I have a question regarding powering electrical motors, variable reluctance motors to be more precise (ie. Stepper motors). This kind of motor, in a perfect situation would like to be powered with current thats shape is a sin wave and a cosine wave (for stepper). Even when doing microstepping, one should try to follow the shape of sin and cos to have the smoothest rotor rotation. Also if VRM was used as generator, it would generate sinusoidal current. This all seems logical, looking at the circle construction of the machine. I believe if one was to unroll the vr motor and make it drive in a plane motion way, it wouldnt have to be powered with sin/cos and also wouldnt generate current in that shape. My question is- would someone please explain me in a more "fact and proof" way why does the current shape has to be sinusoidal for a vr motor? Also, please correct me if anything i wrote was not true. I would apreciate all help!
Because a sinusoidal current will make the torque applied to the motor constant, whetever the position of the shaft.
Let's say we have winding A and B, and supply current I. If you apply a square current to both windings, you'll have:
- a phase where a current I is applied to winding A, and no current in winding B
- a phase where a current I is applied for both A and B, resulting in more power being applied to the motor then in the previous phase
- a phase where a current I is applied to winding B, and no current to winding A
So you see, the power given to the motor varies (sometimes I, sometimes 2*I), depending on the position of the shaft, so it will not run smoothly.
To solve this, you have to apply sinusoidal currents. Then, even when both winding are powered, the torque is kept constant.
Why a sine and not a triangle wave ?
Think of what you need to provide when the shaft is at 45° (both windings powered): the power provided to the motor is twice V*I (once for each winding). V and I are linked by Ohm's law (if we assume steady state and rule out inductance). So the power is twice RI². Whereas when the shaft is at 0°, the power is only once RI². Now, how to make this constant ? By setting the I at 45° to sqrt(0.5)*I at 0°. Indeed : 2*R*(sqrt(0.5)I)² = RI². Now, what is sqrt(0.5) ? It is cos(45°). So you can start visualising the sine wave. Basically, what is required is that I² in winding A + I² in winding B is constant. That is the definition of sin and cos.
And yes, basically, it comes from the fact that the motor turns in circle.