Magnetic interaction between resolver & motor windings?

Question

Scenario: Synchronous electric motor whose rotor position is measured by a resolver.

1. Won't the magnetic field created by the motor stator & rotor, link with the primary & secondary windings of a resolver?
2. If there's no such linkage, what engineering methods are being used to prevent this?

Resolver secondary winding's voltage equations are often simplified as follows: $$V_1=kV_0\cos\theta$$ $$V_2=kV_0\sin\theta$$ $$\theta=\arctan(V_2/V_1)$$

Vo is the primary winding voltage, theta is the rotor angle and the gain is 0 < k < 1. The above equations make sense if we consider the resolver as a simple transformer.

3. Assuming stator/rotor flux also contributes to an induced voltage in resolver coils, shouldn't that be included in the above equations to compute rotor angle/speed?

In a simple transformer, voltage induced in the secondary coil is due to a change in primary current alone. In a resolver, the primary coil can be in motion with respect to the secondary. This would mean that an additional voltage proportional to rotor speed will be induced in secondary coils (equation below) $$V_1=\frac{d}{dt}(\vec{B}.\vec{A})=\frac{d}{dt}(BA\cos\theta)=\frac{dB}{dt}A\cos\theta-BA\frac{d\theta}{dt}\sin\theta$$

4. Shouldn't this speed-dependent voltage term be included for angle/speed computation? If not, what's the rationale for neglecting it?
5. Wouldn't this speed-dependent voltage create a risk of overvoltage at high rotor speeds?

Answer 1

You will get some image of the motor current in the resolver signals.

But the frequency will be much lower than the resolver drive frequency.

The usual method of mulyipying in (V_1,V_2) by V_0 before applying arctan2() to the integrated (or low-passed) result will eliminate most of that crosstalk.

The integration will add some small, but, predictable lag. but the multiplications will mix the perterbations up to a high frequency where they will be mostly swallowed by the integrator.

As you know the approximate rotational speed of the resolver it may be possible to get more precision by some other method that takes this into account. (perhaps multiplying by a frequency shifted image of V_0? - that should cancel out the generator voltage mentioned in (3) )

4. it's near constant and can be predicted, especially with a synchronous motor, so it can be compensated for empirically.

5. yes, but assuming you have a reasonable amount of headroom (like 10%) the speeds will need to be very high to cause over voltage. (like spinning at 1/10 the resolver drive frequency)