| This thesis is mainly concerned with the principle of conjugate surface in singular points. In the light of this principle, a new -type worm gear drive, namely 0?involute-enveloping worm gear drive, is systematically investigated from the aspect of theoretical analysis and experimental research.This thesis classifies the conjugate boundary among the category of singular question on conjugation. Based on the first -type limit and the second -type limit, a detailed research is carried out on the conjugate problem in singular points on a much profounder level. This paper also presents the basic conditions of conjugation in singular points and the two-order necessary conditions of the singular solution existence. As one of the characteristics, this paper puts forward the concept of mapping space in order to study the properties of mesh functions. It is much beneficial to further studying on singular conjugation. By giving the definition of mapping space, some abstract and basic conjugation elements can be impressed by direct geometric graphics. Also, resort to the mapping space, the fundamental theorem of singular conjugation is proved. Furthermore, derived in the paper is the sufficient and necessary condition of the singular conjugation, which the feature function is just as a perfect square formula of identical equaling zero. It is very important to the follow-up jobs.As for the engineering application of the singular conjugation, just like what the paper has exactly indicated, double-envelope is an effective means, but not the only one. If some special kinematic and geometric conditions are satisfied, the singular conjugation can also be gained by single - enveloping method. Owing to the key conclusion, this paper lays emphasis on the possible ways of realizing the singular conjugation by single-enveloping method. It is proved that the hyperbolic normal arc surface and the involute helicoid both may conjugate in singular points on the condition of single - envelope. Thus, two types of drive of the singular conjugation, are developed, one is the hyperbolic normal arc surface worm gear drive, the other 0?involute - enveloping worm gear drive. The latter is one of major issues discussed in the paper.Taking advantage of the moving frame method of differential geometry,this paper deeply studies the theory of numerical simulation for conjugate surface. Several representations of numerical simulation, such as induced curvature, the conditions of first-type limit, second-type limit and singular solution , are presented under continuous and differential conditions. A new system of numerical simulation, which is relative as well as independent to traditional theory, is established. The method of numerical simulation converts the question of conjugate surfaces into the problem of mathematical programming. The conjugate process can be directly described by numerical simulation. In considering the significance of target rod function, this paper mainly discusses the intrinsic relations between the nature of target rod function and the feature of conjugate surface. Therefore, a simulation method of computing bearing contact is also given.In addition, depending on the method of numerical simulation and theoretical analyses, some kinematic and geometric features of 0 involute- enveloping worm gear drive, such as meshing surface, first -type limit, second -type limit, worm surface, the numerical representation of contact line and bearing contact, are systematically studied. These relevant conclusions provide an important basis for the design and manufacture of new type worm gear set. As we predict, the method of numerical simulation has special effect in solving the question of complex conjugate surface.According to the drive theory of 0 involute-enveloping worm gear, its concrete design method is given. This makes the design of new- type worm gear set possible. Three machining methods relying on gear-hobbing machine and technological procedure are presented. It not only meets the meshing principle of wo...
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