Re: how to model motor+gearbox
 

Thanks Clem! Interesting paper. I don't know how I missed it.

For grins, I checked your analytical solution to eq_14 using my favorite* CAS, Maxima. I got the same answer as you, but I don't like the way Maxima factored it [see attached PDF]. What CAS did you use?

You modeled the gearbox by using a constant parasitic torque. I'm looking for something just a bit more realistic.


*it's my favorite because it's free and therefore anyone can afford it:-)

Re: how to model motor+gearbox
 

They are all simplified models of very complex interaction forces... There are many many more than two forces/torques at work. Every model has it's boundaries.

This one (load dependent plus windage) actually has some undesirable behavior about zero speed. You would expect the gearbox to stay stationary until the torque exceeds some threshhold torque boundary. This won't happen here and the slightest torque still transmits 90% and will result in motion. This aberant behavior may or may not be important to your application. A "constant parasitic torque" model you've described does prety well in this case and can even approximate some non-back-drivable gearbox behaviors.

The "constant parasitic torque" is often the dominant force in tight fitting pin joint type rotational systems. Here the coulomb friction is a function of the "clamp load" in the joint and approximated as constant. Unless you have an air bearing, this behavior is always present to some extent. A "next best" model could be to apply all three. As you combine effects you need more measurements/observations to determine the values of the parameters.

The bottom line is that we can say "bad things" about any model. A good model minimizes complexity of understanding, implementation, and/or measurements while giving a desirable approximation. A bad model is one which gives inferior results to models of similar or lesser complexity. I haven't seen any bad models in our discussions, and we certainly don't want to steer anybody away from what has been proven to work!

Hopefully that about does it for the "simple" models discussion. :)

Re: how to model motor+gearbox
 

Attached screenshot "tetrix.png" shows Tetrix data gleaned from Richard Wallace's posts.

The purple dots are the two data points from post #1. These are actual dynamometer data on a Tetrix motor-plus-gearbox.

The blue dots are eyeballed from the dyno data graph attached to post #15 for the same motor, but without the gearbox. To facilitate visual comparison, this data was then adjusted for a "perfect" (100% efficient) 52:1 gearbox so it could be compared graphically to the data with the actual gearbox.

It's quite apparent that, for this gearbox at least, the "threshold torque boundary" consideration can be ignored, and a "constant torque loss" assumption is not valid¹. The torque loss in this gearbox is essentially zero with no load torque, and increases linearly² as the load torque is increased. This data suggests that modeling torque loss as a linear² function of load torque would work well for this gearbox.


Assuming this data is typical, the answers to the questions raised in the original post would be:



¹ the assumption is not valid, but it may still be possible to come up with an average value which can be tweaked to give useful results for certain problem domains

² probably roughly linear, but can't tell for sure from only two data points :-(