EFFECT OF
INTERFERENCE FITS ON ROTORDYNAMICS
A recurring problem in rotordynamics is the whirl
instability caused by internal friction in a built-up rotor. The work of Newkirk
and Kimball (1924), Gunter (1966), Lund (1974), Black (1976) and others
verified that rotors with shrink (or press) fits are susceptible to
subsynchronous whirl instability once the rotor speed exceeds the first
critical speed.
Unlike passing through a
resonance, where the amplitude of vibration increases and then decreases, the
vibration of an unstable system continually grows. In most cases, this whirl
instability has been found to be correctable with hardware fixes, such as
changing the bearings (to ones that are more flexible and have asymmetric
stiffness), adding more external damping to the system, and tightening the
interference fits. However, internal
friction remains a persistent problem, because all rotor assemblies have some
amount of internal friction and quantitative predictions are very difficult.
Dr. Vance and his graduate
students at Texas A&M worked for a number of years
to develop an improved capability to predict threshold speeds of whirl
instability for built-up rotors with shrink and other types of interfaced
joints. A very challenging subservient goal was to develop a measurement
procedure to determine the correct numerical value of the internal friction
coefficient (for any particular rotor assembly) for use in rotordynamic
computer codes that compute stability (typically logarithmic decrement).
One of the first tasks accomplished in this project was
to experimentally investigate the prediction of Black (1976) who predicted that
there could be a finite speed range of whirl instability that could be passed
through safely. Ying and Vance (1994) verified Black’s prediction by performing
tests on a built-up rotor.
In 1994 the project began to develop a test procedure for
assessing the stability of a built-up rotor (Parker, 1997, Vance, 1996). A rotor was suspended free-free and excited
with a shaker. It was discovered that
the first mode shape of the rotor on bearings could be closely approximated in
a free-free test by attaching additional masses to the ends of the rotor. But
the required weights turned out to be double the weight of the rotor, which
makes the procedure impractical for larger rotors.
In 2000-2001 Mir measured the logarithmic decrement of a
simple free-free rotor assembly with variable interference fits and used these
values in a computer code to predict the threshold speeds of instability within
1000 rpm.
In
2002 Srinivasan developed a procedure using shaker
tests (producing larger amplitudes) to measure the internal friction in a
simple rotor assembly, and converted the measurements to appropriate parameters
for input to a rotordynamic computer code
for predicting threshold speeds of rotordynamic instability.
Jafri (2004-2007) worked to make
the tests more repeatable and to generalize the procedure for a more complex
rotor assembly with multiple press fits. Jafri
determined that the cross-coupled stiffness model used by many previous
investigators is incorrect. The correct model was first described by
References
1) Jafri, S., Shrink Fit Effects On Rotordynamic Stability: Experimental And
Theoretical Study, Ph.D. Dissertation in Mechanical Engineering,
2) Kimball, A.L. Jr., 1924,
“Internal Friction Theory of Shaft Whirling”, General Electric Review, 27,#4, pp.244-251.
3) Gunter, E.J.,1966,“Dynamic Stability of Rotor-Bearing Systems”, NASA
Technical Report, SP-113.
4) Walton, J.F. Jr. and Martin,
M.R., 1993,”Internal Rotor Friction Induced Instability in High-speed Rotating
Machinery”, Vibration of Rotating Systems, DE-Vol.60, pp. 297-305.
5)
6) Kimball, A.L. Jr., 1925,
“Measurement of Internal Friction in a Revolving Deflected Shaft,”, General Electric Review, 28, pp.554-558.
7) Kimball, A.L. Jr., Lovell, D.E.,1926,
“ Internal Friction in Solids,” Transactions of ASME, 48,pp.479-500
8) Walton, J., Artiles, A.,
9) Artilles, Antonio F., 1991, “ The Effects of Friction in Axial Splines on Rotor System
Stability,” IGTA Congress and Exposition, pp. 1-7.
10) Black, H.F., 1976, “The
Stabilizing Capacity of Bearings for Flexible Rotors with Hysteresis”,
Transactions of the ASME, pp.87-91.
11) Ehrich, F.F., 1964, “Shaft Whirl
Induced by Rotor Internal Damping”, Journal
of Applied Mechanics, 31, pp. 279-282.
12) Vance, J.M., Ying, D., “Effects
of Interference Fits on Threshold Speeds of Rotordynamic Instability”, Paper
No. 2007, Proceedings of the International Symposium on Stability Control of
Rotating Machinery, August 20-24, 2001, South Lake, Tahoe, California.
13) Mir, Mohammad M., “Effects
of Shrink Fits on Threshold Speeds of Rotordynamic Instability”, MS Thesis,
2001,