720 Budynas-Nisbett:Shigley's IIL Design of Mechanical 14.Spur and Helical Gears T©The McGraw-Hill Mechanical Engineering Elements Companies,2008 Design,Eighth Edition 722 Mechanical Engineering Design Setting Sa=Sm and solving the quadratic in Sa gives 4S2 -1+1+ Setting Sa =a/2,Sur =S2/0.5 gives -忌[-1+1+405 =1.66S% and ky =o/S=1.66.Since a Gerber locus runs in and among fatigue data and Goodman does not,we will use k =1.66. The second effect to be accounted for in using the miscellaneous-effects Marin factor k is stress concentration,for which we will use our fundamentals from Chap.6. For a 20 full-depth tooth the radius of the root fillet is denoted rf,where 0.3000.300 rf= P =0.0375in 8 From Fig.A-15-6 1=1_0.0375 a=7=0.250 =0.15 Since D/d=oo,we approximate with D/d =3,giving K,=1.68.From Fig.6-20, q=0.62.From Eq..(6-32) Kr=1+(0.62)(1.68-1)=1.42 The miscellaneous-effects Marin factor for stress concentration can be expressed as 1 1 =142=0.704 k好= The final value of k is the product of the twok factors,that is,1.66(0.704)=1.17.The Marin equation for the fully corrected endurance strength is Se kakpkekakekf Se =0.934(0.948)1)(1)(1)1.17(27.5)=28.5kpsi For a design factor of n=3,as used in Ex.14-1,applied to the load or strength,the allowable bending stress is Se28.5 0all=兰 3 =9.5 kpsi nd The transmitted load W is wr=FYou=1-50.296950 =3471bf KuP 1.52(8) and the power is,with V=628 ft/min from Ex.14-1, WV347(628) hp=33000=33000 =6.6hp Again,it should be emphasized that these results should be accepted only as prelimi- nary estimates to alert you to the nature of bending in gear teeth.Budynas−Nisbett: Shigley’s Mechanical Engineering Design, Eighth Edition III. Design of Mechanical Elements 14. Spur and Helical Gears 720 © The McGraw−Hill Companies, 2008 722 Mechanical Engineering Design Setting Sa = Sm and solving the quadratic in Sa gives Sa = S2 ut 2S e  −1 +  1 + 4S2 e S2 ut  Setting Sa = σ/2, Sut = S e/0.5 gives σ = S e 0.52 −1 + 1 + 4(0.5)2  = 1.66S e and kf = σ/S e = 1.66. Since a Gerber locus runs in and among fatigue data and Goodman does not, we will use kf = 1.66. The second effect to be accounted for in using the miscellaneous-effects Marin factor kf is stress concentration, for which we will use our fundamentals from Chap. 6. For a 20◦ full-depth tooth the radius of the root fillet is denoted rf , where rf = 0.300 P = 0.300 8 = 0.0375 in From Fig. A–15–6 r d = rf t = 0.0375 0.250 = 0.15 Since D/d = ∞, we approximate with D/d = 3, giving Kt = 1.68. From Fig. 6–20, q = 0.62. From Eq. (6–32) Kf = 1 + (0.62)(1.68 − 1) = 1.42 The miscellaneous-effects Marin factor for stress concentration can be expressed as kf = 1 Kf = 1 1.42 = 0.704 The final value of kf is the product of the two kf factors, that is, 1.66(0.704) = 1.17. The Marin equation for the fully corrected endurance strength is Se = kakbkckd kekf S e = 0.934(0.948)(1)(1)(1)1.17(27.5) = 28.5 kpsi For a design factor of nd = 3, as used in Ex. 14–1, applied to the load or strength, the allowable bending stress is σall = Se nd = 28.5 3 = 9.5 kpsi The transmitted load Wt is Wt = FYσall Kv P = 1.5(0.296)9 500 1.52(8) = 347 lbf and the power is, with V = 628 ft/min from Ex. 14–1, hp = Wt V 33 000 = 347(628) 33 000 = 6.6 hp Again, it should be emphasized that these results should be accepted only as prelimi￾nary estimates to alert you to the nature of bending in gear teeth