Electric Motors

AC Motors and DC Motors

Motors contain:

• Stator: Non-moving outer part which creates the magnetic field via current in windings, a permanent magnet, or an electromagnet
• Rotor: The moving inner part of the motor which is connected to the output shaft, this turns due to the magnetic field
• Armature: A part of DC rotors which contain windings which creates the magnetic moving force when placed in a magnetic field

The magnetic field induced by a current running through a coil which causes the rotor to rotate. AC Motors use an alternating current to switch the direction of current flow to switch the polarity of the electromagnet to keep the motor rotating in one direction along with inertia.

DC Motors work in the same way as AC motors except they use brushes and a commutator to switch the direction of the electromagnet polarity to keep the rotor rotating in the same direction, brushless DC motors use a controller to switch the direction of the current instead

Tesla uses induction motors…

• 3 phase AC windings which when a current rotates through them creates a rotating magnetic field, the rotor has no external connections to the power source so all the current is induced from the stator, the rotors induced magnetic field interactions with the other one causing the motor to spin
• Doesn’t need PM’s
• High speed control
• Higher durability

Selecting Motors

• 1st stage involved applying motor performance principles (choosing gears, kinematics, dynamics) required at the motor
• 2nd stage involves determining the type and specifications of the motor itself (actually selecting the motor)
  • Control objectives, motor drives, DC / AC

Torque-Speed Characteristics

• Involved understanding P, T, v, and $\omega$ requirements to select a motor
• Torque Equation $T=-\frac{k_t{k}_e}{R}\omega +\frac{k_t}{R}V=\frac{k}{R}\left(V-k\omega \right)$

Referred Inertia

• The effective load inertia is the inertia seen by the motor through the gears as seen in Equivalent Mass and Inertia
• Gears lower the inertia from the load (referred inertia)
• Speed reduction: $N{\theta }_l^{{}^{\prime \prime }}={\theta }_m^{{}^{\prime \prime }}$
• Torque amplification: $N{\tau }_1={\tau }_2$
• The effective load or referred inertia is: $J_{eff}=\left(J_m+\frac{J_l}{N^2}\right)$ which has a reduction of $N^2$
  • If there is no armature motor, $J_m$ is 0

Motors with Gears Example

• Theory: We want to minimize the size of your motors and the inertia load which increases the gear ratio and decreases the motor size for torque so we don’t need to design huge structures
• Problem: From previous example (in-wheel motor), Find the torque, max speed and power when motors are used with gears
  • $T_m=\alpha \left(J_w+\left(m_w+g\right)r^2\right)$ where $J_l$ is considered as the terms multiplied by alpha
  • $T^{\prime }={\alpha }^{\prime }\left[{\frac{J_l}{N^2}}_{}\right]$
  • Now after finding $J_l$ find $J_{eff}$
  • After finding ${\alpha }^{\prime }$, you can use $J_{eff}$ and ${\alpha }^{\prime }$ to find $T_m^{\prime }$
  • Where ${\omega }_{\max }^{\prime }=N{\omega }_{\max }$
  • Where $P_{\max }=T^{\prime }{\omega }^{\prime }$ where ${\omega }^{\prime }=N\omega$ for the new gear ratio
• Problem: From rotary indexing example
  • Find $T^{\prime }$ using $J_{eff}{\alpha }^{\prime }$
  • Where ${\omega }_{\max }^{\prime }=N{\omega }_{\max }$
  • ${\omega }_{\max }^{\prime }=N\left({\alpha }_{\max }\right)$
  • Which we use in our $T_m^{\prime }$ equation
  • This is essentially the exact same setup and steps as our last example

Primitive Motor Models

• See models of different Electromechanical Systems and their relationships
• As well as different models of DC Machines
• Induction Motors