Question

A helical compression srping is to be made of oil-tempered wire of 4 mm diameter with a spring index of C = 10. The spring is to operate inside a hole, so buckling is not a problem and the ends can be left plain. The free length of the spring should be 80 mm. A force of 50 N should deflect the spring 15 mm. Su = 1750 Mpa, allow for a 10% clash allowance and G = 79 GPa. a) Determine the spring rate. b) Determine the minimum hole diameter for the spring to operate in c) Determine the total number of coils needed. d) Determine the solid length. e) Determine the static factor of safety based on the yielding of the spring if it is compressed to its solid length

Answer 1

Ans a) Determine the spring rate! - o=ca Ce spring andex d= diameter of helical spring D = 10x4 = nomm obtain the torsional stiffness, G for oil tempered wire with umm from G= 79 Gpa When the spring is compressed, the spring force is Fir ky y = deflection of the spring. k= spring state Here F50N 4, 15m :50 = kx15 ke 3.333 NIM

diameter - b) Determine the minimum hole for the spring to operate in. Do = vad D=lomm, da um DE = 40th Do= uumm c) Determines the total no. of coils needed id 4G Ma 803k OOR D de diameter of helical compression spring G= torsional stiffness D= Mean spring coil diameter k = spring rate d = 4mm. G= 79 GPä o= comm. k = 3.333 (m. N -99 (79x103) 8 (40)3 (3:333) 1.85 Na = 485

d) Determine the solid length Na=ne Ne=the total no. of coils. L-d Caleti) dumm N =11.85 then, a = 4(1.85+1) A Tin = 5065mm e) Determine the static factor of safety based on the yielding of the spring if it is compressed to its solid length Sura Im A = 1855 MPa. mm n - 0187 Suri = 18 18 - 1431:39 MPa fet Say.co.5 Sut substitute Sur = 1750 MPa by given data Sxy = 0:5 (1750) 875 MPa 1855 40.187 RESTITVI

w the deflection of the spring considering solid length : Y-10- Lo= somm, n = 150.4mm 9. So -50.44 --996 mm. Faky, R = 3.33311m 41=29:6 MM F = 3:333x29.6 =98:66, Calculate the factor to kB = uct2 uc-3. c=10, k to ULID+2 B – 4110)-3 = 1.135, Cakulate shear stress due static load Te = KB. (SF. 1 2 3 ks 21.135 , F,- hemm..98:66 D-Ommdum

8 x 98.66 Xuo sol to (4): 2 T= 178.22 MPa Calculate the static factor of based on the yielding of the Szy safety spring UX Sava 75 875MPa tx=178.22 MPa: 875MPa 178.22 MPa cy:9096. [ Solid length = 4,9096 .