Engineering DC Machine motor constant equation

[slain4ever]

Homework Statement

Given the no-load test results of a DC motor connected in shunt to be:
Speed: 3000rpm
Applied voltage: 239V
Field current: 0.25A
Calculate the motor constant K_m, where K_m = K

Homework Equations

not really sure about the equations to use
i have these:
Km = T/ SQRT(P)
Km = Kt / SQRT(Rt)
but not really sure how I can use these to help solve the problem.

The Attempt at a Solution

I'm sure it's just a matter of finding the right formula than just plugging the values in. So if someone can give me the correct equations it would be very helpful, thank you

 

[slain4ever]

ok I found this site which helped a lot, something about a conversion factor for the torque so i managed to get a bit further but I am still confused about those two differing formulae

T Nm * 3000RPM * 0.1047 (conversion factor) = P
T * 3000 * 0.1047 = 239 * 0.25
T = 59.75 / 314.1
T = 0.190226 Nm

Km = T/ SQRT(P)
Km = 0.190226 / SQRT(239 * 0.25)
Km = 0.02461

OR
Km = Kt / SQRT(Rt)
Kt = T/I
R = v/i ?
Km = (0.190226/0.25) / SQRT(1436)
km = 0.0200795

these two values are very similar
just wondering if the methods are correct

 

[CWatters]

I'm a bit rusty but I'd look at the speed equation.

N = K × Eb ÷ f

Not sure if/how you calculate the flux f but perhaps it's enough to say

N = K_m x Ev

where k_m = K/f ?

I think the flux f is fairly constant due to high resistance of the windings.

 

[CWatters]

Deleted.

 

[slain4ever]

not sure about those formulas

is this working right?

E_a = (k_m)(W_m)
V_T = E_a + (I_a)(R_a)
No load test, therefore I_a = 0
Therefore E_a = V_T
V_T/Wm = k_m
k_m = 239/(3000*(1/60)*2pi = 0.76

 

[rude man]

What is your definition of "the motor constant"?