Study On The Manufacturing Error And Geometric Characteristics Of Globoidal Cam Mechanisms

The globoidal cam mechanism is an intermittent indexing transmission mechanism. Due to the compact structure, high reliability, and high loading capacity, the globoidal cam mechanisms are widely used in food machinery, packaging machinery, tobacco machinery, and the automatic tool changer(ATC) of CNC machines. It is a complicated task to manufacture the globoidal cams, for the complexity of the mechanism motion. At present, we still do not have the self-production capacity for high-grade globoidal cam mechanism(ATC), thus mainly depend on imports. In order to increase manufacturing capability and master the manufacturing technology, it is highly desired to study on the globoidal cam mechanism and provide the theoretical basis for production manufacturing.Firstly, the surface deviation of the globoidal cam is analyzed, which is machined by a 4-axes special machine tool with two-coordinated axes for manufacturing globoidal cams. Based on the differential geometry and conjugate theory, the machined surface and the surface deviation of a globoidal cam are derived by considering rotational angle errors, the squareness errors, and linear offset errors of the special machine tool. The sensitivity model is applied to analyze the effects of machine tool errors on the machined surface deviation. Manufacture easiness index which can evaluate the level of manufacture difficulty and can also indirectly imply manufacture cost is proposed. Then, the tolerance optimization problems are formulated to maximize manufacture easiness index subject to quality target of cam surface and manufacture constraints. The optimization results are obtained by using optimization methods, and are applied as a guideline to tolerance design of the special machine tool for manufacturing globoidal cams.Secondly, the rib-thickness of globoidal cams is studied for the occurrence of the thin rib in manufacturing. A systematic approach based on the geodesics in differential geometry for calculating the rib-thickness of the globoidal cam is proposed. In the proposed approach, the analytical description of the rib-thickness is derived and calculated using coordinate transformation, conjugate theory and differential geometry. In addition, the mathematical expressions for the contact curves of the conjugate surfaces, intersection curves of the ribbed surfaces with the torus, and the geodesics of the torus surface are conveniently derived. Then these curves and the ribbed surfaces are all simulated with the help of Creo Software after the calculation results are obtained by using VC programming. By comparing the rib-thickness with respect to different motion curves, the influencing factors of the rib-thickness is studied. The results of this research are necessary for both the selection of motion curves, and the investigations of the rigidity and the strength of the globoidal cam mechanisms.Thirdly, geometric characteristics of the globoidal cam surface are studied. On the premises of the first, the second and the third fundamental forms, the principal curvatures and directions, the Gaussian curvature, and the asymptotic directions of the globoidal cam surface are derived and calculated. Then, the local shapes of the globoidal cam surface varying with different motion periods are analyzed. All these results are obtained with the help of VC++ Software, and simulated by using Creo Software. The existence of straight lines on the globoidal cam surface is investigated. In order to obtain exact solutions, the asymptotic curves on the cam surface are calculated and simulated. The curvatures of the asymptotic curves are calculated to verify whether the cam surface is a ruled surface or not. The calculation results show that the globoidal cam surface is not a ruled surface in the indexing period, which is an important issue to determine the machining process of the globoidal cam.Fourthly, a complete and systematic method for the analysis and simulation of geometric characteristics of mating surfaces of globoidal cam mechanisms is presented. The Dupin’s indicatrix for all kinds of local shapes is summarized, and then the Dupin’s indicatrices for the globoidal cam surface and roller surface are depicted as well. The characteristic curves of relative normal curvature which reflect the change of relative normal curvature on the common tangent plane are compared with respect to different contact points. Based on the Dupin’s indicatrix, the indicatrix of conformity is first applied to analyze the contact geometry of mating surfaces of globoidal cam mechanism. The indicatrix of conformity in the case of contact of saddle-like surface with convex parabolic-like surface is first discussed by considering the contact condition between globoidal cam surface and roller surface. The investigation of the indicatrix of conformity also provided a new and intuitive method to determine whether the interference occurs in differential vicinity of the contact point. The results of the research will provide a strong theoretical basis for the study on the contact strength, contact stress and contact deformation of mating surfaces.At last, the measuring technology of surface deviation of globoidal cam and the testing technology of overturning position accuracy of cutting tools in globoidal cam type magazine are studied. The machined surface deviation of globoidal cam which is manufactured by the newly designed special machine tool is measured. Moreover, the detailed measuring procedures and the measuring results are presented. A platform for testing position accuracy of cutting tools in globoidal cam type magazine after overturning is developed, and its testing principle and methodology are investigated. It provides a dynamic testing technology of overturning position accuracy of cutting tools for industrial plants.