DYNAMIC ANALYSIS OF MULTI CRACKED ROTOR THROUGH EXTENDED LAGRANGIAN MECHANICS

Abstract

The initiation of fatigue cracks or other defects in structures or machines or their elements cause a reduction in stiffness and also change the dynamic characteristics of the machine. Dynamic analysis of cracked rotor is an emerging area of research due to its practical importance and several issues are associated with this analysis due to its complexity and increasing demand of reliable crack detection techniques. It has been found in archival literature that various crack detection methodologies have been used to analyze the dynamic behaviour of a cracked rotor. The vibration problems of cracked rotor generally pose nonlinearity due to its breathing phenomena. Moreover, the theoretical and computational analysis of the non-linear problems seems to be complex and very expensive even with today’s powerful computers. In this work, extended Lagrangian formalism is used for the dynamic analysis of multi-cracked rotor. Another significant issue for the analysis of vibration of cracked rotor, is the analysis of symmetry breaking of cracked rotor, which is also analyzed in this work. However, this symmetry of rotor is disturbed if there is a small difference in material or geometric properties, caused due to initiation of a crack. The study investigates the dynamic behaviour of a finite asymmetric rotor through extended Lagrangian mechanics. Two case studies are analyzed and presented to develop analytical framework for these systems. Computational models are also developed through bondgraph modeling technique and simulations are carried out and compared with analytical results.

vi Further, an extended Lagrangian–Hamiltonian formalism is employed to a continuous multi-cracked rotor system. Analytical formulation for amplitude and natural frequency is being derived through this extended Lagrangian–Hamiltonian methodology. Computational model through bondgraphs are being created. Simulations are carried out for various crack depth to analyze the dynamic behaviour of multi-crack rotor system. Finally, an experimental framework is being developed for the validation of simulation and analytical results. Variation of stiffness due to crack depth and effects of second crack are also determined. Amplitude of vibration at various speeds and different crack depths of multi-crack rotor are examined. NVGate® software is being used for capturing the various signals in running mode of machines. Experimental results validate the analytical and computational results to a great extent. Therefore, it is concluded that the extended Lagrangian methodology is one of the effective and accurate methods to determine dynamic characteristics of a multi-cracked shaft. It may be used for real-time monitoring of the rotor system in various industries.