In a DC motor, is there one commutation point that is optimal in all respects?

This recent question got me thinking about commutation timing, and why advancing it can be desirable. However, I wanted to consider more deeply the underlying phenomena, and I'm pretty sure my understanding is incomplete, so I thought I'd try a new question.

The stator and rotor fields combine to make a rotated overall field, and some motors advance the commutation timing to reduce commutator arcing. Here's an illustration, from this article on submarine electrical systems: The section where this appears is discussing generators, so the arrow labeled "rotation" is backwards if we are thinking of this as a motor. If this were a motor, with the currents and field drawn, we'd be expecting it to turn in the opposite direction, counter-clockwise.

Since at the point label "new neutral plane" the rotor is not passing through any magnetic lines of force, there is no induced voltage, so if commutation is performed here there will be minimal arcing.

But, by moving the commutation point, have we sacrificed some other parameter? Have we reduced torque? Efficiency? Or is this the optimal commutation point in all respects?

• Why are people voting to close this? It seems like a well asked and on-topic question to me. – Olin Lathrop Jan 14 '13 at 15:15
• Just a thought on the potential energy statement. I would say the motor rotates because there is torque. The torque is the integral of the forces acting on anything attached to the rotating axis. You are trying to maximize this force at any given time by controlling the current to the different phases. Think about the static case in a brushless motor (the motor is holding a fixed position), that shows you how the magnetic field is oriented. When things are moving you'll get back EMF but I think the relative orientation doesn't change. – Guy Sirton Jan 20 '13 at 5:01
• From a quick Google search there appear to be two factors in play regarding the physics of the delay vs. speed: inductance and magnetic saturation. – Guy Sirton Jan 20 '13 at 5:40
• @GuySirton in the case of a brushless motor holding a fixed position (more likely a stepper motor), the fields are aligned and look like figure A, if there is no significant torque on the rotor. – Phil Frost Jan 20 '13 at 12:37
• @PhilFrost What I'm trying to say is think about isolating the static portion from the dynamics. Take your holding motor and start rotating it in a constant velocity through another motor. The only thing you'll see is back EMF (AFAIK) which will cause a drop in torque across the board but you will not see a phase change if you graph torque vs. position. I'm pretty sure the phase is advanced when driving the system due to the factors in my comment above, inductance (it takes time for the current to change through the inductor) and non-linearities related to the magnetics (saturation etc.) – Guy Sirton Jan 20 '13 at 19:17

My understanding is that the motor wants to turn counter-clockwise because this represents a lower potential energy by untwisting the field and aligning the stator and rotor fields. Is this correct?

It turns due to the forces acting around it's axis of rotation. Those forces create torque which in turn creates angular acceleration of the rotor.

But if we move the commutation point to there, haven't we rotated the stator field, leading to a new new neutral plane? If we repeat this adjustment, does it converge on a optimal commutation point or do we just keep twisting all over the place? Is this commutation point optimal in all respects, or are there some compromises to be made?

By definition whenever you rotate one of the fields you have a new neutral plane. The entire point of commutation in a motor is to keep the neutral plane at the angle where torque is maximized.

I've always heard that the timing must be more advanced at higher speed. But is this strictly true, or is it a function of winding current / field strength, which just happens to be correlated with speed in the case of a constant mechanical load?

I think you are mixing two effects here. Let's consider a brushless motor. Given a current flowing through its windings it will settle in its neutral plane. At this point the torque is zero (ignoring friction). Now start rotating it slowly by hand and graph the torque vs. position. The maximum of that graph is your "optimal slow speed" commutation point. You could derive a very close approximation of that graph using mathematical models. I wouldn't call this advancing the timing. Depending on the number of phases and poles it would be at some fixed angle from the neutral plane. In a closed-loop brushless system with a position encoder and no hall effect sensors you would typically go through a sequence where you put some current through the windings to discover the position of the neutral plane.

In a dynamic situation you want to keep rotating the field under your control to keep the same phase vs. the fixed magnets. Because of inductance and various non-linear effects such as magnetic saturation and temperature, the control timing needs to change as a function of speed to try and maintain the same phase between the fields. Essentially there is a delay between the time a command is given and the actual change in the field so the command is given earlier, "advanced", to compensate for that. In a brushed motor you can only have one fixed phase advance so you need to make some sort of compromise if you plan to operate in different speeds. There are also static compromises in brushed motors, e.g. the size of the brushes and the on/off nature of the control. In some situations this delay is negligible anyway.

Is a sensorless BLDC driver which detects back-EMF zero crossings to find the commutation point an example of such a motor?

