# Relation between armature voltage and mechanical power in electrical Engineering

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 $$P_{mech}$$.

• Number of windings? – Solar Mike Dec 9 '20 at 4:48
• I don't need calculations just the theoretical aspect – joseph Dec 9 '20 at 10:12

Some formulas for you on Wikipedia.

• I'm searching for a specific relation between the armature voltage and the mechanical power, which I didn't find on web. – joseph Dec 9 '20 at 9:47

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.

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 2𝜋 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.