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To utilize these equations, each factor must be evaluated. The tangential load Wt is given by Wt = 2TP d (10.19)
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where TP = pinion torque in inch-pounds (in lb) and d = pinion operating pitch diameter in inches. If the duty cycle is not uniform but does not vary substantially, then the maximum anticipated load should be used. Similarly, if the gear set is to operate at a combination of very high and very low loads, it should be evaluated at the maximum load. If, however, the loading varies over a well-defined range, then the cumulative fatigue damage for the loading cycle should be evaluated by using Miner s rule. For a good explanation, see Ref. [10.2]. Application Factors Ca and Ka. The application factor makes the allowances for externally applied loads of unknown nature which are in excess of the nominal tangential load. Such factors can be defined only after considerable field experience has been established. In a new design, this consideration places the designer squarely on the horns of a dilemma, since new presupposes limited, if any, experience. The values shown in Table 10.3 may be used as a guide if no other basis is available.
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TABLE 10.3 Application Factor Guidelines
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The application factor should never be set equal to unity except where clear experimental evidence indicates that the loading will be absolutely uniform. Wherever possible, the actual loading to be applied to the system should be defined. One of the most common mistakes made by gear system designers is assuming that the motor (or engine, etc.) nameplate rating is also the gear unit rating point. Dynamic Factors Cv and K v . These factors account for internally generated tooth loads which are induced by nonconjugate meshing action.This discontinuous motion occurs as a result of various tooth errors (such as spacing, profile, and runout) and system effects (such as deflections). Other effects, such as system torsional resonances and gear blank resonant responses, may also contribute to the overall dynamic loading experienced by the teeth. The latter effects must, however, be separately evaluated. The effect of tooth accuracy may be determined from Fig. 10.4, which is based on both pitch line velocity and gear quality Qn as specified in Ref. [10.3]. The pitch line velocity of a gear is vt = 0.2618nD (10.20)
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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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FIGURE 10.4 Dynamic factors C and K . (From Ref. [10.1].)
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where
vt = pitch line velocity, feet per minute (ft/min) n = gear speed, revolutions per minute (r/min) D = gear pitch diameter, in
Effective and Net Face Widths FE and FN. The net minimum face width of the narrowest member should always be used for FN. In cases where one member has a substantially larger face width than its mate, some advantage may be taken of this fact in the bending stress calculations, but it is unlikely that a very narrow tooth will fully transfer its tooth load across the face width of a much wider gear. At best, the effective face width of a larger-face-width gear mating with a smaller-face-width gear is limited to the minimum face of the smaller member plus some allowance for the extra support provided by the wide face. Figure 10.5 illustrates the definition of net and effective face widths for various cases. Rim Thickness Factor Kb. The basic bending stress equations were developed for a single tooth mounted on a rigid support so that it behaves as a short cantilever beam. As the rim which supports the gear tooth becomes thinner, a point is reached at which the rim no longer provides rigid support. When this occurs, the bending of the rim itself combines with the tooth bending to yield higher total alternating stresses than would be predicted by the normal equations. Additionally, when a tooth is subjected to fully reversed bending loads, the alternating stress is also increased because of the additive effect of the compressive stress distribution on the normally unloaded side of the tooth, as Fig. 10.6 shows. Both effects are accounted for by the rim thickness factor, as Fig. 10.7 indicates. It must be emphasized that the data shown in Fig. 10.7 are based on a limited amount of analytical and experimental (photoelastic and strain-gauge) measurements and thus must be used judiciously. Still, they are the best data available to date and are far better than nothing at all; see Refs. [10.4] and [10.5].
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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