Question

1- A helical compression spring 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. (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 a static factor of safety based on the yielding of the spring if it is compressed to its solid length.

Answer 1

@. When the spring is compressed, the spring force is givers by K Fg = k Yg 50 = KX15 SON 15mm K= 3.333 N/mm 6). the means spring coil diameter is determine by using relation is D= cxd D = 10 X 4mm D = Gommy Mechanical properties of oil tempered wire with diameter 4mm obtain torsional stiffness iq G=77.2 Gpa the minimum hole a diameter for the spring is Dtd 4014 Do Do Do 44 mm the total number of coils by using relation is d G N = 80K

N= (414 67.2x103) 8(90) (3.333) N = 11.58) a Now the solid length is Written as Ls = d (N+1) Lg 4 (11.58+1) Ls 50.32 mm le the ultimate tensile strength and yield strength of the material is o am For helical compression spring with oil tempered mure of diametes d=amm obtained the intes cept "Å and slope mo forsom estimating minimum tensile storendth common Spring A=18575 Mpa.mn m= 0.187 Sut wires mi from 1855 Sut 20.187 d 1855 Sut (5)0.187 Sut 1431.39 MPa

The yield Storen 7th in Shean, forows connes pon- -ding ultimate tensile strength by wing the relation 18 Sogy 0.5 Sut Yg Soy 0.5 (1431:39) Ssy 715.695 MPa The deflection of spring considering the solid length is Lo Yg -Lg (80 – 50.32) mm 29.68 mm The spring force based on compression to solid length is KX Yg E = ( 3. 333 N/mm) x (29.68mm) 98.9234 N Now comperssate curvatiore effect is Yg FS = FE writters as KB KB 40+2 46-3 GCO) +2 4 (10) - 90+2 Кв 60-3 1.135135 KB

KB 3 ) Tg 3 The shear stress due to static load is gevens by 8 FG D To a ď 1.135135 ( 8x98.9234890 TX G T = 178.717 MPa The static factor of safety based on yielding of of spring is Say the ng 715.695. 178.717 4.0046 ng