From Gear Geometry and Applied Theory, Second Edtion
Involute gears, spur and helical ones, are widely used in reducers, planetary gear trains, transmissions, and many other industrial applications. The level of sophistication in the design and manufacture of such gears (by hobbing, shaping, and grinding) is impressive. The geometry, design, and manufacture of helical gears was the subject of research presented in the works of Litvin et al. [1995, 1999, 2001a, 2003], Stosic , and Feng et al. .
The advantage of involute gearing in comparison with cycloidal gearing is that the change of center distance does not cause transmission errors. However, the practice of design and the test of bearing contact and transmission errors show the need for modification of involute gearing, particularly of helical gears. Figure 15.1.1 shows a 3D model of a modified involute helical gear drive.
Figure 15.1.1: Modified involute helical gear drive.
The existing design and manufacture of involute helical gears provide instantaneous contact of tooth surfaces along a line. The instantaneous line of contact of conjugated tooth surfaces is a straight line L 0 that is the tangent to the helix on the base cylinder (Fig. 15.1.2). The normals to the tooth surface at any point of line L 0 are collinear and they intersect in the process of meshing with the instantaneous axis of relative motion that is the tangent to the pitch cylinders. The concept of pitch cylinders is discussed in Section 15.2.
Figure 15.1.2: Contact lines on an involute helical tooth surface.
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A hypoid gear is a style of spiral bevel gear whose main variance is that the mating gears' axes do not intersect. The hypoid gear is offset from the gear center, allowing unique configurations and a large diameter shaft. The teeth on a hypoid gear are helical, and the pitch surface is best described as a hyperboloid. A hypoid gear can be considered a cross between a bevel gear and a worm drive.
Herringbone gears, also called double helical gears, are gear sets designed to transmit power through parallel or, less commonly, perpendicular axes. The unique tooth structure of a herringbone gear consists of two adjoining, opposite helixes that appear in the shape of the letter 'V'.
Bevel gears are gears designed to transmit motion between intersecting axes. Perpendicular arrangements are most common, but bevel gears can be manufactured for nearly any angle. The teeth bearing surface of the gear, or surface pitch, is conically shaped or tapered. Miter gears are bevel gears manufactured in a 1:1 ratio, with the same number of teeth on mating gears and with perpendicular axes.
Spur gears are the simplest type of gear. Transmitting power between parallel axes, the teeth project radially on the disc.
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