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9.2 TOOTH DIMENSIONS AND STANDARDS
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The American Gear Manufacturer s Association (AGMA) publishes much valuable reference data. The details on nomenclature, definitions, and tooth proportions for spur gears can be found in ANSI/AGMA 1012-F90. Table 9.2 contains the most used tooth proportions. The hob tip radius rf varies with different cutters; 0.300/Pd or 0.300m is the usual value. Tables 9.3 and 9.4 list the modules and pitches in general use. Cutting tools can be obtained for all these sizes.
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See Chap. 10 for a special note on AGMA.
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TABLE 9.2 Standard and Commonly Used Tooth Systems for Spur Gears
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TABLE 9.3 Diametral Pitches in General Use
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TABLE 9.4 Modules in General Use
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SPUR GEARS 9.7
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SPUR GEARS
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9.3 FORCE ANALYSIS
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In Fig. 9.3 a gear, not shown, exerts force W against the pinion at pitch point P. This force is resolved into two components, a radial force Wr , acting to separate the gears, and a tangential component Wt , which is called the transmitted load. Equal and opposite to force W is the shaft reaction F, also shown in Fig. 9.3. Force F and torque T are exerted by the shaft on the pinion. Note that torque T opposes the force couple made up of Wt and Fx separated by the distance d/2. Thus T= where Wt d 2 (9.7)
T = torque, lb in (N m) Wt = transmitted load, lb (N) d = operating pitch diameter, in (m) dnP 12 dnP 60
The pitch-line velocity v is given by v= ft/min v= m/s (9.8)
FIGURE 9.3 Force analysis of a pinion. A, operating pitch circle; d, operating pitch diameter; np , pinion speed; , pressure angle; Wt , transmitted tangential load; Wr , radial tooth load; W, resultant tooth load; T, torque; F, shaft force reaction.
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SPUR GEARS 9.8
GEARING
where nP = pinion speed in revolutions per minute (r/min). The power transmitted is P= Wtv 33 000 Wtv hp (9.9) kW
9.4 FUNDAMENTAL AGMA RATING FORMULAS
Many of the terms in the formulas that follow require lengthy discussions and considerable space to list their values. This material is considered at length in Chap. 10 and so is omitted here.
9.4.1 Pitting Resistance The basic formula for pitting resistance, or surface durability, of gear teeth is sc = Cp where sc Cp Wt Ca Cs = = = = = WtCa Cs CmCf Cv dF I
(9.10)
Cm = Cf = Cv = d = = = C = mG = F = I =
contact stress number, lb/in2 (MPa) elastic coefficient, (lb/in2)1/2 [(MPa)1/2]; see Eq. (10.77) and Table 10.4 transmitted tangential load, lb (N) application factor for pitting resistance; see Table 10.3 size factor for pitting resistance; use 1.0 or more until values are established load distribution factor for pitting resistance; use Tables 9.5 and 9.6 surface condition factor; use 1.0 or more until values are established dynamic factor for pitting resistance; use Fig. 10.4; multiply v in meters per second by 197 to get feet per minute operating pitch diameter of pinion, in (mm) 2C/(mG + 1.0) for external gears 2C/(mG 1.0) for internal gears operating center distance, in (mm) gear ratio (never less than 1.0) net face width of narrowest member, in (mm) geometry factor for pitting resistance; use Eq. (10.24) with C = 1.0
Allowable Contact Stress Number. The contact stress number sc , used in Eq. (9.10), is obtained from the allowable contact stress number sac by making several adjustments as follows: sc sac CLCH CT CR (9.11)
See Ref. [10.1].
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