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

2021 ◽  
pp. 35-46
Author(s):  
S. Ryazanov ◽  
M. Reshetnikov
Keyword(s):  
Cutting Tool ◽  
Worm Gear ◽  
Geometric Parameters ◽  
Kinematic Chains ◽  
Gear Cutting ◽  
Working Surface ◽  
Worm Wheel ◽  
Worm Gearing ◽  
Worm Gears ◽  
High Level

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].

A Geometrical Model Producing a Surface Equivalent To the Working Surface of the Gear Tool «Hob»

2019 ◽  
Vol 7 (2) ◽  
pp. 56-60 ◽  
Author(s):  
С. Рязанов ◽  
S. Ryazanov
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Geometrical Model ◽  
Worm Gear ◽  
Analytic Description ◽  
Geometrical Parameters ◽  
Computer Algorithms ◽  
Kinematic Chains ◽  
Worm Wheel ◽  
Worm Gears

Existing mathematical models for calculating worm gearing [34; 38] are quite complex and do not always provide an opportunity to quickly and accurately obtain the desired result [1; 3; 24–26]. A simpler way to find a suitable gearing option that satisfies the task is using computer simulation methods and computer graphics, and in particular solid modeling algorithms [4; 5; 30–33; 36; 37]. This information can be entered into the computer in order to simulate control of the movement of the cutting tool. Ultimately, this boils down to the problem of analytic description and computer representation of curves and surfaces in three-dimensional space [18–20]. Despite the diversity and good development of the calculation methods, and the analysis of the geometrical parameters of the worm gear, there is a lack of means and methods for displaying the process of forming the working surfaces of the worm gear elements [28; 29; 41]. There are no computer algorithms for obtaining the producing surfaces of a worm cutter, which are obtained by a tool with a modified producing surface. A change in the geometric shape of the tool producing surface will lead to a change in the working surfaces of the worm wheel and turns of the worm, which may lead to an improvement in their contact. This article shows the application of the developed methods and algorithms of geometric and computer modeling, which are designed to form the helical surface of the turns of the worm and the teeth of the worm wheel. Their use will speed up the process of calculating intermediate adjustments of machines used for cutting worm gears, bypassing complex mathematical calculations that, under conditions of aging of the gear-cutting machine fleet, their wear and inevitable reduction in the accuracy of their kinematic chains. This can be achieved only by applying a deliberate modification of the contacting surfaces, which reduces the sensitivity of the worm gear to the manufacturing errors of its elements, which allows to maintain the quality of the gears produced at a sufficiently high level.

scholarly journals Module and functionally-oriented techniques in designing and manufacturing worm gears

2017 ◽  
Vol 2 (3) ◽  
pp. 37-44
Author(s):  
Сергей Лагутин ◽  
Sergey Lagutin ◽  
Александр Сандлер ◽  
Aleksandr Sandler ◽  
Евгений Гудов ◽  
...  
Keyword(s):  
Machine Tools ◽  
Mechanical Engineering ◽  
Cutting Tool ◽  
Theory And Practice ◽  
Training Manual ◽  
Worm Wheel ◽  
Production Experience ◽  
Worm Gears ◽  
And Performance ◽  
Required Quality

Worm gears of different purposes and dimensions belong to those objects of mechanical engineering which are connected with science intensive design works (computations and development of design arrangements) and with their not less science intensive technological realization in the course of production. In 2016 the authors published a training manual “Theory and practice of general worm gears production” (M. Infra-Engineering, 2016. – pp. 346) where there is generalized a scientific-production experience of enterprises of mechanical engineering and machine tools manufacture for the formation of the complex of modular and functionally-oriented technologies ensuring required quality and performance characteristics of such objects. As a distinctive feature of such a complex is the interconnection of design and production processes of gear basic parts: a worm, a worm wheel with similar processes in the formation of a producing surface in a gear-cutting tool for a worm wheel.

