Modeling compliant motor mounting

[VELCROW]

I have a system where the motor has a torsionally compliant mounting to ground. When I accelerate the motor, I get a ringing in the output, and I am not accelerating the load nearly as much as I would expect given the motor torque available and the estimates for (reflected) load inertia and friction. The acceleration is measured at the motor shaft, so windup between the shaft and load is not being measured.

1. Is the energy lost to ringing responsible for the lack of acceleration?

2. I would like to model this in Excel. I can do this with a straightforward system of springs, dampers, and masses by just iterating the dynamic equations ( for linear systems, acceleration is the sum of forces divided by mass, v=v_prev+a*dt, x=x_prev*v*dt, spring force based on x pos of ends, etc.) My problem is that for a constant torque motor it does not seem like the output is at all affected by the compliance.

As a mental model, if I provide current to get torque T on a motor solidly mounted to ground, the motor shaft and load will accelerate with alpha=T/J. If the mounting is now just a frictionless surface, the housing will spin. But doesn't the motor shaft and load see the same torque as it did before, with the reaction provided by the opposite acceleration of the housing? For a limited time with true constant torque, and no limit on speed, it seems like the load acceleration is independent of the motor mounting. Is this right? If so, the compliance of the motor mounting should not be causing the ringing, and I need to look at the rest of what I thought was a pretty stiff system.

Thanks

 

[BobM3]

When you say "ringing" are you looking at the response of the shaft (displacement, velocity or accel) on a scope? You could have "ringing" even with the motor body rigidly attached to ground (no compliance). The shaft and the load inertia and the shaft springiness comprise a spring/mass system that will oscillate.

Is this a high performance system (servo)? It's common to get ringing on a closed loop servo system. You would adjust the tuning parameters to limit it.

 

[VELCROW]

Thanks for the reply.

I have some control software that records the encoder position every msec. The ringing is most obvious in acceleration, but it can be seen in velocity as well, during what is supposed to be a constant acceleration.

This is a servo system. The motor appears to be underpowered (not enough accel, as I mentioned) so during the accel the motor command, that is the current, is saturated to 16Amps. As long as that is saturated, the servo should have no effect on the motor. But I am getting a pretty good ring in the accel plot.

I am using Excel to calculate velocity from position data, and accel, from velocity data. I have to take a moving average of 10 pts or so to smooth things out enough to see a clear wave form, otherwise it looks more like PWM.

So essentially I have a constant current input to the motor, and the accel is ringing at about 18Hz. The system is very stiff, but I have a reducer and a coupling to ground, so I think they may be to blame, since they have torsional stiffnesses in the 8-10*10^5 Nm/rad.

I came to the conclusion that without significant damping, I can't be losing much energy to the resonance.

I'm still interested in modeling the system to find out how much damping I would need to get the results I see. I'm also curious about the mental model I mentioned.

 

[IRstuff]

18Hz might be believable for a resonance in the engine mounts. Anything that's springy can have resonance, even with "steady-state" inputs.

TTFN

FAQ731-376

 

[BobM3]

When you originally estimated your expected acceleration, did you include the inertia of the motor's rotor also?

For your modeling, I'd start with the fact that the air gap torque accelerating your rotor is equal and opposite to the air gap torque acting on your motor body. I believe that gives you two parallel spring/mass/damper paths to ground.

Of course the model would only be accurate with the controller open loop (as you currently have if the current is maxed out). Have you tried a smaller amplitude signal to see if the control damps out the oscillation without maxing out?

 

[VELCROW]

At lower accelerations, the control damps out properly without saturating the current command. And I did account for the motor inertia.

I almost see what you are saying about the two parallel spring/mass/damper paths to ground, but I think one of them (the shaft) does not go to ground.

I understand that when the motor accelerates, it exerts equal and opposite torques on the shaft and the housing. What I don't know is if the torque to the shaft is at all affected by what the housing is doing. If I rigidly mount the housing, or mount it on a spring, or just set it on the table, does that make a difference to the torque on the load?

Thanks.

 

[BobM3]

Open loop, the housing movement will affect the torque produced on the shaft. Using your extremes, if you had a motor body supported with frictionless bearings and it had no damping forces and it had no inertia, then you would not be able to develop any torque.

Using an electrical analogy, if the applied torque had a "source" impedance of zero then it would not change with varing load. The torque applied by the magnetics does have a finite "source" impedance. If you change the load (let the motor body rotate) then the applied torque will change.

 

[VELCROW]

I understand what you are saying about not developing torque with no friction, damping or inertia, but my extreme does not assume there is no inertia.

I don't quite understand about the torque changing with load. Do you mean torque changing with speed? If so, I am operating at a pretty flat spot on the torque-speed curve, so that should not be an issue.

If you mean the load changes when you clamp the housing vs. let it spin, I don't think it does. The housing either exerts a reaction torque because it is clamped, or a fictitious torque because it is being accelerated. Again, there is a speed difference between the two, but if I am at a flat spot, it does not affect the torque.

So again, the question is, how does a compliant mounting affect the torque on the output shaft (with a locally flat torque-speed curve)? It seems from my example that it should have no effect, but apparently it does and I can't figure out how to model it.

 

[IRstuff]

But your mounts do not have infinite compliance, so at some point in time in the test, they will act as rigid connections.

TTFN

FAQ731-376

 

[VELCROW]

The acceleration is short enough that the mounts don't reach their limits.

So I still have the question - does the compliance of the mount have any effect on the torque on the output shaft?

After thinking about this, the ringing I see is in the acceleration of the shaft. I thought this meant the torque would have to change, but it may not be the case. If I had a constant acceleration at the output shaft, but I grabbed the housing and wiggled it, the encoder (measuring between shaft and housing) would see variations in acceleration even if the load were under constant acceleration.

 

[Bribyk]

The compliance won't affect torque (equal and opposite reaction), as you've seen, it affects relative rotational velocity and, thus, power during transients.

Think of it as a car's suspension, the springs don't change the amount of weight (torque) on each wheel until you are going over bumps (transients). A rigid suspension (i.e. no suspension) will have the same forces between the tires and the ground as a typical suspension on a perfectly smooth road.

 

[BobM3]

For non-steady state it does. Think about how a motor produces torque. In its simplest form a pole on the stator attracts or repels a pole on the rotor. The magnitude of the force acting between the poles varies with the distance between them. It doesn't matter if I rotate the stator or the rotor - each will change the distance between the poles. Hence, rotating the stator will affect the force exerted on the rotor pole. The effect is mitigated a bit in a real motor because as one set of poles moves further apart, another moves closer together but it's not a linear relationship.