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FIGURE 10.41 Allowable bending stress number sat for steel gears. Lower curve is maximum for grade 1 and upper curve is maximum for grade 2. (From Ref. [10.1].)
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FIGURE 10.42 Effective case depth he for carburized gears based on normal diametral pitch. The effective case depth is defined as the depth of case which has a minimum hardness of 50 RC. The total case depth to core carbon is about 1.5he. The values and ranges shown on the case depth curves are to be used as guides. For gearing in which maximum performance is required, detailed studies must be made of the application, loading, and manufacturing procedures to obtain desirable gradients of both hardness and internal stress. Furthermore, the method of measuring the case as well as the allowable tolerance in case depth should be a matter of agreement between the customer and the manufacturer. (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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A guide for minimum effective case depth he at the pitch line for carburized and induction-hardened teeth, based on the depth of maximum shear from contact loading, is given by he = CG sc d sin o UH cos b (10.78)
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where he = minimum effective case depth in inches and UH = hardening process factor in pounds per square inch. In Eq. (10.78), UH = 6.4 106 psi for carburized teeth and 4.4 106 psi for tooth-to-tooth induction-hardened teeth. You should take care when using Eq. (10.78) that adequate case depths prevail at the tooth root fillet, and that tooth tips are not overhardened and brittle. A suggested value of maximum effective case depth he,max at the pitch line is he,max = 0.4 Pd or he,max = 0.56to (10.79)
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where he,max = suggested maximum effective case depth in inches and to = normal tooth thickness at top land of gear in question, in inches. For nitrided gears, case depth is specified as total case depth hc, and hc is defined as the depth below the surface at which the hardness has dropped to 110 percent of the core hardness. For gearing requiring maximum performance, especially large sizes, coarse pitches, and high contact stresses, detailed studies must be made of application, loading, and manufacturing procedures to determine the desirable gradients of hardness, strength, and internal residual stresses throughout the tooth. A guide for minimum case depth for nitrided teeth, based on the depth of maximum shear from contact loading, is given by hc = CG Uc sc d sin o (1.66 107)(cos b) (10.80)
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where hc = minimum total case depth in inches and Uc = core hardness coefficient, from Fig. 10.43. If the value of hc from Eq. (10.80) is less than the value from Fig. 10.44, then the minimum value from Fig. 10.44 should be used. The equation for the lower or lefthand curve in Fig. 10.44 is
2 hc = (4.328 96)(10 2) Pnd(9.681 15)(10 3) + Pnd (1.201 85)(10 3) 3 4 Pnd (6.797 21)(10 5) + Pnd (1.371)(10 6)
(10.81)
The equation of the right-hand curve is
2 hc = (6.600 90)(10 2) Pnd(1.622 24)(10 2) + Pnd (2.093 61)(10 3) 3 4 Pnd (1.177 55)(10 4) + P nd (2.331 60)(10 6)
(10.82)
Note that other treatments of the subject of allowable gear-tooth bending recommend that the value obtained from Table 10.6 or Fig. 10.41 be multiplied by 0.70 for teeth subjected to reversed bending. This is not necessary within the context of this analysis, since the rim thickness factor Kb accounts for reversed bending.
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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