Research On Nonlinear Dynamics Of Gear System Based On Rolling-element-bearing Excitations

Rolling element bearing is the extremely important basic component in rotating machinery,the gear transmission system supported by rolling element bearings is the most widely used device for power and motion transmission,which is commonly applied in transportation,mining metallurgy,energy and power,aerospace,instrument and military equipment.With the improvement of productivity and manufacturing level,the rotating machinery is developing in the direction of precision,high-power,high-speed and automation.The speed of rotating machinery has been significantly increased,the internal mechanical structure has become more and more complex,and the working environment has become worse.The rolling element bearing in high-speed operation is under the action of variable load for prolonged periods due to the unstable operation conditions,which leads to nonlinear vibration behaviors generated and transmitted.Under complicated working conditions,due to the coupling effects of the rolling element bearing force excitation,the gear mesh excitation and the system unbalanced force excitation,some nonlinear vibration response and instability phenomena of the gear-rolling-element-bearing system cannot be expressed by simplified bearing supporting stiffness model.Therefore,the study of the nonlinear bearing characteristics and its vibration characteristics,the analysis of its nonlinear dynamic behavior in the gear transmission system,the understanding of the bearing characteristics and the transmission path of the vibration behavior of the rolling element bearing,can provide certain theoretical foundation with the actual working condition for the design of the geometric parameters and the selection of the structural model for the gear-rolling-element-bearing system.This study can improve the dynamic characteristics of the system and give some guidance to the stable,safe and reliable operation of the system.As an elastic supporting element in the dynamic model of mechanical system,the importance of rolling element bearing in the research and development process has not been paid enough attention.This study takes the rolling element bearing as the main research object,aims at the vibration and noise induced by the bearing internal nonlinear factors.The geometric kinematic characteristics laws of the rolling element bearing is followed,the modeling method and vibration characteristics of the nonlinear bearing excitation is analyzed.The dynamic transmission path of rolling element bearings in the gear-bearing system is studied.The dynamic model of complex and refined system with multi-source excitation and multi degree of freedom is established and the efficient,accurate and fast numerical calculation methods are developed.The coupling effects between the bearing excitation,the gear mesh excitation and the dynamic unbalance force excitation are analyzed and the influence laws of system parameters and working condition changes on the dynamic performance of the system are explored.The main research contents of this paper are as follows:(1)The kinematic contact relationship between the internal members of the rolling element bearing is analyzed,and the load-displacement distribution curve of the rolling element bearing is obtained.Based on the load-displacement three-dimensional distributions,two calculation methods for the rolling element bearing stiffnesses are proposed and the corresponding physical meanings are summarized,in which the mean stiffness represents the bearing capacity and the alternating stiffness reflects the anti-disturbance capacity.As an elastic element,the mechanism of the excitation function of the rolling element bearing needs to be calculated and analyzed based on the corresponding dynamic system under certain working conditions,and the vibration characteristics of rolling element bearing need to be reflected and evaluated by the mass movement of the inertial element,which is under its supporting action.Therefore,based on the two different bearing stiffness methods,the dynamic models of rigid rotor,which is supported by rolling element bearing,is established to analyze the vibration characteristics of the support characteristics in the rotating system for the elastic element-rolling element bearing.The calculation methods of time-varying bearing stiffness excitation function based on these two dynamic models are proposed.The distribution and frequency characteristics of different time-varying stiffness excitation functions of the bearing are analyzed,the relationship between the time-varying stiffness of rolling element bearings and the contact performance of bearing internal components is studied.The influence law of time-varying stiffness excitations,based on different definitions and calculation methods of rolling element bearing stiffness,on the vibration response characteristics of the system is explored.(2)A dynamic bearing 3D nonlinear excitation model,which can identify the influence of dynamic working conditions on the contact state of the rolling elements inside of the rolling lement bearing,is proposed.The model considers both the mean stiffness representing the bearing capacity and the alternating stiffness representing the anti-disturbance capacity,and updates the coupling effect of bearing support excitation and unbalance force excitation under the influence of vibration displacement fluctuation in time.An improved fourth-order Runge Kutta efficient numerical algorithm is proposed,which can accurately obtain the strong nonlinear characteristics of rolling element bearing under the action of variable load in the complicated working condition and get the vibration characteristics of the bearing 3D nonlinear excitations.Thus the coupling actions between the bearing 3D nonlinear excitation and the dynamic unbalance force excitation on the nonlinear vibration behavior of the system are analyzed.(3)The rolling element bearing 3D nonlinear excitation model is applied to the gear-bearing transmission system.Considering the coupling effects of the gear mesh excitation,the unbalance force excitation,and the effect of dynamic center distance and the pressure angle caused by the nonlinear anisotropic characteristics of the rolling element bearings,combining the geometric kinematic characteristics of each component and the dynamic transmission law,the refined dynamic model of gear-bearing system having multi-source excitation is established.An improved numerical calculation method is proposed,which can calculate in time and accurately the vibration displacement-dependent pressure angle and center distance,update the time-varying meshing excitation,bearing 3D nonlinear excitation and unbalance force excitation with the vibration displacement vector.Then the influence law of the change of multi-dimensional nonlinear characteristics of internal components on the vibration response of the system under dynamic conditions can be obtained.(4)For the multi-source,multi-dimensional and highly nonlinear multi degree of freedom gear-bearing system under complex working conditions,an idea of analyzing the dynamic behaviors of the system is provided through case study.Based on the dynamic response obtained by numerical algorithm,the vibration amplification coefficient is introduced.Combined with the graph distributions in time domain and frequency domain,the effect from the bearing 3D nonlinear excitation on the dynamic behaviors of the system are studied from two aspects of vibration intensity and motion state of dynamic resposnes in a large range of system parameter variation.The coupling effects from the bearing excitations,mesh excitation and external load excitation on the system nonlinear dynamic chatacteristics are explored.The mapping relationships between the working conditions and system parameters with dynamic behavior are analyzed and a research idea for the dynamic stability of a complex strongly nonlinear gear-bearing system is presented.