Theoretical Analysis of the Shaft

This paper represents the dynamic response of a steel shaft which is fixed at both ends by bearing. The shaft is subjected to both axial and bending loads. The behavior of the shaft in the presence of two transverse cracks subjected to the same angular position along longitudinal direction is observed by taking basic parameters such as nondimensional depth ( ), nondimensional length ( ), and three relative natural frequencies with their relative mode shapes. The compliance matrix is calculated from the stress intensity factor for two degrees of freedom. The dynamic nature of the cracked shaft at two cracked locations at a different depth is observed. The compliance matrix is a function of crack parameters such as depth and location of crack from any one of the bearings. The three relative natural frequencies and their mode shapes at a different location and depth obtained analytical and experimental method. Multiple adaptive neurofuzzy inference system (MANFIS) methodology (an inverse technique) is used for locating the cracks at any depth and location. The input of the MANFIS is provided with the first three natural frequencies and the first three mode shapes obtained from analytical method. The predicted result of the MANFIS (relative crack location and depth) has been validated using the results from the developed experimental setup. 1. Introduction Generation and propagation of transverse crack in a shaft or rotor is a common phenomenon for every machine. Nowadays, it becomes a challenging task in front of a designer to identify the crack and take steps for precaution before damaging the whole structure. Zheng et al. [1] have formulated a learning algorithm based on radial basis function neural network for structural damage diagnosis. In their work, they have used fuzzy logic, genetic algorithm, and neural network for development of the proposed model. The model has been designed with the data (modal frequencies obtained from finite element analysis). Their model is capable of predicting the delimitation location and size of the composite laminated beam successfully. They have found that the developed model is capable of predicting the results within an error of 18 percent. Bachschmid et al. [2] have analyzed the vibration response of a shaft line used in a turbo generator unit. They have used the quasilinear approach and finite element method to obtain the vibration signature (modal frequencies and amplitude of vibration). They have found out the effect of a crack along the shaft line on the dynamic response of the system at different speed of the