I would think the back-EMF zero crossings are insufficient. They only reflect the "static" positioning described above. So you would need to know the motor parameters as well before you can optimize your control (e.g. using something like field-oriented control)

• When you say, "You could derive a very close approximation of that graph using mathematical models," that's exactly what this question is about. I know there's some point at which torque is maximized. Where is it, and why? Inductance no doubt would play some part, but I don't think that's everything. And under what circumstances in normal operating conditions would magnetic saturation come into play? Assuming I'm keeping the winding current within specifications, isn't the core designed to not saturate? – Phil Frost Jan 20 '13 at 23:36
• Note I am talking about the static system there. For symmetry reasons I would expect the maximum to be exactly in between two zero torque points (the number of zero torque points is the number of poles times the number of phases divided by 2 IIRC). You can Google for models but here's one: robot2.disp.uniroma2.it/~zack/LabRob/DCmotors.pdf – Guy Sirton Jan 20 '13 at 23:55
• @PhilFrost: This paper discusses modelling magnetic saturation: personal-homepages.mis.mpg.de/fatay/preprints/Atay-AMM00.pdf . Intuitively I think inductance and switching delays are the first order reason for changing the phase with speed. If you're looking for a simple mathematical model to explain everything that happens in a motor I don't think you'll find one. Even the very complicated models are still approximations. For the most part however that doesn't matter. – Guy Sirton Jan 21 '13 at 0:05
• That paper presents a model for magnetic saturation in universal motors, but is it applicable when we aren't talking about universal motors, and, what does it have to do with commutation timing adjustment? – Phil Frost Jan 21 '13 at 0:20
• @PhilFrost: According to scholarsmine.mst.edu/post_prints/pdf/… "The mathematical model of BLDCM must include the effects of reluctance variations and, most importantly, the magnetic saturation whose existence is inevitable when large torques are generated." Saturation changes the dynamic behaviour so it would effect the phase between the current and torque in a rotating motor. At least, that's the way I understand it. – Guy Sirton Jan 21 '13 at 0:44

You're correct that the neutral point is where the brush set point would be nominally located. While the rotor is turning, the fields don't effectively move (much), since the movement of the rotor will cause the next set of armature windings to be energized. Thus the field picture in "C" will just be "wiggling" as the different armature windings move by.

For max torque production, you want the armature flux and field fluxes to be properly aligned and at "full strength". (ignoring that torque is really interaction of a current and a flux...)

Note that there is a time constant for the current to increase in the armature winding due to the winding resistance and inductance. This causes a delay in the armature flux/current. If this delay is not compensated for, then optimal torque production won't be achieved. Advancing the commutation angle is one way of addressing this.

The "correct" advance angle depends on the rotor speed, the time constant of the armature circuit and the number of armature poles. Since the armature time constant is a fixed time, for faster rotor speeds, the advance angle needs to be increased.

• At what point are the armature and field "properly aligned"? See, I had previously assumed that the reason for advancing the commutation point was due to the current lagging behind the voltage as you describe, but if you read some of the answers to the question I linked, you might see how I thought maybe that wasn't all there was to it. – Phil Frost Jan 16 '13 at 18:50
• Here's another point of confusion: let's say we can compensate for any current lag perfectly, so the armature's magnetic field is always exactly as it is in figure B, above. Wouldn't the overall field still be distorted as in figure C, leading to a need to adjust the timing more? – Phil Frost Jan 16 '13 at 18:53

The neutral plane is not dependent on speed, only current. The stator magnetic field (horizontal in your picture above) and the armature magnetic field (vertical in your picture above) don't really "add" together unless you think of each of the fields as a vector. If so, then you should be able to see that the neutral plane can move around as the two fields change in respect to each other (e.g., if the stator magnetic field stays the same and the armature magnetic field increases or decreases, the neutral plane will move). Because of this, you can see why the neutral plane depends on current, not speed. The current through the stator and/or armature (which is dependent on the load) determines the strength of the magnetic fields, which in turn determines the location of the neutral plane.

Brushes can be shifted to align them with the neutral plane. But given the fact that the location of the neutral plane is dependent on the load, there may not be an ideal ("properly aligned") position to shift your brushes because most applications don't have a single load point. This is also important to keep in mind if your application requires rotation in both directions. In my experience, most motor designers rely on a combination of past experience and experiments to determine proper brush alignment for a given application.

• I guess that's more or less what I had guessed would happen. I was considering that the fields add as if they are an array of vectors -- I'm not really a mathematician so I'm not sure of the correct terms. But, I'm still wondering, if we rotate the commutation point to meet the neutral point, doesn't that also rotate the armature's magnetic field, leading to a new neutral point? – Phil Frost Jan 18 '13 at 12:25
• Does shifting the commutation point to the neutral plane (wherever it is) also maximize torque, or does it minimize commutator arcing at the expense of torque? – Phil Frost Jan 22 '13 at 14:55