Tooth Surface Parameterization And Contacting Visualization Of Hypoid Gear

In the information age with rapid development of science and technology, new vital force is being brought to traditional subjects by information technology, different subjects keep on supplementing, crossing over and infiltrating mutually, making their scopes of theoretical research and fields of application expanded continuously. In order to keep up with the revolution in information industry and the development of other subjects, traditional mechanics is going through profound changes in many aspects like research objects, contents, theories and methods, among which the hypoid gear drive is a fairly active field.Based on the domestic and oversea researches on hypoid gear, according to the thought of developing and innovating with inheriting, the method of calculating geometric parameters, parameterization of tooth surfaces, strategy of searching conjugate contact points, visualization of geometrical model and tooth-contacting model are deeply researched in this dissertation. Some research results are presented.According to the method of geometric parameters in Gleason Co. which is based on manual computation, the equations set is expand to twenty equations from the original sixteen. The sequence of calculation is following to three-layer construction for calculating three geometric parameters accurately. It solves the difficult problems of shortage of precision and large difference among the results and the presented values by the calculation method of Gleason. The method increases the precision of parameters solution and the stability of iteration process.The method of constructing parameterization of teeth surfaces with cutting parameters, tooth-structure parameters and normalized parameters is brought forward, the conversion relationship among the three parameters is deduced, the definition of position point on tooth surface is unionized, which establishes the base of visualization for geometrical model and tooth-contacting model. The interpolation theory of quartic Hermite parameter curve is put forward and is applied to dedendum easement curve. The method of constructing geometrical model and visualization for parameterized tooth surface, location of point on teeth surface, refinement of teeth surface, configuration of end curve and whole gear is presented based on parameterization of tooth surface. Two solution method, projection method and elliptical function method, are put forward according to Hertz contact theory, which cuts the boundary ellipse along the border of tooth surface, so the instant contact ellipse is illustrated clearly on the three-dimensional tooth surface. The instant contact ellipse is also described as multi-layer structure, on which the different color attributes are defined to make contact ellipse similar to the real contact pattern detected from roll testing machine. That provides a good visualization platform for digitized comparison between theoretical contacting simulation and the actual contact pattern.After discussing the limitation of pure mathematics method for calculating the conjugate contact point on tooth surfaces which are mismatched, the method of ellipsoids-contacting analysis is firstly introduced, which substitutes for conjugate tooth surfaces with ellipsoids, adopts the search strategy of ellipsoid conjugate contact point approaching that of conjugate tooth surfaces. The character of analytic solution of minimum distance between ellipsoids can be utilized to solve the contact mathematic model rapidly and effectively and it has better stability of solution procedure.