Study On Dynamic Response Of The Cylindrical Gear With Variable Hyperbolic Circular-arc-tooth-trace Considering Wear Effect

The variable cylindrical gear with variable hyperbolic circular-arc-tooth-trace(VH-CATT cylindrical gear)is a new type of gear,which has the advantages of involute gear,strong resistance to eccentric load,and insensitive to installation errors.It has broad application prospects in mechanical equipment transmission such as aerospace,transportation,and other fields.During gear service,tooth surface wear leads to increased backlash,reduced meshing stiffness,and increased vibration and noise,which not only affects the normal meshing of gears,reduces transmission stability,but also changes their dynamic characteristics.Therefore,it is necessary to conduct research on the wear characteristics and dynamic response of the gear,striving to achieve vibration and noise reduction,wear reduction and longevity,and optimize design parameters.In response to th e above issues,this paper will conduct research from the following four aspects:(1)Taking a pair of VH-CATT cylindrical gears as the research object,based on tooth surface equations and tooth profile equations,accurate meshing tooth surface data are obtained through numerical calculation.Analyze the relationship between the curvature and speed of the meshing point of the gear pair,and bring in the basic parameters of the gear to obtain the principal curvature,speed,relative speed,and entrainment speed of the concave and convex tooth surface.(2)Based on Archard wear formula and Hertz contact theory,a dynamic load distribution model and a tooth surface wear prediction model are established,and the tooth surface wear depth is calculated.The corre ctness of this model is verified by comparing the results with other literature.Introduce installation error,calculate the tooth surface wear amount under standard installation and non-standard installation in order,reveal the coupling effect of install ation error and geometric parameters on the tooth surface wear amount,and explore its wear characteristics.(3)The time-varying meshing stiffness of a gear pair under different loads is solved using the finite element method,and it is found that it chan ges periodically.A high order fitting method is proposed to replace the piecewise function of the backlash to obtain a continuous and smooth polynomial fitting curve.The lumped mass method is used to establish a six degree of freedom nonlinear dynamic eq uation considering strong nonlinear factors such as backlash,time-varying meshing stiffness,time-varying meshing damping,and bearing clearance.The numerical method is used to solve the equation.The bifurcation diagram and maximum Lyapunov exponent diagram of the system under different operating conditions with varying load,time-varying meshing stiffness,and meshing damping are drawn,and its chaotic bifurcation characteristics are explored.Make a specific analysis of the system’s time history diagram,phase diagram,and Poincare cross section diagram at a specific time.(4)A dynamic model of variable cylindrical gear with variable hyperbolic circular-arc-tooth-trace was established considering wear effects,and tooth surface wear was introduced into time-varying meshing stiffness in the form of random perturbation.The tooth surface wear parameters are represented in the form of normal distribution.For important parameters such as load,time-varying meshing stiffness,meshing damping,etc.,the bifurcation diagrams of the system under different wear degrees and different operating conditions are drawn.The influence of different tooth surface wear degrees on the chaotic bifurcation characteristics of the system is explored using the control variable method.At special moments,the time history diagrams,phase diagrams,and Poincare cross sections for four wear cases are drawn,This reveals the internal influence of to oth surface wear on the dynamic characteristics of the system.