Nonlinear Dynamic And Thermal Behaviors Of A Dual-rotor System With Inter-shaft Bearing

Higher requirements are put forward for dynamic and thermal performances of the supporting system with the development of the rotor system trending toward high-speed and heavy-load.Dynamic and thermal beahviors of inter-shaft bearings,as essential support and transmission parts between the lower pressure rotor and the higher pressure rotor of dual-rotor systems especially in aero engines of fighters,are much more complex or maybe even nonlinear in many cases.Nevertheless,the research about nonlinear dynamic characteristics of the dual-rotor system and nonlinear thermal beahviors of the inter-shaft bearing caused by it are lack of in-depth systematic research at present.Therefore,it is imperative to study nonlinear dynamic characteristics of the dual-rotor system and nonlinear thermal beahviors of the inter-shaft bearing and clarify the effect of dynamic and thermal parameters.The nonlinear dynamic characteristics of the primary resonance of a simple dualrotor system with inter-shaft bearing are analyzed by analytical method,based on which,the effect of the local defect of the inter-shaft bearing on the dynamic characteristics of system,and the effect of the dynamic characteristics on the nonlinear thermal beahviors of the inter-shaft bearing without and with local defect are studied by numerical method.The research contents are as follows:(1)For the simple dual-rotor system,the inter-shaft bearing is considered as a cubic nonlinear elastic spring.The dynamic equations of the system is established by using the assumed mode method and the Lagrange’s equation of the second kind.According to the multiple scales method in the complex coordinate,a simplified method for the nonlinear dynamic equations of the dual-rotor system is proposed,which lays a foundation for the analytical solution of the equations.Mechanism analysis of the nonlinear phenomena,such as jump and bi-stable phenomena,of the primary resonances are clarified.Then three bifurcation modes of the primary resonances are studied.It indicates that two interrelated primary resonances of the dual-rotor system may have different bifurcation modes under the same dynamic parameters.(2)For the dual-rotor system with a local defect on the outer or inner race of the inter-shaft bearing,a modified elastic restoring force model for the inter-shaft bearing with local defect is presented.The nonlinear factors of the inter-shaft bearing such as Hertz contact force,radial clearance and varing complaince are considered.The local defect is considered as a regular dent with a constant depth,thus the radial clearance will increase when rolling elements go through the range of the local defect.The results show that there exist two pair abnormal resonances apart from one couple of primary resonances,one pair are fault-induced resonances caused by the characteristic defect frequency and the other pair are combination resonances caused by the combination frequency.The formula for the resonance frequencies of the fault-induced and combination resonances are given.These abnormal resonances will make dynamic characteristics of the system more complex,put forward a more severe test for the design of aero engine operating speed,and provide a new solution for the problem that the signal is weak and difficult to extract in early fault diagnosis.(3)A new theoretical method is proposed to investigate the thermal beahviors of the inter-shaft bearing under dynamic load by combining heat transfer and dynamics.The dynamic load of the inter-shaft bearing is defined according to the nonlinear dynamic responses of the system.It is found that the dynamic load can reflect the nonlinear dynamic characteristics of the system.A steady-state heat transfer model for the inter-shaft bearing subjected to the dynamic load can be set up with the help of Palmgren’s empirical formula,the steady-state temperatures of the inter-shaft bearing are obtained by using the Gauss-Seidel iteration.The results show that the temperature of the inter-shaft bearing shows nonlinear thermal beahviors,i.e.,jump and bi-stable phenomena,because of the jump and bi-stable phenomena for the dynamic load.It reveals the dynamic characteristics of the dual-rotor system have a great impact on the thermal beahviors of the inter-shaft bearing,which provides a new theoretical basis for the thermodynamic design of bearings.(4)Based on Palmgren’s empirical formula,an unsteady-state heat transfer model of inter-shaft bearing with local defect subjected to dynamic load can be set up considering the viscosity-temperature relationship of the lubricant oil.The transient temperatures of inter-shaft bearing are obtained by numerical method.The results show that no matter the inter-shaft bearing is in unsteady-state or steady-state heat transfer,the temperature of roller is always the highest,the outer ring temperature is always the lowest.The temperatures rise quickly and then slowly,and about 70% of the time is spent on the last 20% of the temperature rise.The temperature of the inter-shaft bearing will also increase abnormally in fault-induced and combination resonance zones,which provides a new method for the fault diagnosis of the bearing.This paper provides a theoretical guiding significance for further understanding the nonlinear dynamic characteristics of the dual-rotor system and its effect on the nonlinear thermal beahviors of the inter-shaft bearing.