1. 1.Modeling of DC motors 2.Transmitting and converting motion (gear trains) ME 431, Lecture 10 Lecture 10: DC Motors 1

2. DC Motor Armature-controlled DC motor model Model resistance and inductance of the coil as lumped parameters Same with mechanical inertia and friction ME 431, Lecture 10 2 θ

3. DC Motor Armature-controlled DC motor model From Lorentz’s law where K is the motor torque constant From Faraday’s law where K b is the back emf constant ME 431, Lecture 10 3 θ

4. DC Motor Armature-controlled DC motor model Electrical domain: Mechanical domain: Two domains are coupled by the previous relations ME 431, Lecture 10 4 θ

5. Example Find the transfer function Θ(s)/E a (s)

6. Example (continued)

7. DC Motor In steady state Slope is constant Intercept changes with e a ME 431, Lecture 10 7 speed T T stall e a1 e a2   no-load torque

8. Transmitting and Converting Motion Gears can be used to convert the speed and direction of motion, and modify the magnitude of transmitted torque ME 431, Lecture 10 8

9. Simple Gear Train Gears mesh without slipping, therefore, and ME 431, Lecture 10 9

10. Simple Gear Train Furthermore, if friction losses are neglected, then the transmitted power is unchanged which leads to tradeoff between speed and torque ME 431, Lecture 10 10

11. Complex Gear Train ME 431, Lecture 10 11

12. Example Find the transfer function Θ L (s)/E a (s)

13. Example (continued)