Torsional analysis-Model Setup

[mechanicaljw]

Hello All,

I am trying to set up a torsional model for a drive train. In the attached picture i am stock at the area that i have circled in red. How do i account for Nodes 10, 11, 12, 15 and 16 in this model? Can setting up an equivalent system with the loads at the nodes be done for such a system? The N denote nodes and G denote gears. The drive train is for a screw compressor.

Thanks in advance for your help.
Jimmy

 

[GregLocock]

Between n15 and n16 I suspect you have a driveshaft or coupling with a rather lower stiffness than the other shafts.

However I don't really understand your question.

Cheers

Greg Locock


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[mechanicaljw]

Hello Greg,

I need to set up a torsional model for the drive train shown to be able to predict the torsional frequencies. In the previous cases I have considered, the synchronization gears (G6 & G7) were on the driven end (opposite end of where they are located now) and so the drive shaft with nodes 11 and 12 was connected ONLY to the male rotor and then to the synchronization gears and then to the female rotor. In that case i was able to treat the system as a reduced system (equivalent system, where the gears and other mass points were put onto a single shaft) and get the torsional model. But from the literature what i have now after node 9 is more like a branched system since i have two shafts sharing the input torque from the drive. It is my first time encountering this type of a system and so i was wondering about how i could set up the torsional model in such a case.

I hope that I have been able to explain myself?

Thanks!
Jimmy

 

[rob768]

You have two options:
Use a program that can cope with a branched system in which you just model every mass and stiffness at eacht respective speed.
or, if you can only model straight lines, sum masses 15-18 with node 7 (remember to account for the speed difference), or, since a gear is of near infinite stiffness, sum nodes 7+15-18 to node 6.
That is an approximation, which is valid only if shafts 7-15 and 16-17 are stiff (no elastic coupling or long, slender shafts)
It will give information on the natural frequency of the main branch (6+11-14), but of course not of the lunped branch. You can repeat this and summ the masses of the main branch to node.
Like I said, this is an approximation. Better is to use a branched model.

 

[mechanicaljw]

Hello Rob768,
Thanks for your input and suggestion. I have been thinking along the same line of using the branch system approach.

I have two additional questions:
1. About the branch system approach. Is there any other method other than using the transfer matrix approach?

2. This is a more general question. When i run some of the torsional models I get imaginary values for some frequencies. What is the exact interpretation if a torsional frequency is imaginary?

Thanks!
Jimmy

 

[rob768]

Hello Jim

if you want only the natural frequencies, you might use a finite element program. Remmember to reduces all masses and stiffnesses to a common speed.

I don't know what you mean by the imaginery values. It may be related to the damping generated, but the program i use only gives real values.

 

[GregLocock]

imaginary frequency implies that either your stiffness or mass term has gone negative. This is unlikely.

By combining the two paralel rotors into one you eliminate an important degree of freedom, there is a very simple mode shape in which the main rotor is nodal and the two rotrs are in antiphase.

As such it seems to me you need a more complex model. What program are you using?

Cheers

Greg Locock


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[rob768]

to get the mode Greg refers to, it is also similar to lump the main branch. I agree it may be an important one, especially if the installation is symmetrical and you might get beating effects.

 

[mechanicaljw]

Hello Greg and thanks for your input. Same to rob768. I am actually setting up the model manually and using MATHCAD for solving for the frequencies and the mode shapes.

I sure want to consider the branched approach as you (rob768) suggested in one of your previous post.

Thanks!

 

[mechanicaljw]

Hello rob768 and Greg,

I just wanted to know if you could recommend any program can do such a calculation (with the branching) for me? I have some limitations in Mathcad with regards to the size of the matrix it can handle.

Thanks!

 

[rob768]

We use an in-house developed program, as well as the DNV-Pilot program. For just natural frequency calculation, any finite element package will do I suppose. I am not familiar with Mathcad, but a model can't be that extensive?

 

[GregLocock]

It can't be more than 20x20 can it? mathcad should knock that over in a flash. If it is bigger than that, matlab, octave (free), or perhaps you could use dymola, adams, simulink or similar to build a component based model.





Cheers

Greg Locock


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[mechanicaljw]

Hello rob768,

I am having some issues with getting the residual torque for the branched system attached in this post @ I3. When I do it for another case where the Inertia of the gears (Ig) is neglected i am getting it right. However, when it is taken into account my residue torque plot versus omega for using the Holzer method is giving me only the first frequency. I am not getting the second. I am not sure what i am doing wrong.I have been also able to compute the angular deformations correctly at end Inertia.

Any input would be appreciated.

Thanks!
Jimmy

 

[GregLocock]

That should give you 4 modes, of which one is trivial.

Cheers

Greg Locock


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[rob768]

It's been some time since i last did it by hand, but with a branched system, you need to add the inertia torque of a secondary branch to that of the main branch. So, considering 1-3-2 as main bracnh, the torque of branch 4 is added to 3.
In the book of Den Hartog you'll find a good example of an iteration scheme for a branched model.
The number of modes is equal to the number of masses and will include a trivial mode.

 

[rob768]

Been playing with the numbers a bit. I noticed that the natural frequencies of each of the "free" masses is 62.5, when considering the central node as fixed. This kind of symmetry may cause the iteration to cause errors or lead to "missed" frequencies.

 

[GregLocock]

Any analysis that cannot deal with branches with equal sdof frequencies needs to be junked and replaced by a proper method.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

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[rob768]

Agreed, most modern programs solve the problem by matrix calculation and will not miss a mode. However, older programs using the Holzer iteration method may go seriously wrong if two (or, as in this case) more modes are within one step of the iteration process. You can see it in the modes, but only if you are very aware of the possibility.
Besides, there is no reason to solve this problem by a holzer tabulation.

 

[mechanicaljw]

Hello rob768,

I had been busy finding the values like the stiffness, Inertias, of the system attached in the NodesDriveTrain.jpg file and so i have not been able to set up the model. I am now at the stage where i can set the model up and I was wondering if you can suggest how the idle shaft between gears G1 and G3 or on the middle idle gear should be included in the drive train network for the torsional model. Also, I would be grateful if you can throw more light on the way you would set the model up in case you wanted to use the branched network approach. I would also want to use the input shaft as the reference shaft as this shaft is connected to the electric drive, which has a large moment of Inertia. I would be glad if a sketch is included.

Thanks for the suggesting the book by Den Hartog. It helped me to understand the way the junction should be treated in torsional systems.

Thanks!
Jimmy

 

[rob768]

Hello Jim

i don't see the attached file you mention. Forgotten?