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].

Analytical Dependences of the Kinematic Forming Primary Surfaces of the Worm Gear

The run-in method for obtaining the screw surface of a worm is based on the use of the worm gearing principle. In this case, the shaping surface (cutting tool) and the workpiece constitute a gear pair [4; 7]. The use of geometric modeling methods [8; 9] to simulate the process of shaping the working surface is based on the relative movement of intersecting objects in the form of a “workpiece-tool” system. This allows to obtain the necessary geometrical model that accurately reproduces the geometric configuration of the surfaces of the teeth of spatial gears [14; 15], where the producing surface of the tool moves in the selected reference system and its position at an arbitrary time is determined by a certain parameter, the motion parameter. The position of the cutting tool at the beginning and at the end of each pass is calculated using parametric equations, which make it possible to calculate the tool path for accurate processing of spatially complex surfaces [16–19]. In the process of mechanical action of a tool on a solid (workpiece), shaping occurs, which consists in the movement of the tool relative to the workpiece [30; 31]. The use of modern methods of three-dimensional computer graphics allows us to improve and accelerate the process of designing technological operations of tooth profiling, providing the final forms of the surfaces of the teeth in the form of visual and accurate computer-based solid-state models [39; 40]. The method is based on a virtual representation of the process of shaping in the form of intersection of solid-state 3D models of two objects (tools and workpieces), which generally perform a screw relative motion. As a result, the working surfaces of the teeth are formed as the envelopes of the tool producing surface [32–34]. For the formation of fission surfaces, mathematical dependences were obtained, which allow one to describe the mutual motion of a worm, a worm gear and a disk cutter [35–37]. These analytical dependences make it possible to simulate the virtual process of forming the side surfaces of the worm gearing elements [1–3; 5; 6]

Development of Computer-Based Model for Design and Analyses of Worm Gearing Mechanism

Current computer software for designing gear systems have limited flexibility and few offer multiple gearing design options. The objective of this study was to develop an interactive package for the design and analyses of worm gearing mechanisms. The worm gears were designed based on full-depth involute teeth. Mathematical models were developed to compute geometry factors for surface durability of single-enveloping worm gearing cases which were extracted from established American Gear Manufacturers Association (AGMA) standards. Maximum percentage errors from the geometry features, bending loads and wear loads are 0.97%, 3.27% and 1.77% respectively and insignificant. A software capable of computing geometry parameters, bending and wear loads, and selecting appropriate materials for worm mechanisms with good accuracy has been developed.

Variable height modification of TA worm drive

The related research shows that a constant contact line, which is negative for the normal operation of the worm gearing, exists on the middle of the unmodified and the constant height modified TA worm wheel surface. To overcome this drawback, a variable height modification method is proposed for the TA worm drive. In line with this modification method, the height modification parameter is variable during the whole processing cycle. Accordingly, the obtained gearing can be named as the variable height modified TA worm drive. The mathematical model for the meshing analysis of this novel worm drive is established according to its generation mechanism and the mesh theory of gearing. The reason why the variable height modification can remove the constant contact line on the worm gear tooth surface is analyzed in detail. In addition, the classification criterion of the transmission type is also derived. The computing methods of the key points on the contact zone boundary and the instantaneous meshing line are elaborated. On the basis of the above theoretical analysis, the meshing characteristics of this novel worm gearing are well investigated. The results manifest that the above theoretical analysis is valid, and the obtained gearing has favorable meshing properties. Furthermore, it is pointed out that the linear variable height modification with larger quantity can be recommended as the ideal strategy in practice.