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Homework Help: DC Machine motor constant equation

  1. Sep 29, 2012 #1
    1. The problem statement, all variables and given/known data

    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

    2. Relevant 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.

    3. 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
  2. jcsd
  3. Sep 30, 2012 #2
    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 im 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

    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
  4. Sep 30, 2012 #3


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    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.
  5. Sep 30, 2012 #4


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  6. Sep 30, 2012 #5
    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
  7. Sep 30, 2012 #6

    rude man

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    What is your definition of "the motor constant"?
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