Study On Meshing Theory Of Normal Arc-toothed Cylindrical Worm Drive

In this paper,the meshing theory of the normal arc-toothed cylindrical worm drive(for convenience,it will be referred to as ZC3K worm drive later)is studied.The spiral surface of the ZC3K worm is turned by a convex arc blade turning tool.The normal section of the worm spiral surface is a concave arc.The machining method of the ZC3K worm helicoid is to place the convex arc blade turning tool in the normal plane of the worm and to make the feeding motion along the worm axis,while the worm rotates around its own axis.The machining method can be used to machine a multi-head worm,thereby improving the meshing efficiency of the worm drive.This paper establishes the mathematical model of ZC3K worm drive meshing analysis,and explores the meshing characteristics and meshing performance of ZC3K worm drive.The main research contents of the paper include:(1)The formation principle of ZC3K worm spiral surface is introduced.The change of tool angle when turning ZC3K worm spiral surface is studied.The mathematical model of ZC3K worm spiral surface is established according to the formation principle of the worm spiral surface.(2)The meshing principle of the ZC3K worm drive.Firstly,the relative motion coordinate system of the worm pair is established according to the relative motion of the worm pair.Secondly,the meshing function and the two kinds of boundary functions and two kinds of boundary equations of the worm pair are calculated.Finally,the judgment basis and judgment method of the meshing performance of the worm pair are given.In addition,the tooth surface equation of the worm wheel is calculated based on the relative motion of the worm pair.(3)Analysis of meshing characteristics of ZC3K worm drive.Firstly,the boundary equation of the worm and the worm gear tooth surface and the range of the worm tooth surface parameters and the arc center coordinates of the circular blade are given.This provides the boundary conditions for the analysis of the meshing characteristics of the worm drive.Secondly,the meshing characteristics of the worm pair is analyzed in detail with specific examples,including the tooth shape and tooth angle of the worm shaft section,the worm pair meshing boundary,the key point of the worm conjugate zone boundary and the instantaneous contact line of the worm pair.Finally,through MATLAB computer simulation technology,different numerical examples are simulated and analyzed,and the relevant conclusions of the meshing characteristics of the worm pair are obtained.(4)Numerical simulation study on the meshing performance of ZC3K worm drive.Using MATLAB computer simulation technology,combined with specific numerical examples to simulate,explore the influence of the parameter change of the turning tool used in machining worm and the parameter change of the worm pair on the meshing performance of the worm pair,and draw relevant conclusions,and thus the selection principle of the above parameters is given.