Coupling Vibration Analysis Of High Speed Gear System

In order to pursue high efficiency,high speed turbine units are more and more widely used in process fluid machinery,and the driving effect of multi-stage gearbox cannot be ignored.The finite element method is used to model the gear shafting system.While ensuring the solution efficiency,the simulation is closer to the actual lateral-torsional-axial coupling vibration by considering the full degree of freedom,gear meshing and casing flexibility.At the same time,high speed is often at the expense of system stabiliy,bearing pad temperature rising,work surface wearing,power consumption increasing and other issues have been closely concerned.Through high-speed transmission,the stress of the flexible and long high-speed shaft is concentrated,so the life estimation of the weak part has certain guiding significance to prevent the vibration damage.According to the coupling steady-state and transient problems of high-speed gear system,the main work and contributions are as follows:(1)The finite element method is used to model the gear shafting,and the rotation axis is simplified into Timoshenko beam element,considering a total of 6 degrees of lateral-torsional-axial freedom.Meshing element is simplified as a pair of linear elastic spring stiffness,which is expressed as a 12×12 meshing stiffness matrix derived by Stringer based on geometric parameters of the gear and force analysis of meshing force,and the dynamic software of lateral-torsional-axial coupling vibration analysis of the gearbox is developed.(2)Taking a tri-parallel shafting expander as an example,the impeller and gear are modeled as concentrated mass;the bearing element is built as a linear spring.The harmonic response of the flexible gearbox is analyzed,and the unit sinusoidal force is applied at the supporting point of the bearings of casing.The response curves of the coupling points witch connect the casing and each shaft are obtained by frequency sweeping,and the frequency response function matrix between bearing support points is deduced.Then the local transfer function of the flexible casing is obtained by fitting.The equivalent stiffness calculation program considering the casing's feedback vibration is developed.A new bearing dynamic stiffness matrix is obtained,and a high-speed gear system coupled with rotating shaft-disk-gear-bearing-casing is established.The dynamic characteristics are analyzed,and based on the test data,the failure of the gearbox is also proposed.(3)The calculation and analysis software of meshing force of gear shafting is developed.Force analysis is carried out on the meshing force of the gear,aerodynamic force,driving torque acting on the impeller and axial force of the thrust ring at the contact point.The COMDYN_Gearload software developed by Matlab is used to calculate the gear-bearing reaction force,which can accurately calculate the bearing load in the working process of the gear shafting and further obtain the bearing characteristic parameters.(4)Based on high stability of the tilting pad bearings,the static and dynamic characteristics of the bearings,the inherent characteristics of the gearbox shafting,the system stability and the influence on vibration response with different rotor loads,width-to-diameter ratios,preloads,and radius clearances are analyzed.Finally,the parameters of tilting pad bearings with low pad temperature,low power consumption,high efficiency and high stability are obtained.(5)For high torque gear compressor unit and startup transient analysis and short circuit conditions,the angular displacement of the elements is solved by newmark-? method.Based on the torque and stress of each shaft segment,the cumulative fatigue analysis of the weak elements of the shaft system is carried out by using the rain flow count and Miner linear rule,and the damage degree of the gear shafting caused by the start-up torque and short circuit fault is obtained.In this paper,a six degree of lateral-torsional-axial freedom coupling model is developed based on the meshing of gears among shafting systems.Based on the characteristic parameters of the structure and the transfer function,the coupling model of shaft-disk-gear-bearing-casing is improved.The basic research of rotor dynamics is carried out in the aspects of unbalanced parallel shafting,bearing characteristics and transient torsion.