Coupled Magnetic Field and Vibration Analysis

for Power Transformer


1. Introduction

The vibration / noise caused by large power transformers were greatly reduced with the adoption of the step lap structure with regards to the iron core. However, with the revision of the JEC-2200 for transformers in November 2014 under the Japan Electrotechnical Committee (JEC) standards, standards for load current noise and its combined noise due to winding vibrations have been added. As a result, further noise reduction of transformers are becoming an important technological theme.


This essay will look at the current state and themes of prior evaluation regarding vibration / noise of large power transformers (transformers from here on) with numerical simulation using JMAG, and introduce case studies.

2. Vibration Phenomenon in Transformer Analysis

The vibration phenomenon that occurs from the transformer are roughly divided into two categories: excitation vibration or winding vibration. Excitation vibration is a vibration phenomenon that occurs with the vibratory force as the vibration source, caused by the magnetic flux that excites the iron core. It is said that magnetostrictive force inside the iron core and the magnetic attraction of the joint part contribute to vibratory force. As opposed to this, winding vibration is a vibration phenomenon that occurs when flux leakage from the winding works on the current inside the winding and produces Lorentz force, which becomes the vibration source. Transformers run with commercial frequency and vibratory force caused by electromagnetic phenomena requires the component of the second harmonics. Commercial frequencies seem like low compared to general electric products; however some large power transformers have iron cores with a few meters in size, and the eigenfrequency becomes equivalent to commercial frequencies. For this reason, since basic wave components of large vibratory force have effect on vibration phenomena, it is important to take vibration prevention countermeasures.

3. Necessity of Magnetic Field – Structural Coupling Analysis

In a vibration phenomena analysis, vibration analysis setting the iron and winding as the vibration source works fine but since the vibration source has distribution, a preciseestimate of distribution will be required for an accurate evaluation.


Excitation vibration occurs with magnetostriction vibration along with the magnetic flux flow inside the iron core and the electromagnetic attraction at the contact part of the yoke and leg as the vibration source. Anisotropic magnetic steel sheet is used for the iron core but anisotropy has large influence not only on the flow of magnetic flux but also on the distribution of magnetostrictive force and electromagnetic force. For this reason, an estimate of excitation force will require electromagnetic field analysis accountring for anisotropy. Lorentz force, which is the vibratory source of winding vibration is greatly influenced by the leakage flux from the winding; however, since leakage flux distribution is also largely influenced by the positioning of the clamp and shield, it is extermely difficult to predict distribution without using magnetic field analysis.


For this reason, it is inevitable to accurately evaluate the magnetostrictive force and Lorentz force as the vibratory source when estimating the distribution of the vibratory source of the transformer. A magnetic field / structure coupling analysis is necessary for a vibration / noise analysis.

4. Vibration Analysis of Large Transformers Using JMAG
Displayed below are results for analysis case studies such as excitation vibration, winding vibration, and vibration of the tank wall analyzed using the magnetic field-structural coupling analysis function. Themes that come up as we progress with the analysis will also be covered.  
5. Excitation Vibration

This example ran an analysis presuming the contribution from the magnetostrictive force as the excitation force of excitation vibration. Since the evaluation of excitation vibration is run with the same excitation condition as the non-load test, it is fine just releasing the secondary winding and adding rated voltage to the primary winding; however, the analysis was run with flowing current simulating the rated voltage. We set directional magnetic steel sheet for the magnetic properties and specified the point sequence of magnetic flux density – striction for magnetstriction properties in the rolling direction and transverse direction, respectively. As the boundary condition, the base of the iron core is assumed to be fixed on the stand. The main stress distribution inside the iron core is shown in Fig.1. It can be seen that due to magnetostrictive vibration along the flow of the main magnetic flux, stress is caused. In response, as for the magnetostrictive force distribution, there is comppressed stress occuring in the direction of the main magnetic flux and the vertical direction (Fig.2). As a result of the iron core extending in the main magnetic flux direction due to magnetostrictive force, compression corresponding to Poisson\’s ratio occurs in the vertical direction of the main magnetic flux and becomes magnetostrictive force. There is also a tendency where magnetostrictive force concentrates along the seams of the joint part. Directional magnetic steel has anisotropy where striction in the main magnetic flux direction gets smaller but the continuity of magnetic flux in the joint part causes magnetic flux in the diagonal direction, increasing magnetostriction, and the magnetostrictive force concentrates along the seams. As for vibration, the main magnetic flux extends and contracts along the iron core, and depending on the current conditions of three-phase AC, it may occur along the upper diagonal direction of both left and right of the iron core. Shows the result of radiated sound pressure distribution with magnetostrictive force as the vibratory force (Fig.2). It can be confirmed that sound pressure distribution relative to the vibration direction of the iron core is obtained.

In this analysis, the iron core is handled as a bulk-shaped model but to run an accurate analysis, the evaluation and the setting of equivalent Young’s modulus and the Poisson ratio is necessary[1]. Modeling the seams, evaluating the constraint state of the iron core would also be necessary.

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