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HELICAL GEARS 10.45
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HELICAL GEARS
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FIGURE 10.43 Core-hardness coefficient Uc as a function of the contact stress number sc. The upper portion of the core-hardness bands yields heavier case depths and is for general design purposes; use the lower portion of the bands for high-quality material. (From Ref. [10.1].)
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FIGURE 10.44 Minimum total case depth hc for nitrided gears based on the normal diametral pitch. (From Ref. [10.1].)
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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 10.45 Variations in hardening patterns obtainable with flame or induction hardening. (From Ref. [10.1].)
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For through-hardened gears, the yield stress at maximum peak stress should also be checked as defined by Eq. (10.83): SayKy where Wt,maxKa Pd Km F Kf Kv (10.83)
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Wt,max = peak tangential tooth load, lb Ka = application factor Kv = dynamic factor F = minimum net face width, in Km = load-distribution factor Kf = stress correction factor Ky = yield strength factor say = allowable yield strength number, psi (from Fig. 10.46)
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The yield strength factor should be set equal to 0.50 for conservative practice or to 0.75 for general industrial use.
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HELICAL GEARS 10.47
HELICAL GEARS
FIGURE 10.46 Allowable yield strength number say for steel gears. (From Ref. [10.1].)
Hardness Ratio Factor CH. It is common practice in using through-hardened gear sets to utilize a higher hardness on the pinion than on the gear. The pinion typically sees many more cycles than the gear; thus a more economical overall design is obtained by balancing the surface durability and wear rate in this manner. Similarly, surface-hardened pinions may be used with through-hardened gears to provide improved overall capacity through the work-hardening effect which a hard pinion has on a soft gear. The hardness ratio factor adjusts the allowable stresses for this effect. For through-hardened gear sets, CH can be found from Fig. 10.47, while Fig. 10.48 provides values for surface-hardened pinions mating with through-hardened gears. Life Factors KL and CL. The allowable stresses shown in Tables 10.5 and 10.6 and Figs. 10.40 and 10.41 are based on 10 000 000 load cycles. The life factor adjusts the allowable stresses for design lives other than 10 000 000 cycles. A unity value for the life factor may be used for design lives beyond 10 000 000 cycles only when it is justified by experience with similar designs. Insufficient specific data are available to define life factors for most materials. For steel gears, however, experience has shown that the curves shown in Figs. 10.49 and 10.50 are valid. In utilizing these charts, care should be exercised whenever the product of KL and sat equals or exceeds say, as shown on Fig. 10.46, since this indicates that localized yielding may occur. For low-speed gears without critical noise vibration or transmis-
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HELICAL GEARS 10.48
GEARING
FIGURE 10.47 Hardness ratio factor CH for through-hardened gears. In this chart, HBP is the Brinell hardness of the pinion, and HBG is the Brinell hardness of the gear. (From Ref. [10.1].)
sion accuracy requirements, local yielding may be acceptable, but it should be avoided in general. Reliability Factors CR and KR. The allowable stress levels are not absolute parameters. Rather, a specific probability of failure is associated with each allowable level. The values shown in Figs. 10.40 and 10.41 and Table 10.5 are based on a 99 percent probability of success (or a 1 percent probability of failure). This means that in a large population, at least 99 percent of the gears designed to a particular listed allowable stress will run for at least 10 000 000 cycles without experiencing a failure in the mode (that is, bending or durability) addressed. In some cases it is desirable to design to higher or lower failure probabilities. Table 10.6 provides values for CR and KR which will permit the designer to do so. Before deciding on the reliability factor which is appropriate for a particular design, the analyst should consider what is meant by a failure. In the case of a durability failure, a failure is said to have occurred when the first pit, or spall, is observed. Obviously a long time will elapse between the occurrence of a durability failure and the time at which the gear will cease to perform its normal power-transmission function.
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