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HELICAL GEARS 10.12
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FIGURE 10.5 Definition of effective face width. (a) FE1 = F1, FE2 = F1 + 2WD; FN = F1; (b) FE1 = F1, FE2 = F2, FN = F1; (c) FE1 = FE2 = FN.
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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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HELICAL GEARS 10.13
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FIGURE 10.6 Stress condition for reversing (as with an idler) loading. (a) Load on right flank; (b) load on left flank; (c) typical waveform for strain gauge at point C.
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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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HELICAL GEARS 10.14
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FIGURE 10.7 Rim thickness factor Kb. The backup ratio is defined as the ratio of the rim thickness to the tooth height. Curve A is fully reversed loading; curves B and C are unidirectional loading.
For gear blanks which utilize a T-shaped rim and web construction, the web acts as a hard point, if the rim is thin, and stresses will be higher over the web than over the ends of the T. The actual value which should be used for such constructions depends greatly on the relative proportions of the gear face width and the web. If the web spans 70 to 80 percent of the face width, the gear may be considered as having a rigid backup. Thus the backup ratio will be greater than 2.0, and any of the curves shown may be used (that is, curve C or B, both of which are identical above a 2.0 backup ratio, for unidirectional loading or curve A for fully reversed loading). If the proportions are between these limits, the gear lies in a gray area and probably lies somewhere in the range defined by curves B and C. Some designer discretion should be exercised here. Finally, note that the rim thickness factor is equal to unity only for unidirectionally loaded, rigid-backup helical gears. For fully reversed loading, its value will be at least 1.4, even if the backup is rigid. Load-Distribution Factors Km and Cc. These factors modify the rating equations to account for the manner in which the load is distributed on the teeth. The load on a set of gears will never be exactly uniformly distributed. Factors which affect the load distribution include the accuracy of the teeth themselves; the accuracy of the
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HELICAL GEARS 10.15
HELICAL GEARS
housing which supports the teeth (as it influences the alignment of the gear axes); the deflections of the housing, shafts, and gear blanks (both elastic and thermal); and the internal clearances in the bearings which support the gears, among others. All these and any other appropriate effects must be evaluated in order to define the total effective alignment error et for the gear pair. Once this is accomplished, the load-distribution factor may be calculated. In some cases it may not be possible to fully define or even estimate the value of et. In such cases an empirical approach may be used. We discuss both approaches in some detail. The empirical approach requires only minimal data, and so it is the simplest to apply. Several conditions must be met, however, prior to using this method: 1. Net face width to pinion pitch diameter ratios must be less than or equal to 2.0. (For double-helix gears, the gap is not included in the face width.) 2. The gear elements are mounted between bearings (not overhung). 3. Face width can be up to 40 in. 4. There must be contact across the full face width of the narrowest member when loaded. 5. Gears are not highly crowned. The empirical expression for the load-distribution factor is Cm = Km = 1.0 + Cmc(CpfCpm + CmaCe) where Cmc = lead correction factor Cpf = pinion proportion factor Cpm = pinion proportion modifier Cma = mesh alignment factor Ce = mesh alignment correction factor The lead correction factor Cmc modifies the peak loading in the presence of slight crowning or lead correction as follows: Cmc = 1.0 0.8 for gear with unmodified leads for gear with leads properly modified by crowning or lead correction (10.21)
Figure 10.8 shows the pinion proportion factor Cpf, which accounts for deflections due to load. The pinion proportion modifier Cpm alters Cpf based on the location of the pinion relative to the supporting bearings. Figure 10.9 defines the factors S and S1. And Cpm is defined as follows: Cpm = 1.0 1.1 when S1/S < 0.175 when S1/S 0.175
The mesh alignment factor Cma accounts for factors other than elastic deformations. Figure 10.10 provides values for this factor for four accuracy groupings. For double-helix gears, this figure should be used with F equal to half of the total face width. The mesh alignment correction factor Ce modifies the mesh alignment factor to allow for the improved alignment which may be obtained when a gear set is adjusted at assembly or when the gears are modified by grinding, skiving, or lapping to more closely match their mates at assembly (in which case, pinion and gear
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