calculating shaft critical speed by hand 1

[hector002]

I am trying to calculate(estimate) the critical shaft speed of a rotating shaft.

When i did this back in school we solved for the eiganvalues of the 4th order diff equation:

d^4/dx^4 - B^4*y=0 where B^4=rho*A/(E*I)*omega

however this assumes A (shaft area) to be constant. The shaft i an interested in steps from 1" to 2" and back down to 1" between the bearings. Does anyone have some tips or references to solve eigenvalue problems for a shaft with non uniform diameter. thanks

 

[hector002]

the concept for the rig is a pretty standard 'floating' bearing design. I will be using Two 2"x7:x15" bearing pillars to support the rotation shaft. One pillar will clamp the bearings axially the other will be floating. the pillars will bolted to a 1" thick positioning plate which will then be clamped to a bed plate. The shaft will be direct driven with a flex coupler. The test fluid bearing will be mounted on the shaft between the two bearings free to move radially wrt the shaft. Static and dynamic loads are applied directly to the bearing housing.

yes the 4" diameter shaft is to simulate larger diameter fluid bearing applications as well as allow for some space to instrument the bearing and shaft

 

[electricpete]

With a flexible rotor, that bearing in the middle probably would have changed the mode shape and made a big difference. With this rigid rotor, I think it won’t make much difference (other than another bearing stiffness to add in parallel).

Since the bearing and support stiffness will represent a fairly big uncertainty, a bump test would of course be a great way to check the results if you have the luxury of access to an assembled unit at this point in time. Try to bump the shaft horizontally near the center and measure vibration response on the bearing housing. Also can try vertical but expect that’ll be higher.

I'll be interested to hear what Greg and others estimate for support stiffness. Seems pretty low to the ground and stout compared to most machines.

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[hector002]

unfortunately this is all in the design phase so far so no real world testing is possible yet.

Question though, in your 'bump test' why would you bump the shaft horizontally- it seems that the direction of interest would be the vertical, longitudinal modes of the supports (yes the transverse/bending modes would of the pillars would be lower-but there really is no excitation in that direction)- maybe i didnt descibe the rig very well. The shaft is mounted horizontally, supported by two vertical bearing pillars. Any static or dynamic loads would be applied perpendicular to the shaft axis

when i get home im going to calc the longitudinal modes for a basic 2"x7"x15" steel bar (thats basically what the pillars are just with a 90mm hole bored at the top)- im guessing this is going to be quite high and what you guys mentioned before-- that its going to be the stiffness of the bearings that will be the weak link. I guess a call to the manufacturer will be in order.

 

[GregLocock]

Most of the energy goes into the lowest frequency mode, and a spinning hsfat thinks only about radial and axial, it doesn't undertsand vertical and horizontal.

Of the pedestal modes, vertical is axial compression of the structure, which is inherently stiff, whereas horizonatl is bending of the structure (typically) which is likely to be less stiff.

For our work at 500 hz we use cast iron bedplates tied to the reinforcement in the concrete floor and grouted in place- anything less and we see spurious effects due to the mounting system.



Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[electricpete]

What he said.

If it were a flexible rotor and bearing/support very stiff in comparison, there is only one first critical speed.

In this case with the rotor very rigid compared to bearings/support, the bearings and support determine the critical. The support as Greg described typically much lower stiffness in the horizontal direction. So you have a "split" critical, with the lower frequency determined by the horizontal direction stiffness.

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[electricpete]

To clarify my previous, I was agreeing with Greg.

"in your 'bump test' why would you bump the shaft horizontally- it seems that the direction of interest would be the vertical, longitudinal modes of the supports (yes the transverse/bending modes would of the pillars would be lower-but there really is no excitation in that direction)"

#1 - Mode shapes and frequencies are characteristic of the system, not the excitation.

#2 - A mode shape is of concern if excitation is present to excite that mode shape at it's natural frequency. In the case of this horizontal rotor, there are numerous potential sources of running speed radial force which can excite resonance in either radial direction H or V. These would include unbalance, eccentricity, bowed shaft, misalignment of drive etc. That's why we never like to operate machines near critical speed or resonance. In the specific case you mentioned, the water is alittle muddier. I believe there was a concern for 1/2 speed whirl to excite critical or resonance (oil whip).

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