Vibration Characteristic Analysis Of A Cracked Gear-rotor System

Gear pair is one of the most widely used movement transmission devices in all sorts of mechanical equipment and its mechanical behavior and working performance have direct effect on the overall performance and reliability of the mechanical system. Since the force case of the gear is quite complicated, even the design of the gearbox is precise, gear fault may appear. This unexpected failure may bring huge economic damage and even endanger life safety. Therefore, it is of important engineering significance to analyze the early gear fault feature and identify the fault as early as possible. In this paper, a test rig gear rotor system is chosen as the research object, and a gear mesh stiffness model and a finite element model of the gear rotor system are established, then the effects of tooth root crack on gear mesh stiffness and dynamic responses of the system are studied. An experiment is also performed to validate the results of theoretical analysis. The main contents of the study are as follows:(1) Three mesh stiffness solving methods, namely deformation method, energy method and finite element method, are introduced in detal. Based on the traditional mesh stiffness model, an improved mesh stiffness model for a healthy gear pair is proposed. The comparison results show that the finite element method could consider more practical factors, so its calculation results are more accurate, but its efficiency is relatively low. In traditional mesh stiffness model, the gear tooth is modeled as a nonuniform cantilever beam on the base circle and when the number of teeth is larger or smaller, this method will produce large error. In the improved mesh stiffness model, the accurate transition curve is considered and the gear tooth is modeled as a nonuniform cantilever beam on the root circle. This model accords with the shape and force case of the tooth, so its results are more accurate than traditional method.(2) Considering a more realistic crack propagation path and weakening effects of tooth root crack on the tooth effective thickness, the gear mesh stiffness when there is a crack in tooth root is analyzed. The effects of crack depth, width, initial position and crack propagation direction on mesh stiffness are discussed. The research shows that it is acceptable to assume the crack path to be a straight line and choseing a parabolic curve as a limiting line for reducing the tooth thickness is appropriate under large crack condition. The stiffness reduction increases with the growth of crack depth and width, decreases with the increasing crack initial position angle and the stiffness firstly decreases and then increases with the increasing crack propagation direction angle.(3) The effects of tooth root crack and its parameters on dynamic responses of the gear rotor system are discussed. When the tooth root crack appears, distinct impulses are found in time domain vibration responses, and the time interval between every two adjacent impulses is exactly equal to the rotating period of the cracked gear. In frequency domain, side frequency components appear around meshing frequency and its harmonics. Amplitudes of impulses, sidebands and statistical indicators ascend with the growth of crack depth and width, decrease with the increasing crack initial position angle, and firstly increase and then decrease with the growth of propagation direction angle.(4) Based on finite element model, the influences of extended tooth contact phenomenon caused by elastic deformation of the tooth on gear mesh stiffness and dynamic responses of the gear rotor system are analyzed. It can be seen that extended tooth contact makes the entry and exit of a gear tooth smooth and with the increase of torque, the phenomenon becomes more and more apparent. In addition, vibration responses of the gear rotor system in time domain and frequency domain will also change.(5) An experiment is performed to validate the results of theoretical analysis and effective methods to identify gear root crack are explored. When the tooth root crack appears, periodic impulses are found in instantaneous energy in the time distributions of the experiment and simulation signals, and amplitudes of the impulses will increase with the growth of crack depth. So, through Hilbert instantaneous energy, gear tooth root crack can be detected easily.