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I am searching for an effect chain that leads to the mechanical power $P_{mech}$ of a DC motor, starting with the applied armature voltage $U_{A}$. My request also includes all the electrotechnical quantities with cause, effect and linking formula, which are created 'on the way' between $U_{A}$ and $P_{mech}$.

Thanks in advance!

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    $\begingroup$ Number of windings? $\endgroup$
    – Solar Mike
    Dec 9 '20 at 4:48
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    $\begingroup$ I don't need calculations just the theoretical aspect $\endgroup$
    – joseph
    Dec 9 '20 at 10:12
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Some formulas for you on Wikipedia.

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    $\begingroup$ I'm searching for a specific relation between the armature voltage and the mechanical power, which I didn't find on web. $\endgroup$
    – joseph
    Dec 9 '20 at 9:47
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A DC motor is modelled as a gyrator, in which the output RPM (a flow variable) is proportional to the input voltage (an effort variable.)

As always, the input power = (flow variable x effort variable) = (current x voltage) and similarly the output power = (torque x RPM)

Mind the units.

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Mechanical Power: $$P_{m} = \omega \ T_m = \frac {9.55 \ T} {n} \ \ (W)$$

$\omega$ = angular velocity in rad/s.

n = speed in rpm.

9.55 = constant to eliminate 2đťś‹ radians and 60s/min.

Torque: $$T_m = k_b\ I_a\ -\ T_f \ \ (N \cdot m)$$

$k_b$ = torque constant in N•m/A.

$I_a$ = armature current.

$T_f$ = motor friction torque in N•m.

Armature Circuit KVL:

$$U_a = I_a\ R_a -\ U_b \ \ (V)$$

$V_a$ = armature voltage.

$I_a$ = armature resistance in Ω.

Back emf:

$$U_b = k_e\ \omega \ \ (V)$$

$k_e$ = back emf constant in V•s/rad.

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