Research On Principle Of Moulding-Surface Conjugation And Technology Of Toroid Worm Transmission With Spherical Meshing Elements

Using "Research of Transmission Theory and New Transmission Technology based on the Bertrand Surface" supported by National Natural Science Foundation of China as the background,many kinds of tooth flanks of gears are re-understood by promoting them to the concept of moulding surface in the dissertation,and on this basis,the basic principle of moulding-surface conjugation and its branch—the general principle of normal circular-arc gear transmission are investigated,and toroid worm drive with spherical meshing elements are studied by the analytic and experimental method.Moulding surface was firstly proposed by G.Monge in 19^th century,but the engineering society is unfamiliar with some of its surface Characteristics.Actually,many surfaces used widely in the engineering,including tooth flanks,can be boiled down to moulding surface,so it is necessary to re-understand and re-research on this surface.Based on the directrix and basic frame,the generation and geometric properties of moulding surface are studied from a new point of view by the application of Curvature Stripe Method in Modern Differential Geometry. The skeleton and the cross-section of surface are decided respectively by the directrix and the generatrix,and the surface normals along the generatrix are coplanar.The multiformity of shape and the simplicity of structure make moulding surface meet different practical demands, and also provide a good platform for this research.The basic principle of moulding-surface conjugation is an important theoretical foundation in this dissertation.According to the idea of surface-curve transformation,the conjugate problems are boiled down to the relationships between a pair of directrixes. Because of the difference of generatrix shape,moulding-surface conjugation is divided into three cases,and respective conjugate conditions and differential relational equations are presented.On this basis,Motion Group Method is applied to solve the consistency of conjugate conditions,i.e.the structure condition of conjugation,and it is arranged as a Pythagoras Equation for the convenience.As the succession and development of Oliver's Theorem,the principle of intermediate conjugation and indirect generating method for moulding surface are studied,and the motion condition and the geometric condition are presented to realize this conjugation.As an important branch of moulding-surface conjugate principle,the general principle of normal circular-arc gear transmission is studied.According to the driving characteristics,a theoretical platform for the research is constituted by taking the meshing line as the program, datum surface as the support and the directrix as the skeleton,and based on the meshing line, the conjugate condition,the limit condition and the non-interference condition are presented, and three kinds of gear drives with parallel axes,intersecting axes and non-parallel non-intersecting axes are systematically studied,a theoretical model of hyperbolic-type normal circular-arc gear drive is proposed.As a result,normal circular-arc gear transmission is developed into one drive suitable for every possibility of axial arrangement,and so an integrated theoretical system is set up.As one of the combinations of moulding-surface conjugate principle and gear transmission technology,toroid worm drive with spherical meshing elements is proposed.It is a special case of normal circular-arc gear with the steel ball mediums,and has some basic characteristics,such as the point-curve conjugation,the three-body two-pair and the mismatch treatment in the technology,etc.By combining theory with technology,the quantitative researches on toroid worm drive with spherical meshing elements are executed,such as the mismatch treatment and the contact area control,the redundant motion and the force analysis of steel ball,the sensitivity and adaptability to error,etc.On this basis,some special problems, such as the profile design of worm and the anti-dropping of steel-bail,are discussed,and the design method of worm pair is introduced.Aiming at NC machining,the design of tool,the accuracy analysis and the machining method are also discussed.By the development and the running test of prototype machine,the results show that the principle is correct and the techniques are realizable,and the anticipative purposes are achieved.