Nonlinear Vibration Mechanisms And Modeling Of Defects In Rolling Element Bearings

30%and44%present of the total number of failures in rotating machinery andlarge induction motors are caused by bearing failures. When a rolling element passesover the defect, an unacceptable impulse will be generated. The amplitude andwaveform of the impulse is determined by the shape and sizes of the defect. Theunderstanding of the relationships between the shape of the defect, the sizes of thedefect, and the waveform of the impulse, and as well as the vibration characteristics ofthe impulse is very useful for the accuracy and reliability of the determination of theoperation status of the rolling element bearing. Therefore, it is an important theoreticaland practical task to investigate the nonlinear vibration mechanism of the defect andthe vibration characteristics of the impulse cause by the defect for the accuracy of thedetection and diagnosis of the early bearing faults, and the prevention of the severeeconomic, personal and equipment losses cause by the bearing failures.However, the relationships between the shape of the early localized defect, thesizes of the early localized defect, and the characteristics of the impulse caused by thedefect in the rolling element bearing are not completely understood due to the effectsof the nonlinear contacts in the bearing, the coupling with the shaft and housing, thetime-varying rotating speed, and the time-varying loads on the vibration characteristicsof the bearing. Therefore, it is of great theory value and engineering significance toinvestigate the nonlinear vibration mechanism and the dynamic modeling method ofthe rolling element bearings with early defects.This thesis is focused on the nonlinear vibration mechanism and the dynamicmodeling method of the defects in the rolling element bearings, including the vibrationmechanism of the waviness and the localized defect, the dynamic modeling of therolling element bearings considering the time-varying displacement excitation and thetime-varying contact stiffness excitation, the dynamic modeling of the rolling elementbearings due to a localized defect with edge topography progress, the dynamicmodeling of the impulse vibration transmissibility characteristics in a rotor-rollingelement bearing-housing system, and the corresponding experimental validation. Themain works done in this study are as follows:①The time-varying contact stiffness excitations between the rolling element andthe races for the uniform and nonuniform waviness cannot be accurately described by the current waviness model considering the time-varying displacement excitation. Toovercome this problem, a new dynamic model coupling the time-varying displacementexcitation and the time-varying contact stiffness excitation for a rolling elementbearing with waviness is proposed. The effects of the wave numbers and the amplitudeof the waviness on the contact stiffness between the rolling element and the races ofthe bearing, and the vibrations of the bearing are investigated. The relationshipsbetween the waviness and the rolling element passing frequencies are investigated, aswell as the sidebands around the maximum peak frequency of the rolling elementpassing frequencies.②The complex practical topography of the localized defect cannot be accuratelydescribed by the time-varying displacement excitation localized defect models basedon single functions. To overcome this problem, a simplified model for describing thetopography of the defect is proposed according to the practical topography of thedefect. The impulse mechanism of the defect with different topographies and thevibration characteristics caused by the defects are investigated. A main function modelfor the waveform of the impulse generated by the defect is also presented. In addition,an experimental investigation is performed to validate the proposed model.③The effects of the elastic deformations at the edges of the localized defect andthe defect depth on the vibration characteristics of the rolling element bearings cannotbe described by the current localized defect models considering the time-invariant andthe time-varying displacement excitation based on single functions. To overcome thisproblem, the current localized defect models based on single functions are extended,and a new dynamic model based on the piecewise response function for the rollingelement bearings with a localized defect coupling the time-varying displacementexcitation and the time-varying contact stiffness excitation is proposed. Anexperimental investigation is also developed to verify the proposed model. Itovercomes the problems of dynamic modeling methods for the different localizeddefects in the rolling element bearings.④The effects of the topographies progresses at the defect edges on the contactstiffness between the rolling element and the defect edge, and the vibrationcharacteristics of the bearing caused by the defect cannot be accurately described bythe current localized defect models considering sharp defect edges. To overcome thisproblem, the relationship expressions for the time-varying displacement excitation andthe time-varying contact stiffness excitation caused by the localized defect with the topographies progresses at the defect edges are derived according to the ratio of therolling element diameter to the minimum defect size and the ratio of defect length to itswidth. Based on Hertzian contact theory, a dynamic model of a rolling element bearingwith a localized defect on its races considering the topographies progresses at thedefect edges is proposed. The current defect models considering the sharp defect edgesare extended. It provides the theoretical bases for the accurate dynamic modelingmethod of the rolling element bearings with a localized defect considering thetopographies progresses at the defect edges.⑤The dynamic model of the rotor-rolling element bearing-housing systemconsidering rigid connection between the outer race and the housing cannot accuratelyexplain the differences of the vibrations between the outer race and the housing.Moreover, it cannot represent the vibratory motion transmitted from the outer race intothe housing and other connecting components. To overcome this problem, a newvibration transmissibility dynamic model of the rotor-rolling element bearing-housingsystem considering elastic interfaces between the rolling element and the races, andbetween the outer race and the housing is proposed. The dynamic model of therotor-rolling element bearing-housing system considering the rigid connection betweenthe outer race and the housing is extended. The vibration transmission characteristicsthrough the rotor-rolling element bearing-housing system are studied. An experimentalvalidation is applied and shows agreement with the numerical results from theproposed model.