Analysis Of Contact Stress And Vibration Characteristics Of Helical Face-gear Transmission

In this paper,the helical face-gear transmission system is taken as the research object.The forming of the gear surface,the limiting condition of the tooth width,the contact path of the tooth surface,the elastic contact of the tooth surface and the nonlinear dynamic characteristics of the transmission system are studied systematically.Based on envelope theory and gear meshing principle,the expression of helical face-gear tooth surface equation is studied with the aid of tooth surface equation and coordinate transformation relation of machining tool.The minimum internal radius and maximum outer radius of helical face-gear are calculated by differential geometry,and the influence of helical angle on the tooth width of helical face-gear is analyzed,and the method of establishing 3D virtual model of helical face-gear with 3D modeling software is studied.According to the characteristics of helical face-gear point contact transmission and the imaginary meshing relationship among cutter,face-gear and meshing pinion,the calculation formula of tooth surface contact track of helical face-gear is studied.By establishing a meshing coordinate system which includes the angle of the axis,the staggered axis and the axial installation error,the influence of various installation errors,helical angle and the parameter combination of the tooth number difference between the meshing pinion and the cutter on the tooth surface contact trajectory of the helical face-gear is analyzed.According to the basic theory of elastic contact problem and linear programming theory,the tooth surface contact problem of helical face-gear is expressed as linear programming problem.The simplex algorithm of linear programming is improved to solve the tooth surface contact problem of helical face-gear.Through this method,the load distribution,deformation and maximum contact stress in the tooth surface contact region are analyzed.Based on vibration theory and lumped mass method,a nonlinear dynamic model of helical face-gear with time-varying meshing stiffness,side clearance,support stiffness and bearing clearance is established,and the dynamic differential equation of the system is derived.The calculation method of time-varying meshing stiffness of helical face-gear pair is studied.The inherent characteristics of the system are analyzed,and the effects of input speed,meshing damping,tooth clearance and bearing clearance on the bifurcation characteristics of the system are studied.