Brushless Gimbal Motors

Camera gimbals have become widely and cheaply available since Alexmos has shown nearly a decade ago that the cheap brushless RC hobby motors can be used for building them. During the „high time“ of DIY brushless gimbal building all the information on which motors are the best and what properties to look for were described in many posts in the various fora (and I am responsible for a good number of them LOL), but – while this info is of course still there – this knowledge has become kind of lost since it is now „deeply“ buried in the web (well, with the right key words they are easily found with google, but …). So I’ve decided to write it up in this article.

1. Electrical: Resistance
2. Magnetical: Cogging and Pole Number
3. Mechanical: Friction
4. Electrical: Inductance
5. Conclusions

 
Electrical: Resistance

Fundamentally, in comparison to the usual application of RC hobby motors for spinning rotor blades, gimbal motors are spinning at negligibly slow rotation rates. Well, they are not actually spinning in the sense of spinning around, but they do constant back and forth movements. The angular velocity with which they do that is however much smaller than the angular velocity in the case of spinning blades, where it is let’s say 500 – 3000 rpm. For a gimbal motor the (time-averaged) angular velocity can in fact safely assumed to be zero.

This is the single most important factor which distinguishes a normal brushless motor from a gimbal motor: The rotation rate is nearly zero.

The key insight can be obtained from the simplest model one can devise to describe a brushless motor, which is also sufficiently realistic for the purpose:

 U = RI + L \dot{I} + k \omega
 M = kI

where the symbols assume the usual meaning. Since, as we were just arguing, the angular velocity is essentially zero, the second and third term in the first equation disappear (\omega \approx 0), and we arrive at

 U \approx RI
 M = kI

That’s really simple, isn’t it! In order to calculate the current, all we have to do is to measure the resistance of the motor wire, know the voltage, and apply Ohm’s law. Well, these motors are 3-phase types, and hence an additional prefactor enters, but we will not be concerned with this detail, as it is irrelevant for our purpose (taking the prefactor into account will not modify a single statement below). We arrive at this conclusion:

The key factor to consider in the selection of a brushless motor is its resistance, and not the KV value.

One now may think that a low resistance is good as then a larger current can flow and the motor can produce more torque. Unfortunately, a second factor comes into play, namely that each motor can handle only so much heat power before it gets too hot and burns. For a gimbal motor the Joule’s heat is given by

 P = UI

Normally, for a spinning motor, most of the electric power is converted into mechanical power and not heat, and the motor can accept quite high currents. For a gimbal motor the rotation speed is however nearly zero and thus nearly no mechanical power is produced, and thus all electric power goes directly into Joule’s heat! Accordingly, the motor can sustain only relatively low currents without overheating.

(one should not confuse mechanical power, which is P_{mech} = M \omega, with the torque M; a gimbal motor is producing torque but not mechanical power)

Therefore you will find that when used in a gimbal the motor will get hot already at comparatively low currents. The heat a motor can accept is for all motors essentially only determined by its size (= volume = mass = weight). That is, the only way to get a stronger motor is to use a larger motor.

The result of balancing these two factors is:

The resistance comes out to about 10 Ohms (2 -20 Ohms).

This is so for all motors, from motors for micro gimbals to motors for huge gimbals. The „best“ resistance depends on the voltage as well as on whether a sinusoidal or FOC driving scheme is used. Lower voltage equals lower resistance, and FOC also permits lower resistance (where it is actually of advantage). For instance, the Phantom P3 gimbal motors run a FOC scheme at 5 V and have a resistance of ca 2 Ohms. For big gimbal motors you find resistances of up to 20 Ohms. This gives you a range of 2 – 20 Ohms. The typical rule is 10 – 15 Ohm for sinusoidal drives at 2S – 4S voltages, 5 – 10 Ohm for FOC drives at 2S – 4S voltages, 5 – 10 Ohm for sinusoidal drives at 5 V, and ca. 5 Ohm for FOC drives at 5 V.

Note that motors used for spinning rotors have an as low resistance as possible, and their resistance is in the mOhms range and thus hundreds and more times smaller than what is needed for gimbal motors. They thus cannot be used without rewinding. Disk motors as found in hard drives and similar units however tend to have resistances in the Ohm range and can be suitable as is.

(if you are unsure if you are using a sinusoidal or FOC scheme in your gimbal, it’s easy to figure out: If it is using encoders it is FOC, if not then sinusoidal)

Since the current (or maximal current in case of a FOC scheme) is now given (see Ohm’s law) and is nearly equal for all gimbal motor sizes, it follows that more torque can only be obtained by motors with lower KV value (= larger torque constant k; k \propto KV^{-1}), i.e., motors of larger size. You thus find that the larger the gimbal the larger the motors need to be. Well, this makes sense, right, and you also find this trend for motors used for spinning blades. So, you won’t find this surprising. The situation and thus the motor design criteria is however indeed somewhat different, since in the case of gimbal motors it is about torque production while in case of spinning motors it is about mechanical power production. As a result, gimbal motors are much bigger (= heavier) for what they appear to do and what one may expect them to be. Gimbal motors need to be relatively big since size (= mass) is the only way to handle the heat, and as explained before, all electrical power goes directly into heat for them.

