Load shared by concentric springs, Mechanical Engineering

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 × 103 N/mm2 and the maximum permissible shear stress is 800 N/mm2, 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 R3 n / G d 4

2138_Load shared by concentric springs.png

          168_Load shared by concentric springs1.png----------- (1)

τmax      = 16 W R  /π d3

499_Load shared by concentric springs2.png ------- (2)

  n1d1= 55mm   ⇒  n 1 = 551 /d1                           --------- (3)

From Eq. (1) and (3), we get

1111_Load shared by concentric springs3.png--------- (4)

From Eq. (2) to Eq. (1), we get

 

∴          d1  = 15.67 mm ; 15.7 mm

∴ W1  = 3.93 × 15.73  = 15 129 N = 15.1 kN

  W1  + W2  = 60 kN

  W2  = 44.9 kN

Outer Spring

R2 = 80 + 15.7 + 2 × 3 + d2 /2= (50.85 + 0.5 d2) mm

τ max  =16 W R  / π d3

16 × 44.9 × 103 × (50.85 + 0.5 d 2 )

1491_Load shared by concentric springs4.png

∴          d2  = 24.4 mm

∴ R2  = (50.85 + 0.5 × 24.2) = 63.05 mm

Posted Date: 1/21/2013 1:43:08 AM | Location : United States







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