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Crowning and side relieving are tooth surface modifications in the
axial direction. See Figure 12-2. Crowning is the removal of a slight amount of tooth from the center on out to reach edge, making the tooth surface slightly convex. This method allows the gear to maintain contact in the central region of the tooth and permits avoidance of edge contact with consequent lower load capacity. Crowning also allows a greater tolerance in the misalignment of gears in their assembly, maintaining central contact. Relieving is a chamfering of the tooth surface. It is similar to crowning except that it is a simpler process and only an approximation to crowning. It is not as effective as crowning. 12.3 Topping And Semitopping In topping, often referred to as top hobbing, the top or outside diameter of the gear is cut simultaneously with the generation of the teeth. An advantage is that there will be no burrs on the tooth top. Also, the outside diameter is highly concentric with the pitch circle. This permits secondary machining operations using this diameter for nesting. |
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Semitopping
is the chamfering of the tooth's top corner, which is accomplished
simultaneously with tooth generation. Figure 12-3 shows a semitopping
cutter and the resultant generated semitopped gear. Such a tooth tends to
prevent corner damage. Also, it has no burr. The magnitude of semitopping
should not go beyond a proper limit as otherwise it would significantly
shorten the addendum and contact ratio. Figure 12-4 specifies a
recommended magnitude of semitopping.
Both modifications require special generating tools. They are
independent modifications but, if desired, can be applied simultaneously.
SECTION 13 GEAR TRAINS
The objective of gears is to provide a desired motion, either rotation or linear. This is accomplished through either a simple gear pair or a more involved and complex system of several gear meshes. Also, related to this is the desired speed, direction of rotation and the shaft arrangement.
A meshed gear is the basic form of a single-stage gear train. It consists of z1 and z2 numbers of teeth on the driver and driven gears, and their respective rotations, n1 & n2 The speed ratio is then:
speed ratio = Z1 = n2 (13-1)
Z2 n1
13.1.1 Types of Single-Stage Gear Trains
| Gear
trains can be classified into three types: 1. Speed ratio > 1, increasing: n1 < n2 2. Speed ratio =1, equal speeds: n1=n2 3. Speed ratio < 1, reducing: n1> n2 Figure 13-1 illustrates four basic types. For the very common cases of spur and bevel meshes, Figures 13-1(a) and 13-1(b), the direction of rotation of driver and driven gears are reversed. In the case of an internal gear mesh, Figure 13-1(c), both gears have the same direction of rotation. In the case of a worm mesh, Figure 13-1(d), the rotation direction of z2 is determined by its helix hand. In addition to these four basic forms, the combination of a rack and gear can be considered a specific type. The displacement of a rack, i, for rotation 0 of the mating gear is: i
= pmz1f
(13-2) |
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