Why EUCs Fail
The importance of not pushin
g it too much
Francisco Gorina
October 2016
Why EUC’s Fail
Don’t push your wheel
Introduction
As most of you know, forums are full of EUC’s accidents in which the wheel seems to abruptly stop working, usually at high speeds. Just an example
Sometimes this behavior is blamed on the soft, the BMS, the mainboard… But while probably some cases are just that, soft or hard failures, there are many in which a sudden failure is just a consequence of the EUC’s workings.
Most of us are aware that as we increase speed, motor torque is reduced. In fact, the relation between torque and angular speed is :
so it is a neat, linear relation. If we go too fast, we will fell because we have a “lack of torque” and eventually if in a climb we push too far we may “overlean” and get a faceplant. All that seems clear and simple but under this simple and neat relation hides a much nasty truth, the sudden failure without any signal, without any evident reason.
A simple model for an EUC
To understand what happens we need either perform many experiments (not very healthy usually) or have a mathematical model that allows to perform virtual experiments without crashing.
In the model the wheel tries to maintain its level, moving the rider with it. As the driver moves its cog to the front, you will add a moment to the paddles and the motor will put a moment back so you don’t fall. But doing this, it will generate a reaction of the floor which will accelerate the wheel.
It will be accelerating forever but air resistance and friction will finally arrive to an equilibrium and stabilize the speed.
So the open loop wheel model (without motor) is something like :
α''[t] - g Sin[α[t]] == 0
which is essentially Newton’s second law. For small alfa Sin[α] ~ α and the equation may easily be solved analytically.
If α[0] = 0 and α’[0] = 0 nothing happens and α[t] = 0 for every t but if not it diverges and you fall down.
So we put the motor and we have :
α''[t] - g Sin[α[t]] + mr[mm[α[t], α'[t]], ω[t]] == 0
where mm is the filter that is a PD and mr is the motor response to the signal.
I don’t know if real controllers are PD or PID but just the PD makes a very good work stabilizing the wheel :
Here is a graph of a stable 55 N*m drive (aprox 4º inclination of your body) and a decrease to 0. As you can see, wheel angle changes very little.
Signal is the signal from the controller, from -1 to +1 (includes direction).
As the torque mades the wheel accelerate maximum torque of the motor decreases and the signal has to increase.
Also, as the controller is a PD it always needs a small offset to drive the motor so alfa will never be 0 when driving.
Anyway in this case everything is controlled and no problems.
But what happens when we don’t have not enough torque?, when we already have signal at +/-1 and the motor doesn’t give enough?
As you can see things are very different. As speed increases, signal increases to maintain motor torque but eventually all plateau so finally alfa goes nuts.
But the interesting point is the last graph where you may see the detail of alfa. It is essentially flat till it begins to fall and you fall with it. It is not progressive but very fast and very difficult to detect.
But not all is so simple. Let’s get a situation with 0 drive, you are perfectly aligned and are in a descent. The wheel accelerates because gravity pulls it down and then suddenly you move a little, just a little. What happens?
Here we have zero drive (we are perfectly vertical) except at 40-45 seconds where we tilt just a little. No need of extern action like a bump, etc.
As we are in a descent we have accelerated a lot and at second 40 are well beyond the motor maximum speed. The controller tries to get a torque but it fails, motor have no torque and we go down.
In the detail you may see than going from a stable wheel to a fall is very very fast.
Conclusion is that we don’t need bumps, etc to fall. We don’t need an electric failure, the controller shutting down the wheel but just going fast enough. Our movement is enough.
OK, now we found ourselves going too fast, so try to stop gently no?. No, Same result, we fall down as the motor is not able to maintain equilibrium.
So that means we need a lot of torque reserve. And responsible wheel manufacturers know it too well.
Ninebot famous tiltback is just a way of not letting it go too fast.
Ninebot E+ kicks back at about 23 km/h. If you let the wheel run without load it arrives at near 40km/h and probably the motor has some reserve as it is able to maintain that speed sometimes. So that is near half.
I am a little impressed that Ninebot software doesn’t cut it immediately at a speed but waits a little to confirm it is not a fault.
And think you may find situations in which at half the speed you unestabilize the wheel. Reasons may be low battery, or the typical overlean in a climb. Please, be cautious and don’t try to pass the security limits. Once over them the wheel gives you NO warning and that is just physics so no way to go over it, sorry.
Don’t push your wheel1