The Study About The Influence Of A Transverse Crack On The Elastic Wave Propagation Characteristics Of Rotating Shafts With Variable Cross-sections

The propagation characteristics of elastic waves in the shaft are affected by the geometrical dimensions,rotational speed and crack depth.In this paper,based on the national natural science foundation project ‘Research on method of crack detection for shafts of large rotating machinery based on propagation characteristics of elastic wave',the influence of transverse crack on the elastic wave propagation characteristics of the variable cross-section shaft is studied by means of transfer matrix method.At first,according to different fracture modes,the transfer matrix of the crack was derived.Then the transfer matrix for the whole cracked rotating shaft was deduced by combing the transfer matrix of a single rotating shaft and that of a crack.After that the results of theoretical analysis are solved by numerical method,and then the FEA method and experiment are used to simulate the analysis to the further study.This study is organized as follows.Chapter one expounds the background meaning of the research.The development,research methods,application prospect and existing problems on studying the elastic wave propagation in mechanical components such as rotor,beam with cracks are summarized.The content of this study is proposed at last.Firstly,three types of fracture modes are briefly introduced,which can be divided into three basic types according to the stress and displacement characteristics of the cracks in chapter 2.Then three different fracture modes are established through the relationship among the strain energy density function,the stress intensity factor and the local flexibility coefficient,and then the transfer matrix of the shaft with a variable cross-section and emerging a transverse crack is obtained.Solved the eigenvalue of the transfer matrix using the MATLAB numerical calculation tool,the crack model which is more consistent with rotating shafts with variable cross-sections is obtained.At last,based on the most reasonable crack model,the influence of rotational speed and crack depth on the elastic wave propagation characteristics of the crack shaft is studied.In chapter 3,the finite element analysis method is carried out according to the theoretical model and relevant conditions in chapter 2.Firstly,the constructed model is imported into ANSYS.Secondly,the reasonable boundary condition and loads are applied,then transient analysis is carried out on the crack shaft.Obtained the results of ANSYS,time-frequency analysis through MATLAB(STFT)is necessary to gain the passband and the stopband frequency and to further study the elastic wave propagation characteristics from the perspective of energy.In chapter 4,according to the relevant conditions in theoretical analysis,the designed experimental scheme is used to further study the propagation characteristics of elastic waves in the variable cross-section of the cracked shaft.The experimental results are compared using the MATLAB software.The results of the experiment agree with the theoretical analysis and the finite element simulation analysis,and further verify the influence of transverse crack on the elastic wave propagation characteristics in the rotating shaft.In chapter 5,this paper summarizes and prospected the next research work.