DC Machine motor constant equation

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Discussion Overview

The discussion revolves around calculating the motor constant \( K_m \) for a DC shunt motor using no-load test results. Participants explore various equations and methods to derive \( K_m \) based on given parameters such as speed, applied voltage, and field current.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant presents initial equations for \( K_m \) but expresses uncertainty about their application.
  • Another participant calculates torque using a conversion factor and derives two different values for \( K_m \) using different formulas, questioning the correctness of their methods.
  • A different participant suggests looking at the speed equation and relates \( K_m \) to the back EMF and flux, indicating that the flux might be constant due to high winding resistance.
  • Another participant proposes a formula involving armature voltage and speed, concluding with a calculated value for \( K_m \) but expresses uncertainty about the formulas used.
  • A later reply asks for clarification on the definition of "the motor constant," indicating potential confusion about terminology.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the correct method to calculate \( K_m \), and multiple competing views and formulas are presented without resolution.

Contextual Notes

There are unresolved assumptions regarding the definitions of terms and the applicability of the various formulas presented. Some participants question the accuracy of their calculations and the interpretation of the motor constant.

slain4ever
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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
 
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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
 
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.
 
Deleted.
 
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
 
What is your definition of "the motor constant"?
 

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