A Study on Average Eigenvalue Sensitivity for the Improvement of Rotordynamic Stability of Integrally Geared Centrifugal Compressors

This paper presents a study on the average eigenvalue sensitivity to design variables of an integrally geared centrifugal compressor pinion-bearing system and its application to the improvement of the rotordynamic stability. The average eigenvalue sensitivity is the approximation of the eigenvalue sensitivity, i.e., the central difference of eigenvalue is substituted for the partial derivative of eigenvalue with respect to a design variable. Hence, the average sensitivity coefficients can be calculated using a rotordynamic analysis program integrated with a bearing analysis program. The results are presented in a new frequency versus logarithmic decrement diagram, which is designed for multiple analysis cases. The average eigenvalue sensitivity to the mass properties of an impeller can not only predict how much an eigenvalue of interest varies with the mass properties, but also indicate where the impeller should be modified. The average eigenvalue sensitivity to a bearing design variable strongly depends upon pad length, bearing load and pivot offset. The sensitivity study tells what design variables should be changed for satisfactory rotordynamic stability and bearing performance. The effects of main shaft dimensions on the average eigenvalue sensitivity are examined to select and tune certain dimensions for the rotordynamic stability. This numerical method has been implemented to improve the rotordynamic stability of two compressor pinions.