Numerical analysis and vibro-acoustic improvement of a thin-walled power

transformer tank

Michael Ertl1, Hermann Landes2

1 Siemens PTD Transformers, 80641 Nuremberg, Germany, Email: michael.ertl@siemens.com2 WisSoft GmbH, 91054 Buckenhof, Germany, Email: h.landes@wissoft.de

Introduction

Oil-immersed power transformers tanks with characteris-tic dimensions in range of 3-13m made up of rib-stiffenedthin steel plates with a characteristic wall thicknessof 10mm. This cost-optimised tank design showsdisadvantageous vibro-acoustic properties. Mechanicalresonances of tank fields can regularly identified as amajor contributor of an increased noise emission abovethe expected design level (Fig. 1). The response of thisfluid-loaded structure is dominated by the resonancemodes if exposed to a periodic excitation [1, 2]. Anoise-reduced transformer design needs to eliminate thisvibro-acoustic flaws.

Figure 1: Bottom-up structured modelling of oil-immersedtransformer tanks (left). Resonant sound transmission withstrong lateral vibration of tank stiffener (right).

In power transformer manufacturing the production ofsingle-units or small series is dominant, having in com-mon solely the same tank design guidelines and stan-dardised substructures. This situation does not allow atime-consuming numerical or experimental investigationof each individual unit. Instead the need for a strategicapproach of an automated, fast modelling and analysisprocedure arises to improve varying tank designs to avoidresonant sound transmission.

Modelling and analysis environment

An efficient and accurate FEM-based analysis of thevibro-acoustical properties of thin-walled vessels requires

an optimised structured hexahedral mesh of high quality.Further, an accurate geometric model needs to includeall structural details which affects the overall dynamicresponse of the system (Fig. 2). To reach reasonablecomputational costs, the model size has to be minimisedas far as possible. These demands are contrary to theneed for a fast and robust analysis tool for daily use inthe design process.

Currently, no usable mesh generator is available to allowa hexahedral meshing of complex geometric structuresbased on imported CAD-data which meets the aboveprescribed requirements. The solution is a highlyautomated and parameterised bottom-up model gen-eration based on geometry data transfer via interfacesto existing construction tools. Therefore the MATLABenvironment is used to define and setup a virtual modelgeometry with a continuous structured mesh based on alldefined tank substructures (Fig. 1). This parameterisedand script based geometry setup gives the necessaryflexibility for automatised design parameter variations,which are the base for design improvement or optimi-sation algorithms. The continuous fluid-element meshwithin the oil-filled tank is generated simultaneouslywithout any further bottom-up modelling efforts for theanalysis of the fluid-structure interaction.

Using text files as interfaces, the geometric setup isused to generate and analyse the FEM-model within theANSYS-CAPA environment. This method gives full con-trol about the mesh structure. Thus, geometric shear-locking phenomena can be reduced by limiting the ra-tio of element side dimensions. After applying a har-monic frequency response analysis by distributed localforce excitation at the transformer tank, the calculatednodal displacements are transferred back to the MAT-LAB environment for a fast postprocessing of the level ofstructure-borne sound (SBS). The SBS-level can be de-rived from the surface normal vibration of the tank andis defined as

LSBS = 10 lgS v2

⊥S0 v2

0

. (1)

In (1), S denominate the total tank surface, v2⊥ the time-

and space- averaged mean-squared normal velocity of thetank surface and S0 v2

0 is an appropriate reference value.The SBS-level can be taken as a measure of the vibra-tional sensitivity of a structure when exposed to mechan-

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ical loads and further as an estimator of the total soundtransmission behaviour of the transformer tank [3, 4].

a

b

ab

Figure 2: Detailed hexahedral meshing of oil-filled trans-former tank (left). Parametric change of stiffener positionswithin the vibro-acoustic improvement routine (right).

Vibrational behaviour of fluid-loaded tank

The numerical frequency response analysis shows the typ-ical high mode density of thin-walled power transformertanks (Fig. 3). Comparing the frequency response of an”empty” tank structure with the one-sided fluid-loadedtank, the additional fluid mass loading strongly lowersthe natural frequencies. Hereby the structural modeshapes remain unchanged in most cases. If the princi-pal dimensions of the confined fluid volume meets thedimensions of standing waves within this cavity, coupledfluid and structural mode shapes can be observed.

Figure 3: Frequency response of an oil-filled and emptytransformer tank. The forbidden frequency bands surround-ing the excitation frequencies are highlighted.

Design improvement procedure

The parameterised model allows a fast change of anysubstructure within the iterative vibro-acoustic improve-

ment process. Using the number and position of stiffenersas the variation parameters, the optimisation parametersare the natural frequencies. The target is to shift thenatural frequencies of the oil-immersed tank outside the”forbidden” frequency bands. These frequency bandssurrounds the excitation frequencies of the transformerhumming noise (fundamental frequency of 100Hz andhigher harmonics) (Fig. 3). As an improved design isconsidered if the mean SBS-level LSBStot within all for-bidden frequency bands is distinctly reduced (3-4dB(A)).

Hereby the optimisation design space at the tank surfaceis restricted, e.g. regions for fittings are excluded.Further restriction are mainly based on assembly andcost considerations. Thus, only horizontal and verticalrow- and cross-stiffening can be applied. Because ofthis widely restrictions, no mathematical optimisationalgorithms are applied so far. Instead the results ofthe parameter variation process are used as a basefor the decision process of the engineer to evaluate anappropriate design for the final tank structure.

Typical processing times for a frequency response anal-ysis using 80 000 finite elements are < 1h for modellingand meshing, 3h for the frequency response analysis of50 frequencies and < 1h for post processing

Conclusions

Sound emission of power transformers is increased incase of resonant sound transmission of the thin-walledtransformer tank. The resonance frequencies of tanksfilled with a heavy fluid (mineral oil) are far from thein-vacuo frequencies. Thus, a vibro-acoustic optimisa-tion of this devices needs to consider the strong cou-pled fluid-structure system. The presented automatised,script-based modelling and analysis routine allows toavoid vibro-acoustic flaws in advance. The accuracy andcomputational costs are suitable for daily use to improvetransformer tank design.

References

[1] Filippi, P.; Habault, D.; Mattei, P.; Mairy, C.: Therole of the resonance modes in the response of a fluid-loaded structure. Journal of Sound and Vibration239(4) (2001) , 639-663

[2] Fahy, F.; Gardonio, P: Sound and Structural Vibra-tion. Academic Press, London, 2007

[3] Bos, J.: Numerical optimization of the thickness dis-tribution of three-dimensional structures with respectto their structural acoustic properties. Struct Multi-disc Optim 32 (2006), 12-30

[4] Kollmann, Schosser, Angert: Praktische Maschine-nakustik. Springer, Berlin, 2006

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