Newkirk Effect: Thermally Induced Dynamic Instability of High-Speed Rotors

The Newkirk Effect is the vibration change due to thermal distortion of a rotor caused by rubbing on stationary components. B. Newkirk first noticed this phenomenon in 1924 and gave a qualitative explanation for it. The effect is not yet well enough understood. This and the importance of it in designing high-speed turbine rotors demand further work in this area. In this work an analytic study was undertaken. The static bow due to an arbitrary heat input can be found from a convolution integral of a source bow function and a heat function. Utilizing the dynamic response of the system, the resulting dynamic bow was computed. This dynamic bow controls the generated heat and the associated heat function. The resulting model can be described by a complex integral equation which can be transformed into two nonlinear differential equations. The stability and the modes of these equations have been studied. The equations themselves were solved with numerical methods. Three modes of the Newkirk Effect were discovered: spiralling, oscillating, and constant modes. It was found that critical speeds only indirectly influence the modes. The important factor is still the dynamic characteristics of the system in the form of a phase angle. It is believed that this analysis can be used for the design of rotors free of rubbing at wide ranges of speeds.