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GEARING
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FIGURE 9.1 Terminology of gear teeth. A, addendum circle; B, pitch circle; C, clearance circle; D, dedendum circle; E, bottom land; F, top land; G, flank; H, face; a = addendum distance; b = dedendum distance; c = clearance distance; p = circular pitch; t = tooth thickness; u = undercut distance.
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meshing gears. Line E is the pressure line, and the angle is the pressure angle. The resultant force vector between a pair of operating gears acts along this line. The pressure line is tangent to both base circles C at points F. The operating diameters of the pitch circles depend on the center distance used in mounting the gears, but the base circle diameters are constant and depend only on how the tooth forms were generated, because they form the base or the starting point of the involute profile.
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TABLE 9.1 Basic Formulas for Spur Gears
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FIGURE 9.2 Layout drawing of a pair of spur gears in mesh. The pinion is the driver and rotates clockwise about the axis at O. A, addendum circles; B, pitch circles; C, base circles; D, dedendum circles; E, pressure line; F, tangent points; P, pitch point; a, initial point of contact; b, final point of contact.
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Line aPb is the line of action. Point a is the initial point of contact. This point is located at the intersection of the addendum circle of the gear with the pressure line. Should point a occur on the other side of point F on the pinion base circle, the pinion flank would be undercut during generation of the profile. Point b of Fig. 9.2 is the final point of contact. This point is located at the intersection of the addendum circle of the pinion with the pressure line. For no undercutting of the gear teeth, point b must be located between the pitch point P and point F on the base circle of the gear. Line aP represents the approach phase of tooth contact; line Pb is the recess phase. Tooth contact is a sliding contact throughout the line of action except for an instant at P when contact is pure rolling. The nature of the sliding is quite different during the approach action and the recess action; bevel-gear teeth, for example, are generated to obtain more recess action, thus reducing wear. Instead of using the theoretical pitch circle as an index of tooth size, the base circle, which is a more fundamental distance, can be used. The result is called the base pitch pb. It is related to the circular pitch p by the equation pb = p cos (9.5)
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If, in Fig. 9.2, the distance from a to b exactly equals the base pitch, then, when one pair of teeth are just beginning contact at a, the preceding pair will be leaving contact at b. Thus, for this special condition, there is never more or less than one pair
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SPUR GEARS 9.6
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of teeth in contact. If the distance ab is greater than the base pitch but less than twice as much, then when a pair of teeth come into contact at a, another pair of teeth will still be in contact somewhere along the line of action ab. Because of the nature of this tooth action, usually one or two pairs of teeth in contact, a useful criterion of tooth action, called the contact ratio mc , can be defined. The formula is mc = Lab pb (9.6)
where Lab = distance ab, the length of the line of action. Do not confuse the contact ratio mc with the module m.
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