Development of Geometric Descriptors for Gears and Gear Tools

Abstract

Important parameters of a gear tool are values of deflection of the machined surface at its different points, appearing due to errors of tool set-up, its re-sharpening and so on. An important parameter of a gear is its sensitivity to variation in the mutual arrangement of links appearing at gear assembly and due to deformations by loads and temperature influence. It is almost impossible for a production engineer, designer, product assembler or repairman to find this information; it can be obtained through complicated computer-aided analysis, individually tailored to each specific tool and gear. The place for keeping this information may be geometric descriptors of tools and gears proposed in this paper. The geometric descriptor will allow the manufacturers to solve multiple complex tasks quickly and reliably: (a) to obtain the proper location of the bearing contact in a gear; (b) to estimate the behavior of the bearing contact and the value of cyclic variations of the gear ratio when a gear is operated; (c) to assign deviations in tool-setting parameters in order to compensate for organic errors in the re-sharpening of tool front surfaces; (d) to determine the re-sharpening parameters in order to decrease organic errors in re-sharpening or obtain the required modification of tooth surfaces and other tasks. Theoretical basics for creating geometric descriptors are kinematic methods of the classical theory of gearing, developed later in the theory of real gearing. Choosing the most valuable references for development of geometric descriptors, we have to list works [11,12,13,14,15,16,17,18,19,20, 22,23,24]. The previous theoretical works written by the author are essentially useful for computer-aided design of generating processes, which precedes the development of geometric descriptors [2,3,4, 6, 7]. In these works, investigations of generating processes are carried out through applying: (i) the concepts of fans, wedges and bunches of normal lines [2,3,4, 7] (one can determine surfaces generated by jogs on generating solids, including those of secondary cutting); (ii) multi-parametric enveloping [2] (surfaces of shear are determined within tool supply and withdrawal); (iii) interrelated systems of curvilinear coordinates: integral, natural, unified, regulated [3] (one can even describe the geometry of all cutting edges for any edge-type tool as a continuous, smooth surface differentiable at all points with two unified regulated curvilinear coordinates on it [7]). The paper also presents: (a) analysis of features for gear machining cutting by edge-type tools and requirements for the geometry of operating flanks of teeth; (b) specification of types of geometric descriptor (paper, computer-aided and combined) and of tasks solved by their means; (c) statement of theoretical basics of development of geometric descriptors; (d) approximate contents of works on development of a system of geometrical descriptors for tools and gears; (e) theoretical investigations and specification of developed computer-aided programs aimed at development of geometrical descriptors; (f) results of computer-aided simulation through these programs for generation of helical surfaces by solids of revolution, i.e., fundamentals of geometric descriptors for disk-type cutters and disks for profile grinding; (g) structure of paper geometric descriptors and basic components of one sheet of such a descriptor. The present paper does not provide examples of geometric descriptors for specific tools and gears.