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.
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
λeff = effective slenderness ratio = α L0 /D
δ = spring material density (kg/m2)
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.
Table showing α for different end conditions
|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|
Absolute stability occurs when C'2 /λeff2 is greater than unity. The condition for absolute
stability is therefore.
For more detailed notes refer to Surging of Springs
The equation for the lowest natural frequency of a compression spring
located between two flat plates is..
Forcing frequencies near the above lowest natural frequency and at whole multiples (2,4,6...) of this frequency.