Question

Two concentric helical compression springs made of steel and having the same length when loaded and when unloaded are used to support a static load of 3 kN. The outer spring has D = 50 mm, d = 9 mm, and N = 5; the inner spring D = 30 mm, d = 5 mm, and N = 10. Determine the deflection and the maximum stress in each spring.

Answer 1

see explaination for all the answers and full working.

Step-by-step explanation:

deflection=8P*DN/Gd^4

G(for steel)=70Gpa=70*10^9N/m^2=70KN/mm^2

for outer spring,

deflection=8*3*50^3*5/(70*9^4)=32.66mm

for inner spring

deflection=8*3*30^3*10/(70*5^4)=148.11mm

max stress=k*8*P*C/(3.14*d^2)

for outer spring

c=50/9=5.55

k=(4c-1/4c-4)+.615/c=1.2768

max stress=1.2768*8*3*5.55/(3.14*9^2=.66KN.mm^2

for inner spring

c=6

k=1.2525

max stress=2.29KN/mm^2

Answer 2

Step-by-step explanation:

Data

Load = 3kn = 3000N

Modulus of rigidity = 80Gpa= 80000mpa

Outer spring diameter = 50mm

d. = 9mm

N = 5

Inner spring diameter = 30mm

d = 5mm

N = 10

Fo = outer force

Fi = inner force

Ki = stiffness of inner spring

Ko = stiffness of outer spring

Ks = stress factor