The Production of Small Worm Gears for Experimental Work

1947 ◽  
Vol 156 (1) ◽  
pp. 368-372
Author(s):  
A. M. Gunner
Keyword(s):  
Experimental Work ◽  
Research Laboratory ◽  
Single Point ◽  
General Rule ◽  
Worm Gear ◽  
Pressure Angle ◽  
Worm Wheel ◽  
Worm Gears ◽  
Shaft Angle ◽  
Gear Drives

Small worm gear drives are a common feature in the design of many types of apparatus, and the following description of the methods used for producing them in an experimental establishment may be of interest. Quantities are small, one or two to each pattern being the general rule, but there is certainly no lack of variety. The worms and wheels most often called for range in size up to 1½ inches and 6 inches diameter respectively, while pitches vary from 10 to 60 d.p. (diametral pitch). Addendum and dedendum proportions of 1/ PN and 1·25/ PN have been standardized, and a pressure angle of 20 deg. is adopted throughout. The gears are designed as hollow-faced helical (spiral) gears, and all calculations are based on the normal pitch. This is to enable standard hobs and cutters to be used for the worms. The shaft angle is usually 90 deg., but the angle of crossing may be varied up to 10 deg. either way on the particular machine employed for cutting the wheels. For many applications, backlash must be reduced to the very minimum consistent with smooth running; and to avoid the extreme accuracy of workmanship which an exact centre distance would necessitate, provision is usually made for adjustment of the worm. Although the Reinecker tangential feed method of worm wheel generation by a single-point tool —representing one tooth of a hob—is generally known, very little information on cutter forming is available. The method outlined was developed at the Admiralty Research Laboratory. Given the use of a modern worm grinder (not available), it should be possible to profile-relief grind these cutters after hardening.

PROSPECTS FOR THE USE OF WORM GEARS IN VEHICLE DESIGNS

2020 ◽  
Vol 5 ◽  
pp. 67-72
Author(s):  
M.Yu. KARELINA ◽  
N.V. ATAMANENKO ◽  
Т.Yu. CHEREPNINA
Keyword(s):  
Comparative Analysis ◽  
Carbon Steels ◽  
Worm Gear ◽  
Cast Irons ◽  
Sliding Speed ◽  
Medium Carbon ◽  
Worm Wheel ◽  
Medium Carbon Steels ◽  
Worm Gears ◽  
Selection Of

The article analyzes the prospects for the use of worm gears in the construction of vehicles. A review of the method of calculating the worm gear has been carried out, approaches to the selection of materials for the worm itself and the worm wheel have been analyzed. A comparative analysis of the characteristics of improved and normalized medium-carbon steels and cast irons has been carried out. The characteristics of materials characterized by the best antifriction and anti-seize properties, in particular, tin bronzes, are given. The methods for predicting the reliability of a worm pair as well as methods for increasing the resource have been considered. The choice of the material of the worm gear depending on the sliding speed has been justified. Calculations have been given to prevent failures in the worm pair: chipping of the working surfaces of the teeth, kinking of the worm wheel tooth, seizing and wear, breakage of the worm's body, overheating, jamming of the gear and others.

Efficiency of worm gearboxes

2016 ◽  
Vol 230 (16) ◽  
pp. 2952-2956 ◽  
Author(s):  
Eva-Maria Mautner ◽  
Werner Sigmund ◽  
Johann-Paul Stemplinger ◽  
Karsten Stahl
Keyword(s):  
Experimental Test ◽  
Carrying Capacity ◽  
Worm Gear ◽  
Experimental Investigations ◽  
Load Carrying Capacity ◽  
Test Results ◽  
Research Project ◽  
Worm Wheel ◽  
Load Carrying ◽  
Worm Gears

Within a research project, experimental investigations of large-sized worm gears (pairing steel worm with bronze worm wheel) with centre distance a = 315 mm are carried out. The primary aim is to gain verified knowledge regarding load-carrying capacity and efficiency for this worm gear size. The paper describes the conducted tests in detail and shows basic examples of experimental test results. In the course of these investigations, an overall worm gearbox efficiency of up to η = 96% is measured.

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

2019 ◽  
Vol 7 (2) ◽  
pp. 65-75
Author(s):  
С. Рязанов ◽  
S. Ryazanov ◽  
М. Решетников ◽  
M. Reshetnikov
Keyword(s):  
Solid State ◽  
Geometric Modeling ◽  
Tool Path ◽  
Cutting Tool ◽  
Three Dimensional ◽  
3D Models ◽  
Mechanical Action ◽  
Worm Gear ◽  
Worm Gearing ◽  
State Models

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]

Worm gear wear and coefficient of efficiency during their running-in period

2021 ◽  
pp. 22-25
Author(s):  
Keyword(s):  
Friction Coefficient ◽  
Velocity Vector ◽  
Worm Gear ◽  
Worm Gears ◽  
Contact Surfaces

The process of worm gear wear is considered. The reasons for the change in the coefficient of efficiency of worm gears during the running-in period are analyzed. Keywords: worm gear, line of engagement, contact surfaces, involute worm, velocity vector, friction coefficient. [email protected]

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