STRESS ANALYSIS OF HELICAL COMPRESSION SPRING FOR FATIGUE LOADING

This calculator was developed to check stresses occurred at a compression spring which works under a 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.

Sinusoidal cycling loading in spring design

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 mechanical 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:

 INPUT PARAMETERS
DIMENSIONAL PARAMETERS
Parameter Symbol Value Unit
Wire diameter d
Maximum cyclic force Fmax
Minimum cyclic force (preload) Fmin
SPRING MATERIAL &  STRESS RELEATED PARAMETERS
Parameter Symbol Value Unit
Material selectionx
Material tensile strength Sut
Shot peening process
Design factor for fatigue nf ---
 

Note 1 : x Material properties are from Ref-1 except "User defined" selection.


 RESULTS
Parameter Symbol Value Unit
Wahl factor Kw --- ---
Shear stress amplitude
τa ---
Midrange shear stress
τm ---
Ultimate tensile strength of material Sut ---
Shearing ultimate strength Ssu ---
Shear endurance limit ( according to Gerber) Sse ---
Shear endurance limit (according to Goodman) Sse ---
Strength amplitude component ( according to Gerber) Ssa ---
Strength amplitude component ( according to Sines) Ssa ---
Strength amplitude component ( according to Goodman) Ssa ---
Factor of safety (Acc. to Gerber)+ fosgerber --- ---
Factor of safety (Acc. to Sines)+ fossines ---
Factor of safety (Acc.to Goodman)+ fosgoodman ---
Material ASTM No. ---

Note 1 : + Shall be larger than the design factor for fatigue (nf ≤ fosgerber , nf ≤ fossines ,nf ≤ fosgoodman)



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 104 cycles

Dynamic Loading: A loading which varies with time with a number of load cycles over 104 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. [Ref-1]. 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).

Gerber fatigue criteria

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

Goodman fatigue criteria: A fatigue  failure criteria with characteristics shown in the figure.

Zimmerli's Data: Data reported in Ref-2 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 Ssa Ssm
Unpeened 35 kpsi (241 MPa) 55 kpsi (379 MPa)
Peened 57.5 kpsi (398 MPa) 77.5 kpsi (534 MPa)

Supplements:

Link Usage
Formulas For Compression Spring Fatigue Design List of formulas used in the calculator.


Reference:
  • Budynas.R , Nisbett.K. (2008) . Shigley's Mechanical Engineering Design . 8th edition.  McGraw-Hill
  • 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 13906-1: 2002 - Cylindrical helical springs made from round wire and bar – Calculation and design – Part 1: Compression springs