COMPRESSION SPRING DESIGN (DIMENSIONAL & RATE BASED)

The compression spring design calculator can be used to calculate  design parameters of compression springs with the knowledge of spring design type (dimensional or rate based), compression spring wire diameter, spring diameter, spring free height, number of active/total spring coils, spring rate, compression spring end type and material selection. Material selection of compression springs can be done from listed spring steels including music wire, stainless steel wire, chrome vanadium, etc. Calculation results generated by the calculator are spring rate, spring solid height, torsional shear stress at solid height, factor of safety at solid height, buckling check, outer diameter expansion, load-deflection curve, stress–deflection curve, spring index.

This calculator can be used to design statically loaded compression springs. For compression springs which work under a cyclic loading, first use this calculator for sizing according to static loading and then visit the "Critical Frequency of Coil Springs" and "Stress analysis of Coil (Helical) Compression Spring for Fatigue Loading" calculators to check the compression spring design against cyclic loading.

The formulas and parameters used in the calculator are given in the " Supplements " section of this page.

Note: This calculator was developed by mainly using Shigley's Mechanical Engineering Design book. If further information on the subject is needed, this reference source can be used.


Calculator:

Mechanical springs - Compression spring terminology
 INPUT PARAMETERS
Design Type
DIMENSIONAL PARAMETERS
Parameter Symbol Value Unit
Spring wire diameter d
Spring free length (height) Lf
---
Spring rate k
End types for compression spring
SPRING MATERIAL &  STRESS RELEATED PARAMETERS
Parameter Symbol Value Unit
Spring material selectionx
Elastic modulus E
Poisson's ratio v ---
Material tensile strength Sut
Prestressing (Set romoval)
Allowable torsional strength  (% of Sut) + %
Design factor at solid height against torsional stress ns ---
SPRING STABILITY (BUCKLING)
Parameter Symbol Value Unit
Spring stability (buckling) check
End condition*
End condition constant α ---
Design factor for buckling nb ---
 

Note 1 : x Spring material properties are from Ref-2 except "User defined" selection.

Note 2 : + Equals maximum allowable torsional stress in static applications. See "Supplements" for reference values.

Note 3 : * Ends supported by flat surfaces must be squared and ground [Ref-2] .


 RESULTS
DIMENSIONAL PARAMETERS
Parameter Symbol Value Unit
Number of active coils Na --- ---
Number of total coils Nt ---
Spring index C* ---
Spring rate k ---
Spring wire diameter d ---
Spring outer diameter OD ---
Spring mean diameter D ---
Spring inner diameter ID ---
Outer diameter at solid length ODat solid*** ---
Spring free length (height) Lf ---
Spring solid height Ls ---
Maximum deflection (Lf to Ls) Δx ---
Pitch at free length p** ---
SPRING MATERIAL &  STRESS RELEATED PARAMETERS
Parameter Symbol Value Unit
Load at solid height Fs ---
Shear stress at solid height τs ---
Ultimate tensile strength of material Sut ---
Allowable torsional strength Sall ---
Factor of safety at solid height against shear stress foss
(Sall / τs )#
--- ---
Modulus of rigidity G ---
Elastic modulus E ---
Material ASTM No. ---
SPRING STABILITY (BUCKLING)
Parameter Symbol Value Unit
Stability condition (includes nb) ---
Factor of safety against buckling fosb+ --- ---

Note 1 : * The preferred index range is 4 to 12 according to  [Ref-1] . Compression springs with high indexes tangle and may require individual packaging, especially if the ends are not squared. Compression springs with indexes lower than 4 are difficult to form [Ref-1] .

Note 2 : ** According to no yielding assumption and Lf length shall be same after loading.

Note 3 : *** Does not include the effect if the spring ends are allowed to unwind.

Note 4 : + Shall be larger than the design factor for buckling (nb ≤ fosb )

Note 5 : # Shall be larger than the design factor at solid height  (ns ≤ foss )

Force vs Deflection
 
Shear Stress vs Deflection

Note 1 : The load deflection curve for helical compression springs is essentially a straight line up to the elastic limit, provided that the amount of active material is constant. The initial spring rate and the rate as the spring approaches solid often deviate from the average calculated rate. When it is necessary to specify the rate, it should be specified between two test heights which lie within 15 to 85 % of the full deflection range. [From Ref-1]


Definitions:

Link Usage
Compression Coil (Helical) Spring Definitions Terms and definitions about compression coil springs.

Supplements:



Link Usage
Spring Steels for Coil Springs List of spring steel materials given in the calculator.
Formulas For Compression Spring Design List of formulas used in the calculator.
Allowable Torsional Stresses for Helical Compression Springs in Static Applications Supplementary tables about the material strength properties of helical compression springs.
End Condition Constants For Helical Compression Spring Stability Analysis End condition constants for helical compression spring stability and buckling analysis.

Reference:
  • Courtesy of Associated Spring (1987)., Design Handbook
  • Budynas.R , Nisbett.K. (2008) . Shigley's Mechanical Engineering Design . 8th edition.  McGraw-Hill
  • 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