Constraint equations for rotating shafts

barrti

Hi

Thanks for the earlier help with the spaceframe chassis and suspension. FYI - It did actually model the weight transfer at each end of the car and accounted for the varying suspension stiffness as you would expect. It avoided the usual graphical calculation of roll center or resorting to hand calculations etc (as per Milliken's book).

I am currently working with forced torsional vibration for shaft and flywheel combinations.

1. I've successfully built the simple model below with one shaft (using beam elements)and one flywheel mass using one nodal rotational inertia and analysed it with Dynamic Response 3D. Is there a way to use more nodal inertias or must I model additional flywheels as shell or solid elements attached to the shaft?

2. If I have several parallel shafts, is there a way using constraint equations, to connect the two ends of the shafts to transmit torque? I'm thinking of using the constraint equation method to replace say a vee-belt.

Cheers,

Tim

Victor

1) Yes, you can add more rotational inertias as separate loads. It just doesn't allow a single one to be spread over more than one node.

2) Yes, you can couple torsion between, say, nodes 1 and 4 with a constraint equation like 0 = 1 rx4 + -1 rx1, which you'd enter as:
1 1/rad rx 4
-1 1/rad rx 1

barrti

Hi Victor

Thanks for this. I think I now understand why I was fooled. If I remember correctly, I must have selected more than one node when I added the inertia.

Thank you also for pointing out what I found later about the constraint equations (sorry Victor! I should have persevered). I now have a 3:1 reduction belt drive between 2 shafts with about 1 minutes work!

The attached files show that the angular velocities and torques are at a 3:1 ratio

I continue to be very impressed by Mecway. Not only is the software versatile, amazingly cost effective but the support is exceptional. Well done Victor.

Tim

barrti

Greetings again
Thinking about the use of mecway for geared and belt drive shaft systems, is it possible to model rotational backlash with beam elements? I am thinking about when one has clearance between gear teeth or between coupling elements. I realise that one could use contacts and solid elements to do this but computationally, these could be slow?

Could there be a way to use constraint equations for this or possibly a custom non-linear material?
Tim

Victor

There's no simple way to do backlash. I expect you could use a compression-only or tension-only material, which CCX has. You'll have to enter the definition manually. It's a nonlinear problem so at least you'll need to use the CCX solver with nonlinear dynamic response. That means some other features won't be available, like rotational inertia. You might end up having to make the whole thing with solids.

barrti

Thanks for that. Just a question about applying torque to the shaft mass system. If I apply a short torque pulse of say 2. Milliseconds, I notice a high frequency sintorsion result in the shaft. Initially I thought it was the result of the natural frequency of the system. It is about 500 Hz. The natural frequency is actually closer to 15 Hz.
What is this?
Tim

Victor

That vibration will be higher frequency modes above the fundamental natural frequency. The sharp edge of a pulse contains high frequency components that will activate them.

You can change the analysis type to Modal vibration with about 10 modes to see the natural frequencies. There's one around 450 Hz. It doesn't show any near 15 Hz though.

barrti

Thanks Victor

I did some more work and have answered some of my questions...

If we refer to the attached model and screenshots:


I make the torsional natural frequency of the shaft mass system to be 17.5 Hz (ignoring shaft mass and its own torsional natural frequency).


Since the torque pulse is shut off after 24 msec and the system is free to vibrate in an undamped manner, then I now realise that it is not reasonable for me to expect to see 17.5 Hz in the results.

What we are seeing from what you have said must therefore be the 25 mm steel 1m long shaft vibrating independantly from the flywheel. I have not calculated the torsional natural frequency of the shaft alone but it must be high.

If you look at my screenshots, there seems to be about a 410 Hz torsional vibration of some magnitude occurring over the whole shaft.

What is suprising and therefore my main question here is the magnitude. It is about +/- 60 Nm close to the fly wheel and about 10 Nm close to the left of the shaft. Is this to be expected or am I missing something?


Tim

barrti

Hi Victor
Just a question related to the natural frequencies:
I have used both solid elements and beam elements for the shaft.
None of them seem to have any torsional modes? Does Mecway give torsional modes?
Tim

Victor

I don't have an intuition for the magnitude of those high frequency torques. I tried refining the mesh but it didn't change it. I suppose that's just how it is. If you look at longitudinal stress, and turn on the animation, you can see the shaft twisting much more than its overall rotation, so I suppose that's alright.

In torsionalshaft03.liml, I found the fundamental torsion mode at 711 Hz (mode 10). Look at the Rotation about X field variable to find a mode where it's not ~10^-13.

barrti

Victor
Thanks for your help here. If you use the equations here (https://perso.univ-rennes1.fr/lalaonirina.rakotomanana-ravelonarivo/Stokey_chapter7.pdf) for a uniform shaft alone, you get about 700 Hz natural frequency (ignoring the flywheel) so I guess this fits in this case.

I tried a slower ramp up/down time of 0.1 sec and get 714 Hz ripple in angular velocity. Interestingly, with this case, their does not seem to be any ripple in torque. So I supose that the gentler ramp being less impulsive and excited only the 1st natural frequency of the shaft.

Correction.
I checked my earlier work from torsionalshaft03.liml (also see the word doc) and found that somehow, I calculated the frequency of the torque ripple wrongly. Its about 700 Hz not 410 Hz.



Anyway, there is obviously a lot going on here and as you say, I guess thats how it is!

cheers, Tim

barrti

Greetings,
FYI - This last piece of info may help.
I made an error when I calculated the natural system frequency of the flywheel and shaft.
Its 2.8 Hz not 17.5 Hz. I mistakenly did not convert from Rad/sec to Hz. In actual fact for a 1.1m long 25mm dia shaft and a 10 kgm^2 inertia, the natural frequency with the shaft end clamped is 2.6Hz.

I then fixed the end of the shaft and ran modal analysis in Mecway and got 2.606 Hz (Rotation about X). This mode of course will not appear without fixing the drive end.

Tim

Victor

Oh, I see that mode now. Surprisingly very low compared to the unconstrained one! Makes sense now since it's dominantly a flywheel mode compared to the higher one being mostly a shaft-only mode.