Explanation and Application of the SAFE Diagram

Vibration of compressor and turbine bladed wheels, interacting with the fluid distributed by the stator vanes, can be reason of fatigue failures when resonance conditions are excited. Avoid resonances is a strategic requirement in bladed wheels design. The Campbell diagram approach just excludes the matching between the natural mode frequency and the excitation frequency. However, bladed wheels show many natural frequencies that are very near each other, so it is difficult to avoid any resonance matching. The Singh’s Advanced Frequency Evaluation (SAFE) diagram approach introduces also the shape matching instead of just the frequency matching. Many frequency matching can be identified as non-critical and then tolerated. The present paper explains the SAFE diagram and introduces an analytical expression to identify the critical shape interactions. The matching map is introduced, showing the shape of the mode that fully interact with each excitation harmonic order. Full resonances are distinguished from partial resonances that are not identified on the SAFE diagram. Finally, an application is reported on a family of bladed wheels, identifying the optimal geometry configuration to avoid any critical resonance.