Determine the ratio between moment and load, Mechanical Engineering

Determine the ratio between moment and load:

Any close coiled helical spring of circular section extends 1 mm while subjected to an axial load of W and then given an angular rotation of 1 radian while a moment M is independently applied around the axis. Determine the ratio M / W

Solution

For a close coiled spring :

Δ=64 W R3 n/ Gd 4 (Δ = 1 mm)

∴          W = Gd 4/64 R3 n                   ------------- (1)

φ= 128 M Rn  / Ed 4

∴          M =      E d 4/128 R n                        -------------- (2)

Eq. (2) divided by Eq. (1), we get

M/ W = (Ed 4/128 R n) × (64 R3n/ Gd 4)

=   E   R2 / 2 G                      E = 2 G (1 + ν)

M / W  = R2  (1 + ν)

Posted Date: 1/21/2013 1:21:41 AM | Location : United States







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