Research On Vibration Characteristics Of Cracked Rotor And Asymmetrical Rotor System Based On Three-dimensional Transfer Matrix Method

The rotor is a core component of the rotating machinery,and the accurate expression of a rotor model is one of core problems in the vibration analysis.In order to describe a crack in the rotor more accurately and to improve the accuracy of the rotor model,a novel stereoscopic crystal format model(SCFM)of a rotor system is proposed in the paper.The SCFM is made up of crystal grains which are dispersed into a spatial network structure.Two adjoining crystal grains in the axial direction are connected by a massless rod,and they are imaged to connect by a massless spring and a torsion spring in the longitudinal direction.In addition,the distance between the grains in the longitudinal direction is ignored.The transfer matrix method is an effective and convenient method to describe the multibody system,and the traditional TMM is mostly used to describe the simple onedimensional linear multibody system.In order to describe the SCFM,a novel three-dimensional transfer matrix method(3-DTMM)is proposed in this paper,the dynamic equations of the SCFM are deduced by using the 3-DTMM.By combining the extended transfer matrix method and the discrete time transfer matrix method(DTTMM)with the 3-DTMM,the application range of the 3-DTMM can be extended from the frequency domain to the time domain,and the applicable objects are extended from the linear system to the nonlinear system.Firstly,the natural frequency of a single disk rotor is studied by using the 3-DTMM,and the steady-state responses of the rotor system under the unbalanced mass with and without damping are investigated,the correctness of the SCFM of the rotor system is verified by comparing with the results calculated by the FEM.The influence of the depth and position of an open crack on the critical rotational speed of the rotor system is investigated by using the SCFM.The results show that the major critical speed of the rotor system decreases with the increase of the crack depth,especially the secondary critical speed is more affected by parameter changes.At the same time,the position of the open crack is also the key factor affecting the major critical speed of the rotor system.When the open crack is located near the disk or in the middle of the span,the major critical speed of the rotor decreases obviously,and when the open crack is located at both ends of the rotor,it has a small impact on the major critical speed of the system.In addition,the vibration characteristics of the rotor system with the effect of the breathing crack at different depths are investigated by using the SCFM,and the results show that the existence of breathing cracks reduces the major critical speed and causes the super harmonic resonance of the rotor system.With the increase depth of the breathing crack,the unstable range of rotor system expands.The results show that when shallow cracks appear in the rotor,the SCFM can also be accurately reflected,and the results also verify the accuracy and practicability of the model.Secondly,the vibration characteristics of the rotor system with the influence of an asymmetry are investigated by using the SCFM.This paper calculates the natural frequency of the symmetrical rotor and the vibration response under the action of unbalanced mass,and analyzes the asymmetry influence of the rotor to be shown on the inertial moment of the section.The vibration characteristics of the rotor system is analyzed with different depths,positions and lengths.The results show that asymmetry can cause complex super harmonic and sub-harmonic resonance of the rotor system.When the asymmetry increases,the major critical speed of the rotor system decreases gradually,especially the secondary critical speed varies more.When the asymmetric position changes,the asymmetric factors located in middle of the span and near the disk have a greater impact on the major critical speed of the rotor system.When the asymmetric length increases,the high order critical rotational speed of the rotor system attenuates greatly,while the shorter asymmetric length may increase the major critical speed of the rotor system.Finally,this paper makes a series of corresponding experiments to verify the simulation results,and the experimental results are in good consistency with the simulation results,which proves the correctness of the SCFM and the accuracy of the 3-DTMM established in this paper.