×
INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS

Log In

Come Join Us!

Are you an
Engineering professional?
Join Eng-Tips Forums!
  • Talk With Other Members
  • Be Notified Of Responses
    To Your Posts
  • Keyword Search
  • One-Click Access To Your
    Favorite Forums
  • Automated Signatures
    On Your Posts
  • Best Of All, It's Free!
  • Students Click Here

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

Students Click Here

Jobs

Induction Motor Design - Circulating Strand Currents

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

RE: Induction Motor Design - Circulating Strand Currents

Welcome to the site.

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

Correction:
"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

Correction/Clarification:
"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

(OP)
Thank you for the very quick reply and explanation!

Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

Reply To This Thread

Posting in the Eng-Tips forums is a member-only feature.

Click Here to join Eng-Tips and talk with other members!


Resources