paper: MINIBOT acceleration solution

[vamfun]

Originally Posted by Ether

Good catch. I was thinking about that just the other day. The model assumes there is enough friction between the "wheel" (drive shaft) and the pole so that the wheel never slips. But if your shaft diameter is small enough and your normal force isn't high enough, the stall torque of the Tetrix can "burn rubber" (like a dragster). The model does not account for this. I could add another user input: coefficient of friction, and include that to model wheel slip. But not only would that number be fuzzy (so many factors can cause it to vary), it would also make the system nonlinear and not solvable analytically. Numerical methods would have to be used. Of course, once you say goodbye to the analytical solution and start using numerical methods, you can introduce all sorts of clever nonlinear refinements. Maybe a fun project for the off season.

It is important to have the wheel slip modeled if you want to get the optimum wheel radius and normal force. I have done the modeling a couple of times... once for my own excel dynamic model and I also posted the numerical solver as a modified version of Team 1640 Drivetrain model on my blog here for others to use.
This has the spec motor curves built in but by playing with the parameters, you can easily make it look like the dyno model.

I measured the coefficient of drag as .22 for our minibot model using a high speed camera and a drop test. The coefficient of drag is defined as Drag_force/Normal_force. This model used Tetrix kit bearings. Typically the friction force is 6 to 7 newtons for our 2.5lb minibot. We always measure it with a newton scale prior to each run.


A excellent approximation to the climb time can be made by using your variable definitions.

The steady state climb speed v_ss = D/B (should be the same as peak_pwr/W)
System time constant tau = 1/B
Dist = pole height.
Then
time_to_climb = Dist/v_ss + tau

This falls out of the exponential solution when the time > 5 tau which is typically the case for the minibot. To include the effects of drag... simply replace W with W + Drag.

Glad to see you are spending some time to document the physics for others. I have been a little lax this year on my posts.