 
Magnetical: Cogging and Pole Number

Another factor to be concerned about are the magnets, and the key factor here is actually cogging. This might be a bit surprising at first, since the first factor coming to mind is probably the number of motor poles. However, the cogging also sets which number of poles is best, as you will see shortly.

Cogging

Motor cogging describes the effect that the amount of torque produced by the motor which is available to turn the load depends on the actual position of the motor. You can easily feel it when you take the motor in your hand and rotate it with a finger of your other hand. You will (for most motors) clearly feel that the motor wants to snap into particular positions; this is due to motor cogging.

The magnitude of the cogging is actually not that relevant, what is most relevant is how much the cogging torque changes with varying motor position, i.e., the rate of change with respect to motor position. This brings non-linearity into the feedback loop, and any PID control loop has difficulties with handling this. Basically, what cogging means is that the optimal tuning of the PID controller depends on the position of the motor, and since in a gimbal the position varies permanently, an optimal tuning cannot be found. That is, the tuning is necessarily worse than it could be.

Most people settle for a compromise, that is a tuning which is such that for some positions the tuning is too weak but for others too strong. This leads to a typical snarring then one is moving the gimbal, and shows up as micro vibrations in a video. The alternative is a generally weak tuning, which however means less stability, which in a video may show up as jello or a „drunken sailor“ effect.

You see, cogging is not good. Fortunately, it is well known how to minimize or even avoid it. Unfortunately, the large majority of gimbal motors which are available to us do the worst possible (you don’t believe it? You will in a second).

The major factor is the type of magnets used in the motor. They can be largely classified into „assembly of strong magnets“ and „ferrite rings“. The rational for using an assembly of magnets is simple: Strong magnets such as NdFe can be used and thus the power density of the motor much increased. And indeed, this is what you find in all RC model motors which should produce mechanical power (such as spinning blades). However, this construction necessarily produces lots of cogging. The alternative is to use a ferrite ring, which can be precisely magnetized as needed and cogging be much minimized. This construction is what you find in motors which should rotate as constantly as possible such as in hard drives.

Motors with ferrite ring have much less cogging than motors with a magnet assembly.

For our gimbal motors, we obviously want the ferrite ring type. As said, unfortunately, the large majority of gimbal motors available to us don’t have that but an assembly of magnets (my guess is that these gimbal motor producers simply use their available motors and tools and just rewind them to achieve the larger resistance). Visual inspection often allows us to immediately determine this.

Another method for minimizing cogging is to not use metal slots for the stator, but a coreless design. The ideal is a combination of ferrite ring and coreless design, which then really gives zero cogging. Such motors are available, but too pricey and special for us (e.g. the Maxxon motors which are/were reportedly used in DJI Zenmuse gimbals are of this kind). Large-scale gimbal manufacturers have a huge advantage here.

However, the situation is not totally lost. Usable motors with ferrite ring are available, mostly as replacement parts for commercial gimbals, such as e.g. the DJI Phantom and Mavic series. They however usually need some tweaking if one wants to use them in a DIY gimbal. Every once in a while also specific gimbal motors with ferrite rings show up on the market accessible to us, but they can be difficult to identify since it’s not mentioned in the description or the closed constructions of the motor makes it difficult to see the type of magnet.

Number of Poles

The number of poles describes how many magnetic south and north poles there are in the magnetic ring. For an assembly of magnets this is easy to tell, as it is just the number of magnets in the ring. Also ferrite rings are magnetized such that they have alternating north and south poles on the ring, with a certain number of them, which is the number of poles. Note that often the number of pole pairs is discussed instead, which is just half of the number of poles however.

The number of poles also affects the cogging, and the result might be counter-intuitive at first. More poles indeed usually reduce the magnitude of the cogging, and this is what is often desired as it gives smoother rotation. However, with more poles on the ring, they obviously need to come closer together, which means that the rate of change of the cogging with motor position in fact increases! And as we have just discussed, for our gimbal motors, it is the latter which mostly matters. Thus, motors with lower pole count are in fact better for gimbal applications than high-pole motors.

Motors with lower pole number are better than motors with a high pole number.

This was not understood in the early days of the DIY gimbal building, and it is still sometimes misunderstood. It was believed that high-pole motors provide better „angular resolution“ (like it would be for a stepper motor) and hence would be better. This is however incorrect. Usually, high-pole motors bring the disadvantage of large cogging effects. High-pole motors also tend to have large inductance, which is a further disadvantage (see below). Thus, the conclusion is clear: Low pole number is better.

