# COMPRESSION SPRING DESIGN (DIMENSIONAL & RATE BASED)

Compression spring calculator to find  spring parameters with the knowledge of design type (dimensional or rate based), wire diameter, spring diameter, free height, number of active/total coils, spring rate, end type and material. Material selection 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.

### Compression Spring Calculator:

 INPUT PARAMETERS Design Type DimensionalRate based DIMENSIONAL PARAMETERS Parameter Value Spring wire diameter [d] mm m inch ft Spring outer diameter - [OD] Spring mean diameter - [D] Spring inner diameter - [ID] Spring free length (height) [Lf] Number of active coils - Na Number of total coils - Nt --- 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 Value Spring 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 Value 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 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 Value Number of active coils [Na] --- --- Number of total coils [Nt] --- Spring index [C*] --- Spring rate [k] --- N/mm lbf/inch lbf/ft Spring 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 Value Load at solid height [Fs] --- N kN lbf Shear stress at solid height [τs] --- MPa psi ksi 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] --- GPa psi*10^6 Elastic modulus [E] --- Material ASTM No. --- SPRING STABILITY (BUCKLING) Parameter Value 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 . (2014) . Shigley's Mechanical Engineering Design . 10th edition.  McGraw-Hill
• EN 13906-1: 2002 - Cylindrical helical springs made from round wire and bar – Calculation and design – Part 1: Compression springs