Generalization Process of the Integrated Mathematical Model Created for the Development of the Production Geometry of Complicated Surfaces
Year: 2024
Type: article
Abstract: Computer modeling of the construction and operation of technical structures is increasingly done using software that includes more detailed knowledge, which requires an increase in the level as well as an expansion of the scope of the geometric knowledge. A significant part of the motion transmission mechanisms are the worm drive pairs, for which the separation of the parts dealing with the theoretical and practical problems found in the literature can be experienced in numerous instances. Due to the different technical features, in many cases the screw surfaces are not designed and manufactured in a geometrically correct way, or the best solution is not necessarily chosen. The geometric model describing the production process of the screw surfaces provides the basis for examining the deviation between the surface mathematically determined by the designer and the surface produced. An integrated mathematical kinematic model was developed for the production geometrical analysis of the elements of cylindrical and conical worm gear drive pairs for machining with a traditional thread grinding machine, which causes a serious pitch fluctuating error among several other problems in case of machining the conical worm. During the geometrical research of production modelling, running parallel to the analysis of these errors, the idea was formulated, since the geometric modelling always is created with the toolbox of descriptive geometry, in which the application of projective invariants proves useful in many cases, it may be advisable to create a projective relationship between the reference surfaces of conical and cylindrical spiral surfaces. As a result of the research conducted for the mathematical generalization of the integrated model, the improved constructive geometric model was created, in which the method of analytically creating the projective geometric relationship between the reference surfaces of conical and cylindrical helicoid surfaces has been described for the first time in this article. The significance of the further development presented in this article is that during the production of the conical helicoid surface, the thread pitch fluctuation has been eliminated, and that the algebraic form of the central collineation relationship between the reference surfaces of the conical and cylindrical worms has also been determined. In accordance with the improved constructive geometric model, the technological environment and tools must be rearranged and relocated during further work.
Source: Symmetry
DOI: 10.3390/sym16121618
Author: Zsuzsanna Balajti Óváriné
Institution: University of Miskolc
Language: English
Subfield: Mechanical Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,728
OpenAlex ID: W4405113254