Research On Nonlinear Vibration Characteristics Of Ball Bearing-Misaligned Rotor System

As one of the most important supporting components,the rolling bearing has been widely used in aircraft engine,railway and wind turbine.The specialties of rolling bearing contain the high rotating speed,small volume and convenient installation,etc.During the preliminary application of ball bearing,the researchers paid less attention to the vibration problems,for the operating parameters were not high and the system possessed enough safety margin,which could not lead to large vibration amplitude or instability.With the development of scientific level and meets of human lives,the rotating machineries develop towards high speed and automation.The structures are more complex and the working conditions are more rigorous.The nonlinear vibration problems induced by ball bearing usually occur,which brings huge challenge to traditionally linear theories,such as the vibration jump and double stable state in the aircraft engine rotors,the bifurcation behaviors of periodic vibration in the principle roller systems of high speed machine tools,and the chaotic vibration of the fan gear box bearing,etc.The complex dynamics behaviors are essentially caused by the nonlinearities,which can not be explained by the linear theory.To understand and control the dynamical behaviors should be based on the study of dynamic mechanism of system essence.Thus,the thesis will be listed in the aspects as follows:Two intrinsic nonlinearities of ball bearing are considered,for one is bearing clearance nonlinearity,and the other is Hertz contact nonlinearity.A single degree of freedom(DOF)reduced ball bearing-cantilever rotor model is established.The average method is applied to calculate the analytical solution of primary resonance.Some important characteristics of backbone curves are discussed: extreme values,smoothness,the fixed point and error.The backbone curves of primary resonance(equivalently linear natural frequency)are smooth and derivable,moreover,the equivalently natural frequency approximates to infinite as the vibration amplitude increases,which is a significant symbol to distinguish the piecewise linear systems.On account of the effect of Hertz contact(3/2 order stiffness nonlinearity),the backbone curve upwarp as the increase of system amplitude,which is an important symbol that Hertz contact system differs from cubically nonlinear Duffing system.The effects of bearing stiffness,clearance,damping and the eccentricity of the disc on the resonant curves are analyzed.Then the singular theory is applied to study the bifurcation behaviors of resonant solutions.Five different bifurcation forms in the parametric plane are provided.Some bifurcation forms should be avoided,e.g.the bifurcation form of large vibration amplitude,vibration jump,etc.These forms will affect the stable operation of rotor system.The numerical simulation of twoDOF dynamical model(the coupling of horizontal and vertical direction)is used to verify the rationality of the single-DOF reduced model and the efficiency of the analytical method.Thus the theoretical basis for the vibration control of this class of rotor system is provided.The effects of nonlinear supporting force of ball bearing and misalignment of coupling are considered.The dynamical model of rotor with eccentricity and set of gear coupling is established.The characteristics of nonlinear response impacted by unbalanced excitation of rotor and misalignment excitation of coupling are studied.The harmonic balance and alternating frequency time(HB-AFT)method is applied to calculate the periodic solutions of the dynamical equation with piecewise and fractional exponent strong nonlinearity,then the efficiency of the HB-AFT method is verified through comparing with the numerical integration results.The Floquet theory is applied to analyze the stability of periodic solution and provide the speed range of instability.The bifurcation mechanism is revealed,the period-doubling bifurcation,the saddle-node and secondary Hopf bifurcation forms emerge.Then the arc length continuation method is combined to analyze the super-harmonic resonance properties of rotor system.Several super-harmonic resonant domains are discovered in the low rotating speed domains,and the triple super-harmonic resonance is more obvious.The twice super-harmonic resonance occur in the high rotating speed domains.The hard spring characteristics of the resonant curve are obvious,and the resonant peak values are large,thus the dramatic vibration jump occurs easily.The vibration jump causes impact and damage to rotor,which must be controlled.The effects of bearing clearance,damping,misalignment quantity and the external force(constant load)on the super-harmonic resonance curves are discussed,which provide the reference frame to formulate control strategies.The action mechanism of constant load is illustrated based on Duffing system,stating the primary cause of the arise of soft characteristics in hard spring system.The clearance,Hertz contact and varying compliance effect of ball bearing is considered.A four-fulcrum dual rotor model supported by intermediate bearing is established.The nonlinear dynamic response of system is obtained by using the numerical integration method,and the vibration properties of varying compliance of ball bearing are studied.The varying compliance frequency of the supporting bearing is the principal frequency of inner rotor,and all the varying compliance frequency components in outer rotor response are obvious,which are caused by supporting forms of inner and outer rotors.The vibration characteristics of rotor unbalance are studied,and the self-alignment of inner and outer rotor occur when the primary excitations pass the second order critical speed,thus the resonance of outer rotor occur before inner rotor in the case of system acceleration process.The effects of speed ratio,bearing clearance,misalignment of dual-rotor on vibration characteristics are analyzed,and we found that speed ratio has large effect on the critical speed of rotor system.The increase of bearing clearance will lead to the weak chaotic vibration,and further causes the increase of chaotic attractor size.The misalignment fault can lead to the increase of twice frequency of the system response,which can cause twice super-resonance,and orbit of shaft center appears as ‘banana' form.The results provide guidance significance to the optimal design of dual-rotor system.Finally,a multi-disc misaligned rotor-ball bearing system is designed and tested under different working conditions.The nonlinear factors of ball bearing at the supporting position are considered.The discrete dynamical model of actual rotor system is established by finite element method,and the dynamical response of the system is obtained by the numerical simulation method,which is compared with the experimental results.Numerical results agree well with the testing data.