Influence of Axial Loads to Propagation Characteristics of the Elastic Wave in a Non-Uniform Shaft

Yimin Wei,Qi Liu,Zhiwei Zhao,Wenhua Chen

doi:10.1186/s10033-019-0385-z

Abstract

The vibration propagates through the shaft in the form of elastic waves. The propagation characteristics of the elastic waves are affected by the axial loads. The influence of the axial loads to the propagation characteristics of the elastic waves is studied in this paper. Firstly, the transfer matrix of the elastic waves for the non-uniform shaft with axial loads is deduced by combining the transfer matrix without axial load and the additional equation caused by the axial load. And then, a numerical method is used to study the influence of the axial load, non-uniformity and the rotating speed to the propagation characteristics of the elastic waves. It’s found that a new Stop Band will appear due to the axial force, and the central frequency of which will decrease as the increase of the force, while the band width of which remains the same. The central frequency of the new Stop Band will also increase as the increase of the cross-section area ratio; however, the rotating speed of the shaft doesn’t affect the propagation characteristics of the elastic waves obviously. Finally, an experimental rig is built up for further study, even though there are some small local errors, the results of experiments match well with the numerical ones, which indicates the validation of the theoretical results. The result can help to study the influence of the axial load to the dynamics of a non-uniform shaft and help to reveal the vibration propagating mechanism in such a shaft.

Highlights

The rotating shaft often suffers axial loads in real applications and the loads increase gradually as the unstop development of the machinery, e.g., the shaft of a large compressor, the rotor of a heat pump system, the dynamics of the rotating shaft with axial loads have drawn people’s attention [1,2,3]
Vibration propagates in the media such as a shaft in the form of elastic waves, the study to the propagation characteristics of the elastic wave can help to know the dynamics of the rotating shaft
Huang et al [13] presented a method for assessing the dynamic stability of supported columns with damping under arbitrary periodic axial loading owing to parametric resonance

Summary

Introduction

The rotating shaft often suffers axial loads in real applications and the loads increase gradually as the unstop development of the machinery, e.g., the shaft of a large compressor, the rotor of a heat pump system, the dynamics of the rotating shaft with axial loads have drawn people’s attention [1,2,3]. The rotating shaft are often non-uniform, e.g., with non-uniform cross-section, with variable elastic modulus [4,5,6] These factors have a non-negligible influence on the vibration propagating in the shaft. An important question of interest, which to our knowledge have not been addressed in most previous studies, is the influence of axial loads to the dynamics of the rotating shaft and to the propagation characteristics of the elastic waves, which need to be studied further. The axial load of the non-uniform rotating shaft is considered, the influences of the axial load, the area-ratio and the rotating speed to the propagation characteristics of the elastic wave are studied. An experimental rig is built up to verify the results of the theoretical study

Theoretical Study

Part 1 Part 2 Part 3

Conclusions