Conference material: "Proceedings of the International Conference on Computer Graphics and Vision “Graphicon” (23-26 September 2019, Bryansk)"
Authors:Ryazanov S.A., Reshetnikov M.K.
Geometrical Model of the Manufacturing Surface of the Equivalent Working Surface of the Fine Tooth Dolbyak
Abstract:
Existing mathematical models for calculating gearing are quite complex and do not always make it possible to quickly and accurately obtain the desired result. A simpler way to find a suitable gear option that satisfies the task is to use computer modeling and computer graphics methods, and in particular solid-state modeling algorithms. The use of geometric modeling techniques to simulate the process of shaping the working surface of gearing is based on the relative movement of intersecting objects in the form of a “workpiece-tool” system. This allows you to obtain the necessary geometric model that accurately reproduces the geometric configuration of the surfaces of the teeth of spatial gears, taking into account the technological features of their production on gear cutting machines. This information allows you to perform on the computer imitation control the movement of the cutting tool. Ultimately, this boils down to the problem of analytic description and computer representation of curves and surfaces in three-dimensional space. As the gear cutting tools, the most widely used are disk and worm modular mills (shaver), gear cutting heads, dolbyaki and lath tools. At the moment there are no computer algorithms for obtaining the “dolbyak” producing surfaces, which are obtained by a tool with a modified producing surface. A change in the geometric shape of the tool producing surface will lead to a change in its working surfaces, which may lead to an improvement in their contact. This article shows the application of the developed methods and algorithms of geometric and computer modeling, which are intended for shaping the working surfaces of the Dolbyak tool. Their application will speed up the process of calculating intermediate adjustments of machines used for cutting gears, bypassing complex mathematical calculations that, under conditions of aging of the gear-cutting machines, their wear and the inevitable reduction in the accuracy of their kinematic chains.
