Question

2, A helical compression spring is to be designed to carry a variable load. The load varies from a minimum of F,=4 lbf to a maximum of F, = /8 lbf. The corresponding spring length varies from a maximum of L, 2.5 in to a minimum of L, =1 in. The outside diameter of the spring is Do = 0.638 in; the material is hard-drawn wiree of diameter d = 0.080 in. The free length of the spring is L 5.561 in. The rigidity is G =10.0x10° psi. The Zimmerli's endurance data of the unpeened spring is used in this case, i.e. S = 35 kpsi and S55 kpsi (30% (A). To find the required spring rate k and spring index. (B). To find the shear stress amplitude r of the spring and the safety factor of the fatigue load by employing Zimmerlis fatigue failure criterion, i.e n, S0/t,. Is it possible to have a fatigue failurc? (C). To find the shear yield strength S of the spring material. (Hint! The shear ultimate strength S., = A/d" (kpsi) and A=169 kpsi, m=0.146. The shear yield strength is Spy = 0.35S.) (D). To find the rcquired number of active coils N and the total number of coils N if both ends are squared (the number of inactive coils is 2) (E). To find the solid length Ls, the force F, and the stress r, when the spring is compressed to the solid length. (F). To find the safety of factor n, = S/t,. of the spring when L = L.. Is it possible to have a static failure at L= L,.?

Answer 1

(A) Def ledin,8- 4--2.5-1 -1.5m P= F-h 18-4 Sprig rate, b in 14 9 22 1-5 Sprng inder C=D D= D-da 0.628-0.08 Do D0.558 n 0.5S C- b.975 0 08 IB Pa (F2-F,) (18-4) Pa-7 2 2 4xb 475- t0lal5 6.175 40-1 + Db15 4X6-175-4 4C-4 C Kp-1-21 21X8X D AX0 0 8 Pa D 3 Ta 23 58X10 psil 558 1 35KI02 23-58 X103 2n Sse Ca L48 T61 X103 M - 24.44X 1O Sut (C) pSL A Sut 0-35X 24 44 XIo 0.25 Set = Ssy 85.53KID psi 1

(D) 8=8D3PNa Na Sadt 8PD Na= 5X1OXIDx0.0s4 X O Adeve oils Na 32 wils 8X 14X 0-5583 Na 21.57 22 Nt=Nat inachive coils 2+2 (E Ls NIKd34XD.O8 L2.72in SeLo- Ls = 5.S-2.72 ds= 2-P41 in F k&1.33X 2.841 & Fs= 26.51 lb s8 F D 8X21 K26-5IXD 552 DD 8101 XLO pr 8553X10 81.01KI0 state fai lure facha possible to have It ar IS lesr than 1 of safety