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TABLE 11.10 Formulas for Computing Blank and Tooth Dimensions of Hypoid Gears (Concluded)
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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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area.The recommendations and rating formulas which follow are designed for a tooth contact developed to give the correct pattern in the final mountings under full load. 11.6.1 Formulas for Contact and Bending Stress The basic equation for contact stress in bevel and hypoid gears is Sc = Cp 2TpCo 1 N 1.2CmCf Cv FD2 n I (11.1)
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and the basic equation for bending stress is St = where 2TG K o Pd 1.2K m K v FD J (11.2)
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St = calculated tensile bending stress at root of gear tooth, pounds per square inch (lb/in2) Sc = calculated contact stress at point on tooth where its value will be maximum, lb/in2 Cp = elastic coefficient of the gear-and-pinion materials combination, (lb)1/2/in TP, TG = transmitted torques of pinion and gear, respectively, poundinches (lb in) Ko, Co = overload factors for strength and durability, respectively Kv, Cv = dynamic factors for strength and durability, respectively Km , Cm = load-distribution factors for strength and durability, respectively Cf = surface-condition factor for durability I = geometry factor for durability J = geometry factor for strength
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11.6.2 Explanation of Strength Formulas and Terms The elastic coefficient for bevel and hypoid gears with localized tooth contact pattern is given by Cp = where 3 1 2 2 2 (1 P )/EP + (1 G)/EG (11.3)
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P, G = Poisson s ratio for materials of pinion and gear, respectively (use 0.30 for ferrous materials) EP, EG = Young s modulus of elasticity for materials of pinion and gear, respectively (use 30.0 106 lb/in2 for steel) The overload factor makes allowance for the roughness or smoothness of operation of both the driving and driven units. Use Table 11.11 as a guide in selecting the overload factor. The dynamic factor reflects the effect of inaccuracies in tooth profile, tooth spacing, and runout on instantaneous tooth loading. For gears manufactured to AGMA class 11 tolerances or higher, a value of 1.0 may be used for dynamic factor. Curve 2 in Fig. 11.18 gives the values of Cv for spiral bevels and hypoids of lower accuracy or for large, planed spiral-bevel gears. Curve 3 gives the values of Cv for bevels of lower accuracy or for large, planed straight-bevel gears.
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BEVEL AND HYPOID GEARS 11.32
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TABLE 11.11 Overload Factors Ko, Co
FIGURE 11.18 Dynamic factors Kv and Cv.
The load-distribution factor allows for misalignment of the gear set under operating conditions. This factor is based on the magnitude of the displacements of the gear and pinion from their theoretical correct locations. Use Table 11.12 as a guide in selecting the load-distribution factor. The surface-condition factor depends on surface finish as affected by cutting, lapping, and grinding. It also depends on surface treatment such as lubrizing.And Cf can be taken as 1.0 provided good gear manufacturing practices are followed. Use Table 11.13 to locate the charts for the two geometry factors I and J. The geometry factor for durability I takes into consideration the relative radius of curvature between mating tooth surfaces, load location, load sharing, effective face width, and inertia factor. The geometry factor for strength J takes into consideration the tooth form factor, load location, load distribution, effective face width, stress correction factor, and inertia factor.
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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