In this paper an examination has been outlined a possibility of further generalization respecting the Dudás's kinematic-mathematical model, which is suitable for the production geometric development of elements of helicoid drive pairs. The positioning of the rolling surfaces of the cylindrical and conical surfaces, as axoids of worms, in the extended model to the projective space under the right conditions, based on the surfaces invariant to projective transformations can be a right extension of the model, as the projective space model includes the Euclidean space model in full. The machining of the conical worm surfaces modelled in this method involves the clarification of the kinematic-geometric relations of production geometry in the Euclidean space model, which shows the possibility of further development of production geometry. The goal of generalization of the mathematical description is the systematization by creating central collinear projective connection between axoids (rolling cones and rolling cylinders). Managing the production geometry of the worms in a system is also a further improvement in manufacturing precision.
The difference between the mathematical defined shape of the conical helicoid surface and the operating surface of the spiroid worm produced with axis adjustment on a thread grinding machine results – among other things –in thread pitch fluctuation. During the manufacturing of conical helicoid surfaces the transmission of the rotation from the main spindle to the worm shaft can be realised by a driving pin and an adjusted lathe dog. This article deals with the examination of the fluctuation of the thread pitch parameter occurring when using a counter-conical drive pin. The fluctuation is described here as a function of the position and the shape geometry of the drive pin.
The aim of the paper to show the localising the bearing pattern and exploring the relations between the geometrical parameters of the worm in the new model.
ÖsszefoglalásA cikk célja ez esetben egy új modellben a hordkép lokalizálás és a csiga geometriai paraméterei közötti kapcsolatok feltárásának bemutatása.
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