Induction Motor Design - Circulating Strand Currents
Induction Motor Design - Circulating Strand Currents
(OP)
Hello!
I have just signed up as this looks like a good place to hopefully get some help. This is a rather specific design question - I'll understand if no one is able to easily help.
My question comes from the book: "Polyphase Induction Motors - Analysis, Design, and Application" by Paul Cochran
In section 9.4 circulating currents in the strands are calculated. Prior to this section eddy current loss densities are calculated. The circulating currents are then shown to be a certain percentage of the eddy current losses depending on turns per coil and stranding configuration.
Two cases are examined based on two turns per coil:
- 2 vertical strands
- 3 vertical strands
They go through the derivation for the 2 strand case and end up with a constant of 3/16 or 0.188 in front of the expressions. They then say that if the same derivation is taken for the 3 strand case that the multiplier becomes 0.5. I don't see how this is accomplished. If I follow their calculations I end up with the same numbers in both cases. I would like to be able to calculate this coefficient for other TPC and strandings.
I may be missing something very simple or maybe there is a mistake somewhere?
I've attached pages 204 through 209. The top of page 205 has the expression for eddy current loss density in the top strand "Dts", then section 9.4 follows for circulating strand currents. The value of Bav comes out to Bm/4 in both cases I believe. K2 is the value I'm confused about in equation 9.48 on page 209.
I'm hoping someone will have some idea of what I am talking about and be able to help me figure this out as it is driving me crazy!
Sorry if this is way too long winded and stupid...
Thanks,
Michael
I have just signed up as this looks like a good place to hopefully get some help. This is a rather specific design question - I'll understand if no one is able to easily help.
My question comes from the book: "Polyphase Induction Motors - Analysis, Design, and Application" by Paul Cochran
In section 9.4 circulating currents in the strands are calculated. Prior to this section eddy current loss densities are calculated. The circulating currents are then shown to be a certain percentage of the eddy current losses depending on turns per coil and stranding configuration.
Two cases are examined based on two turns per coil:
- 2 vertical strands
- 3 vertical strands
They go through the derivation for the 2 strand case and end up with a constant of 3/16 or 0.188 in front of the expressions. They then say that if the same derivation is taken for the 3 strand case that the multiplier becomes 0.5. I don't see how this is accomplished. If I follow their calculations I end up with the same numbers in both cases. I would like to be able to calculate this coefficient for other TPC and strandings.
I may be missing something very simple or maybe there is a mistake somewhere?
I've attached pages 204 through 209. The top of page 205 has the expression for eddy current loss density in the top strand "Dts", then section 9.4 follows for circulating strand currents. The value of Bav comes out to Bm/4 in both cases I believe. K2 is the value I'm confused about in equation 9.48 on page 209.
I'm hoping someone will have some idea of what I am talking about and be able to help me figure this out as it is driving me crazy!
Sorry if this is way too long winded and stupid...
Thanks,
Michael





RE: Induction Motor Design - Circulating Strand Currents
Going from 2-turns/2strands to 2-turns/3-strands, the factor increase from 3/16 to ½.
That is a change of [1/2] / [3/16] = 8/3.
We can explain that 8/3 change as follows
Bav does not change. Look at figure 9.13.. both upper and lower coil are both symmetrical about B/4. Bav remains B/4.
First look at 2 parallel strands shorted at both ends
1---------------
V0~ t
2---------------
They are separated by distance t and the voltage induced in each is proportional to t^2.
Now look at 3 parallel strands shorted at both ends
1---------------
V0~ t
2---------------
V0~ t
3---------------
They are again separated by distance t and the voltage induced in each is proportional to t^2. But draw a CCW loop between each pair of lines. I think you see there is no flow in strand #2!
So we can redraw it without the strand in the middle as follows:
1---------------
V~ (2t)~ 2*V0
3---------------
Compare this final simplified 3-strand system to the original 2-strand system. It has twice the voltage, but same resistance. So P ~ V^2/R is a factor of 4 higher.
Now express that P on a per strand basis. We have 4 times the losses P distributed among 3/2 of the strands. The loss per strand is 4/[3/2] = 8/3.
Q.E.D.
But... they didn't consider flux from the other coil in the slot. That can make life more complicated.
=====================================
Eng-tips forums: The best place on the web for engineering discussions.
RE: Induction Motor Design - Circulating Strand Currents
"the voltage induced in each is proportional to t^2"
should've been
"the voltage induced in each is proportional to t"
=====================================
Eng-tips forums: The best place on the web for engineering discussions.
RE: Induction Motor Design - Circulating Strand Currents
"the voltage induced in each is proportional to t^2"
should've been
"the voltage induced in each loop is proportional to t"
=====================================
Eng-tips forums: The best place on the web for engineering discussions.
RE: Induction Motor Design - Circulating Strand Currents