Geometrical- and Tooth Contact Analysis of the Areas and Perimeters on the Archimedean Worm Wheels Depending on the Modification of the Axial Module

With the knowledge of the recommendations from reference literatures - six types of Archimedean worm gear drives were designed with the modification of the axial module. After that computer aided models were generated. These pairs were loaded by the same torque to analyse the mechanical parameters on the tooth contact zone. Due to the geometrical establishment, three teeth are connected with the worm surface at the same time, that is why these teeth are analysed. Polygon method was used to approach the kinematical impression on the worm wheel surface. As a result, we were able to define the area- and perimeter percentages of these impressions on the worm wheel surface for each tooth. We also determined the correlation between the axial module and the analysed mechanical parameters supposing average values on the contact surfaces.

Calculation of the Digital Prototype for Modification of the Initial Straight Profile to the Form of the Tooth-Cutting Tool’s Producing Surface

Spatial helical gears, worm gears with a cylindrical worm, globoid gears, etc., are widely used in most of modern engineering products [1-3; 37; 42]. Cylindrical worm gears are actively used in the creation of metalworking equipment (push mechanisms of rolling mills, presses, etc.), in lifting and transport machines, in drives and kinematic chains of various machine tool equipment where high kinematic accuracy is required (dividing machine tools, adjustment mechanisms), etc. In a worm gear a cylindrical worm or its cylindrical helical surface can be cut by various technological methods [49-51], but no matter how the shaping of the worm gear elements’ working surfaces is carried out, the worm wheel is cut with a gear cutting tool, whose producing surface coincides with the worm thread’s lateral surface [19; 22; 23]. In this regard, the working surface of the cylindrical worm wheel’s tooth, even with a non-orthogonal arrangement of axes, is an envelope of a one-parameter family of surfaces that gives a linear contact, which presence makes it possible to transfer a large load using a worm gear. For high-quality manufacturing of worm gears, it is necessary to design and manufacture a productive gear cutting tool - an accurate worm cutter, whose shaping (working) surface must be identical to the profiled worm’s shaping (working) surface [24-27; 54]. One of the most important tasks in the implementation of worm gearing is the problem of jamming of the cylindrical worm and the worm wheel’ contacting surfaces. This problem is excluded by relieving the contacting surfaces’ profile along the contact line. Considering that any violations of contacting surfaces’ geometric parameters affect the change in their geometric characteristics, the tasks of accurately determining the adjustment parameters of the technological equipment, used for shaping the worm and worm wheel, enter into in the foreground of the worm gearing elements production. In modern conditions of plant and equipment obsolescence, and in particular, of gear cutting machines used for worm gears manufacture, these machines physical wear, implies an inevitable decrease in the accuracy of their kinematic chains. Therefore, in order to maintain the produced gears’ quality at a sufficiently high level, it is necessary to use deliberate modification of contacting surfaces when calculating the worm gearing’s geometric parameters; such modification reduces the worm gear sensitivity to manufacturing and mounting errors of its elements [28-31].

FORMATION OF WORKING SURFACES OF A WORM WHEEL AND A WORM WITH A TOOTH-CUTTING TOOL WITH A MODIFIED PRODUCING SURFACE BY THE METHOD OF COMPUTER SIMULATION

Substantiated the relevance of theoretical studies on the use of modern CAD systems, which make it possible to move away from the analytical description of interacting surfaces and focus on the implementation of algorithms for their interaction. The use of geometric modeling tools for virtual imitation cutting of elements involved in the formation of a worm pair is shown. The use of a modified generating surface is shown to introduce errors that inevitably arise when trying to form and use a real worm pair.