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TABLE 12.3 Ratio Correction Factor Km
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WORM GEARING 12.11
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TABLE 12.4 Velocity Factor Kv
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24, from Table 12.3, Km = 0.823 by interpolation. The pitch line velocity of the worm is VW = dnW = (3)(1800) = 16 965 in/min The sliding velocity is VS = VW 16 965 = = 17 024 in/min cos cos 4.767
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Therefore, from Table 12.4, Kv = 0.215. The transmitted load is obtained from Eq. (12.18) and is WGt = Ks d 0.8Fe Km Kv = 700(60.8)(1.5)(0.823)(0.215) = 779 lb To find the friction load, the coefficient of friction is needed. Converting VS to feet per minute and using Fig. 12.5, we find = 0.023. From Eq. (12.13) we find Wf = = WGt sin cos n cos 0.023(779) 0.023 sin 4.767 cos 14.5 cos 4.767
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= 18.6 lb
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Next, using Eq. (12.17), we find the input horsepower to be hp(in) = = Wf VS WGt DnW + 126 000mG 396 000 779(6)(1800) 18.6(17 024) + 126 000(24) 396 000
= 2.78 + 0.80 = 3.58
12.6 HEAT DISSIPATION
In the last section we noted that the input and output horsepowers differ by the amount of power resulting from friction between the gear teeth. This difference represents energy input to the gear set unit, which will result in a temperature rise. The capacity of the gear reducer will thus be limited by its heat-dissipating capacity. The cooling rate for rectangular housings can be estimated from n + 0.01 84 200 n + 0.01 51 600 without fan (12.19) with fan
C1 =
where C1 is the heat dissipated in Btu/(h)(in2)( F), British thermal units per hour inch squared degrees Fahrenheit, and n is the speed of the worm shaft in rotations per minute. Note that the rates depend on whether there is a fan on the worm shaft. The rates are based on the area of the casing surface, which can be estimated from Ac = 43.2C1.7 (12.20)
where Ac is in square inches. The temperature rise can be computed by equating the friction horsepower to the heat-dissipation rate. Thus hp(friction) = or T( F) = hp(friction)(60)(33 000) 778C1 Ac (12.22) 778C1 Ac T 60(33 000) (12.21)
The oil temperature should not exceed 180 F. Clearly the horsepower rating of a gear set may be limited by temperature rather than by gear strength. Both must be checked. Of course, means other than natural radiation and convection can be employed to solve the heat problem.
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WORM GEARING 12.13
WORM GEARING
12.7 DESIGN STANDARDS
The American Gear Manufacturer s Association has issued certain standards relating to worm-gear design. The purpose of these publications, which are the work of broad committees, is to share the experience of the industry and thus to arrive at good standard design practice. The following relate to industrial worm-gear design and are extracted from [12.1] with the permission of the publisher. Gear sets with axial pitches of 3 16 in and larger are termed coarse-pitch. Another standard deals with fine-pitch worm gearing, but we do not include these details here. It is not recommended that gear and worm be obtained from separate sources. Utilizing a worm design for which a comparable hob exists will reduce tooling costs. 12.7.1 Number of Teeth of Gear Center distance influences to a large extent the minimum number of teeth for the gear. Recommended minimums are shown in Table 12.5. The maximum number of teeth selected is governed by high ratios of reduction and considerations of strength and load-carrying capacity. 12.7.2 Number of Threads in Worm The minimum number of teeth in the gear and the reduction ratio determine the number of threads for the worm. Generally, 1 to 10 threads are used. In special cases, a larger number may be required. 12.7.3 Gear Ratio Either prime or even gear ratios may be used. However, if the gear teeth are to be generated by a single-tooth fly cutter, the use of a prime ratio will eliminate the need for indexing the cutter.
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