COMPRESSION SPRING CALCULATOR (LOAD BASED DESIGN)

The Compression spring calculator has been developed to calculate compression springs design parameters with the knowledge of design type (one load & free height, one load & spring rate, two loads), compression spring wire diameter, spring diameter, spring free height, loads at specific heights, 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 compression springs calculator are solid height, torsional shear stress at solid height, factor of safety against yielding, buckling check, spring 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 cyclic loading, first use this calculator for the sizing according to static loading and then visit "Critical Frequency of Helical Springs" and "Stress Analysis of Coil Compression Springs 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:

 INPUT PARAMETERS Design Type One Load & Free HeightOne Load & Spring RateTwo Loads DIMENSIONAL PARAMETERS Parameter Symbol Value Unit Wire diameter d mm m inch ft Spring outer diameter - [OD] Spring mean diameter - [D] Spring inner diameter - [ID] Spring free height (length) Lf Height 1 L1 Height 2 L2 Load 1 @ height 1 F1 N kN lbf Load 2 @ height 2 F2 Spring rate k N/mm lbf/inch lbf/ft End types for compression spring Plain (Open) Plain (Open) and Ground Squared (Closed) Squared (Closed) and Ground SPRING MATERIAL &  STRESS RELEATED PARAMETERS Parameter Symbol Value Unit Material selectionx User defined Music Wire Hard-drawn wire Chrome-vanadium 302 Stainless wire Phosphor-bronze wire Oil tempered Elastic modulus E GPa psi*10^6 Poisson's ratio v --- Material tensile strength Sut MPa psi ksi Prestressing (Set romoval) Unprestressed (Set Not Removed) - Default Prestressed (Set Removed) 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 Stability control End condition* Ends are fixed with flat parallel surfaces One end flat & fixed, other end pivoted (hinged) Both ends pivoted(hinged) One end clamped, one end free User Defined End condition constant α --- Design factor for buckling nb ---

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 --- N/mm lbf/inch lbf/ft Wire diameter d --- mm m inch ft 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 --- N kN lbf Shear stress at height 1 τ1 --- MPa psi ksi Shear stress at height 2 τ2 --- Shear stress at solid height τs --- Ultimate tensile strength of material Sut --- Allowable torsional strength Sall --- Factor of safety against torsional yielding at solid height foss (Sall / τs )# --- --- Modulus of rigidity G --- GPa psi*10^6 Elastic modulus E --- Material ASTM No. --- SPRING STABILITY (BUCKLING) Parameter Symbol Value Unit Stability condition (includes nb) --- Factor of safety against buckling fosb+ --- ---

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

 Force vs Spring Height Shear Stress vs Spring Height

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