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Diameter Changes in Compression Springs Formulae and Calculator

Diameter Changes in Compression Springs Calculator and Equation

Most compression springs are open coil, helical springs which offer resistance to loads acting to reduce the length of the spring. The longitudinal deflection of the springs produce shearing stresses in the spring wire. Where particular load deflection characteristics are desired, springs with varying pitch diameters may be used. These springs may have any number of configurations, including cone, barrel and hourglass. They may be made from wire of round, square or rectangular cross section.

When a helical compression spring is compressed, an increase in the outside diameter occurs because the angularity of the coils changes so that it is nearly at a right angle to the axis. The outside diameter when the spring is compressed solid, can be obtained from the following formula:

Eq. 1

${\displaystyle O{D}_c=\sqrt{D^2+(p^2-<!--\; -\; -->d^2)/{\mathrm{\pi <!--\; \pi \; -->}}^2}+d}$

where:

D = mean coil diameter, in
p = load, lbs
d = diameter of wire or side of square, in
OD_c = outside diameter change, in

Source

Bell Helicopter Structural Design Manual, 1977

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