Theoretical Study On Meshing Of A Xial Arc Tooth Cylindrical Worm Pair

The axial arc-tooth cylindrical worm drive is a promising form of worm drive.I built a mathematical model,and derived the tooth surface equation through the cutting edge curve,and obtained the geometrical properties such as the unit method vector and the curvature parameter of the spiral surface of the worm,and established the active frame on it.New explorations and research have been carried out through the above methods.The main research contents of the thesis include:(1)Through reviewing domestic and foreign literatures,we can understand the development history and current situation of this field at home and abroad,and understand the superiority of the worm drive.In view of the shortcomings of the straight-line cylindrical worm,a new circular-arc cylindrical worm drive,namely axial arc-tooth cylindrical worm drive,is proposed,and its tooth surface forming principle is introduced.(2)Establish a mathematical model for meshing analysis of axial arc-tooth cylindrical worm drive.Calculate the geometric properties of the worm helicoid,such as unit method vector,normal curvature,short-range torsion.And establish an activity frame.The relative velocity of the two tooth surfaces at any one of the meshing points is obtained,and the meshing function of the hob to form the worm wheel is derived,and the worm gear tooth surface equation of the axial arc tooth cylindrical worm drive is obtained.Using the active frame,the normal vector of the instantaneous contact line is calculated.Thereby the inductive curvature is calculated.And the meshing limit function and the curvature interference limit function are introduced.(3)Based on mathematical models and meshing characteristics,a program for numerical simulation was developed.Proper selection of the main parameters,geometry and tool parameters of the worm drive.The nonlinear equations of the key points in the conjugate zone are established respectively.The nonlinear equations of the key points in the conjugate zone are solved by MATLAB software.The geometry and instantaneous contact line of the conjugate zone are drawn in the axial section of the worm and the worm wheel respectively Distribution.(4)Using the built simulation simulation platform,the numerical simulation of the worm pair with different parameters is carried out,and the meshing characteristics,analysis of design parameters,process parameters and influence on meshing characteristics are studied.Finally,some principles and strategies for parameter selection are proposed.