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## Spring Stability Notes

INTRODUCTION

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 λeff = effective 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.

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

Absolute stability occurs when C'2 /λeff2 is greater than unity. The condition for absolute stability is therefore.

Surging

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.

 Links to Spring Design Mitcalc ...A excel based software package -very convenient to use

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Last Updated 17/09/2009