Stiffness of gaps in rotordynamics

[VibFrank]

Hy,
I start in rotordynamics and are a little bit confused of the stiffness of gaps.
The situation is: a rotating shaft (d=200mm) with a small gap (1mm) to the stationary part. No fluid flow across the gap (only in tangential direction of course)
Calculated according to Black, I get negative kxx and kyy and very high additional masses. Is this realistic ? How do you handle the influence of such gaps ?
If I take them as journal bearings, I would get positive stiffness and no additional masses from our "journal bearing program"
Thanks
Chris

 

[vanstoja]

For shaft rotation in an relatively wide annular fluid-filled gap there is a so-called "virtual mass effect" where the effective mass of the rotating fluid can be several times higher than the mass of the shaft depending on fluid density (water is much worse than air for example). In rotordynamics jargon this is an inertia effect that results in negative spring action, ie, increasing rotor radial displacment with eccentricity increase due to rotor unbalance leads to higher loading and more displacement and still higher loading. Increasing shaft stiffness and/or minimizing rotor unbalance are possible remedies for preventing rotor-stator contact and rubbing which can lead to other kinds of rotor whirling instabilities. Besides H.F.Black, fluid annulus inertia effects have been studied and reported by R.J.Fritz of General Electric, Chris Brennan of Cal Tech and Dara Childs of Texax A&M among others.

 

[VibFrank]

Hy,
thanks for your answer. I still have problems to understand:

1.) Where is the difference between Black, Fritz ... with decentrating forces and on the other side the journal bearing theory with centrating forces ? If I have a gap that isn't defined as journal bearing, which theory could be applied ??
2.) If I have additional inertial masses in my model, the weight of the complete machine is about 10x higher than in reality. So the pendular frequency of the whole machine changes dramatically compared to the machine, when the shaft does not rotate and no inertia forces exist. Is this reality ?
Thanks
chris

 

[vanstoja]

I haven't seen an explicit definition of the critical radius ratio that results in a transition from fluid film radial bearing clearance gap decentering forces to wide gap inertial negative spring forces but radius ratios below one-tenth of typical bearing clearances (R/C=333 for bearings at 1.5 mils per inch diameter clearance)certainly produce the inertia forces. We had a long water cooled rotor with an R/C of about 58 and an L/D of about 4 that had high virtual mass-induced rotor loads and decreased critical speed. Fritz [1970, "The Effects of an Annular Fluid on the Vibrations of a Long Rotor"ASME, J.Basic Engineering, Dec., pp.923-937]tested R/C ratios of 25, 16 and 10 in water, glycerol solution,and oil and found hydraulic mass to motor mass ratios greater than 1.0 for water and glycerol which lowered the rotor critical speed. Fritz's rotor L/D ratios were about 0.75. For much smaller L/D ratios such as exist in centrifugal pump impeller wear ring seals, the inertia effects apparently don't occur. Thrust balance drums and liquid cooled motor rotors are applications where inertia forces of large annular clearance gaps must be considered.

 

[alexit]

I have always wondered about this theory as applied to gaseous-fill gaps. How will the fluid density affect the negative spring (linear, square, etc.)

Has anyone done more recent testing with density or are they continuing with fluid-states?

 

[vanstoja]

Fluid inertia effects in wide annular gaps are directly proportional to fluid density which for air is some 5 orders of magnitude lower than water so air gap inertia effects should be insignificant. Fritz also tested in air at the three R/C ratios of 25, 16 1nd 10 but showed no results for hydraulic to rotor mass ratio increases nor any changes in rotor critical speeds which were tested at 897, 960 and 1077 RPM , respectively, for the three radius ratios.