EXTENSION SPRING CALCULATOR FOR FATIGUE LOADING
This calculator has been developed to calculate fatigue resistance of ordinary
extension springs with full twisted end.
The points at extension spring hook where
maximum stresses occurred (tensile stress at point A and shear stress at pont B) are shown in the following figure. In
addition to these points, high shear stresses are occured at the body of the extension
springs. This calculator can be used to check these critical
points fatigue resistance against dynamic loading. Gerber and Goodman failure
criterias are used in this calculator for the fatigue evaluation of the spring.
For the fatigue resistance calculations of
the points where shear stresses occur (body of the spring and point B at extension spring
end), Zimmerli's data [Ref 2] are used to
calculate shear endurance limit value. Zimmerli's data is based on torsion
in spring so it has not been used for the points where
tensile stresses occur. See the "Definitions" section for more information about the Zimmerli's Data.


Location of Maximum Bending and Torsion
Stresses in Twisted Loops 
For the point where maximum tensile stresses occur (at
pointA) due to bending, fatigue calculations are
done by using maximum allowable tensile stress
value , which is entered as an input parameter in the calculator. Values given in
the "Supplement" section can
be used as a reference for maximum allowable tensile stress.
The calculator is valid for dynamic loading case, unpeened spring steel material
and ordinary extension spring with full twisted end as shown in the figure.

Extension Spring Design
with Twisted End 
For the extension spring design
which works under dynamic loading, first define the design
parameters with the "Dimensional Design of Extension Spring". Then use "Stress
Analysis of Extension Spring for Static Loading" calculator to check spring against yielding and use "Stress Analysis of Extension Spring for
Fatigue Loading" calculator to check spring against fatigue.
The formulas and parameters used in the calculator are given in " List of Equations " section of this page.
Note: This calculator was
developed by mainly using Shigley's Mechanical Engineering Design book. For
further information on subject , this reference source can be used.
Calculator:
Note 1 : ^{x} Material properties are from Ref2 except "User defined" selection.
Note 2 : ^{+} See supplements for reference values.
Note 3 : ^{o} The design factor value that used for all of the points
of interest ( Tensile stress at pointA, shear stress at pointB and shear
stress at spring body).
RESULTS 
Parameter 
Symbol 
Value 
Unit 
STRESS RELEATED PARAMETERS 
STRESS PARAMETERS AT SPRING BODY 
Factor of safety (According to Gerber)^{+} 
fos_{gerber} 


 
Factor of safety (Acc.to Goodman)^{+} 
fos_{goodman} 


Shear stress amplitude 
τ_{a} 



Midrange shear stress 
τ_{m} 


STRESS PARAMETERS AT POINT B 
Factor of safety @ B (According to Gerber)^{+} 
fos_{gerber} 


 
Factor of safety @ B (According to Goodman)^{+} 
fos_{goodman} 


Shear stress amplitude @ B 
τ_{a} 



Midrange shear stress @ B 
τ_{m} 


STRESS PARAMETERS AT POINT A 
Factor of safety @ A (According to Gerber)^{+} 
fos_{gerber} 


 
Factor of safety @ A (According to Goodman)^{+} 
fos_{goodman} 


Tensile stress amplitude @ A 
σ_{a} 



Midrange tensile stress @ A 
σ_{m} 



SPRING MATERIAL PARAMETERS 
Ultimate tensile strength of material 
S_{ut} 



Shearing ultimate strength 
S_{su} 


Material ASTM No. 


Note 1 : ^{+} Green color means, fos ≥ n_{d}, red color means
fos ≤ n_{d}
Definitions:
Design factor (nd): The ratio of failure stress to allowable stress.
The design factor is what the item is required to withstand .The design factor is defined for an application
(generally provided in advance and often set by regulatory code or policy) and is not an actual calculation.
Dynamic Loading: A loading which
varies with time with a number of load cycles over 10^{4} and torsional stress range
greater than 10 % of fatigue strength (or endurance strength) at:
• Constant torsional stress range

• Variable torsional stress range

Extension spring: Extension /
tension springs
are coil springs which work under tensile loading. In order to carry and transfer tensile loads, extension springs require special ends in the form of hooks or loops. These special ends are generally produced by using the last coil of the spring or a separate component like screwed inserts. Generally, extension springs are connected to other component via these ends. If there is a motion to extend extension spring, it exerts force to component to move it back.
Extension springs are usually
coiled with an initial tension which keeps the extension spring coils closed. Due to initial tension incorporated into spring, spring can’t be extended theoretically until a force that is greater than initial tension. In practice, extension springs extends slightly with smaller forces than initial tension due to deflection of end loops.
Tension springs are generally used to return back the component to its default position by providing return force.
Factor of Safety (Safety Factor):
The ratio of failure stress to actual/expected stress. The difference between the factor of safety (safety factor)
and design factor is: The factor of safety gives the safety margin of designed part against failure. The design factor
gives the requirement value for the design. Safety factor shall be greater than or equal to design factor.
Gerber fatigue criteria: A
fatigue failure criteria with characteristics shown in the figure.
Goodman fatigue criteria: A
fatigue
failure criteria with characteristics shown in the figure.
Spring index: Ratio
of spring mean diameter to coil diameter.
Spring rate: Parameter which shows relation between applied force and deflection. In other words, reaction force per unit deflection or spring resistance to length change.
Static/Quasistatic Loading:
Following loading cases are defined as Static/Quasistatic loading:
• A constant loading

• A cycling loading with torsional shear stress range up to 10 % of fatigue
strength (or endurance strength)

• A cycling loading with torsional shear stress range more than 10 % of fatigue
strength (or endurance strength) up to 10^{4}
cycles

Zimmerli's Data: Data reported in Ref2 about the torsional endurance limits of spring steels. According to these data, spring steel material and its tensile strength has no effect on the torsional endurance limit for the wire size under 3/8 in (10mm).
The endurace strength components for infinite life are reported as follows:
Shot Peended 
S_{sa} 
S_{sm} 
Unpeened 
35 kpsi (241 MPa) 
55 kpsi (379 MPa) 
Peened 
57.5 kpsi (398 MPa) 
77.5 kpsi (534 MPa) 
Supplements:
Reference:
 Budynas.R , Nisbett.K. (2008) . Shigley's Mechanical Engineering Design. 8th
edition. McGrawHill
 F. P. Zimmerli, “Human Failures in Spring Applications,” The Mainspring, no. 17, Associated Spring
Corporation, Bristol, Conn., August–September 1957.
 Shigley J.E. , Mischke C.R. (1996), Standard Handbook of Machine Design, 2nd
edition
 EN 139061: 2002  Cylindrical helical springs made from round wire and bar –
Calculation and design – Part 1: Compression springs