Helical Gears Bevel Gears and Wormgearing 395 E A z B z A y B y B x W rP 108 lb

# Helical gears bevel gears and wormgearing 395 e a z b

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Helical Gears, Bevel Gears, and Wormgearing 395 E A z B z A y B y B x = W rP 108 lb 43.5 lb 43.5 36 lb z y 2.22 b a E W xP 1.03 36 lb 36 lb 0 H11002 64.5 (lb) V x 64.5 lb B x H11005 99 99 lb b 2.22 W tP 313 lb a 1.03 214 lb W xP H11005 36 lb V (lb) 0 H11002 214 0 M (lb · in) H11002 66.4 H11002 96.6 H11005 M E y M E y 2 H11005 M E z 2 H11001 220 2 H11001 96.6 2 Resultant H11005 H11005 H11005 240 lb · in ( b ) Vertical plane ( x-y ) Maximum bending moment H11002 220 H11005 M E z ( a ) Horizontal plane ( x-z ) M (lb · in) 0 0.84 FIGURE 10–11 Pinion shaft bending moments Summing moments about B yields 0 = W rP ( b ) + W xP ( r m ) - A y ( L P ) 0 = 108(2.22) + 36(0.84) - A y (3.25) A y = 64.5 lb Step 3. To find B x : Summing forces in the x -direction yields B x = W xP = 36 lb This 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 = 4 A y 2 + A z 2 = 2 64.5 2 + 214 2 = 224 lb B = 4 B y 2 + B z 2 = 2 43.5 2 + 99.2 2 = 108 lb Bearing Reactions, Gear Shaft: Bearings C and D Using similar methods, we can find the forces in Figure 10–12. C z = 142 lb C x = 41.1 lb f C = 148 lb (radial force on C) D z = 171 lb D x = 77.1 lb f D = 188 lb (radial force on D ) D y = W xG = 108 lb (thrust force on D) Summary In selection of the bearings for these shafts, the following capacities are required: Bearing A: 224-lb radial Bearing B: 108-lb radial; 36-lb thrust Bearing C: 148-lb radial Bearing D: 188-lb radial; 108-lb thrust 396 PART TWO Design of a Mechanical Drive 10–9 STRESSES IN STRAIGHT BEVEL GEAR TEETH This 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, P d , 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, P d , and metric module, m. 10–8 BENDING MOMENTS ON SHAFTS CARRYING BEVEL GEARS Because 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  • • • 