Vibration of transformer sheets using non-linear characteristics

Intensive research has been carried out over the years to reduce acoustic noise resulting from the vibration of transformer plates. The noise of transformer sheets excited by electromagnetic field can be mostly attributed to induced forces between the plates. The vibration generated from transformer structures causes abnormal vibration, breakage of the machine, and noise. Vibration measurement and analysis of the structure is important to prevent this phenomenon. This chapter presents the research resulted by measurement and Finite Element Method of the resonance of the transformer sheets. The goal of this research is to introduce the coupling of the developed nonlinear hysteresis model and the Finite Element Method. The COMSOL and MATLAB based finite element simulation method combines the electromagnetic, structural mechanics and acoustic models. The moving mesh (ALE) geometry of the transformer sheets leads on a valid model and assures the calculations of the electromagnetic properties in different deformed shapes. The measurement of the natural frequencies of the plates yields the relation between the excitation frequency and the resonance of the system. The goals of the developed model are: to derive the magnetic field intensity H and with hysteresis nonlinearity the magnetic flux density B properties inside the transformer sheets with d = 0.35 mm and l = 150 mm; to compute the induced current density J(i) inside the plates; to calculate the Lorentz force F distribution along the sheets; to derive the plane stresses the horizontal and vertical displacements along the sheets are calculated; applying the ALE moving mesh the deformation of plates can be simulated. For modelling the nonlinear characteristic of the magnetic material M = H{H} a novel developed hysteresis model is used. The advantages of the hysteresis model are its easy identification, past memory representation and numerical simplicity [1]. So, the hysteresis characteristic can be determined as B = H H, partial derivative B/partial derivative H,psi(i)(H(i), B(i)).