On Crack Detection in Tuned and Mistuned Repeating Structures Using the Modal Assurance Criterion

Repeating structures in the form of multiple‐bladed rotors are used widely in turbomachinery. Mistuning in turbomachinery is caused by small differences in individual blade properties because of inevitable material and manufacturing variations, resulting in the splitting of vibration modes of the tuned system. Modal characteristics of the blades are quite sensitive to the level of mistuning present inside the structure. In addition, the existence of damage also results in changed dynamics of the complete system. This paper introduces a modal assurance criterion (MAC)‐based approach for the investigation of small defects such as cracks in a repeating structure. In order to understand the key issues involved, initial work involved a numerical study of a simple comb‐like repeating structure, followed by a detailed numerical and experimental investigation of a tuned and mistuned bladed disc. Changes to the system mode shapes and mode order arising from damage are related to the location and severity of damage. Damage, in the form of small, open cracks, is modelled using different techniques such as follows: material removal, monotonic reduction in the modulus of elasticity of selected elements at the required location and mass modification. Damage indices based on differences in the MAC that give a measure of the change in the mode shapes are introduced. MAC matrices are obtained using a reduced number of data points. The damage index is obtained from the Frobenius norm of the MAC matrix subtracted from the AutoMAC of a reference tuned model without crack. A clear correlation between the damage indices and the crack depth/location is shown. Application of this approach to the limited data obtainable from developing techniques such as blade tip timing is also explained.