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Geometry Factor J. The bending strength geometry factor is J= where Y = tooth form factor Kf = stress correction factor C = helical factor mN = load-distribution factor YC K f mN (10.46)
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The helical and load-distribution factors were both defined in the discussion of the geometry factor I. The calculation of Y is also a long, tedious process. For helical gears in which load sharing exists among the teeth in contact and for which the facecontact ratio is at least 2.0, the value of Y need not be calculated, since the value for J may be obtained directly from the charts shown in Figs. 10.11 through 10.25 with Eq. (10.47): J = J QTRQTTQAQH where J = QTR = QTT = QA = QH = basic geometry factor tool radius adjustment factor tooth thickness adjustment factor addendum adjustment factor helix-angle adjustment factor (10.47)
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In using these charts, note that the values of addendum, dedendum, and tool-tip radius are given for a 1-normal-pitch gear. Values for any other pitch may be obtained by dividing the factor by the actual normal diametral pitch. For example, if an 8-normal-pitch gear is being considered, the parameters shown on Fig. 10.11 are Addendum a = 1.0 = 0.125 in 8 1.35 = 0.168 75 in 8 0.42 = 0.0525 in 8
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Dedendum b = Tool (hob) tip radius rT =
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The basic geometry factor J is found from Figs. 10.11 through 10.25. The tool radius adjustment factor QTR is found from Figs. 10.14 through 10.16 if the edge radius on the tool is other than 0.42/Pd, which is the standard value used in calculating J . Similarly, for gears with addenda other than 1.0/Pd or tooth thicknesses other than the standard value of /(2Pd), the appropriate factors may be obtained from these charts. In the case of a helical gear, the adjustment factor QH is obtained from Figs. 10.23 through 10.25. If a standard helical gear is being considered, QTR, QTT, and QA remain equal to unity, but QH must be found from Figs. 10.23 to 10.25. These charts are computer-generated and, when properly used, produce quite accurate results. Note that they are also valid for spur gears if QH is set equal to unity (that is, enter Figs. 10.23 through 10.25 with 0 helix angle). The charts shown in Figs. 10.11 through 10.25 assume the use of a standard fullradius hob. Additional charts, still under the assumption that the face-contact ratio is
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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 10.11 Basic geometry factors for 20 spur teeth; N = 20 , a = 1.00, b = 1.35, rT = 0.42, t = 0.
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.
HELICAL GEARS 10.23
HELICAL GEARS
FIGURE 10.12 t = 0.
Basic geometry factors for 221 2 spur teeth; N = 221 2 , a = 1.00, b = 1.35, rT = 0.34,
at least 2.0 for other cutting-tool configurations, are shown in Figs. 10.26 through 10.36. For these figures, mN = PN 0.95Z (10.48)
where the value of Z is for an element of indicated number of teeth and a 75-tooth mate. Also, the normal tooth thicknesses of pinion and gear teeth are each reduced 0.024 in, to provide 0.048 in of total backlash corresponding to a normal diametral pitch of unity. Note that these charts are limited to standard addendum, dedendum, and tooth thickness designs. If the face-contact ratio is less than 2.0, the geometry factor must be calculated in accordance with Eq. (10.46); thus, it will be necessary to define Y and K f . The definition of Y may be accomplished either by graphical layout or by a numerical iteration procedure. Since this Handbook is likely to be used by the machine designer with an occasional need for gear analysis, rather than by the gear specialist, we present the direct graphical technique. Readers interested in preparing computer codes or calculator routines might wish to consult Ref. [10.6]. The following graphical procedure is abstracted directly from Ref. [10.1] with permission of the publisher, as noted earlier. The Y factor is calculated with the aid
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