[JesseK]

Thanks for solving a question I've had for a while about the non-constant force applied by an electric motor to accelerating a robot. I couldn't quite finalize any equations to get concrete undisputable answers.

Perhaps a more accurate way to model motor load due to robot mass is to assume that some percentage of the normal force (Fn) is transferred through the bearings to create a load on the motor. Typically roller bearings are >99% efficiency if perfectly aligned, yet this is not always the case; I've usually model 1% of the mass per bearing. Increasing number of wheels in contact with the floor as well as increasing robot weight creates higher motor loads, thus reducing top maximum speed as well. An important point is that the load is distributed among all of the motors in the model as well.

For example, in your spreadsheet tool, reduce the # of CIM Motors from 4 to 1. The top speed in reality would not remain the same after the reduction, though I suspect the shape of the acceleration curve is the same.

A simple recalculation for Vmu is all that's needed since the load is a constant Vmu_new = (1-(total_loss_load/total_system_stall_torque))*Vmu. Gearbox efficiency loss should also be similarly modeled, and could be a fraction of stall torque depending on the number of gearing stages (0.98*0.98*Tstall).

Another graph I found to be useful is a velocity vs distance traveled graph. This shows how much of the field it takes to accelerate to maximum speed and allows for readjustments based upon available motors and gearing options. It doesn't matter what the top is speed if it takes the whole field to get up to it! It's a simple graph of existing data.