The most frequently found number of poles is 14, in combination with 12 slots; the motor is then labeled as 12N14P (N for „nuts“ and P for „poles“). Typical high-pole motors would have 22, 24 or 28 poles, but gimbal motors with even more poles are found. In commercial gimbals, especially the micro-sized ones, one frequently finds lower pole numbers (the number of slots is e.g. only 9 and the number of poles could be 8 or even as low as 4).

These are useful overviews of suitable pole/slot combinations:
http://www.powerditto.de/Kombinationstabelle.html
https://www.emetor.com/windings/

 
Mechanical: Friction

Yet another factor of relevance is the mechanical friction, when rotating the motor. Unfortunately, even though it is a very critical factor, we usually cannot do much about it – except of not using motors with large friction!

Friction is mainly produced in the bearing of the motor axle. It has disastrous effects on the performance of the PID control loop, which is at the heart of any gimbal controller. The PID controller can then not be tuned to large gains, and this directly reflects itself in a poor stability of the camera, which you then see in the video as jello or micro vibrations. Thus, the rule only can be to use motors with as low friction as possible. We often may have little choice here, but one should just not use motors with large friction. The gimbal won’t work well and the only result of this would be to have wasted time.

Unfortunately, it is not easy to answer „What is large friction?“. Generally, larger gimbals allow larger friction, and for large gimbals it is often actually not a problem. Small gimbals are very sensitive to friction, and here it is often a major problem.

Friction can also come from the wires which are needed to connect the IMU and motors to the gimbal controller, and other required wiring. However, this is very much under our control, and we can (and have to) ensure that this source of friction is minimal.

A word of caution: Large friction can give a smooth feel to the motor, and can hide the cogging. In fact, it seems that in some motors the manufacturer exploits this, and one might think „wau, what a good motor“. But it should be clear from the above: It isn’t. It might be not a bad motor, but it isn’t a good motor in the sense of this article.

 
Electrical: Inductance

Finally, we should also discuss the relevance of the inductance of the motor coils. However, this factor is usually not under our control. That is, we hardly have a choice here, but have to use the motors as they are available to us and as selected by the above criteria. I mean, at the end of the day we need to chose a motor and cannot just rule out all of them, right. This point is thus mentioned here for completeness and knowledge. Large-scale gimbal manufacturers have again a definite advantage here.

In the above it was argued that the (time averaged) rotation speed is essentially zero, and that the inductance L drops out. This is absolutely justified for discussing the power production, but it is not for discussing the dynamics or band-width of the system. The latter tells you up to which frequencies the gimbal can stabilize the camera. The video rate of 30 fps or 60 fps gives you an indication of the desired bandwidth. The actual bandwidth of any gimbal is however much lower than that, typically 10 Hz and even much lower for big gimbals, and it is illusory to reach the desired bandwidths. Therefore what mostly matters is the roll-off at frequencies above the cutoff frequency, which should be as gentle as possible. The inductance however adds another pole to the transfer function and thus steepens the roll-off. The frequency above which this additional roll-off sets in is given by the ratio R/L, which shows that a large inductance is of disadvantage.

As general trends, motors with metal slots have much higher inductance than coreless motors. Also, motors with higher pole number tend to have higher inductance.

It should be noted that the negative effect of the inductance can be largely overcome by employing a current loop in the motor driver. This however implies more costly electronics, and (much) more difficult setup for the user. Gimbal controllers like the STorM32 or BASECam/Alexmos don’t use a current-loop. It is often used in the high-quality commercial gimbals (at least as much as I can tell with the limited info available to me).

 
Conclusions

This article has listed the relevant factors, in order of relevance, to the best of my knowledge. The reading may give the impression that for us DIY gimbal builders it is essentially impossible to find a good motor. And for small gimbals, of GoPro size and smaller, this is – IMHO – indeed the case!

This is at least my own experience. In all these years I’m doing this I have never had the luck of being able to build a gimbal which really satisfied me. To a large extend this is due to the limited mechanical tools available to me (a CNC or lathe would be really handy), and to a good extend also to the much raised expectations (the expectations have in fact increased enormously over the years, thanks to DJI). At then end, however, I always come back to concluding that it are the motors which I’m using which diminish the performance (and in some cases even ruin it). The only exception had been the PS2 disc motors which I used for my micro gimbal builds, with which I started all my gimbal efforts. Even after all these years it are still the best gimbal motors I had the chance to use. Not coincidentally, they had been the only ones with ferrite ring, while all others on my bench have magnet assemblies. So, my search for the ideal motor for building a good (!!) smaller gimbal is still ongoing :).

Of the above points, the only one the gimbal motor sellers appear to have adapted to is the higher resistance, but in all other points they usually fail to check the mark. It is quite unclear to me why not every gimbal motor on the market could have ferrite rings, since such motors are a commodity in other areas. Very sad for us, but it is as it is, right ­čÖé

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