Vibrational resonances of centrifugal compressor and radial inflow turbine impellers are usually identified using either Kushner’s or Singh’s parametric equations in product design and failure analysis. These equations were developed based on positive work accumulated within a certain time period. However, some resonances observed in simulation and testing cannot be understood with those resonance equations.

This paper presents an alternative method to derive vibrational resonance conditions. A new model of general pressure pulsations is developed by taking into account the disturbances resulting from stationary obstacles and rotating blades. Analytical solutions of the forced vibration responses of a rotating disk subjected to different pressure pulsations are then formulated. From the forced responses, both Kushner’s and Singh’s equations can be derived. They can further prove to be equivalent though they focus on different physics.

A general resonance condition is derived from the analytical solutions. This condition is a necessary condition, i.e. all resonances must meet this condition while a system following the condition may or may not be in resonance, depending upon excitation sources. It is noticed that the excitation sources could be related to harmonics due to stationary obstacles, harmonics with combined harmonic orders, or even harmonics to be understood. This general resonance condition can hence provide more “possible resonance points” and assist identifying resonances from more representative modes and more excitation sources. It has been validated by predicting vibrational resonances observed in three centrifugal compressors. This condition has also been successfully employed in the failure analysis and design modification of a radial inflow turbine impeller.

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