Simulating Flywheel with Servo Motor

Model the torque curve over the speed range of interest as would be presented by the actual load.

Modelling an ideal flywheel is trivial, but the big question here is the nature of the drag: For instance, is the drag torque proportional to speed, or is it some other function of speed (or of some other parameter or of more than one)? What causes the drag? Is the drag temperature-dependent? A cylinder rotating in viscous liquid that becomes less viscous as energy is imparted to it, for example? A paddle rotating in air? Is the drag torque a linear function? A nonlinear one? Is it linear over the range of interest? What are its dependencies? Lots of questions that only you can answer.

If the mathematical model of the drag torque vs (independent variable(s)) is overly complex or unknown, one thing you could do is measure it via your servomotor system - if it makes certain parameters available, servomotor torque (computed or inferred via motor current), speed and so forth. If so, program your servo to apply a schedule of speeds (typically the 'independent variable') and measure the applied torque to maintain this speed, for each speed, for example.

Knowing more about the cause and nature of the drag torque would be very helpful.

You hit on so many important points here that I had to give you a GA. The actual questions asked by the OP were not directly answered and are in reverse order of what I think is the method to solve this.

First then is the second question, the mathematics are differential equations and/or calculus to attempt simulating a flywheel with a servo motor. You, europium mkII, rightly describe the various models for linear and some of the possible non-linear effects of a flywheel. If this was my task, I would use a LaPlace transform version of these equations. [A valid shortcut around the complications of diff/eq and calc.] Additionally this will then allow for an easier design of the control circuits needed in the end. Once a suitable flywheel model has been established the suitability of the servo and controller can then be identified.

Second then is the first question, this does make sense in that it is theoretically possible to do this and it has been done by others before. However can the motor and controller the OP has in hand be capable of simulating the flywheel(s) needed to be simulating, maybe.

Will it be financially worthwhile to simulate a flywheel instead of just attaching the actual flywheel, for just one invariant flywheel it probably will not be cost effective. For many different possible flywheels it certainly will be cost effective.

I would look for some software....but it seems you could use the servo motor to drive the flywheel at different acceleration rates recording the current and perhaps translate that to torque....but I would think a test of the results would be prudent....

http://www.wescottdesign.com/articles/Friction/friction.pdf

http://www.mcasco.com/Answers/qa_ldot.html

Last question first...

What math do I need to work through?

To simulate the flywheel, you would need to measure the rotation rate and calculate its rate of change. The reaction torque from spinning up and slowing down the flywheel would be the rate of change of rotation velocity times the moment of inertia. The reaction torque from the drag load, or course, is constant. So the amount of load torque you would need would be the sum of these two.

What you need to simulate this load is a programmable torque. The torque from a dc motor can be controlled by varying the motor current...

So your motor has to generate torque that is the sum of the constant drag and the rate of change of rotation velocity times moment of inertia. A dc motor driven by a controlled current supply to generate the necessary torque would work.

My understanding of servo motors is that they drive to a certain position, much like a stepper motor and controller. I don't see how a servo motor would work in this application.

The drag is function of speed and NOT at ALL constant! It depends on the type of fluid in which the flywheel rotates and the boundary conditions along the radius.

The shear stress will be τ=η*(dv/dn) where dv/dn= velocity gradient normal to the surface. If this value is constant all over the flywheel then the friction torque is T=4*PI*τ*(Re^3-Ri^3)/3 -(2 friction surfaces). dv/dn will depend on the rotation speed ω and on the flow rat along the radius. It can be laminar and the equation is valid or present a transition and a turbulent zone and the equation is not any more valid.

The OP specified a constant drag torque...

"We have a hydraulic motor/gearbox comb that currently is tested with a 1000 in-lb drag load"

... so I assumed it was constant, as you would expect with sliding friction.

Wouldn't the torque absorbed by the servo be at least partially represented by heat? Is this a synchro servo or servo actuator?

Were you there, originally during original development of this test method, and understand why it is performed this way? Or did a kid do this, and no one knows why it's tested this way?

My experience is from the avionics use of +28VDC DC servo motors (precision torque) with low backlash gears.

So from a production test standpoint, just what qualities are being tested by the current method?

Are you testing just the hydraulic motor-gearbox, or is the servo amplifier with hydraulic valves included?

What are you trying to achieve by changing the test method?

I've seen production mess with PTRs (production test requirements), and ship junk as they did not see the long history of the test revisions to add tests that detect different production assembly issues. Our servos had to match the Kt (torque vs current constant) to less then 2% error.

My point is do you understand why the test is the current method, and will changing it defeat some quality aspect. Or was this just a random selection of 1 of a ~1000 different tests that could prove the product before shipping?

Spinning up and down a flywheel does some thermal aspects of the servo amp and hydraulic valve leakage, maybe, was that the intent.

So it becomes a Taurus with magneto hydrodynamics of a ferro fluid, modulated electrically between Newtonian and non-Newtonian phases.

Thanks guys for the enthusiasm here. I used poor word choice to describe the situation. We don't have access to the current test bench. We have the test procedure for the component with that bench and some engineers that were on this program years ago saw the bench but we don't have any real details about it. I can't give 100% of the details because I don't know who is viewing these boards, but I have some more info I left off the first post (sorry). The motor drives a wing structure from stow (for packing it into the carrier) to deployed. I think the drag load is from the mechanical linkages connecting everything. The flywheel isn't sitting in fluid, it's just a big heavy rotating disk. The test procedure calls to rotate it for 10 revolutions and it can't reach a speed faster than 50rpm and has to complete all the rotations in 20 seconds. I think the time requirement comes from a requirement of the maker of the aircraft that was likely driven from the government for how quick the wing structure needed to convert from stowed to deployed and vice versa.

I don't have the servo model number handy but through the gearbox we currently have installed it can do ~30000 in-lb at around 60 rpm or something like that. Servo motor runs at 3000rpm.

My first comment was not a direct answer to your question.

When you spin up and down should it be a linear speed rise and fall or any other time-function?

If it is linear then the flywheel is a constant moment load for the test object. So that you load in fact with the sum of the two constant moments+the flywheel friction moment. If you work in air the last can be neglected.

For your drive it is a step loading function which could be only approximated by a load-drive as you think since the simulator will not be able to bring a step but only a stiff ramp.

Of course it is a problem of relative values it could be possible that the simulation is satisfactory but as you asked if it is justified to do in such a way I would answer it is not.

Mr. Buzz Kill here.

It sounds like this flywheel simulator is to be used with a QTP/ATP for a product. If so, you may be required to Qualify your test equipment and have a Calibration Schedule with traceability to NIST standards. Most inspectors will assume that the flywheel has not evaporated mass and therefore the flywheel test equipment should be pretty stable. However, home brew software running motors and other items held together with duct tape . . . . . . . . . Maybe the Fred Flintstone method has some merit.

Your feedback or output from the flywheel/drag simulator is torque. The input to the flywheel/drag simulator is angular acceleration. The flywheel/drag simulator has to take its measurement of angular speed ω, calculate rate of change α=dω/dt (acceleration) and then generate a torque T to feed back to the driving motor.

T = K+Iα, where K is the constant torque of the drag, I is the moment of inertia of the flywheel, and α is the angular acceleration in radians/sec2.

To generate the feedback torque, you can drive a dc motor with the appropriate current to generate the necessary torque.