Spring Fatigue Design

Springs subjected to repeated or fluctuating loads may fail by fatigue even when the maximum working stress is below the material's static strength. Fatigue is therefore an important design consideration for valve springs, vehicle suspension springs, press-tool springs and other springs operating through large numbers of load cycles.

This page summarises the treatment of mean and alternating spring loads, torsional fatigue strength and fatigue safety factors. For the more general theory of fatigue failure, stress-life behaviour and modifying factors, see the RoyMech Fatigue Index.

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Spring Fatigue Loading
Nomenclature
Mean and Alternating Loads
Mean and Alternating Shear Stress
Spring Endurance Strength
Yielding and Low-Cycle Loading
Finite-Life Fatigue
Goodman Fatigue Criterion
Practical Fatigue Design Considerations

Spring Fatigue Loading

Components subjected to repeated cyclic loading can fail by fatigue as a result of the initiation and progressive growth of cracks. The severity of fatigue loading depends on the stress range, mean stress, number of cycles, material, surface condition, environment and component geometry.

Fully reversed loading, in which stress alternates between approximately equal tensile and compressive values, is particularly severe for many materials. Springs, however, frequently operate with a substantial non-zero mean stress because they are installed with preload and then fluctuate between minimum and maximum operating loads.

Conventional helical compression and extension springs normally retain the same basic sense of loading throughout their working cycle. Their stress therefore commonly fluctuates between two non-zero values rather than being fully reversed.

This does not remove the fatigue requirement. Any spring subjected to a sufficient number of fluctuating stress cycles can be susceptible to fatigue failure.

Typical high-cycle spring applications include:

Internal-combustion-engine valve springs
Vehicle suspension springs
Press-tool and die springs
Repeatedly operated mechanism and actuator springs

Nomenclature

Symbol	Description	Typical Unit
F_max	Maximum axial spring force	N
F_min	Minimum axial spring force	N
F_m	Mean axial spring force	N
F_a	Amplitude of alternating axial spring force	N
n_s	Factor of safety	Dimensionless
S_se	Torsional endurance strength / endurance limit used in fatigue analysis	MPa
S_sl	Torsional fatigue strength at a specified low cycle count	MPa
S_sy	Torsional yield strength	MPa
S_sf	Torsional fatigue strength at the required finite life	MPa
τ_max	Maximum spring shear stress	MPa
τ_min	Minimum spring shear stress	MPa
τ_m	Mean shear stress	MPa
τ_a	Alternating shear-stress amplitude	MPa

Mean and Alternating Spring Loads

A spring operating between a minimum and maximum load can be represented by a mean load with an alternating load superimposed upon it.

Cyclic spring loading showing maximum, minimum, mean and alternating load

The mean force and force amplitude are calculated from the maximum and minimum operating forces:

F_{a} = \frac{F_{max} - F_{min}}{2}

F_{m} = \frac{F_{max} + F_{min}}{2}

Mean and Alternating Shear Stress

The corresponding maximum and minimum spring stresses are used to determine the mean shear stress and alternating shear-stress amplitude.

τ_{a} = \frac{8 D K_{w} F_{a}}{π d^{3}}

τ_{m} = \frac{8 D K_{w} F_{m}}{π d^{3}}

The spring stress values used here should include the appropriate stress correction applicable to the spring geometry. For a helical spring, for example, the corrected wire shear stress rather than an uncorrected nominal torsional stress should normally be used for fatigue assessment.

Spring Endurance Strength

For springs intended for a large number of fluctuating load cycles, the alternating and mean stresses must remain within the appropriate fatigue design criterion.

The original RoyMech spring-fatigue method expresses the safety factor for torsional endurance using:

n_{s} = \frac{S_{se}}{τ_{a}}

Legacy Experimental Spring-Wire Values

The original RoyMech notes use the following empirical values for spring steel wire below approximately 10 mm diameter:

Property	Unpeened	Shot Peened
S'_se	310 MPa	465 MPa
S'_sa	241 MPa	398 MPa
S'_sm	379 MPa	534 MPa

Legacy preliminary-design values: These empirical values are retained from the original RoyMech spring design notes. They should not be regarded as universal fatigue allowables for all modern spring steels. Spring fatigue strength depends on material grade, wire diameter, surface condition, heat treatment, shot-peening process, residual stress, operating environment, required reliability and the specified number of cycles. For final design, use fatigue data applicable to the actual spring material, manufacturing condition and required service life.

