Research On Nonlinear Dynamics And Fault Mechanism Of Gear System

Spur gear,as one of the most common basic parts of vehicles,plays an essential role in railway,highway and aviation,etc.The spur gear system is an elastic structure system with nonlinearity and parametric excitation due to its complexity of structure and the interaction of internal and external excitations,which shows complex dynamic response characteristics in the meshing process.In addition,local faults caused by fatigue,overload,and poor lubrication are easy to occur in the working process,which seriously affects the work efficiency and safety of the whole mechanical equipment.Therefore,it is of great theoretical significance and engineering value to study deeply the nonlinear dynamic behavior and the mechanism of gear failure for early fault diagnosis,gear design,and safety maintenance in mechanical equipment.This dissertation takes the single-stage spur gear reducer as a subject,investigates its nonlinear dynamic response,and analyses the fault mechanism and vibration characteristics of root crack and tooth pitting.The main contents of this dissertation include:(1)The periodic solution and the system response are obtained by means of the incremental harmonic balance method(IHBM).Firstly,the torsional vibration model of spur gear pairs is obtained,in which the main factors are the backlash,time-varying mesh stiffness(TVMS),and static transmission error.Based on the fractional-order calculus theory,three kinds of nonlinear parametric excitation torsional vibration models of spur gear pairs with fractional-order differential/integral are established.The nonlinear ordinary differential equations describing gear systems are transformed into algebraic equations by using IHBM.Then the approximate periodic solutions of these models are derived.At last,the dynamic behavior of the gear system with the change of important parameters is investigated,including the impact state,vibration amplitude,transition frequency,primary and super-harmonic resonances.The research shows that the analytical solution obtained by the IHBM is in good agreement with the numerical solution derived by the power series expansion method.The results can provide some theoretical guidance for the design and optimization of gear parameters and lay the foundation for the study of fault mechanism.(2)The parametric resonance of the gear system with multi-degree-of-freedom is studied.A multi-degree-of-freedom spur gear model is established,where the vertical vibration of the supporting system of the gear pair,and the clearance of the supporting bearings of the driving gear and driven gear are considered.Under the 3:1 internal resonance condition,the steady-state solutions of the principal parametric resonance and the combined parametric resonance of this system are derived based on the multi-scale method(MSM),and the stability of the steady-state response is analyzed by using Lyapunov’s first method.The influence of important parameters,such as backlash,bearing damping,gear meshing damping,on the amplitude and stability of the steady-state solution of gear pairs is discussed at last.From the point of view of dynamics,the stable and unstable regions of the steady-state solution are defined,and the factors affecting the stability of the system are determined.(3)The variation of TVMS and vibration characteristics of gear system under the influence of root crack are studied.Based on the energy principle,the TVMS of spur gear with tooth root crack in the single-tooth engagement region and the double-tooth engagement region is calculated when the crack propagates beyond the central line of the tooth.Considering the actual shape of the gear tooth,an improved beam model for evaluating the TVMS is developed in which the gear tooth is assumed to be a cantilever beam with variable cross-section starting from the root circle.Four types of root crack models are presented and the TVMS of 13-crack levels is calculated.The fault vibration characteristic of a single-stage spur gear reducer with root crack is analyzed and the correctness is qualitatively verified by the acceleration vibration signals of an experimental gearbox with crack or missing failure.The research shows that the presence of the tooth root crack can significantly reduce the TVMS,the improved variable cross-section cantilever beam model reduces the calculation error,and the TVMS of gear can be calculated more accurately.(4)Based on the new tooth surface pitting model,the TVMS is calculated and the vibration characteristics of the gear system with pitting are investigated.A novel model for describing tooth pitting is proposed where the pitting shape is considered as approximately a part of an ellipse cylinder,and the gear tooth is assumed to be a cantilever beam with variable cross-section starting from the root circle when the number of teeth is considered.Three damage levels are defined based on the position and number of pits: slight pitting,moderate pitting,and severe pitting.The TVMS of perfect gear and that of gear with different pitting severity levels are solved and compared by the potential energy method.The effect of the position and size of pits on TVMS is discussed.The fault dynamic response of one-stage spur gear transmission is studied and the results are verified by the Drivetrain Dynamics Simulator(DDS).The overlap between different pits is considered in the new model,which is closer to the shape of the pitting in experimental and practical engineering applications.The results indicate that it is important to investigate the evolution and control of nonlinear dynamic behavior of gear system and the mechanism of root crack and tooth pitting to reveal the deep dynamic characteristics of the gear system and to understand the possible causes of vibration and noise of mechanical equipment.Furthermore,it is of great theoretical value and long-term engineering significance to promote the development of nonlinear dynamics and control,and ensure guarantee the safe and stable operation of equipment.