Load shared by concentric springs:
Two concentric springs are subjected to an axial load of 60 kN. The maximum permissible deflection of the springs is 45 mm & the solid length is 55 mm. If the springs are of the material having G = 80 × 10^{3} N/mm^{2 }and the maximum permissible shear stress is 800 N/mm^{2}, determine
a. load shared by the springs, and
b. wire diameter and outer spring radius.
Take inner spring radius = 40 mm & radial clearance = 3 mm.
Solution
The springs are in parallel. Deflection of both of the springs is similar.
Δ= 64 W R^{3} n / G d^{ 4}
----------- (1)
τ_{max} = 16 W R /π d^{3}
------- (2)
n_{1}d_{1}= 55mm ⇒ n 1 = 55_{1 }/d_{1} --------- (3)
From Eq. (1) and (3), we get
--------- (4)
From Eq. (2) to Eq. (1), we get
∴ d_{1} = 15.67 mm ; 15.7 mm
∴ W_{1 } = 3.93 × 15.73 = 15 129 N = 15.1 kN
W_{1} + W_{2} = 60 kN
W_{2} = 44.9 kN
Outer Spring
R_{2} = 80 + 15.7 + 2 × 3 + d_{2 }/2= (50.85 + 0.5 d_{2}) mm
τ max =16 W R / π d^{3}
16 × 44.9 × 103 × (50.85 + 0.5 d 2 )
∴ d_{2} = 24.4 mm
∴ R_{2} = (50.85 + 0.5 × 24.2) = 63.05 mm