Calculation of the coordinates of the modified profile of the generating surface of the gear cutting tool

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].