Does Resonating an Inductor at Its Physical Frequency Improve Efficiency?

[dlbeeson]

1. 
   17:47 - dlbeeson:
   Is there any benefit of setting capacitance of an LC tank to resonate an inductor at its natural physical resonance frequency, like a tuning fork frequency? Like a brass pipe hanging on a string in a wind chime, the inductor must also have some physical resonating frequency, from vibration, like a wine glass. Does setting the electrical resonant frequency to that same physical resonant frequency accomplish anything? More efficiency? Sharper Q??

 

[zoki85]

If it does anything, it could just lower Q

 

[sophiecentaur]

The mechanical resonance (due to the spring stiffness and mass - excited by the varying magnetic field) would modulate the measured value of inductance by loading the basic EM property of the coil. You would have an equivalent lightly coupled tuned circuit connected to the Inductor. If the Inductance measurement were done over a range of frequencies around that resonant frequency you would get a small 'blip ' wiggle in the Inductance / frequency plot. A copper spring would have a pretty soggy resonance but a suitable alloy could have a high enough Q resonance to be detectable (sucking energy into the mechanical resonator) if you got things right. The spring would have to be self supporting, though. If it were wrapped around a former, the friction would spoil the effect.
I wouldn't mind betting it has been known to upset sensitive measurement of 'something' in the past and provided a headache for someone.

 

[NascentOxygen]

So with a current of frequency f_r, the solenoid would contract in length at a rate of 2f_r. If this were to result in the turns touching (assuming enameled wire), expect it to make an annoying buzz/squeal.

http://thumbnails112.imagebam.com/37333/0363e9373324851.jpg

 

[sophiecentaur]

Many mains transformers rattle and hum. The laminations make it even worse.

 

[NascentOxygen]

Many mains transformers rattle and hum. The laminations make it even worse.

I've always assumed it is lamination hum, in domestic appliances. It might be difficult to differentiate the two? Maybe 60Hz would indicate lamination hum, and 120Hz the winding?

 

[zoki85]

AFAIK, transformers noise(hum) peaks near 50 (60) Hz.

 

[sophiecentaur]

The rattles / clicks will surely be 100 (120)Hz and produce as many harmonics as the mechanical arrangement will allow. The basic Hum could well be at twice mains frequency because the magnetic shortening of the coils will peak at both - and + current peaks (second harmonic distortion).

 

[zoki85]

The rattles / clicks will surely be 100 (120)Hz and produce as many harmonics as the mechanical arrangement will allow. The basic Hum could well be at twice mains frequency because the magnetic shortening of the coils will peak at both - and + current peaks (second harmonic distortion).

That's right, one click "up" and one click "down" per cycle of the mains frequency (100/120 Hz as you say).
Interesting ly, 3rd harmonic (6th of the mains frequency) at 360 Hz is typically almost as strong as fundamental beat at 120 Hz:
http://tdworld.com/site-files/tdworld.com/files/uploads/2014/04/typical-frequency-spectrum-of-nose-produced-by-60Hz-power-transformer_20140407.png

 

[sophiecentaur]

That's right, one click "up" and one click "down" per cycle of the mains frequency (100/120 Hz as you say).
Interesting ly, 3rd harmonic (6th of the mains frequency) at 360 Hz is typically almost as strong as fundamental beat at 120 Hz:
http://tdworld.com/site-files/tdworld.com/files/uploads/2014/04/typical-frequency-spectrum-of-nose-produced-by-60Hz-power-transformer_20140407.png

Now that's surprising because I should have thought it was a symmetrical effect and the third (sorry, sixth) harmonic is only 3 or 4 dB down. Must be more complicated than I thought (naturally).
You are not showing 3 Phase Transformer results are you ??

 

[zoki85]

This is for a power transformer (I guess must be a 3 phase one). But I wouldn't expect much change in a single phase case. It is always "messy"

 

[jim hardy]

Odd harmonics in a sine-like wave arise from symmetric distortion about zero - for example flat tops and bottoms or peaky tops and bottoms...mirror image distortion.
Even harmonics are not mirror image, they'd give perhaps a flatter top peak and more sharply pointed bottom peak.

Transformer core is operated not far from knee of B-H curve.
http://ttradio.net/images/magcurrent.jpg
image from: http://ttradio.net/basic-concept-of-tube-amp-output-transformers/

So magnetizing current will have a peak around time of the voltage zero crossing , to push flux on around the curvature of approach to magnetization curve's knee.
It'll be mirror image distortion.
Here it is in color...

image courtesy http://www.ibiblio.org/kuphaldt/electricCircuits/AC/AC_9.html

Think about the physical force between laminations - will it not be greatest at flux peaks, when current peaks to push flux through that higher reluctance ?

