How much motor-power can be obtained from a stator core? 1

[zlatkodo]

I'm interested in whether there is a simple procedure to determine the motor- power from the stator core measures?
Let me explain.
Suppose we have the stator core of a motor without a nameplate.
Suppose we know the number of poles for which the motor is provided (this is a separate topic for another time).
We know that power depends on the measures of the stator core (or vice versa). The most important measures are the internal diameter, length of core, back-iron, the width of the teeth, etc.
Is there an easy way to determine the power (in continuous operation - S1) which the motor can give? Of course, for the known voltage and frequency.
In practice it is usually performed by comparison with a similar core from some database.
Zlatkodo

 

[electricpete]

I'm sure there are a number of ways to do it approximately. Probably someone can come up with a fairly simple approximate equation using a small number of variables.

There is another more brute force way. There is a book called "Computer Aided Design of Electrical Machines". You may be able to get your hands on a copy if you search the internet. He goes step by step through design and sizing process at each step providing Matlab code. At the end is the complete Matlab source code. You enter the rating of the motor, the speed, voltage, and some other parameters. And it comes up with a design including dimensions of cores, slot, conductor arrangement etc. I haven't cut/pasted from the book into Matlab yet, but I'm going to try it soon.

Also if you don't have Matlab, you can get a number of free clones including Scilab and Octave

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(2B)+(2B)' ?

 

[electricpete]

Another thing you can do is use the formula:
#2 - Tmotor = R· N ·I· L· Bgap· pf
where
N = number of conductors
L = length of each conductor in the slot section
I = rms value of the fundamental current in each conductor
Bslot is rms of the fundamental radial flux density in the slot section
Bgap is rms of the fundamental radial flux density in the airgap
p.f. is cosine of angle between B and I which represents a power factor
Tmotor = total motor torque (sum of conductor torque and iron torque)
This is based on section 12.1 here:

http://home.comcast.net/~electricpete1/torque_web/attach/TheLongVersion091207.pdf

And there is example application of the formula to an real motor in 12.4.1.

You don't know the winding configuration, so you can adapt it to replace N ·I with (A*rho) where A is the total slot area (adding up all the slots) and rho is the assumed current density in amps per area.

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(2B)+(2B)' ?

 

[edison123]

That would depend on the cooling of the motor and the slot size. For example, the capacity of turbo-generators is almost doubled when the cooling is changed from air to hydrogen.

Muthu

http://www.edison.co.in

 

[zlatkodo]

Thanks to both for answers.
Electricpete wrote:

you can adapt it to replace N ·I with (A*rho) where A is the total slot area (adding up all the slots) and rho is the assumed current density in amps per area.

I think there is a major problem: how to determine the value of current density (amps per area) for each motor. Generally speaking, it is the range of 3-8 amps per square millimeter. This range is too large for any serious calculation.
I know that the value of amps per area strongly depends on: the number of poles, type of ventilation (TENV, TEFC), motor frame etc.
Are there any data that determine the value of current density (in a smaller range) for each of these categories?
Here we are talking only about the low voltage motors with air ventilation.
Zlatkodo

 

[electricpete]

I agree it's not exact. The more exact you want to be, the more you need to sharpen your pencil.

I don't think poles is a very big factor since we are calculating torque, not power. The size of the core dictates the torque it can produce. We calculate power from torque only when we know the target speed or poles.

I agree cooling is among the biggest factors for consideration.

Per Table 8.3 of "The Handbook of Small Electric Motors" by Yeadon & Yeadon, conductors are typically designed for steady state current density in the range of 2-4 kA/inch^2 for enclosed type motors (TEFC, TEAO, TENV) and 6-8 kA/inch^2 for open constructions (ODP). That takes into account the cooling in a very rough appoximate way.

There are other books that address machine sizing in other ways.

Liwschitz Garik's Electrical Machines Volume 2 has a vert detailed writeup in one of his appendices. He uses specific tangential torque loading as key parameter and has many many empircal charts that show how these paramters vvary with machine size, voltage etc . But I wouldn't use the values listed because the books is from the 1940's. (By the way it is a pretty good book and I see it is available for about $30. In addition to this and the fractional slot stuff, he also has an outstanding discussion of space harmonics)

Another References is "Design of Rotating Electrical Machines". He looks at the product A * J where J is current density (A/m^2) the same as we have been discussing, and A is linear current density (A/m).... i.e. the current located in one slot divided by the circumferential length of one slot pitch. He says that this quantity is more steady accross a range of motor sizes than the current density. However the range is still pretty broad 10E10 to 35E10 A^2/M^3 for "air-cooled machines" which I assume means open.

Here is that link to the info discussed above:

http://books.google.com/books?id=_y...machines, the product AJ ranges from"&f=false

Starting with current density seems like an easy approach but not the only and maybe not the best. This morning I studied the book "Computer Aided Design of Electrical Machines". It seems like a cookbook way to transform the performance specifications of the motor (horsepower, speed, etc) into a design. The first step involves sizing the machine dimensions (including core inner diameter) based on an output coefficient, which is proportional to the ratio of torque per volume. More specifically output coefficient C0 = P / (D^2*L*N). where P is machine KVA, D^2 is diameter in meter, L is length in meter, N is speed in RPM.
They provide an empirical relationship:
Output Coefft(CO) = 11 x Kw x Bav x q x effx pfx 1E-3
KW is KW rating. Bav is average airgap flux density, q is average electrical loading in amps per meter of airgap circumference (very similar to the A parameter of Design of Rotating Eelectrical Machines)., eff and pf are efficiency and power factor. Empircal values of Bav, q, eff, pf are given in tables included in the attachment and it provides an example how these are used to calcualte the core inner diameter. As far as I can tell they don't say anything about the type of cooling (open or TEFC). Also even later in the design they calculate the temperature rise and it doesn't seem like they take the type of cooling into account there either. So, I have a small doubt about this reference already.... unless it's buried in the book somewhere that I can't find.


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(2B)+(2B)' ?

 

[electricpete]

Correction in bold:
[tab]Output Coefft(CO) = 11 x Kw x Bav x q x effx pfx 1E-3
[tab]KW is KW rating. Bav is average airgap flux density, q is average....
should have been...
[tab]Output Coefft(CO) = 11 x Kw x Bav x q x effx pfx 1E-3
[tab]Kw is Winding Factor. Bav is average airgap flux density, q is average....


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(2B)+(2B)' ?

 

[MotorStuff]

Electricpete:
I just finished reading the "motor mythbusters" paper, which you wrote. It is indeed a good paper. On a side note, somehow I thought that there was a direct relationship between the "D^2L" with the motor horsepower.
I was once told that to size a motor using an existing motor(Induction), assuming that you will use the same O.D, all you had to do is use the (D^2L)= H.P, to find the new length of the new motor.