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Electric potential, torque and energy equation

Electric potential, torque and energy equation 
Electric potential, torque and energy equation (1)  Electric potential (Figure 6)
From V=E+2△U+I*r we get E=V-2△U-I*r
Meanwhile E=KE*Φ*n(armature back EMF)
V: power supply voltage (Unit: V)
2△U: brush voltage drop (Unit: V)
I: armature current (Unit: A)
R: rotor resistance (Unit: Ω)
KE: EMF constant = Z/60 (for a 2-pole motor.
Z: number of conductors)
Φ: magnetic flux (Unit: Weber) = average magnetic flux density B * width of magnetic pole *effective length of rotor 
N: speed (Unit: rpm)
(2)  Torque
TE=KTΦ*I(electromagnetic torque: N.M)                 KT: torque constant = Z/2π
Φ: magnetic flux (unit: Weber)                                  I: armature current (unit: A)
(3)  Relationship between power and torque:
P=T*n/97500        P: power(unit: W)        T: torque (unit: g.cm)        n: speed (unit: rpm)
When the unit of T is “N?m”, P=T*n/9.55(unit: W)
(4)  Energy equation(Figure 7):
Electric potential, torque and energy equation P1=2△U*I+I2r+PE
PE=P2+PFe+Pmec
PE: electromagnetic power   P2: output power
Pmec: mechanical loss      PFe: iron loss
P2=P1-2△U*I-I2r-PFe-Pmec (unit: W)
Efficiency: η=P2/P1*100%
PFe+Pmec is also called no load power
P0=PFe+Pmec
PE=P2+P0 and TE=T2+T0


(5)  Energy transmission graph: (Figure 8)
Electric potential, torque and energy equation


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