Koen Delaere

Comparison of induction machine stator vibration spectra induced by reluctance forces and magnetostriction

For rotating electric machines, the reluctance forces (Maxwell stresses) acting on the stator teeth are a major cause of noise emission. Next to the reluctance forces, magnetostriction is a potential cause of additional noise from electric machines. First, a thermal stress analogy is used to introduce magnetostriction in the finite-element framework. Next, we present the computation and comparison of the stator vibration spectra caused by these two effects separately, by example of a 45 kW induction machine. Moreover, two kinds of magnetostriction characteristics of the stator yoke material are compared: a quadratic /spl lambda/(B) curve and a /spl lambda/(B) curve with zero-crossing around 1.5 Tesla.

Local magnetostriction forces for finite element analysis

The magnetic materials deformation caused by magnetostriction is represented by an equivalent set of mechanical forces, giving the same deformation to the material as magnetostriction does. This is done in a way similar to how thermal stresses are usually incorporated. The resulting magnetostriction force distribution is summed to other force distributions (external mechanical forces, magnetic forces) before starting the mechanical deformation or vibration analysis. This procedure is incorporated into a weakly coupled cascade solving of the magnetomechanical problem.

Influence of rotor slot wedges on stator currents and stator vibration spectrum of induction machines: a transient finite-element analysis

The stator currents and stator vibration spectrum of a 45-kW four-pole induction machine is computed using a transient two-dimensional finite-element analysis. The analysis is performed for two different rotor geometries: with open and with closed rotor slots. Open rotor slots increase the harmonic content of the air gap field and also the harmonic content of the stator currents. Open rotor slots thus increase the stator vibration level for frequencies higher than 1 kHz.

Finite element based expressions for Lorentz, reluctance and magnetostriction forces

The magnetic and mechanical finite element systems are combined into one magnetomechanical system. Investigating the coupling terms results in a finite element expression for the magnetic forces (Lorentz force and reluctance force) for both the linear and nonlinear case. The material deformation caused by magnetostriction is represented by an equivalent set of mechanical forces, giving the same strain to the material as magnetostriction does. The resulting magnetostriction force distribution is superposed onto other force distributions (external mechanical forces, magnetic forces) before starting the mechanical deformation or vibration analysis. This procedure is incorporated into a weakly‐coupled cascade solving of the magnetomechanical problem.

Statistical energy analysis of acoustic noise and vibration for electric motors: transmission from air gap field to motor frame

A large number of vibration measurements are performed on the stator of a standard 5.2 kW electric motor. The rotor and the end-caps are removed. First, vibration measurements are performed on the stator without coils, i.e. consisting of the stator yoke (ferromagnetic iron) and the motor frame (cast iron) only. Second, vibration measurements are carried out on an identical stator with a standard coil system in the stator slots. Subsequently, a statistical energy analysis (SEA) is performed using these experimental data, in order to quantify the internal losses in the stator yoke and in the coils. The SEA also allows us to quantify the transmission of vibrations from stator yoke to motor frame (coupling loss factors), and to consider the influence of the presence of the coil system.

Weak coupling of magnetic and vibrational analysis using local forces

A weak coupling between magnetostatic and elasticity equations is derived from energy considerations for electric machines. The coupling term results directly into a finite element expression for the nodal electromagnetic forces, which can be used as source terms for an elasticity or vibration analysis. The relative contribution of the stators modal shapes in the deformation excited by this force distribution is calculated. As an example, the coupling is used to analyse the vibrational behaviour of a 6/4 switched reluctance machine.

Strong coupling of magnetic and mechanical finite element analysis

A strong coupling between the magnetic and the mechanical finite element model is presented. The two coupling terms represent magnetic forces and magnetostriction, respectively. The coupled system is solved using a fixed point iteration (successive substitution) with relaxation. The influence of physical parameters (low or high magnetostriction) and numerical parameters (scaling factors) on the convergence is investigated.

Highly accurate 3D field gradient computation using local post-solving

To enhance the accuracy of finite element based computations of field quantities and their derivatives, a post-solving technique with superconvergent properties is presented. This technique uses an analytical expression for the magnetic field potential inside a closed region. The coefficients of the analytical expression are evaluated using a FE solution as boundary condition. All second derivatives of the analytical expression are calculated, leading to values for the flux density B and its derivatives. These values are highly accurate, even when based upon a FE solution. As an example, the (edge) write gradient in a notch write head is evaluated.