Unbalanced magnetic pull

[odradek7]

Hello all.

I am studying the dynamic behaviour of a squirrel-cage rotor. I have some reports where its natural frequencies have been determined experimentally in a free suspended state (only the rotor, out of the motor). Trying to make a relation of this results with the ones that coud be expected with the rotor installed and running i know that bearing system would stiffen the shaft and increase the values of the natural frequencies. However, i have a doubt about other fact: unbalanced magnetic pull. From information i have gathered it is possible to assume it as NEGATIVE STIFFNESS SPRINGS (for FEM simulations, for example). ¿Would this fact lower the values of the natural frquencies in an unstiffen-like phenomenon?.

I would thank any kind of information about the calculation of the forces produced by the Unbalanced Magnetic Pull.

Thank you.

 

[electricpete]

Yes, the unbalanced magnetic would act to reduce the total effective stiffness of the rotor support and decrease the natural frequency.

Note that if we offset the rotor from the centerline there is a dc component of the force and a 2*LF component. I believe it is the dc component that would act to modify (reduce) the effective spring constant. The 2*LF component would need to be considered separately.

 

[odradek7]

Thank you for the informationbut, sorry, i don't understand what do you mean with dc and 2*LF components. In the only formula i have for calculating the radial force produced by the unbalance it depends on some geometrical parameters and coefficients, the square of the magnetic flux (constant for me) and the eccentricity. This way i obtain a linear stiffness law (linear spring).

 

[electricpete]

If you move the rotor off-center, there are two components acting on it:

#1 "dc" = force with no time variation

#2 "2*LF" = sinusoidal time varying force with frequency = twice line frequency.

A basic idea of these two components would come from assuming a fixed geometry displaced from the center.

F ~ B^2 ~ [Bmax*sin(2*Pi*f*t)]^2
~ Bmax^2*sin^2(2*Pi*f*t)
~ Bmax^2 * [0.5-0.5*cos(4*Pi*f*t)]

The 0.5 part is the dc part. The 0.5*cos(4*Pi*f*t) is the 2*LF part. Although the simple equation above suggests that these components have equal maximum magnitudes, they are not equal when the full problem is modeled.

 

[odradek7]

Thanks.

Any bibliographycal reference or standar for the calculation of this force??? Sorry but i don't use to deal with electrical problems...

 

[GregLocock]

Hmm, interesting. One problem you'll have is that the magnet is a non linear negative spring, the more it deflects the higher the rate. Therefore simple modal models will struggle with this, ie you'll need to do a non linear dynamic analysis.





Cheers

Greg Locock

 

[GregLocock]

Damn, hit reply too quick.

You may find that an energy method (Rayleigh Ritz) may give you a more tractable insight into the change in modal frequency, if you can write a good equation for PE.

Rayleigh Ritz is adequately described in William Thomson's vibration book.

Cheers

Greg Locock