Motor Characterization for Small Running Robots

a.k.a. HobbyKing Cheetah.Bear with me, this is going to be a long one.Tl;DR: I characterize a bunch of cheap brushless motors to investigate their usefulness in small running robots.  Each motor gets a mechanical teardown and brief characterization.  Scroll to the bottom for conclusions.BackgroundI've worked on small running robots in the past, in the Biomimetic Robotics Lab.  That robot was designed to be extremely low-cost, built out of super cheap off-the-shelf DC gearmotors, which proved to be a hugely limiting factor in terms of the kind of running the robot was capable of.So here's the basic idea:  The hobby remote-control-things market has produced an abundance of cheap, light, super powerful motors.  This type of motor has showed up in my fleet of small electric vehicles, and many other people's vehicles, multi-copters, airplanes, etc. long before me.  But not in robots as precision or fast, torque controlled actuators.There are a couple reasons for this, I think.  First, suitable motor controllers don't really exist.  There are super expensive small brushless controllers made by companies like Maxon, and slightly less expensive (but larger) industrial-grade servo drives by the likes of AMC.  These could be convinced to work by appending your own sensor array to a hobby motor.  However, these motors tend to be wound for low torque constant, low resistance, low inductance, so they want lots of amps and relatively few volts, which doesn't play nicely with the fancy servo drives.  On the other end of the spectrum, there are the hobby grade controllers which usually are awful for anything other than RC vehicles, as they lack any form of current or torque control.As I'm interested in using these motors in dynamic running robots, all these motor control options become even less useful.  The fancy industrial drives might output 10 amps all day, but won't give you a drop more than 10 amps ever.  For running, on the other hand, that's not what you want.  Instead, you want many times your continuous current for short bursts and much less current the rest of the time.  So more dynamic current limiting is required.Thanks to Nick's last semester at MIT working on the Derpbike (a.k.a Bremsthesis), I'm making this a senior thesis project.  While I technically don't need to do one to graduate as I'm doing course 2A (the flexible MechE option), it's an excellent excuse to spend all of next term at MITERS working on my own project for credit.  My end-goal for the semester is to get all the necessary motor control stuff worked out and build a prototype 2 degree-of-freedom leg using hobby RC motors.Motor CharacterizationI've started out this project by acquiring a pile of small brushless motors I thought would be suitable for this kind or robot, and characterizing them to figure out which are the best.  These were visually narrowed down from the vast array of available motors by geometry.  In general, pancake-shaped (large diameter, small depth) is best for high torque density1.This can be seen with a little motor dimensional analysis.  Assume your rotor and stator are two rings of constant thickness, and radius and depth can be varied (not too unreasonable, although not all-encompassing).  Motor torque will be proportional to both air gap surface area and air gap radius.  So for a fixed air gap surface area (which means fixed mass, in this case)  increasing diameter means increasing torque per mass.Obviously there are many practical reasons why this might not be perfectly true (motor supporting material mass may scale differently, thinner motor means larger percent of windings in the end turns, etc.) but it's a good place to start from.Here's the pile of motors I ended up with.  From left to right, the Turnigy HD 5208 Gimbal Motor, Turnigy Multistar Elite 5010, Gartt ML 5208, Turnigy Multistar 4830, Turnigy Multistar 4822, and Flycat i-Rotor 5010:MethodologyThe goal of this motor characterization is to get a good first-order understanding of each motor's electromagnetic performance, as well as gauge the quality of construction and ease with which these motors could be adapted to legged robot applications.  All the characterization was done with a benchtop power supply, a pair of multimeters, a cordless drill, and an oscilloscope:The two parameters I measured were line-to-line resistance and line-to-line back-EMF waveform at constant speed (hence the cordless drill).  From these numbers, I can calculate the torque constant (Kt) and  "motor constant" (Km) by finding Kt/sqrt(R).  This number tells how much torque a motor can produce for a given amount of power dissipation in the windings (the units also work out to N*m/sqrt(watts).  It is important to note that this number is independent of how the motor is wound (assuming constant pattern and same amount of copper).  In other words, rewinding a motor to have twice the turns will give it twice the torque constant and four times the resistance, meaning the motor constant is unchanged.  