Magneto-elastic resonance



Magneto-elastic resonance , magneto-mechanical resonance or magnetostrictive resonance - a resonance of a given structure magnetised at a frequency close to the frequency of its mechanical resonance.

Mechanical structures resonate mechanical sense - that is they can amplify certain frequency of mechanical vibrations. Such mechanical resonance frequency is dictated by the shape, size, mechanical inertia and stiffness of a given structure.

Magnetic materials usually exhibit some level of magnetostriction, which causes mechanical vibrations. If the mechanical vibrations caused by the process of magnetisation have a frequency close to the mechanical resonance then the magneto-elastic resonance can occur.

Practical significance
Such conditions lead to increased power loss and for brittle materials (like for instance ferrites) can cause cracks or even destruction of the core.

Power transformers generate acoustic noise due, mostly due to magnetostriction or electrical steel. They must be designed in such a way, as to avoid the magnetoelastic resonance, which would lead to exacerbated level of acoustic noise.

Calculations
The frequency f of fundamental extensional mode of vibration of toroidal cores is given as:

$$f = \frac{1}{2 \cdot \pi \cdot r} \cdot \sqrt{\frac{E}{\rho}}$$

where: r - average radius of a ring core (m), E - Young's modulus of the core material (N/m), &rho; - specific density of the material (kg/m).

For ferrite cores Ferroxcube gives the following equation. The result of the calculation is in kHz:

$$f = \frac{5700}{\pi \cdot \left( \frac{OD + ID}{2} \right)}$$

where: OD - outer diameter of the toroidal core (mm), ID - inner diameter (mm).