The Improved Meshing Theory And Meshing Characteristics Analysis Of TA Worm Pair With Modification

The double enveloping worm gearing with straight side profile,which is widely used in metallurgical machinery,mining machinery,lifting machinery,marine machinery,petrochemical machinery,precision machinery and other industries,has a series of good characteristics.Therefore,the research on the meshing theory of this worm drive has some practical significance.Although some scholars have carried on the research,but there are still a series of problems.It is still active to study this content.The research on the TA worm gearing is carried out,and its mathematical model is established.the meshing theory of TA worm gearing is improved.Based on this,the meshing characteristics of the TA worm gearing is explored.The main research work of this paper is as follows:(1)A new calculation for tooth surface curvature parameters and the selection of the calculation method is proposed based on the differential geometry knowledge,compared with the commonly method used in the literature,the calculation process is simplified and more convenient for beginners to understand and master.(2)Using the properties of rotary vector to simplify the calculation of the meshing function,and obtained the beautiful meshing function,more conducive to subsequent theoretical derivation and MATLAB programming calculation.(3)Combined with the characteristics of modified TA worm pair tooth face area and study of related examples,gives the nonlinear equations to solve key points of TA worm gear surface conjugate boundary,it is useful for beginners and provides the basis to computing conjugate tooth face area.(4)In the research,the method of solving the nonlinear equations of boundary critical points is studied,including the assignment problem of the parameters u,and the initial value problem for two groups of different solutions.To some extent,it can improve the calculation efficiency.(5)A new method for computing instantaneous contact line is presented,which can make up the blank of the existing literature,and provide the basis for the following research.(6)Through the research of the meshing characteristics of the TA worm pairs of the type II,the method and the reasons for the avoiding curvature interference of the worm pairs of the type II are aiso explained.It was found that the appropriate to reduce modification parameters,can change the curvature interference position in relation to the boundaries of meshing zone,in the meshing zone outside,no longer engaged,eliminate the worm wheel tooth surface curvature interference region,thus avoiding the curvature interference.(7)The influence of the variation of the worm head number and the center distance of the worm pair on the meshing characteristics of the worm pair is explored.It is found that the number of the worm head can enlarge the contact area of the worm gear,and can account for half of the worm gear tooth surface.But instantaneous contact line is relatively concentrated in the recess end,will lead to worm gears in the meshing process is not uniform heat dissipation.In the head is the same as the number of cases of worm,worm gear center distance increases,the worm wheel tooth surface contact area will be offset to the middle of the worm wheel tooth surface,but contact zone size and the instantaneous contact line distribution does not change significantly,and the micro mesh qualities of meshing area will improve.