DC Motor Model

[candu6]

I need to mathematically model a DC motor (with brushes) to determine the motor's load profile for battery sizing. I want to include the inrush and it's effect on the battery voltage. Does anyone have suggestions or links to sites that are useful.

 

[baltic]

Armature equation:
Va=La*(dIa/dt) + Ra*Ia + E;

Field winding equation:
Vf=Lf*(dIf/dt) + Rf*If;

Mechanical equation:
J*(d2W/dt2)+D*(dW/dt)=T

Motor back EMF:
E=Ke*If*W

Motor torque:
T=Kt*If*Ia

There are also shunt, series and compound field winding connections.

For permanent magnet DC motor you just have:

Va=La*(dIa/dt) + Ra*Ia + E;

J*(d2W/dt2)+D*(dW/dt)=T

E=Ke*W; T=Kt*Ia; Ke=Kt