Research On Dynamic Characteristics Of Gear Transmission System Under Fatigue Pitting Of Tooth Surface

With the five core developmental ideology,such as,innovation,coordination,green,openness,and sharing,were put forward.The development of national industrial equipment was needed,and industrial products were needed to be improved urgently.The strict requirements were proposed for the bearing capacity,stability,vibration and noise of the gear transmission system.Vibration and noise as one of the important indexes to measure the dynamic response of gear transmission system,is very important to predict and discover the uneven response which was caused by the fatigue pitting or peeling off of the tooth surface and the misalignment of the shaft under the premise of meeting the design requirements of geometric components.Based on the mature basic theory,different types of mathematical models of gear systems were established to describe its physical movement characteristics,and to studied the dynamic response characteristics of gear systems deeply.The evolution process of fatigue pitting characteristics of tooth surface and the accompanying response characteristics were analyzed through the contact fatigue test platform.According to the mesh kinematics of gear pair,the analytical equations of engage in or out limit positions of tooth and the process of single-double mesh alternate motion of tooth were derived in detail along the line of action.With the principle of energy method,a fine mathematical model of time varying mesh stiffness of gear was established by considered the fine geometric parameters of gear tooth profile which was composed of fillet foundation curve and involute curve.The example with the different tooth parameters was analyzed,and the influence of different basic parameters of gears,such as module,pressure angle,tooth width,bore diameter,etc.,on the component stiffness and comprehensive time-varying mesh stiffness was studied in detail.The results show that the stiffness has different response characteristics by the different basic parameters,and its main performance characteristics are the numerical charge of time-varying mesh stiffness and the domain charge of single-double mesh stiffness.The calculation results are basically consistent by compare FE model of elastic three-dimensional gear pair with the proposed energy method for evaluating time-varying mesh stiffness,the both parties are mutually verified.The verified result show that mathematical model of refined gear for evaluating time-varying mesh stiffness has certain feasibility and reliability,which improve the calculation efficiency and timeliness,and make a preliminary research foundation for the rapid simulation analysis of stiffness excitation of system dynamics.Considered the macro interface friction coefficient,the action load equation along the direction of tooth profile was derived.And the mathematical model of time-varying mesh stiffness of spur gear pair with friction effect was established,the example was selected for simulation analysis.The results show that friction effect with the alternation of friction direction causes a sudden change in meshing stiffness.The greater friction coefficient,the more obvious difference in meshing stiffness changes.When the gear pairs are fully lubricated,the fluctuation of time-varying mesh stiffness curve of gear pair can be reduced.In the micro scale space,a fractal mathematical model for evaluating normal load and normal contact stiffness was established by using fractal theory,and the effect of different micro characteristic parameters on macro characteristic such as normal load and contact stiffness was studied.The results show that the normal contact stiffness of multi rough surface features of tooth surface can be better explained or cover by the established fractal contact mathematical model.And different calculation models can be selected according to the application scenarios of gear for simulation analysis.The pitting morphology of tooth surface was simulated by using rectangular geometry quickly and approximately,and the mathematical model and analytical equations of physical characteristics of simple pitting,multi-pitting and random distribution of pitting were introduced in detail.Therefore,the time-varying mesh stiffness is quickly predicted or evaluated under the characteristics of fatigue pitting of tooth surface.The results show that the meshing stiffness of gear under the different rectangular geometric parameters of pitting and number of pitting has different response characteristics.The greater geometric parameters of pitting or the greater number of pitting,the more obvious the effect on meshing stiffness.The meshing stiffness value decreases more obvious at the location where pitting occurs especially.The different types of tooth surface pitting can be simulated completely by the analysis model of three different pitting,and there is a certain engineering application significance.Based on the fractal theory,a prediction model of normal contact stiffness of gear was introduced under the micro-pitting characteristics of tooth surface.The calculation results are consistent with change trend of engineering application situation.It will be used as a foundation for the later analysis of dynamic response of micro-pitting and the extension of micro-pitting.A simplified six-degree freedom dynamics mathematical model of gear system and a rigid body dynamics analysis model of gear system with advanced gear feature modules and bearing modules were established.The effect of pitting characteristics of tooth surface on system response characteristics was discussed.The results show that a local unbalanced dynamic response in system is produced by the pitting characteristics of tooth surface,such as the increase of response amplitude,the decrease of meshing stiffness and so on.Under the action of cycle period,the rapid fatigue pitting of tooth surface will be occurred and expanded.The evolution process of gear fatigue pitting and the vibration response characteristics of gear system in the process were studied by the test rig of contact fatigue of cylindrical gear.The results show that the fatigue pitting phenomenon of tooth surface is an evolution process in which the tooth surface undergoes various features such as running in,wear,local gray spots,expanded gray spots,initial pitting marks,obvious pitting zones and so on.The final pitting phenomenon is caused by the small features of tooth surface which undergoing cumulative damage step by step under the action load.The amplitude effect of dynamic response caused by fatigue pitting on tooth surface is more than 2 times of that without pitting,which as a reference for the alarm value set in the system during the real-time monitoring of test rig.The pitting characteristics of tooth surface will be distinguished in early,and lays a foundation for the later diagnosis and identification of gearbox faults.