Metody modelowania i obliczania rozkładu obciążenia w zazębieniach ślimakowych
Sabiniak, Henryk Grzegorz
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Compactness, silent running and possibility of achieving large transmission ratio at one degree make worm gears one of the most popular reducer types. There exist actually two problems to be solved during designing and exploitation of cylindrical and globoid worm gears: the gliding speed and the distribution of load in teeth. Great gliding speeds in the teeth are a characteristic feature of worm gears. It is a disadvantage because it results in power losses. The losses, in tum, change into heat during the gear work. The problem is already known to worm gears designers. This negative effect may be reduced in various ways by proper selection of teeth outline geometry as well as materials choice and correction. Y et the distribution of load in the teeth of worm gears is unknown or almost unknown. The knowledge of distribution of load along the contact lines between the pairs of cooperating teeth and of the associated tension in the tooth root as well as of the proper physical laws will enable achieving through constructional operations at the designing stage of such a load distribution that will enable increasing the working life or load endurance and consequently increasing the efficiency of the gear. Due to their specificity, globoid teeth, including worm teeth, are an extremely difficult area for theoretical as well as for experimental research. The knowledge and information about this type of teeth should be looked for in basie engineering problems, like the theory of plates, the theory of friction, lubrication and wearing out or the theory of surface pressure. Obviously not whole the research run in these areas can be directly applied to globoid teeth. Only a small part of them can be applied in practice here. The basie theory used in the worm teeth modelling was the theory of plates, specifically the theory of circular and rectangular, thin and thick support plates with constant and variable thickness. The mathematical and physical models of these teeth were step by step adjusted to the engineering reality. In the research a number of problems in the area of the support plates theory were solved with special possibility to adjust them to the teeth of globoid and cylindrical worm gears. Particular problems of the plate theory were solved with the use of different methods: analytical, analytical-empirical, empirical. Obtaining the information on stress and deformations in the worm teeth was based on mathematical models, including the graphic ones projecting the real systems considerably well. In the experimental research the measuring methods and apparatus selection were presented enabling obtaining as accurate results as possible, which did not demand further recalculating of the measurements. Thus issues formulated in the above way were considered. The presented results and their processing enable calculating in a short time deformations of support plates under any load as well as finding the distribution of load (knowing the inter teeth stress) that caused these deformations. The knowledge of the distribution of load along the contact line of the pairs of cooperating teeth in any type of gears enables a detailed analysis of the gear work. Through proper correction or even modification of the outline of working surface of the worm teeth and work wheel the load cumulating and stress at the tooth root can be avoided, which in consequence improves the durability of the whole gear. The results achieved in the work can serve for making the further calculations of the plates themselves more precise as well as specifying the analysis of the real systems projected by the support plates, e.g. in other types of drives, machines themselves or mechanical constructions in which such models can be applied.