Roymech engineering encyclopedia

Compression Spring Stability and Buckling


Long compression springs can become laterally unstable when compressed. Instead of continuing to shorten along their intended axis, the spring may deflect sideways and buckle. Spring stability should therefore be checked where the free length is large relative to the coil diameter.

Where buckling cannot be avoided by the spring proportions, the spring may require lateral guidance using a suitable guide rod, tube or bore. Guidance must provide adequate clearance for normal spring movement without causing unacceptable friction, wear or interference.

Need help choosing or understanding a spring arrangement?
See the Spring Selection and Design Guide before using the detailed spring design pages.

Contents

Compression Spring Buckling

A compression spring can lose lateral stability in a manner broadly analogous to the buckling of a slender column. The tendency to buckle increases as the spring becomes longer relative to its coil diameter and is also influenced by the way its ends are supported.

For a given spring geometry and end condition, a critical axial deflection can be calculated. If the required working deflection approaches or exceeds this value, the spring should not be assumed to remain laterally stable without suitable guidance.

Spring diameter: The stability equations on this page use the spring diameter D as defined by the original buckling method. Ensure that the diameter definition used in the calculation is consistent with the spring geometry and design method being used.

Nomenclature

Symbol Description Unit
C'1 Elastic constant Dimensionless
C'2 Elastic constant Dimensionless
E Young's modulus Pa
G Shear modulus Pa
d Spring wire diameter m
D Spring diameter used in the stability calculation m
L0 Free length of spring m
L'0 Limiting free length for absolute stability m
ycrit Critical axial deflection for onset of buckling m
α Constant determined by spring end conditions Dimensionless
λeff Effective spring slenderness ratio Dimensionless

Elastic Constants

The elastic constants used by the original RoyMech stability relationship are:

C 1 ′ = E 2 ( E − G )
C 2 ′ = 2 π 2 ( E − G ) 2 G + E

Effective Slenderness Ratio

The effective slenderness ratio is:

λ eff = α L 0 D

Critical Deflection for Buckling

As with a slender column, a sufficiently long compression spring can become laterally unstable when its axial deflection exceeds a critical value.

The critical axial deflection is:

y crit = L 0 C 1 ′ [ 1 − 1 − C 2 ′ λ eff 2 ]

where:

λ eff = α L 0 D

The end-condition constant α is selected from the table below.

Spring End Conditions

The effective slenderness of the spring depends on its end restraint. The original RoyMech method uses the following values of α.

End Condition α
Spring between two flat parallel surfaces 0.5
One end on a flat surface, other end hinged 0.707
Both ends hinged or pivoted 1.0
One end clamped and the other free 2.0

The end condition used in a stability calculation should represent the actual restraint provided by the spring seats and surrounding mechanism. Idealised end conditions may not exactly reproduce the behaviour of a practical installation.

Absolute Stability

In the original RoyMech buckling method, absolute stability occurs when:

C 2 ′ λ eff 2 > 1

The corresponding limiting relationship for absolute stability is:

L 0 ′ < π D α 2 ( E − G ) 2 G + E

A spring satisfying this condition is considered absolutely stable under the assumptions of this buckling model. The end-condition constant α should correspond to the actual spring support arrangement.

Spring Guidance

Where a compression spring is too slender to remain stable over its required working deflection, lateral guidance may be provided by:

  • A guide rod passing through the inside diameter of the spring.
  • A bore, tube or sleeve surrounding the outside diameter of the spring.
  • A mechanical arrangement that reduces the unsupported spring length or otherwise restrains lateral movement.

Adequate clearance must be provided between the spring and its guide. Deflection changes the coil geometry, and insufficient clearance can produce rubbing, wear, friction, noise and local damage.

A guide should therefore be treated as part of the spring installation rather than simply as a means of correcting an otherwise unsuitable buckling calculation.

Spring Surge and Dynamic Stability

Buckling is a lateral stability problem and should not be confused with spring surge. Surge is a dynamic phenomenon associated with longitudinal stress waves and the natural vibration modes of the spring.

If a spring is excited at or near one of its natural frequencies, dynamic motion and stress can become significantly greater than those predicted by a static spring calculation.

Spring surge and natural frequency are treated separately on RoyMech and should be considered for springs subjected to rapid cyclic loading.

For dynamic spring calculations:
See Spring Surge and Natural Frequency for natural-frequency equations and dynamic design considerations.

Practical Stability Considerations

A spring stability calculation should be considered together with the physical installation. Important factors include:

  • Free length and coil diameter: increasing spring slenderness generally increases the tendency to buckle.
  • Working deflection: a spring that is stable at small deflection may become unstable further into its operating travel.
  • End seating: spring seats influence the effective end restraint and therefore the buckling behaviour.
  • Alignment: eccentric loading, angular misalignment and poorly aligned seats can promote lateral deflection.
  • Guidance: a rod or bore can prevent gross lateral buckling but must provide sufficient clearance throughout the operating stroke.
  • Friction and wear: contact between the spring and guide can affect spring force and may damage the wire surface, which can also reduce fatigue performance.
  • Dynamic operation: rapidly cycled springs should also be checked for surge and resonance.
Engineering reference: Compression-spring buckling should be checked against the actual spring geometry, working deflection and end restraint. Where adequate stability cannot be demonstrated, suitable guidance or a revised spring geometry should be considered.
See Also