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 Lund in 1986 and was verified by Jafri. It uses cross-coupled internal moments instead of cross-coupled forces to ground.




1)      Jafri, S., Shrink Fit Effects On Rotordynamic Stability: Experimental And Theoretical Study, Ph.D. Dissertation in Mechanical Engineering, Texas A&M University, August 2007.


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)      Lund, J.W.,1986, “Destabilization of Rotors from Friction in Internal Joints with Micro-slip”, International Conference in Rotordynamics, JSME, pp. 487-491


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., Lund, J., Dill, J., Zorzi, E., 1990, “Internal Rotor Friction Instability”, MTI 88TR39.


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, Texas A&M University, College Station