Analysis of Gearing of Worm-Helical Gears in Generalizing Parameters

Worm-helical gears occupy an intermediate position between the worm gears and helical gears, which are widely used in machines. A cylindrical gear or a cylindrical worm-screw that has a large number of threads and a limited length of the cut part, serves as the basic link in these gears. To fully reveal the geometric-kinematic capabilities of the gearing, the method of synthesis and analysis in generalizing parameters in the generalized area of existence is used. The method involves using local areas of existence, corresponding to specific geometric-kinematic indicators of the gearing. However, in the literature there is neither the information on the subject with regards to different schemes of worm-helical gears, nor the recommendations on the choice of parameters for a forming rack contour for forming working surfaces of the gear-wheel teeth and the worm-gear threads that provide the most favourable set of gearing indicators. The studies have revealed that the areas of existence in the scheme with the basic worm-gear are much smaller than those in the scheme with the basic gear-wheel, wherein in the former case, the local area is limited by a curve corresponding to the points of the teeth tips of the enveloping link, and in the latter case, by the axis of face angles of the gearing and only a part of the aforementioned curve. It has been established that the best set of quality indicators of the gearing can be obtained utilizing the forming rack contour with a 28° profile angle used in manufacturing highly-stressed cylindrical involute gears for aircraft engines. The corresponding values of these indicators are presented in comparison with the indicator values for a standard basic contour with a 20° profile angle. These results can be used to improve the strength and durability of the threads of worm-gears and the teeth of gear-wheels in worm-helical gears.

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