Research On Meshing Theory Of Offset Normal Arc-toothed Cylindrical Worm Pair

In this paper,the meshing theory of the offset normal arc-toothed cylindrical worm pair is studied.The offset normal arc-toothed cylindrical worm is a kind of ZC3 type worm.The worm gear is a line contact meshing transmission with concave and convex arc tooth profiles,so it has the characteristics of small contact stress,high precision,large bearing capacity and compact structure.The spiral surface of the offset normal arc-toothed cylindrical worm is formed by a circular blade turning tool.The convex circular turning tool is placed on the offset plane of the normal plane of the worm,and the spiral surface of the worm is surrounded by the turning tool.The axis is formed by relative spiral motion,and the worm gear matched with it is processed by the worm hob with the same shape as the worm.The meshing theory of the offset normal arc-toothed cylindrical worm pair is mainly studied as follows:(1)The equation of the helical surface of the offset normal arc-toothed cylindrical worm is established.Firstly,the relative coordinate system of the turning worm is established,and the spiral surface equation of the worm is written by the spherical vector coordinates.Using the knowledge of differential geometry to obtain the curvature parameters of the helicoid,the first and second basic quantities of the helicoid are calculated,and the unit normal vector of the helicoid and the calculation formula of the curvature are derived.(2)The meshing principle of the offset normal arc-toothed cylindrical worm pair is studied,and the coordinate system of the relative motion of the worm pair is established.The two kinds of boundary functions of the worm pair meshing function and the worm pair are derived by coordinate transformation,and then the sliding is calculated.The calculation formulas of the two meshing performance parameters of the angle and the induced principal curvature,and finally derive the tooth surface equation of the worm wheel and the boundary equation of the worm gear.(3)The calculation principle of the conjugate region of the offset normal arc-toothed cylindrical worm pair is studied.The numerical simulation of the conjugate region is carried out by a specific example.The key points and conjugate regions of the conjugate region are determined.The calculation method of the meshing point on the contact line is drawn by numerical examples to obtain the conjugate zone of the worm pair and the specific meshing characteristic parameters of each point are obtained.The curvature interference boundary and the meshing boundary of the worm gear tooth surface are determined,and the Calculate the tooth profile shape and tooth angle of the worm shaft section and the calculation method of the axial tooth profile of the worm wheel.(4)The numerical simulation and analysis of the offset normal arc-toothed cylindrical worm pair are carried out.By changing some parameters of the worm pair and the turning tool in the example,a large number of examples are used to analyze the parameters of the worm pair conjugate.The influence of the meshing performance gives the principle of selecting the worm pair designing parameters and the turning parameters.