How to calculate Torsional Vibration 3

[Tagger]

I understand about lateral vibration, but how do you calculate (formulas) for torsional vibration of a tube?

 

[ivymike]

set up a mass-elastic system to represent your tube geometry, and solve the equations of state... the situation is analogous to lateral vibration, so if you can do one you can do the other.

 

[sreid]

The torsional vibration frequency is determined by the torsional stiffness of the tube and its rotational inertia. The best source for vibration equations is "Natural frequencies and Mode Shapes" by Blevins.

 

[tgmcg]

First step is to define ALL the mass & elastic components of the system. For example, if the tube is connected to masses on either or both ends, possibly via couplings, then you must include the polar inertias of these masses in your torsional model. (It's not often that one would be calculating the torsional natural frequency of a tube by itself.)

If the tube is of non-constant cross section, you may want to use the Mykelstad-Prohl transfer matrix approach, and divide the tube into multiple mass elastic stations of constant cross section. Same approach would apply if calculating the torsional modes for a free-free supported tube.

Best regards,

Tom McGuinness, PE

 

[desertfox]

Hi Tagger

Putting the above posts into formula mode :-


w_n=[√] (T_o / I)



where w_n=natural angular freq in rads/secs

T_o= torque per unit angle of twist

I = moment of inertia of oscillating mass

regards desertfox

 

[sreid]

Tagger,

If you can supply more specific information on your problem we can help you more.

 

[suomifoster]

There is a good book that describes solving torsional vibration by Daniel J Inman, Engineering Vibrations

Terve,
Aaron

 

[Tagger]

Thanks for your help guys. I found some info from what a previous employee did using TK Solver that helps.
Basically what I am determining is the torsional frequency of a vertical shaft for a pump. You not only have to worry about lateral frequency but also torsional. You have to determine the Vane Pass Frequency (VPF) of the system. That is the RPM*# of Vanes of the impellar. The drive shaft torsional natural frequency (TNF) must be designed away from multiples (based on the # of vanes) of the operating speed and the speed of the pump itself.
I am trying to learn how to determine the TNF of a vertical pump shaft from single to multiple sections.
I've been pouring over the data left and it looks like you split the system into mass - spring - mass - spring, etc using the inertias and torsional stiffnesses.

 

[GregLocock]

Holzer's method is what you are looking for.How do you account for the coupled inertia of the fluid in the impeller?




Cheers

Greg Locock

 

[aberta]

As mentioned by GregLocock, you need the Holzer method. In this you must include the motor inertia, shaft stiffness to the coupling, coupling inertia, the pump shaft stiffness, the impeller wet inertia. The latter will approximate to inertia of the impeller and the entrained water. Having determined the natural frequencies, you must ensure that you donot get a nodal point at the coupling. Change inertia or stiffness to get the nodal point away from this location. Your exicitaion frequencies will be the pole pairs of the motor and the vanes in the pump.
Let us know how it works out.