Digital Modeling Of AE-CE Type Ellipsoidal Spiral Curved Surface And Helical Pair Mechanism Design

Spiral curved surfaces can realize the demand for transmission of force,motion and energy in specific occasions because of the unique mechanical properties and kinematic characteristics result from the unique modeling methods and contour features,which are widely applied in industrial fields and the modeling of daily handicrafts.With the progress of science and technology and the development of production,the requirements of the mechanical system and mechanical and electrical products on the working characteristics of the spiral curved surfaces and spiral curved surface related mechanisms are further complicated and diversified.It includes cylindrical spiral curved surface,conical spiral surface,spherical helicoid,etc.Which are difficult to meet the requirements of complex working conditions due to they're limited geometric characteristics.Therefore,it is an important research direction for spiral curved surfaces to find new type of spiral curved surfaces with rich geometric features and working characteristics.Ellipsoidal spiral curved surfaces with various properties can be obtained when the ellipsoidal surface is selected as the matrix of the spiral curved surfaces.The mathematical models of axial equidistant ellipsoidal spiral curved surface(AE type ellipsoidal spiral curved surface)and central equiangular ellipsoidal spiral surface(CE type ellipsoidal spiral curved surface)are set up by two methods in this paper.The first method is the intersection of space surfaces,the second method uses the principle of particle forming motion.Ellipsoidal spiral curved surface motion pairs are designed based on the systematic research on the geometric characteristics,kinematic characteristics and mechanical properties.Using the pair to design ellipsoidal spiral surface motion pair mechanism combined with the existing mechanism,analyze its working characteristics and explore its application prospect.The main research contents are as follows:(1)Research on the mathematical modeling of ellipsoidal spiral curved surface.Mathematical modeling based on the method of intersection of space surfaces: the axial equidistant ellipsoidal spiral curve's(AE type ellipsoidal spiral curve)mathematical model comes from the intersection of equidistant cylindrical helical surface and rotated ellipsoidal surface;The central equiangular ellipsoidal spiral curve's(CE type ellipsoidal spiral curve)mathematical model comes from the intersection of equiangular spiral surface and rotated ellipsoidal surface.The two kinds of Ellipsoidal spiral curves' mathematical models also can be obtained by the principle of space particle forming motion.Then,constructing space generatrix equation,and set up two kinds of ellipsoidal spiral curved surfaces mathematical models by the principle of space generatrix forming motion.Expanding the kinds of ellipsoidal spiral curved surface,cyclic ellipsoid spiral curved surface is established.(2)Research on characteristic parameter set and accurate description of ellipsoidal spiral curve.Based on the ellipsoidal spiral curves' mathematical models,the characteristic parameters especially the change regulation of the helix angle,curvature,and torsion of ellipsoidal spiral curves.Summarizing the characteristic parameters of two kinds of spiral curves which can uniquely distinguish between different ellipsoidal spiral curves and comparing two kinds of ellipsoidal spiral curves.(3)Research on the working characteristics of ellipsoidal spiral curved surface motion pair.Designing ellipsoidal spiral curved surface motion pairs,and constructing mechanical model of the working state of the active part and the driven part of the ellipsoidal spiral curved surface motion pairs.The rolling friction force,pressure angle,critical value of helix angle during self-locking,the law of speed and acceleration change of driven part's mass center,instantaneous transmission ratio and other mechanical and kinematic characteristics will be researched.(4)Research on mechanism design and application based on ellipsoidal spiral curved surface motion pair.Ellipsoidal helical-gear & rack combined speed change mechanism is designed based on the working characteristics of ellipsoidal spiral curved surface motion pair.The working principle,kinematic and mechanical characteristics of the mechanism are explored by analytical method.Using the numerical simulation software to simulate the motion stats of the mechanism,analyzing the motion characteristics of the related parts,and explore the practical application scene of the mechanism.