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12.8 DOUBLE-ENVELOPING GEAR SETS
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12.8.1 Number of Teeth in Gear The number of teeth for the gear is influenced to a large extent by center distance.The recommended number of teeth for various center distances is listed in Table 12.11. Should special considerations indicate a requirement for fewer teeth, it is advisable to consult a manufacturer of this type of gearing before you complete the design. For multiple-thread worms, the number of teeth in the gear should be within the limits listed in Table 12.11. The maximum number of teeth for single-threaded worms is limited only by the machines available for cutting gear sets and manufacturing tooling. 12.8.2 Number of Threads in Worm The minimum number of teeth in the gear and the ratio determine the number of threads for the worm. Generally, one to nine threads are used. In special cases, a larger number of threads may be required.
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See Ref. [12.2].
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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 12.19
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WORM GEARING
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TABLE 12.11 Range of Recommended Gear-Tooth Numbers
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12.8.3 Gear Ratio The gear ratio is the quotient of the number of teeth in the gear and the number of threads in the worm. Either prime or even ratios may be used; however, hob life is improved with even ratios. 12.8.4 Pitch It is recommended that pitch be specified in the axial section. Pitch is the result of design proportions. 12.8.5 Worm Root Diameter The recommended root diameter for the worm is dR = C 0.875 3 (12.23)
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It is desirable that the root diameter be not less than that indicated by this formula, even where the worm threads are cut integral with the shaft. For ratios less than 8/1, the worm root diameter may be increased. This increase may vary from zero for an 8/1 ratio to plus 15 percent for a 3/1 ratio. 12.8.6 Worm Pitch Diameter The pitch diameter of the worm is assumed to be at the mean of the working depth at the center of the worm and is so considered for all calculations. The approximate worm pitch diameter is d= and the corresponding root diameter is dR = d 2bG C 0.875 2.2
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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 12.20
GEARING
where bG is the dedendum of gear teeth in inches. Compare this root diameter with that given by Eq. (12.23). If it does not agree, alter the pitch diameter until the root diameter is within the desired limits. Where horsepower rating is not a factor, there is no limitation regarding pitch diameter of the worm. Where efficiency is not as important as strength or loadcarrying capacity, increasing the worm root diameter and gear face width will result in greater capacity.
12.8.7 Base Circle The base circle may be secured from a layout in the following way. The normal pressure angle is always 20 . The axial pressure angle may be obtained from x = tan 1 tan n cos (12.24)
Once the centerline of the worm and gear, the vertical centerline, and the gear pitch circle are laid out, measure along the common worm and gear pitch circle to the right or left of the vertical centerline an amount equal to one-fourth the axial circular pitch px. Through the point thus established and at an angle to the vertical centerline equal to the axial pressure angle x, extend a line upward. A circle tangent to this line and concentric to the gear axis is the base circle. Adjust this diameter to the nearest 0.01 in. The formula for figuring the base circle diameter is Db = D sin x + 90 NG (12.25)
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