Digital Modeling And Mechanism Design Of Ellipsoidal Spiral Surface

Spiral surfaces can realize complex motion and meet high precision of workplace needs due to their complex shape and surface characteristics. So they are widely used in industrial products, such as precision machining, aerospace, national defense and military industry. With limited application complexity and situations, ordinary spiral surfaces have been unable to meet the current and future needs. So far, the research model of spiral surface lacks systematic, yet on the spiral surface especially new spiral surface formed deep and a series of research, it is difficult to meet the needs of industrial applications in theory and technology. The current study, taking the ellipsoidal spiral surface which has drawn more and more attention but still been in lack of research as the object, intends to systematically investigate the surface forming principle, mathematical modeling, kinematics and mechanic characteristics,and then explores its industrial applications. The specific contents include:(1) Summarize the basic motion combinations of spiral surface forming based on the particle forming movement principle. Analysis forming motion of CC type spiral surface and combining a linear motion, constitute three CCR type resultant motion of ellipsoidal spiral. Using coordinate transformation methods achieve motion in the form of expression vectors. On the basis of particle forming characteristics, obtained ellipsoidal spiral surface mathematical model according to the characteristics of the generatrix. Concluded ellipsoidal spiral surface forming movement accurate mathematical expression by using differential geometry.(2) For industrial applications, research the forming characteristic parameters of ellipsoidal spiral surface, extract the forming characteristic parameters from ellipsoidal spiral surface which has the minimum number of degrees of freedom, and converted into the form of a general visual features, establish ellipsoidal spiral surface feature parameter class of six parameters. Realize section general building of the ellipsoidal spiral surface. Using three-dimensional modeling software and numerical simulation software to drawing and writing three-dimensional graphics ellipsoidalspiral curves and surfaces based on ellipsoidal spiral surface forming characteristics and parameter class, visually verify the correctness of the mathematical model.(3) Study, by using differential geometry, the geometric characteristics of ellipsoidal spiral curve and ellipsoidal spiral surface, including the tangent vector,spiral angle and curvature, et al. Analyze kinematic characteristics of ellipsoidal spiral curve based on the characteristics of particle forming motion; construct the basic ellipsoidal spiral surface kinematic pair, and establish the corresponding mechanical properties of theoretical model. The current study steps into insight of the characteristics of ellipsoidal spiral curve whose equatorial radii are equal and has concluded that the spiral angle has a constant value, and the curvature of the curve changes a little in value over a wide range.(4) On the ellipsoidal spiral surface whose equatorial radii are equal, research the characteristics of the angle between curves of spiral connection with the adjacent point and the equatorial plane- the half spiral bevel angle. Using vector expression and parametric expression of ellipsoid spiral curve, study and establish the equation of this angle. Further analysis has shown that the half spiral bevel angle in the ellipsoidal spiral curve with the same equatorial radius has a constant value.(5) Research on the characteristics and application of the ellipsoidal spiral surface.Design spiral- linear transmission mechanism based on the property of constant value of the half spiral bevel angle. Establish the relevant theoretical models of kinematic pair based on the research of kinematics and mechanical characteristics, clarify the mechanism can realize the linear motion which has the characteristics of ellipsoidal spiral surface. Finally, the possible applications of several ellipsoidal spiral surface pairs are discussed.