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.
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.
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 . Modeling the seams, evaluating the constraint state of the iron core would also be necessary.
FIg. 1 Main stress distribution inside the iron core due to magnetostriction
Fig. 2 Magnetostrictive force distribution and sound pressure level distribution inside the iron core
As for the load current of the transformer, the ratio that the excitation current accounts for is an extremely small proportion and it can be assumed that the primary current and the secondary current flows pretty much in the reverse direction. For this reason, repulsion occurs in the primary and secondary winding (Fig.3). With each winding, the current between wires are the same phase so attraction occurs in the coil axis direction.
The vibration state of winding is determined in the natural mode of the Lorentz force and winding. The natural mode of the winding differs depending on the type of winding. The main mode of cylindrical shaped coils is the elliptical mode where the winding vibrates in the cylindrical side direction but the main mode of disc-shaped winding is the extension and contraction mode that vibrates in the coil axis direction .
This examples assumes cylindrical shaped coils, so the elliptical mode with the basic components of vibration occurs and outputs the predicted results (Fig.4).
Modeling winding in an analysis is not in wire units and is rather modeled in bulk; however, in truth, they contain insulation and press board materials. For this reason, to conduct an accurate analysis, it is necessary to conduct an evaluation of equivalent material characteristics but for this case, the analysis assumes copper material characteristics for the winding of the bulk state.
Fig. 3 Image of flux density distribution occurring in winding, and Lorentz force
FIg. 4 Lorentz force distribution and displacement distribution occurring in the winding
Tank Wall Vibration
As for vibration from the tank wall, generally, excitation vibration or winding vibration occurs through surrounding structures or insulating oil and it is assumed that the tank itself will not be the source. However, analysis results of stray loss suggest that the eddy current and leakage flux occurring in the tank wall causes significant electromagnetic force. In an actual tank wall, it is assumed that the entire tank wall will not vibrate as there are vibration prevention measures with the placements of H steel acting as reinforcements. However, excitation vibration and winding vibration can spread as in the figure above and will shake the tank wall. For this reason, considering vibration along the tank wall is important and it would be interesting to compare their contribution .
This example was an analysis of the electromagnetic force distribution, which was considered vibratory force occurring along the tank wall in the state where load current is flowing. The area of the tank wall is large in the narutal mode so when there are no reinforcements placed, vibration of low frequencies starting from less than 10Hz can be seen, and it can be predicted that it will be easily integrated into the fundamental wave mode of vibratory force (Fig.5). When the noise from the tank wall does not have a sound insulating board, it will be directly radiated to the outside and it is thought to have large effects. From sound pressure distribution, it can be seen that the maximum is greater than 90dB and that vibration prevention measures for the tank wall is important (Fig.6).
The vibration analysis of the tank wall is relatively easy as there are no inclusions such as insulating oil, compared to excitation vibration and winding vibration, which are difficult to model. In the future, in addition to conventional excitation vibration and winding vibration as vibratory sources, it may be important to evaluate vibration from the tank wall.
Fig. 5 Natural mode of the tank
Fig. 6 Excitation force distribution and sound pressure level distribution occurring in the tank