The motor's ability to produce torque (looking at just resistive loss) is not dependent on how high or low a torque constant it is wound for, if copper area is held constant.  I find this to be a common point of confusion.So, motor constant is a very limited motor performance metric, but if you just want a good idea of how much motor you have, it's a useful number.Furthermore, perhaps a good metric of how well your motor's materials are used to produce torque would be Km/sqrt(mass).  Sticking two identical motors end to end would double the mass and increase the motor constant by a factor of sqrt(2), so this number would remain constant.Turnigy HD 5208 Gimbal MotorLinkPrice: $39.20The rotor is axially constrained by a single e-clip.  The shaft and bearings are very small diameter, and there's no extra shaft sticking out of either end.There is plenty of space for more copper on the stator.  The windings are a single strand of very fine wire.Extra-thick laminations.  Another indication that this motor wasn't designed to spin fast:Nice thick magnets.  There's no visible balancing done to the rotor.Back EMF on the scope:  This is nominally a 31 RPM/Volt motor.Torque Constant:  0.3081 N*m/AResistance:  11.7 ΩMotor Constant:  0.0901 N*m/sqrt(watt)Turnigy Multistar Elite 5010LinkPrice: $52.69  $42.15 as of 1/29This is a beautiful motor.  You pay for it, but Hobbyking really outdid themselves here.  For an extra $15 over other motors of similar size, you get absolutely beautiful single-strand, perfect windings, curved N45SH magnets, and an overall just really nice feeling motor.Solid construction all around.  Big shaft and bearings.  Shaft axially constrained by a locktite-ed screw.Rather disappointingly, there's a lot more space for copper on the stator.  However, I think for multirotor-duty, this actually is a good thing.  I bet these motors are exceptionally well cooled with air forced past them by propellers, considering the thick, clean windings and room for airflow between stator slots.  Also take notice of the tapered ends of the stator teeth.  Every other motor tested has right angles at the ends of the stator teeth.  Hard to say what this does without seeing the FEA.As expected, it has nice, thin laminations:A closer look at the curved magnets.  Also some small daubs of blue balancing goop.Drill-o-metered back EMF.  This is nominally a 274 RPM/Volt Motor.  Fairly sinusoidal looking.Torque Constant:  0.0333 N*m/AResistance:  128 mΩMotor Constant:  0.0930 N*m/sqrt(watt)Gartt ML 5208LinkPrice: $38-$45I had high hopes for this motor.  I managed to offer them down to $38 on ebay, making it cheaper than most equivalently sized motors from Hobbyking.  Unlike the two motors above, it has 22 rather than 14 poles.  A nice thing about having more pole pairs is that there's less flux between poles (because each pole is smaller area).  I was hoping this would mean that the rotor can would be less leaky (i.e. less flux leaking out of it).  This indeed appears to be the case - you can barely feel metal objects stick to the can of the motor.Solid construction here too.  Again, big bearings, big shaft, snap ring and screw to axially retain the rotor.  The magnet fill is pretty low though.The windings are "Hobbykinged" with a bundle of parallel strands.  Cleanly done, though.  The cutouts in the stator between the bearings and the windings are interesting.Nice thin laminations:More balancing compound, and a better look at the magnets:Back EMF.  This is nominally a 340 RPM/Volt motor.  Some much more noticeable harmonics on this one.Torque Constant:  0.02498 N*m/AResistance:  97.5 mΩMotor Constant:  0.0800 N*m/sqrt(watt)Turnigy Multistar 4830LinkPrice: $43.29This motor has a different aspect ratio than the rest of them - longer axially, smaller diameter.  Like the one above, it's a 22 pole motor.  Rather annoyingly, it came in a fancy metal box with foam cutouts on the inside.  I'd  have preferred cheap cardboard packaging and a couple dollars less expensive motor.Well constructed here.  Not sure why so many washers at the end of the shaft, but like before it's a screw plus snap ring to hold the can on.Good magnet fill, and a little balancing done to the rotor:Eww, some big 5th harmonic in that back EMF.  This is nominally a 420 RPM/Volt motor.Torque Constant:  0.0212 N*m/AResistance:  102.8mΩMotor Constant:  0.0662 N*m/sqrt(watt)Turnigy Multistar 4822LinkPrice: $32.91I was expecting this motor to just be a shortened version of the 30mm motor, but there are a surprising number of changes between the two besides the stator length.The rotor retention is different - this one just has a snap ring, while the 30 mm one had a snap ring and a screw-on cap to the shaft:The bearings and shaft are also smaller:As usual, there's some balancing goop on the rotor:I was expecting the back EMF waveform to look pretty much the same as the 30mm version of the motor, but to my surprise it showed none of that 5th harmonic, and