The Research Of Some Questions In Approximate Developing About Undevelopable Curved Surface

Approximate developing about undevelopable curved surface has been widely used in the field of machine, aviation, automobile, ship construction and light industry. Exploring a new developing method, analyzing the error of the approximate developing and developing a system of fast surface analysis and developing have an important application value in many aspects, such as to improve the product quality and the surface design quality, to reduce the materials consumption, to raise the production efficiency, to economize resource and to boost production more, faster, better and more economized. In this paper, in-depth research was made on some questions existing in the approximate developing about undevelopable curved surface, and mainly included the several aspects below:Firstly, it was demonstrated that there was a tangent planes tribe along arbitrarily curved Γ on the surfaces Σ, whose envelope surface was developable curved surface, and the solving formula of the plane was deduced. Replacing the curved surface Σ by the planes Σ1could attain a high accuracy. The flattened model of rotating curved surfaces’cylinder replacement and cone replacement was systematically deduced-with the case study of rotating curved surfaces model. The global and local error analysis of the cylinder replacement of sphere surface, ring surface and revolution hyperboloid of one sheet was calculated, and the graph and the flattened curved surface of all evaluation indexes were prepared.Secondly, on the basis of using numerical method, an analytic method of seeking the best flattened base point of the surfaces was presented, with the regularity study of the best base point’s geometry. The best flattened base point’s position of the surfaces could be solved quickly with this method. Sphere surface, ring surface and hyperbola paraboloid were used as examples to solve the best point’s position.Thirdly, the definition and characteristics of area coordinate were introduced.Area coordinate was brought into the mapping calculation of the points of the curved surface and its flattened plane with the triangle line method principle. A one-to-one correspondence between the points of the surface and its flattened plane was established by dispersin,locating and mapping the points on the surface line. The shape of the surface’s line onto the flattened plane was drawn by an example calculation based on the UG redevelopment system.