Research On Meshing Theory Of The Toroidal Surface Enveloping Cylindrical Worm Pair With Offset Worm Gear

In the face of the practical problem that the central area of the worm gear tooth surface is prone to adhesive wear in engineering application,this paper proposes a solution to the problem that the worm gear is designed to be in the offset state.On the basis of the torus envelope cylindrical worm pair using this way to get a new type of worm gearing,the offset worm gear circular enveloping cylindrical worm pair,whose worm gear is in the offset state with a fan-like ring shape.In this paper,the design method of offset worm gear is studied systematically,and the complete meshing theory system and meshing performance analysis of this kind of worm drive are established.The main research work can be summarized as follows:(1)The mathematical model of the two stages in the enveloping process of the circular enveloping cylindrical worm pair with offset worm gear is established,and the relative motion analysis is carried out.The meshing function of the enveloping worm with grinding wheel and the meshing function of the worm pair are derived by means of vector rotation,and the helicoid equation of the worm and the worm gear,as well as the two kinds of limit functions and meshing performance parameters of the worm pair are derived.(2)The solution equations of meshing boundary and curvature interference boundary of worm pair are deduced.The images of two kinds of boundary and their conjugate lines in conjugate area of worm countershaft section are obtained.It can be seen directly that curvature interference boundary does not enter conjugate area of worm pair.By analyzing the value of the sliding angle at the instantaneous contact point in the conjugate area of the worm gear tooth surface,it is found that the position of the bad sliding area of the worm gear tooth surface is close to the conjugate line of the meshing boundary.(3)Through the establishment of the worm gear rotation coordinate system,the nonlinear equations for the solution of the tooth top thickness and the tooth profile of any cross section of the worm gear are derived,and the reasonable initial value is selected for iterative solution by combining the parameter elimination method and the function drawing method.By choosing a reasonable value of the tooth top thickness coefficient,the boundary line of the tooth top of the offset type worm gear is determined to meet the requirements,and by selecting the angle between the boundary oblique lines on both sides of the tooth surface of the worm gear and the vertical and horizontal directions,not only the bad sliding area of the tooth surface is eliminated,but also the meshing area of the tooth surface is ensured,and finally the tooth surface of the offset type worm gear is determined.(4)The boundary of conjugate region is formed by solving and fitting the key points of conjugate region boundary of worm pair,and the instantaneous contact line is formed by solving and fitting the instantaneous contact points,which are drawn in the axial section of worm pair.Using MATLAB computer simulation technology,combined with a specific example,the numerical simulation analysis of meshing performance is carried out,and the meshing performance is compared.The results of this paper show that,compared with the circular enveloped cylindrical worm gearing,the offset gear type circular enveloped cylindrical worm gearing eliminates the bad lubrication area on the tooth surface of the worm gear and improves the lubrication performance significantly.The new worm drive is expected to solve practical engineering problems and provide more choices for production and application.