So, with the driving function for mechanical movement, flux, being in proportion to absolute value of a sinewave having lots of third harmonic, I'm not surprised it has so much 6th (twice third).Great image , zoki !
Isn't a spectrum analyzer just tremendously great fun ?
Ever put one over an old CRT TV set? When i was a kid back in vacuum tube days i could hear the flyback transformer from outside the house.. now it's just tinnitus...
old jim

 

[sophiecentaur]

This is for a power transformer (I guess must be a 3 phase one). But I wouldn't expect much change in a single phase case. It is always "messy"

If you have three phases then you will have two clicks per phase, at current maxima, and the three pairs of clicks are out of phase with each other - giving six clicks per 20ms cycle.
Our ears are very easily deceived when listening to 'low' frequencies and the audible higher harmonics will probably dominate over the fundamental of 50Hz - particularly as the acoustic matching will be better for 300Hz (no sub-woofer structures around a power transformer, usually).

 

[jim hardy]

Myself i can't hear 60 hz, so i have always attributed power supply and transformer hums to 120 hz..

Nobody called me out yet on my mistake in post #12:

So, with the driving function for mechanical movement, flux, being in proportion to absolute value of a sinewave having lots of third harmonic, I'm not surprised it has so much 6th (twice third).

Flux is proportional to mmf but not linearly because we're approaching the knee and that's why current departs from cosine, sprouting those lumpy peaks.
When voltage is a sine sans harmonics , flux will be a cosine sans harmonics .

Magnetorestrictive force that causes the hum is attributed by hyperphysics to the magnetic field which i take to mean flux , so i may be all wet on that current-flux connection as the source of third harmonic.
http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/magstrict.html

You may have noticed the humming sound associated with a transformer or a fluorescent light ballast. For U.S. circuits, that hum will be at 120 Hz since the iron material associated with the transformer core responds mechanically to the magnetic field which is impressed upon it. The effect is called magnetostriction, and it is one of the magnetic properties which accompanies ferromagnetism. For 60 Hz applied magnetic fields in AC electrical devices such as transformers, the maximum length change happens twice per cycle, producing the familiar and sometimes annoying 120 Hz hum.

MMF is proportional to current,
and current has odd harmonics. as shown in two pictures in post 12.
but flux won't unless the applied voltage contains some. d/dt of sine and cosine have same shape.
here's a Wiki showing restriction is unidirectional which is why, as others pointed out , frequency gets doubled.
Observe they plot it vs mmf not flux - . grrrrrr .

http://upload.wikimedia.org/wikiped...trictive_hysteresis_loop_of_Mn-Zn_ferrite.pngThere is mention that magnetorestriction is not linear with flux, and that would be a source for audible harmonics as demonstrated by zoki's analyzer..

The magnetostriction-magnetization curve has initial slope zero in all the cases studied. When the attainable field was sufficient for magnetic saturation the magnetostriction reached a limiting value.

and figure 3 here shows restriction vs flux density
http://encyclopedia2.thefreedictionary.com/magnetostriction

that's pretty nonlinear.

still learning something every day.
and apologiesfor the mistake are hereby tendered ---

old jim

 

[zoki85]

If you have three phases then you will have two clicks per phase, at current maxima, and the three pairs of clicks are out of phase with each other - giving six clicks per 20ms cycle.
Our ears are very easily deceived when listening to 'low' frequencies and the audible higher harmonics will probably dominate over the fundamental of 50Hz - particularly as the acoustic matching will be better for 300Hz (no sub-woofer structures around a power transformer, usually).

Sound level pressure is a logaritmic measure of the rms sound pressure to a reference value. This means it is an objective state of measured things regardless of human perception of sound. For some 3 phase power transformer Lp spectrum is already posted. I don't know the details and procedure regarding these measurements. As concerns 6 beats per cycle remark, I would expect that to be expressed in transformer system with 3 separated magnetic cores/circuits, placed close enough. In that case Lp peak near 300(360) Hz should exhibit higher peak in spectrum than 100(120) Hz peak, shouldn't it? Obviously, this doesn't happen;power transformer cores are built differently. In various transformer designs the most expressed is the fundamental frequency (2xf_mains). However, I am not saying it is impossible to have transformer where higher harmonic peak will beat fundamental one! If mechanical parts of the transformer have their fundamental resonant frequency coinciding with the harmonic, then it is pretty possible (bad/unlucky design I guess). Power transformers are complicated electromechanical systems, and it is hard to predict details about their noise. For instance, compare spectrum graph in Fig.1. in http://www.wseas.us/e-library/conferences/2009/hangzhou/IMCAS/IMCAS37.pdfwith the previously posted. 2nd harmonic of the sound is clearly higher than 3rd. But 4th, 5th, and 6th harmonic of sound are almost at same level. Magnetostriction effect dynamics is the most responsible for sound generated, but it isn't the only thing. In very big, decently loaded power transformers cooling fans can make significant contribution to sound noise as well.