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Helical Gears, Bevel Gears, and Wormgearing 395EAzBzAyByBx=WrP108 lb43.5 lb43.536 lbzy2.22baEWxP1.0336 lb36 lb0H1100264.5(lb)Vx64.5 lbBxH110059999 lbb2.22WtP313 lba1.03214 lbWxPH11005 36 lb V(lb)0H110022140M(lb·in)H1100266.4H1100296.6 H11005MEyMEy2 H11005MEz2 H110012202 H11001 96.62ResultantH11005H11005H11005240 lb·in(b) Vertical plane (x-y)Maximum bending momentH11002220 H11005 MEz(a) Horizontal plane (x-z)M(lb·in)00.84FIGURE 10–11 Pinion shaft bending momentsSumming moments about Byields0=WrP(b)+WxP(rm)-Ay(LP)0=108(2.22)+36(0.84)-Ay(3.25)Ay=64.5 lbStep 3. To find Bx: Summing forces in the x-direction yieldsBx=WxP=36 lbThis is the thrust force on bearing B.Step 4. To find the total radial force on each bearing: Compute the resultant of the y- and z-components.A=4Ay2+Az2=264.52+2142=224 lbB=4By2+Bz2=243.52+99.22=108 lbBearing Reactions, Gear Shaft: Bearings C and DUsing similar methods, we can find the forces in Figure 10–12.Cz=142 lbCx=41.1 lbfC=148 lb (radial force on C)Dz=171 lbDx=77.1 lbfD=188 lb(radial force on D)Dy=WxG=108 lb(thrust force onD)SummaryIn selection of the bearings for these shafts, the following capacities are required:Bearing A:224-lb radialBearing B:108-lb radial; 36-lb thrustBearing C:148-lb radialBearing D:188-lb radial; 108-lb thrust
396PART TWODesign of a Mechanical Drive10–9 STRESSES IN STRAIGHT BEVEL GEAR TEETHThis section generally follows AGMA Standard 2003-C10, Rating the Pitting Resistance and Bending Strength of Generated Straight Bevel, Zerol Bevel and Spiral Bevel Gear Teeth, considered to be the primary standard in the United States (Reference 10). However, only straight bevel gears are treated here. The standard presents design analysis in both the U.S. unit system based on diametral pitch, Pd, and the SI Metric unit system based on metric module, m.This book will maintain similar notations and sym-bols for gear tooth features, allowable stresses, and modi-fying factors that were initially presented in Chapter 9 for spur gear design to facilitate the comparison of design ap-proaches. The reader should note that Standard 2003-C10 presents design analysis in SI units using terminology from ISO standards that employ radically different symbol sets. In this book, we maintain similar notations for factors in both systems except for the basic terms, diametral pitch, Pd, and metric module, m.10–8 BENDING MOMENTS ON SHAFTS CARRYING BEVEL GEARSBecause there are forces acting in two planes on bevel gears, as discussed in the preceding section, there is also bending in two planes. The analysis of the shearing force and bending moment diagrams for the shafts must take this into account.Figures 10–11 and 10–12 show the resulting diagrams for the pinion and the gear shafts, respectively, for the gear pair used for Example Problems 8–3, 10–4, and 10–5. Notice that the axial thrust load on each gear provides a concen-trated moment to the shaft equal to the axial load times the distance that it is offset from the axis of the shaft. Also no-tice that the maximum bending moment for each shaft is the resultant of the moments in the two planes. On the pinion