generator air gap exitation 1

[chjura]

There are two different cases:
The first is when the rotor is radially shifted constantly. This gives an excitation force acting with twice the rotating frequency. However in reality the misalignment is so small, that this force can be neglected. (???)
The second case is more complicated. Due to the operating
deflection shape of the shaft you have a dynamic "eccentricity" which also leads to these forces. If this is developed behaving linear with the deflection it can be expressed as a negative stiffness and is a part of the system properties. Since the change of air gap in x-direction also causes a change of the air gap in y-direction, we probably also have cross coupled terms.

Unfortunately I do not know the formulas to model those two effects.

So the questions are:
How to model the influence of the generator air gap exitation?

Based on which parameters it could be decided that the effect of the air gap could or could not be neglected?

Thanks in advance.
Jura

 

[electricpete]

I think in the static eccentricity case you will expect to see vibration at a frequency of rotating speed times number of poles. (i.e. 2*FL). It is the same as 2*running speed only for a 2-pole machine.

The basic formulation for determing force.

Wm = Integral (0.5*B^2/mu0)dV
Wm = magnetic energy
B = field
mu0 = permeability
dV = integration over airgap volume.

F = -dWm/dx
I will provide more comments and links later

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[chjura]

So that means that I need to know how a magnetic field B change within airgap. When I know the generator data (rated power, terminal voltage, phase current, power factor, field current, field voltage, etc) can I estimate magnetic field within air gap.

Sorry for such basic questions, I am not electrical but mechanical engineer.

 

[electricpete]

You can calculate the airgap flux magnitude from the generator parameters. See:

thread237-82570

Roughly the flux also varies in space and time as sin(2*Pi*FL*t - p/2*theta) where FL is line frequency, p is number of poles, and theta is mechanical angle.

It is not an easy problem but has been extensively studied in many ways. I have a lot of links and also some great literature given to me by a very helpful colleague (thanks John). I'll work on getting those links this weekend.

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[electricpete]

It's probably better to skip my link on detailed calculation of flux from generator design. Instead just use typical values. I have an EPRI document which indicates the normal range of air gap flux for medium voltage induction motors is 36,000 - 50,000 lines per square inch. I believe sync generators will be at the upper end of this range around 50k lines per square inch.

(1 Gauss = 2.54^2 lines per square inch)



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[electricpete]

http://www.brazosport.edu/~pschimpf/forums/airgapforce/here_is_file.htm

At the above link I have placed a file where I solved for for an eccentric rotor the 2*Line-Frequency force and static/unidirectional force.

I solved for 2-pole and 4-pole motor. Dimensions assumed in there 10" radius an 10" length. Bmax=59000 lines per inch squared, eccentricity (offset as fraction of total airgap) assumed 0.33 (very high).

For 2-pole motor it shows the force varies from 15,000 Newtons to 55,000 Newtons over time. This is equivalent to a 35,000 static force plus 20,000 2*LF force.

For 4-pole motor it shows the force varies roughly 35,000 to 37,000. Approximately the same static force as 2-pole but much lower 2*LF force.

This method makes a lot of sense to me. I apologize the presentation may not be too clear. Particularly if you are not familiar with this math program (Maple). Feel free to ask questions if you're interested to try to understand what I have written there.

There are a lot of different twists on this theme published in articles. I will see if I can dig up those links.

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[electricpete]

I am pretty sure that the approach I outlined has a sound basis, within the idealized assumptions made.

At least two significant effects which have not been modeled:
1 - It assumes that the mmf (related to exciting current) remains sinusoidal and the only thing that changes flux is air-gap. However as flux changes, the induced stator emf changes and exciting curent changes. This effect is not large for windings with one path (circuit) per phase. This effect becomes much larger as the number of parallel circuits per phase increases. The excitation current shifts to try to keep the flux more sinusoidal. Final result is lower force. Reduction in force larger for larger number of circuits.
2 - In squirrel cage motors there is similar effect to #1 provided by the squirrel cage. The 'damping' action of the squirrel cage reduces the flux distortion and reduces the force. There ay be a similar effect for damper windings on a generator.

Also I am not positive whether I have made a math error in my unit conversions.

I will look for links. One thing that will be helpful is there are a number of empirical results published. That may end up more helpful than the math approach. If I get a chance I will double check my result against empirical.

For more help from others, I recommend that you re-post your message at the electric motor forum237

Motors and generators are very similar and the same people usually work on both.

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[electricpete]

Here are the promised links:

Article on 2*LF vibration focus mostly on mechanical response vs electromagnetic force:

http://scholar.lib.vt.edu/theses/available/etd-2421171249711311/

The work of Tenhunen in little pieces:

http://lib.hut.fi/Diss/2003/isbn9512266830/article1.pdf

http://lib.hut.fi/Diss/2003/isbn9512266830/article2.pdf

http://lib.hut.fi/Diss/2003/isbn9512266830/article3.pdf

http://lib.hut.fi/Diss/2003/isbn9512266830/article4.pdf

http://lib.hut.fi/Diss/2003/isbn9512266830/article5.pdf

http://lib.hut.fi/Diss/2003/isbn9512266830/article6.pdf

http://lib.hut.fi/Diss/2003/isbn9512266830/article7.pdf

http://lib.hut.fi/Diss/2003/isbn9512266830/article8.pdf

http://lib.hut.fi/Diss/2003/isbn9512266830/article9.pdf

The work of Tenhunen in one big piece:

Go to

http://www.hut.fi/Units/Electromechanics/Publications/pub2003.html

and scroll to bottom and download link labeled "Tenhunen, A.
Electromagnetic forces acting between the stator and eccentric cage rotor, Doctoral Thesis, Helsinki University of Technology, Laboratory of Electromechanics, Report 69,Espoo 2003, 40 p. Abstract, Download Thesis (pdf, 2544Kb) "


Texas A&M University articles
Go here

http://ee.tamu.edu/~empelab/publications.html

and download (free) the following articles:

8 - S. Nandi, R. Bharadwaj, H.A. Toliyat, A.G. Parlos, "Performance Analysis of a Three Phase Induction Motor under Incipient Mixed Eccentricity Condition," submitted to the IEEE Transactions on Energy Conversion.

18 - H.A. Toliyat, N. Al-Nuaim, "Simulation and Detection of Dynamic Air-Gap Eccentricity in Salient Pole Synchronous Machines," IEEE Transactions on the Industry Applications, Vol. 35, No. 1, Jan./Feb. 1999, pp. 86-93.

22 - N.A. Al-Nuaim, and H.A. Toliyat, "A Novel Method for Modeling Dynamic Air-Gap Eccentricity in Synchronous Machines Based on Modified Winding Function Theory," IEEE Transactions on Energy Conversion, Vol. 13, No. 2, June 1998, pp. 156-162.

Browse around on that TAMU site and you might be interested in some of the others as well. There are many similarities between induction motors and sync generators.

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[electricpete]

A previous thread on the subject: thread237-28482

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