It is necessary to check that relatively long compression springs are not are risk of buckling. If buckling is a problem it is necessary to incorporate some method of guiding the spring by placing it in a hole or on a suitable rod.
A longitudinal spring which is subject to rapid cycling may be at risk of surging. This is when the pulses of compression surge along the spring and back. This could continue and magnify if the natural material frequency of the spring is near the frequency of repeated loading.
Nomenclature
C'1 elastic constant = E /(2(E-G))
C'2 elastic constant = 2 π2 (E-G) /(2G+E))
E = Elastic Modulus (Pa)
d = wire diameter (m)
D = Spring diameter (m)
fn= lowest natural frequency (cycles/second)
na = Number of active coils
G = Shear Modulus (Pa)
L0 = Free Length of spring (m) ycrit = critical deflection for onset of buckling (m)
α - constant depending on spring end conditions -see table
γeff = slenderness ratio = α L0 /D
δ = spring material density (kg/m2)
Buckling
Just as a column will buckle when the load becomes too large a long compression spring may buckle when the deflection exceeds a certain value. The critical deflection is given by the following equation.
| End Conditions | α |
| Spring between two flat parallel surfaces | 0,5 |
| Spring on one flat surfaces with other end hinged | 0,707 |
| Both ends hinged (pivoted) | 1 |
| One end clamped and the other free | 2 |
The equation for the lowest natural frequency of a compression spring is
