Application Of Fractal Chaos Theory In Gear Vibration Stability

With the rapid development of industry,gear,as one of the important transmission components,is more and more widely used in production and life.The vibration characteristics of gear system directly affect the performance and reliability of mechanical system and equipment.The vibration characteristics of gear system directly affect the performance and reliability of mechanical system and equipment.Based on the fractal theory and chaos theory,this paper discusses the influence of the micro-topography of the tooth surface on the meshing vibration characteristics of the gear as well as the time-varying stiffness,and studies the dynamic characteristics of the gear through the clearance of the tooth surface.Firstly,two kinds of surfaces with different micro-geometrical morphologies were obtained by electrochemical finishing and grinding,and the corresponding fractal dimension and characteristic scale were obtained by spectral method after data were collected by Taylor hopson's stylus measuring instrument.Applied mathematics fractal geometry,Hertz and W-M contour curve function,set up considering the micro 3 d model of the real surface profile and surface micro convex body contact model,on the basis of analyzing the characteristic of the fractal dimension and scale effect on micro uneven,a deeper analysis of the dynamic characteristics in the process of gear movement with the method of tooth surface to the relationship between the contact stiffness and damping.The results show that the fractal dimension and feature scale can describe the microstructure well.The larger the fractal dimension is,the smaller the feature scale is,the smaller the roughness is,the more complex the surface contour curve is,and the smaller the surface contour amplitude is.Compared with grinding machining,electrochemical finishing machining tooth surface normal contact damping,can reduce the meshing vibration in gear operation,can effectively improve the stability of gear movement.Secondly,the global bifurcation and chaotic nonlinear vibration of gears are discussed.Melnikov analysis is an effective method to analyze homology bifurcation and detect chaotic behavior.The single-degree-of-freedom dynamic model of spur gear system with tooth side clearance,time-varying stiffness,external excitation and static motion error is considered.Melikov method was used to predict the parameter regions of bifurcation and horseshoe chaos in the system's homotopic orbit,and to draw the threshold curves of different parameter Spaces.Runge-kutta method was used to numerically solve the differential equations of motion with one degree of freedom.Combined with the phase diagram of the system,the poincare section diagram and the maximum lyapunov index,the influence of tooth side clearance and time-varying stiffness on gear vibration is analyzed.The results show that Melnikov's prediction is correct and has a good consistency.