Elevator Equations

[narmstro2020]

So I decided to work through the derivation of the set of equations for net Force, net Motor Current, Voltage, and velocity for an elevator (simple gear rolling up and down a linear gear, has a mass, etc.) starting from the torque equation of a DCMotor gearbox

My results are linked here.

These should line up with the equations presented in Controls Engineering except instead of redefining the motor constants in terms of n and G I've kept them separate. K_t, K_v, and R_m are all from the perspective of a single motor.

I get torque due to gravity as -mgr * sin theta

I'm just wondering if this is correct. I'm excluding friction in the motor and gearbox from this setup.

[calcmogul]

I get torque due to gravity as -mgr * sin theta

That's correct assuming m is mass, g is acceleration due to gravity, r is length of the arm, and theta is arm angle measured from vertical (SingleJointedArmSim measures angle from horizontal).

[calcmogul]

I think the carriage on the rack and pinion system works differently then a string/pulley system.

In the rack and pinion system, the "drum" becomes the pinion gear.

It would also seem to me that there might be a need for an argument to ElevatorSim that takes in some sort of effective gravitational acceleration term for the physical system setup and one that takes in kG for the sysId system setup.

I'm not convinced that's necessary. The gravitational acceleration is constant for all elevators (excluding drum MoI), because all masses have the same acceleration under gravity. Drum MoI is probably absorbed by kₐ since it affects all dynamical terms.

[narmstro2020]

In the rack and pinion system, the "drum" becomes the pinion gear.

Yes. And therefore the mass of the carriage would factor into the mass of the drum for moment of inertia purposes the acceleration.

I'm not convinced that's necessary. The gravitational acceleration is constant for all elevators, because all masses have the same acceleration under gravity.

True concerning g. However that would make ElevatorSim more usuable/accurate in terms of inclined elevators and factoring in kG toward the system. From a CD post last year I was informed that kG / kA should equal g, but because of efficiency losses (which I thought factored in kS) it doesn't quite. I don't think I was fully convinced of this reasoning.

[calcmogul]

And therefore the mass of the carriage would factor into the mass of the drum for moment of inertia purposes the acceleration.

The way you phrased this implies you're confusing moment of inertia (distribution of mass around an axis of rotation) with mass. The moment of inertia is still just the distribution of mass of the drum around its rotation axis. The carriage mass is still separate. The physics is the same as the drum case; the rack serves the same purpose as the string.

However that would make ElevatorSim more usuable/accurate in terms of inclined elevators and factoring in kG toward the system.

I don't want ElevatorSim to support inclined elevators; the class is complex enough as it is. Teams who make one should make their own simulation class instead.

[narmstro2020]

The way you phrased this implies you're confusing moment of inertia (distribution of mass around an axis of rotation) with mass. The moment of inertia is still just the distribution of mass of the drum around its rotation axis. The carriage mass is still separate. The physics is the same as the drum case; the rack serves the same purpose as the string.

You're right. I'm convinced.

I don't want ElevatorSim to support inclined elevators; the class is complex enough as it is. Teams who make one should make their own simulation class instead.

Okay. Not a problem.