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American Gear Manufacturer s Association (AGMA), Alexandria, Virginia.
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TABLE 12.5 Recommended Minimum Number of Gear Teeth
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Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
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WORM GEARING 12.14
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12.7.4 Pitch It is recommended that pitch be specified in the axial plane of the worm and that it be a simple fraction, to permit accurate factoring for change-gear ratios.
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12.7.5 Worm Pitch Diameter The pitch diameter of the worm for calculation purposes is assumed to be at the mean of the working depth. A worm does not have a true pitch diameter until it is mated with a gear at a specified center distance. If the actual addendum and dedendum of the worm are equal, respectively, to the addendum and dedendum of the gear, then the nominal and actual pitch diameters of the worm are the same. However, it is not essential that this condition exist for satisfactory operation of the gearing. Although a relatively large variation in worm pitch diameter is permissible, it should be held within certain limits if the power capacity is not to be adversely affected. Therefore, when a worm pitch diameter is selected, the following factors should be considered: 1. Smaller pitch diameters provide higher efficiency and reduce the magnitude of tooth loading. 2. The root diameter which results from selection of a pitch diameter must be sufficiently large to prevent undue deflection and stress under load. 3. Larger worm pitch diameters permit utilization of larger gear face widths, providing higher strength for the gear set. 4. For low ratios, the minimum pitch diameter is governed, to some degree, by the desirability of avoiding too high a lead angle. Generally, the lead is limited to a maximum of 45 . However, lead angles up to 50 are practical.
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12.7.6 Gear Pitch Diameter The selection of an approximate worm pitch diameter permits the determination of a corresponding approximate gear pitch diameter. In the normal case where the addendum and dedendum of the worm are to be equal, respectively, to the addendum and dedendum of the gear, a trial value of gear pitch diameter may be found by subtracting the approximate worm pitch diameter from twice the center distance of the worm and gear. Once the number of teeth for the gear has been selected, it is desirable to arrive at an exact gear pitch diameter by selecting for the gear circular pitch a fraction, which can be conveniently factored into a gear train for processing purposes, and calculating gear pitch diameter from the formula in Table 12.6. Should the actual value of gear pitch diameter differ from the trial value, the worm pitch diameter must be adjusted accordingly through the use of the formula in Table 12.7. It is not essential that the pitch circle of the gear be at the mean of the working depth. Where there are sufficient teeth in the gear and the pressure angle is high enough to prevent undercutting, the pitch line can be anywhere between the mean of the depth and the throat diameter of the gear, or even outside the throat. This results in a short addendum for the gear teeth and lengthens the angle of recess. It is
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Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
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TABLE 12.6 Dimensions of the Gear
also practical for the gear pitch diameter to be located somewhat below the mean of the working depth.
12.7.7 Worm Thread and Gear-Tooth Proportions Pressure Angle. Several factors deserve consideration in the selection of the pressure angle. Smaller values of pressure angle decrease the separating forces, extend the line of action, and result in less backlash change with change in center distance. Larger values of pressure angle provide stronger teeth and assist in preventing undercutting of the teeth where lead angles are larger. The recommended pressure angles are listed in Table 12.8. These, used with the system for stubbing teeth (Table 12.9), will avoid undercutting.
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