Comparative study of vibration analysis in rotary shafts between Rayleigh's and Dunkerley's methods

The importance of vibrations in rotating rotors in engineering applications has been examined, as has the best approach to interpreting vibration data. The most extensively used analytical approaches for rotating shaft vibration analysis have been investigated. In this research, a detailed study was made of the Rayleigh and Dunkerley methods due to their importance in the special calculations to find the amplitude of vibrations in the rotation system. The multi-node method was used to calculate both Dunkerley's and Rayleigh's methods. An experimental platform was built to study the vibrations that occur in the rotating shafts, and the results were compared with theoretical calculations and with different distances of the bearings. It proved that there is very little error between the experimental and theoretical results. The vibration signal from the sensors was analyzed using the LABVIEW program. Rayleigh's method was compared to the exact method, and it was considered the most accurate method. It was found that it made very little difference, up to about 0.06%. As for the Dunkerley method, the difference between it and the proper method is about 4%, which is acceptable. Then a comparison was made between Rayleigh's and Dunkerley's methods, and it was found that Dunkerley's method is the most appropriate in the calculations.