Motor equivalent diagram data

[PrebenJakobsen]

I have an asynchronous motor where the manufacturer has given two sets of data for the equivalent diagram:
* R1/X1 and Rm/Xm which are almost identical at locked rotor and at full speed.
* R2/X2 which are very different at locked rotor and at full speed.

In my calculation program i can only type one value for R1/X1, Rm/Xm and R2/X2 but then i can type Cage Factors Kr/Kx to include the effect of varying R2/X2.

How do I calculate Kr/Kx from the two set of data?

Best Regards
Preben Jakobsen

 

[7anoter4]

KR=Rotor AC Resistance/Rotor DC resistance
KX=Rotor AC Slot Leakage Reactance/Rotor DC Slot Leakage Reactance
Rotor DC Leakage Reactance it is a virtual value-not an actual one.
The resistance of rotor cage depends on a lot of factors as slot shape and size, conductor temperature, conductor material, rotor current frequency and other. The skin effect depending on rotor slip will be high at start and negligible at run.
You could take the rated load rotor resistance as d.c. resistance and the ratio KR(start)=Rstart/Rrated
The problem remains how you could appreciate the KR(slip) and KX(slip) for any slip from 1 to almost 0. If the rotor bar is round and small diameter KR=1
R(slip)=(Rstart-Rrated)*slip+Rrated; slip=1 R(1)=Rstart; slip=0 R(0)=Rrated.
If Xrstart=Xrrated then KX=1.
If the rotor slot depth is more than 25 mm[1 inch] then the skin effect is pronounced.
KR=(A+B*slip^2)/(C+D*slip^2)
The rotor leakage reactance relation:
Xrl=2*pi()*miuo*f1*Length*(Lsl*KX+Ldr+Ler) where:
Lsl= slot leakage coefficients[as inductance factor] ; Ldr= Rotor differential leakage coefficients ; Ler=Rotor end leakage coefficients; miuo=vacuum[or air] permeability [4*pi()/10^7 H/m]; f1=first harmonic current frequency.
KX it is a slot leakage reactance factor -not for entire rotor leakage reactance.
From the above formulae one could extract:
KX=(Xrl/2/pi()/miuo/f1/length-Ldr-Ler)/Lsl or : KX=Xrl*A+B
KX depends also on the shape and size of the rotor slot and the rotor current frequency.
Rotor current frequency=f1*slip.
As you could see it would be very difficult to calculate KR and KX for any slip[ at start].
Typical KR=1 to 5 and KX= 0.2 to 1.
See[for instance]:
"Calculation of the bar resistance and leakage reactance of cage rotors with closed slots"

http://md1.csa.com/partners/viewrec...ecid=8525995AN&q=&uid=789458222&setcookie=yes

or:
"Traditional Design of Cage Rotor Induction Motors"

http://ceme.ece.illinois.edu/seminars/CEME1109HarleyGeorgiaTech.ppt#1