STRESS ANALYSIS OF HELICAL COMPRESSION SPRINGS FOR FATIGUE LOADING
This calculator has been developed to check stresses occurred at
compression springs which work under fluctuating loading. The calculator uses endurance strength
components of Zimmerli data [Ref 2]
to calculate endurance limit of the spring steels using Gerber, Sines and Goodman
fatigue failure theories. Endurance limit indicates infinite life for a
material. This means the calculator is checking the design if it has got
infinite life under given loading conditions. Zimmerli's data is
valid for spring steels with wire
diameter smaller than 3/8 inch (10 mm). See the "Definitions" section for
more information about the Zimmerli's Data.
The user shall first design the compression
spring with the help of other spring calculators according to dimensional, spring
rate and static loading requirements. After dimensioning study, the user
shall check the margin between cyclic frequency of the loading and spring natural frequency
with the "critical cyclic loading frequency" calculator.
Finally, this calculator shall
be used to check coil springs fatigue resistance against given cyclic
loading conditions.
The formulas and parameters used in the calculator are given in the " 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 Ref1 except "User defined"
selection.
RESULTS 
Parameter 
Symbol 
Value 
Unit 
Wahl factor 
K_{w} 


 
Shear stress amplitude 
τ_{a} 



Midrange shear stress 
τ_{m} 


Ultimate tensile strength of material 
S_{ut} 


Shearing ultimate strength 
S_{su} 


Shear endurance limit ( according to Gerber) 
S_{se} 


Shear endurance limit (according to Goodman) 
S_{se} 


Strength amplitude component ( according to Gerber) 
S_{sa} 


Strength amplitude component ( according to Sines) 
S_{sa} 


Strength amplitude component ( according to Goodman) 
S_{sa} 


Factor of safety (Acc. to Gerber)^{+} 
fos_{gerber} 


 
Factor of safety (Acc. to Sines)^{+} 
fos_{sines} 


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


Material ASTM No. 


Note 1 : ^{+} Shall be larger than the design factor for fatigue (n_{f}
≤ fos_{gerber} , n_{f} ≤ fos_{sines} ,n_{f} ≤
fos_{goodman})
Definitions:
Fatigue Failure: Cyclic loading slowly damages materials near microscopic defects. After a number of loading cycles, small cracks initiate. Under continued cycling loading, the cracks grow until the structure suddenly ruptures, often at an unexpectedly low load. This phenomenon is called fatigue failure.
Endurance Level: It’s the stress value at which the number of cycles to failure is infinite.
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

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

Shot peening: Fatigue life can be
severely reduced by pits, seams, or tool marks on the wire surface where stress
is at a maximum. Shot peening is a cold working process improves fatigue life,
in part, by minimizing the harmful effects of surface defects.
Wahl factor: A factor to correct
shear stress to include curvature effect.
Spring index: The ratio of spring
mean diameter to coil diameter. As a general rule, the ratio shall be between 4
and 12. Spring sizes out of this interval increases the cost and manufacturing
process is harder. [Ref1]. According to BS1726:Part 1:1987 , advised index
range is between 3.5 to 16. A low index value indicates a very tightly wound
spring with a relatively large wire or bar being coiled sharply around a
relatively small coil diameter. This results very high axial stiffness. A high
index value means an open wound spring which will be very flexible along its
axis (low spring rate).
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.
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.
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