# Why am I getting Torque although stator and rotor fields are aligned?

I am working on a synchronous machine simulation project using FEMM. I am trying to find the rotor position that produces 0 torque. According to my understanding, this happens when both the rotor and stator fields are aligned. Therefore, I first found the back EMF waveform when the stator is not excited, then I applied rotation to the rotor so that the back EMF on Phase A is a cosine wave. Then, I excite the 3 phases of the stator, making the current of Phase A similarly a cosine wave, so that the back EMF produced in Phase A is in phase with the excitation current in Phase A, and therefore the rotor's field will be in phase with the stator's field when the stator is excited (since both fields are now aligned). However, I am still getting torque when doing so. What am I doing wrong?

• Not enough detail. Can you edit your question with, first, the magnetic field diagram that FEMM shows you in this not-zero-torque case, and -- if it's not apparent from the field diagram -- tell us if the stator or rotor have salient poles (or even slots for windings). Dec 26, 2022 at 2:33
• still getting torque ... are you saying that the rotor is turning? Dec 26, 2022 at 4:10
• @jsotola it sounds like the OP is doing a simulation in which the rotational speed is fixed. I presume that one of the simulation outputs is the torque exerted on the rotor. Dec 26, 2022 at 6:22

From practical experience with BLDC motors I know that applying stator current in-phase with the back EMF produces maximum (or near maximum) torque. So that is an observed fact.

Mathematically, per my understanding, the back EMF is proportional to the rate of change of the magnetic field. This means that the back EMF is proportional to the derivative of the flux. Mathematically, derivation of a sinusoid creates a 90 degree phase shift. So by exciting stator current in-phase with the back EMF you are actually not aligning the stator and rotor fields. In fact, the stator and rotor fields are 90 degrees offset from each other in your simulation.

If you want to simulate the no-torque condition you need to excite the stator such that the current is in quadrature with the back EMF.

Maybe a simple way to summarize is to just say that your excitation is 90 degrees off. The phase of the flux and the phase of the back EMF are offset by 90 degrees. So you have accidentally simulated the max torque condition instead of the zero torque condition.

• Oh, I am a bit mixed about this now, since from my understanding the back emf is in phase with the rotor field, i.e. we can use them interchangeably when discussing load angles and phases, but the explanation you provided makes sense. So by aligning the back EMF with the stator current, I am creating a leading rotor field? I tried correcting this. My machine is a 2 pole one, so instead of rotating the rotor 90°, I rotated it 45° opposite the direction of the rotating magnetic field, since the EMF is lagging (am I correct?). Indeed, I am getting close to 0 torques now (0.35 N.m on average). Dec 26, 2022 at 6:50
• Edit, I rotated it 45° with the direction of the rotating magnetic field, this is where I am getting close to 0 torques. But I am assuming that in this case, my rotor field is leading and I am simulating a generator. When doing it opposite to the stator's magnetic field, I am getting -0.7232 N.m on average. Should it not be the same? Dec 26, 2022 at 7:00
• I am sure of two things: In bench testing three phase motors and motor controllers with the ability to vary excitation angle, I have seen that the torque is maximized when current is in-phase with the back EMF (in my test setup, I had shaft position sensors so I know where the back EMF is even when it is not directly observable). My grasp of motor theory is not very strong. But Faraday's law definitely states that EMF is proportional to the rate of change of the magnetic flux. So I think the back EMF must be in quadrature with the actual flux vector. Dec 26, 2022 at 7:01
• Ideal motors are one thing. Real motors (even in simulation) have saliency and non-sinusoidal back EMF and variable inductance (variable reluctance). So I don't necessarily expect that the torque relationship is perfectly symmetrical in generation and motoring. Also, the null may not be at 45 degrees exactly in a real motor (or detailed model of a real motor). Dec 26, 2022 at 7:05
• This is correct, back EMF voltage is 90 degrees offset from the magnetic field. Similarly, voltage applied to the stator is not aligned with the magnetic field, but the applied current is.
– jpa
Dec 26, 2022 at 14:29