrical machines. In this method, a set of solutions of the original problem is obtained at relatively large intervals, covering the whole cycle. The solutions, known as snapshots, are then used for the linearization as well as the order reduction of the matrices at the intervals. The reduced linearized matrices are then interpolated for time instance within the strides, supplemented with initial guess obtained by interpolating the snapshots. The method enormously reduces the number of matrix projections. Furthermore, it limits the number of the Newton–Raphson iteration to one. The results of applying the method on the magnetostatic analysis of interior permanent magnet motor shows that the method is several time faster than the conventional MOR with almost the same accuracy.

Fast non-linear magnetic field analysis of inverter-driven machines by applying POD on linearized coefficient matrices

A novel model order reduction (MOR) technique based on the proper orthogonal decomposition (POD) is proposed to speed up nonlinear magnetic field analysis in inverter-driven electrical machines where the electrical current contains high frequency harmonics of small amplitude. In this method, a set of static solutions of the original problem, referred to as snapshots, are obtained in one cycle at relatively large intervals. The snapshots are then used for both linearization and order reduction of the matrices. The solution variation around the snapshots at any time instance within intervals is then calculated by interpolating and solving the reduced system at the given time. The results of applying the method on the magneto-static analysis of interior permanent magnet (IPM) motor shows an order-of-magnitude speed gain with a high accuracy.