# Motor Calculations

Does anyone know how to do motor calculations and motor curves and things of that nature? I’ve seen a few posts here and there, but they’ve all thus far involved the old 3-wire motors. Minus insufficient power (torque) and stripping, my team and I have never had any electrical or thermal issues with those motors. These days our designs now call for the possible reliability and strength that the 269’s and 393 can offer. However, over the past season we’ve had a plethora of problems with these motors, so we thought it would be best to do some calculations as our school’s FRC team does.

Although you probably already know most of this stuff given your involvement with an FRC team, this website gives a reasonably good run-down of how power, speed, and torque are related: http://lancet.mit.edu/motors/motors3.html

It’s got pretty much all the formulas you need to be figuring out where the limits are and where the most optimal operation of your motors will be. Here are the specs for the 269 and 393 motors, which you can substitute into the equations to get the right numbers out:

2-wire 393 (High Strength):
Free Speed:100 rpm (As Shipped)/160 rpm (High Speed Option)
Stall Torque:13.5 in-lbs (As Shipped)/8.4 in-lbs (High Speed Option)
Stall Current:3.6A
Free Current:0.15A
All motor specifications are at 7.2 volts. Actual motor specifications are within 20% of the values above.

2-wire 269:
Free Speed:100 rpm
Stall Torque:8.6 in-lbs
Stall Current:2.6A
Free Current:0.18A
All motor specifications are at 7.2 volts. Actual motor specifications are within 20% of the values above.

These three diagrams might help when you’re trying to figure out how you should gear your motors too:

Hopefully that helps! As Rick Tyler quite rightly says in the Lynfield Drive thread, try not to stall your motors!

Thanks! I’ve also heard that somewhere around 60% is the sweet spot for electrical efficiency… can anyone here confirm or disprove that?

Without details of the plethera of problems you’ve had on new motors, we can’t tell if you have new, interesting problems, or just the usual ones (expecting miracles). Can you share your experiences with your new motor problems? (Collaboration is more interesting than neediness.)

If you look at the last graph on the motors3 link from two posts above,
you’ll see that the Max Power (Output) is at 50% of noload RPM,
the mid-point balance between max RPM and max torque.

I’ve previously posted that 60% of noload RPM is a good gearing target to get max power out of Vex motors.
Electrical efficiency (EE) is different; as long as a battery lasts longer than a competition match, most people here don’t care about EE
Efficiency is PowerOut/PowerInput.
PowerOut = RPMTorque as mentioned in the motors3 link.
Power input = Volts
Amps; Volts is relatively fixed by battery, so I’ll ignore it here.
Amps input is proportional to torque output,
which leads to this equation of proportionality:
Electrical efficiency (EE)
== (…PowerOut…) / ( …PowerInput… )
== (RPM*Torque) / ( Volts * (Torque = Amps input ) ).
The Torque terms cancel, so we are left with the results that “higher RPM = more efficient”.

Here are some example EE metrics from the motors3 last graph, moving from right to left across the marked points: (non-Vex specific, not real units, just a comparative metric)
High speed power output 4W / 0.7 = EE metric of 5.7 (higher EE than at max power)
Max______power output 5W / 1.6 = EE metric of 3.1
Low speed power output 4W / 2.5 = EE metric of 1.6

The higher RPM = (lower torque and lower Amps) side of the power graph is more Electrical Efficient.
This also make mathematical sense because power lost in the motor is I^2R, while output power is proportional to I=Torque;
Increasing the current Amps (I) makes the I^2
R losses grow more quickly than the output power.
Excessive IR losses end up as heat, which trips the thermal breaker.

In related soundbites:

• its very instructive to make your own speedchart in excel, to match and combine vex speedcharts.
• Drive train motors are often starting up from 0 rpm = stalled
• A full accel/decel model would include linear acceleration of robot mass, as well as rotational interia of heavy spinning parts (wheels).
• The “Exothermic Hypothesis” is that small-wheeled robots are nimbler, due in part to lower rotational inertia.
• Andrew/Discobots report faster results than Vex speedchart, so your results may vary from anything said on forums.
• Tables and equation are only a guide to point your real experimenting in the right direction: empiracism rules over theory every time.

btw are these pics in the gallery?
so i can “favorite” them like i did with the old speed chart?

:):) (ten char)

It seems as though my team’s problems match up with that which many people on the forum have had. “Expecting a miracle,” kinda sums it up well enough. At times our drive would slow down significantly, if not stop all together. At that point the articulation still seemed to function just properly. We had a four wheel drive with four 3-wire motors geared at 3:5 and a four bar linkage with two 393 motors geared at 7:1. At the end of the linkage was a claw with two servos geared at 3:1.

Hey Rick, How many small double omni-wheels have you ordered for Exo?
10-pair? 20-pair?

Flippin: Thats a good start of description, but You forgot to mention essential facts like:
CPU type, motor port assignment (if Cortex), battery, wheel size and type,
and whether 3:5 means higher-speed or higher-torque when you say it.

Also what does “articulation” reference mean: that the arm still works when the wheels dont?

Another useful metric is “How many hours of driving practice did the robot have between assembly and game-day?”

If you had 4" wheels with a 36-tooth gear driving a 60-tooth gear, four motors should have been OK. If you were driving 60s into 36s and especially if you did not use omniwheels, your robot was *seriously *underpowered. Either gearing would have been fine with 2.75" wheels. All of these comments assume that your robot was in the 12-15 pound class. If you had a sub-8 pound ultralight, your drive might have been OK.

The easiest way to tell if your robot is underpowered, watch it accelerate. If it starts off slow before ramping up to full speed, it’s underpowered. If the robot jumps pretty much right to full speed, it’s not.

It was a first-run cortex (the one without the elevated VEXnet port) One of the 393’s and one of the servo’s were placed on each breaker on the microcontroller. And the drive motors were placed on the power expander. We had 4" wheels (2 omni’s in the back, 2 all-purpose wheels in the front). We had around 2 weeks worth of drive/programming practice, but things seemed to go wrong at competitions often. Perhaps we were driving much more aggressively at competitions? I was taught that gear ratio’s were Driven:Driving, so 3:5 would be speed.

Only six so far, but it’s only May…

and another question:
what are you planning to do with all the old ones?

ultra mobile protobots? just an idea

Sorry if it’s been answered and I missed it but what do the green/yellow/red colors on that chart mean?

They correspond to the “danger zone”, red is not reccomended because it draws too much current or it doesnt have enough torque or it is too fast to be controllable. One of the best examples is a 3:1 speed gearing which is in the yellow because its at the borderline of being feasible

Ah, thanks for clearing that up.

if you have a lightweight robot, then yellow would be ok
but if you have a tank, then its best to stick to green

It’s also worth noting that faster robots take more effort and practice to control. Just keep in mind, it doesn’t matter what the top speed of your drive is, only how long it takes to complete the task.

That’s an issue that some clever programming should be able to fix. For Round Up, my team used stepped motor powers based on ranges on the joystick, so if the joystick was moved just a little bit, the robot would actually have just enough power to move, instead of the usual 15 place gap before the robot actually moved.
Speed is always important, but control is also always better. It is possible to do both.