Where an endurance value is modified for reliability, the original RoyMech method expresses the relationship as:

S_{e} = C_{r} S_{e}^{'}

Yielding and Low-Cycle Loading

For springs subjected to relatively few load cycles or predominantly static loading, yielding or permanent set may govern before a high-cycle endurance criterion becomes relevant.

The original RoyMech method gives the following safety-factor relationship for torsional yielding:

n_{s} = \frac{S_{sy}}{τ_{a} + τ_{m}}

The S_sy ≈ 0.40 S So spring_fatigue_

An approximate relationship historically used for preliminary spring calculations is:

S_{sy} \approx 0.40 S_{ut}

where S_ut is the ultimate tensile strength. See the Spring Materials page for the material notes used by RoyMech.

Preliminary relationship only: The ratio S_sy ≈ 0.40S_ut is an approximation rather than a universal material property. For final design, use shear yield or proof-strength information appropriate to the specified material and condition.

Finite-Life Spring Fatigue

Where the required life is below the endurance region, a finite-life fatigue strength may be used instead of an endurance-limit value.

The original RoyMech method uses a modified torsional fatigue strength S_sf for this purpose:

n_{s} = \frac{S_{sf}}{τ_{a}}

The appropriate fatigue strength depends on the required number of cycles. It may be estimated from suitable fatigue data by interpolation on the stress-life relationship.

See High-Cycle Fatigue Strength for the associated RoyMech fatigue notes.

Goodman Fatigue Criterion

A spring operating with both mean and alternating stress can be assessed using a mean-stress fatigue criterion. The Goodman relationship is one commonly used engineering method.

Fatigue failure criteria diagram showing alternating stress against mean stress

The Goodman criterion represents the interaction between mean stress and allowable alternating stress. The original RoyMech relationship is shown below:

\frac{S_{sa}}{S_{se}} + \frac{S_{sm}}{S_{sut}} = 1

The corresponding factor-of-safety relationship is:

n_{s} = \frac{1}{\frac{τ_{a}}{S_{se}} + \frac{τ_{m}}{S_{sut}}}

Mean-stress criterion: Goodman is one engineering model for combining mean and alternating stress. Other criteria may be appropriate depending on material, spring type, available fatigue data and the design standard being followed. Where spring-specific fatigue test data are available, these should normally take precedence over a generic material fatigue approximation.

Practical Spring Fatigue Design Considerations

Fatigue performance depends on more than the nominal spring stress. Important factors include:

Stress range: reducing the difference between maximum and minimum operating stress generally improves fatigue life.
Mean stress: preload and the minimum operating load affect the mean stress and therefore the available alternating-stress capacity.
Surface condition: fatigue cracks commonly initiate at the surface, making scratches, corrosion pits, seams and other defects particularly important.
Shot peening: properly controlled shot peening can introduce beneficial compressive residual surface stresses and substantially improve fatigue resistance.
Presetting / scragging: controlled preloading during manufacture may alter residual stresses and reduce the risk of permanent set in service.
Spring geometry: stress concentration and curvature effects must be included when determining the actual cyclic stress.
Corrosion: corrosive environments can greatly reduce fatigue strength and may require material selection, coating or other protection appropriate to the service conditions.
Temperature: elevated temperature can affect material strength, relaxation, residual stress and fatigue behaviour.
Dynamic effects: spring surge or resonance can produce cyclic stresses considerably greater than those predicted from a purely static load calculation.

Engineering reference: For fatigue-critical springs, calculations should be based on the actual minimum and maximum operating loads, corrected spring stresses, specified material and surface condition, required number of cycles and an appropriate spring fatigue criterion.

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