# EXTENSION SPRING DIMENSIONAL DESIGN CALCULATOR

Tension/ Extension spring design calculator has been developed to calculate  dimensional parameters of ordinary coil extension springs with the knowledge of different parameter sets such as extension spring rate & spring free length, extension spring diameter & free length, extension spring preload & spring rate, extension spring diameter & spring rate. Calculation results generated by the calculator are tension spring height,  number of body coils,  spring body length, spring rate, spring initial preload range, spring index.

This calculator is valid for ordinary extension springs with twisted end where hook/loop mean diameter is same with spring mean diameter ( R1=D/2). Shape of an ordinary extension coil spring is given in the figure.

 Extension Spring Design with Twisted End

This calculator can be used for dimensional sizing of the tension springs. For the stress calculations of the extension springs, visit "Extension Spring Design for Static Loading" and "Extension Spring Design for Fatigue Loading" calculators.

The formulas and parameters used in the calculator are given in "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 Known parameters in addition to wire diameter Spring rate & Free lengthSpring diameter & Free lengthNumber of body coils & Free length Preload & Spring rateSpring diameter & Spring rate 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] Free length inside hooks Lo Initial Preload Fi N kN lbf Spring Rate k N/mm lbf/inch lbf/ft Number of body coils Nb --- 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 ---

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

 RESULTS DIMENSIONAL PARAMETERS Parameter Symbol Value Unit Number of active coils Na --- --- Number of body coils Nb --- 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 --- Free length inside hooks Lo --- Spring body length Lb --- SPRING MATERIAL &  STRESS RELEATED PARAMETERS Parameter Symbol Value Unit Preferred initial preload range Fi Min Max N kN lbf --- --- Modulus of rigidity G --- GPa psi*10^6 Elastic modulus E --- Material ASTM No. ---

##### Definitions:

Extension spring: Extension / tension springs are coil springs which work under tensile loading. In order to carry and transfer tensile loads, extension springs require special ends in the form of hooks or loops. These special ends are generally produced by using the last coil of the spring or a separate component like screwed inserts. Generally, extension springs are connected to other component via these ends. If there is a motion to extend extension spring, it exerts force to component to move it back.

Extension springs are usually coiled with an initial tension which keeps the extension spring coils closed. Due to initial tension incorporated into spring, spring can’t be extended theoretically until a force that is greater than initial tension. In practice, extension springs extends slightly with smaller forces than initial tension due to deflection of end loops.

Tension springs are generally used to return back the component to its default position by providing return force.

Spring rate: A parameter which shows relation between applied force and deflection. In other words, reaction force per unit deflection or spring resistance to length change.

Spring index: The ratio of spring mean diameter to coil diameter.

##### Supplements:

 Link Usage Spring Steels for Coil Springs List of spring steel materials given in the calculator.

##### List of Equations:

 Parameter Symbol Formula Spring outer diameter OD Spring inner diameter ID Spring index C Spring rate k Number of active coils Na* Extension spring free length Lf* Initial tension stress range τi

###### Note 1 :* Equation is valid for ordinary extension spring with twisted loop where hook/loop mean diameter is same with spring mean diameter ( r1=D/2)

 List of Parameters Symbol Definition Na Number of active coils Nb Number of body coils d Wire diameter Lf Spring free length