Energizing of armature as function of position in electric motor

Question

How is the armature in an electric motor energized (i.e. main conditions on signal as function of position)? Let's consider the following parameters:

• $n_a$,$n_f$ the number of armature and field pole pairs, respectively
• $\gamma_{a,k}={\pi k\over n_a}$, $\gamma_{f,k}={\pi k\over n_f}$ the position of armature and field pole $k$ ($k\in \{1,\ldots,2n\}$)
• $\gamma$, the angular position of the shaft
• $I(\gamma)$, the current in armature as a function of position ($\forall\:\theta\in\mathbf{R}\::\:I(\theta+\pi)=-I(\theta)$)
• $I_k(\gamma)=I(n_f×(\gamma-\gamma_k))$, the current in armature pole $k$.

The most important question is: should $I_k(\gamma_k)=0$ (i.e. should the current commutate whenever a field pole passes an armature pole)?

I created the gif below to illustrate. The vectors represent the magnetic moments: blue is armature, yellow is field.

Answer 1

Synchronous motors can be operated with a VFD in the same way that induction motors are usually operated. To start the motor, the stator is energized at a very low frequency, 1 Hz or so. The motor is then accelerated by increasing the frequency at a rate that is limited by the torque with which it is desired to accelerate the load or the torque that the system has a the capacity to deliver.

The torque can be more tightly controlled by measuring the torque angle and controlling the armature current to provide the desired torque. The torque angle is the angle between the rotor field and the stator field. To control torque, the phase of the armature current would be adjusted so that the moving position of the magnetic poles created by the armature current would lead (for positive torque) the moving position of the field poles as indicated by position encoder feedback. This is called a "flux vector" torque control strategy.

In an electric vehicle, for example, the "gas pedal" could provide a torque command. Pressing the pedal down would call for more torque and accelerate the vehicle. Lifting your foot from the pedal would call for less torque (or perhaps braking torque) and decelerate the vehicle.

The relationship between the physical stator poles and the rotor poles is not relevant. The relevant thing is the angle between the rotating stator field and the rotor field.

Answer 2

Most commonly (in induction motors) it's the other way around, the armature is energized in a arbitrary frequency coming straight from the 3-phase mains power and the rotor can do nothing but follow it along. This is done with 3 sets of coils in the stator.

This fixes the rotation speed to a multiple of the mains frequency. If you need a different rotation speed you can add a gearing reduction as needed.

in a universal engine the rotor is energized using commutator. The field created by the stator follows the input current (stays constant if DC) and the rotor will make its own field offset to that field to create torque.