Deflection of Spring Calculator

✖Axial Spring Force is the force acting at the ends of a spring trying to compress or expand it in axial direction.ⓘ Axial Spring Force [P]			+10% -10%
✖The Mean Coil Diameter of Spring is defined as the average of the inner and the outer diameters of a spring.ⓘ Mean Coil Diameter of Spring [D]			+10% -10%
✖Active Coils in Spring is the number of coils or turns of a spring that actually contributes to the load-bearing capacity of the spring. All of the coils that aren't on the ends of a spring.ⓘ Active Coils in Spring [N_a]			+10% -10%
✖Modulus of rigidity of spring wire is the elastic coefficient when a shear force is applied resulting in lateral deformation. It gives us a measure of how rigid a body is.ⓘ Modulus of Rigidity of Spring Wire [G]			+10% -10%
✖Diameter of Spring Wire is the diameter of the wire of which a spring is made.ⓘ Diameter of Spring Wire [d]			+10% -10%

✖Deflection of Spring is how much the length of a spring changes when force is applied or released.ⓘ Deflection of Spring [δ]

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Deflection of Spring Solution

STEP 0: Pre-Calculation Summary

Formula Used

Deflection of Spring = (8*Axial Spring Force*(Mean Coil Diameter of Spring^3)*Active Coils in Spring)/(Modulus of Rigidity of Spring Wire*Diameter of Spring Wire^4)
δ = (8*P*(D^3)*N_a)/(G*d^4)
This formula uses 6 Variables

Variables Used

Deflection of Spring - (Measured in Meter) - Deflection of Spring is how much the length of a spring changes when force is applied or released.
Axial Spring Force - (Measured in Newton) - Axial Spring Force is the force acting at the ends of a spring trying to compress or expand it in axial direction.
Mean Coil Diameter of Spring - (Measured in Meter) - The Mean Coil Diameter of Spring is defined as the average of the inner and the outer diameters of a spring.
Active Coils in Spring - Active Coils in Spring is the number of coils or turns of a spring that actually contributes to the load-bearing capacity of the spring. All of the coils that aren't on the ends of a spring.
Modulus of Rigidity of Spring Wire - (Measured in Pascal) - Modulus of rigidity of spring wire is the elastic coefficient when a shear force is applied resulting in lateral deformation. It gives us a measure of how rigid a body is.
Diameter of Spring Wire - (Measured in Meter) - Diameter of Spring Wire is the diameter of the wire of which a spring is made.

STEP 1: Convert Input(s) to Base Unit

Axial Spring Force: 138.2 Newton --> 138.2 Newton No Conversion Required
Mean Coil Diameter of Spring: 36 Millimeter --> 0.036 Meter (Check conversion here)
Active Coils in Spring: 10 --> No Conversion Required
Modulus of Rigidity of Spring Wire: 86400 Newton per Square Millimeter --> 86400000000 Pascal (Check conversion here)
Diameter of Spring Wire: 4 Millimeter --> 0.004 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

δ = (8*P*(D^3)*N_a)/(G*d^4) --> (8*138.2*(0.036^3)*10)/(86400000000*0.004^4)

Evaluating ... ...

δ = 0.02332125

STEP 3: Convert Result to Output's Unit

0.02332125 Meter -->23.32125 Millimeter (Check conversion here)

FINAL ANSWER

23.32125 Millimeter <-- Deflection of Spring

(Calculation completed in 00.020 seconds)

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Home » Physics » Design of Automobile Elements » Design of Springs » Mechanical » Stress and Deflections in Springs » Deflection of Spring

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Created by Kethavath Srinath

Osmania University (OU), Hyderabad

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< Stress and Deflections in Springs Calculators

Diameter of Spring Wire given Resultant Stress in Spring

LaTeX Go Diameter of Spring Wire = ((Wahl Factor of Spring*8*Axial Spring Force*Mean Coil Diameter of Spring)/(pi*Shear Stress in Spring))^(1/3)

Mean Coil Diameter given Resultant Stress in Spring

LaTeX Go Mean Coil Diameter of Spring = Shear Stress in Spring*(pi*Diameter of Spring Wire^3)/(Wahl Factor of Spring*8*Axial Spring Force)

Force acting on Spring given Resultant Stress

LaTeX Go Axial Spring Force = Shear Stress in Spring*(pi*Diameter of Spring Wire^3)/(Wahl Factor of Spring*8*Mean Coil Diameter of Spring)

Resultant Stress in Spring

LaTeX Go Shear Stress in Spring = Wahl Factor of Spring*(8*Axial Spring Force*Mean Coil Diameter of Spring)/(pi*Diameter of Spring Wire^3)

Deflection of Spring Formula

LaTeX Go

Deflection of Spring = (8*Axial Spring Force*(Mean Coil Diameter of Spring^3)*Active Coils in Spring)/(Modulus of Rigidity of Spring Wire*Diameter of Spring Wire^4)
δ = (8*P*(D^3)*N_a)/(G*d^4)

Define a Mechanical Spring?

A metal wire spring that functions in a spring mechanism that compresses, extends,rotates, slides, pulls and exerts force when an equal or greater force is applied. A spring mechanism can exert pressure, rotational force or pulling strength in a variety of ways.

How to Calculate Deflection of Spring?

Deflection of Spring calculator uses Deflection of Spring = (8*Axial Spring Force*(Mean Coil Diameter of Spring^3)*Active Coils in Spring)/(Modulus of Rigidity of Spring Wire*Diameter of Spring Wire^4) to calculate the Deflection of Spring, Deflection of Spring formula is defined as a measure of the maximum displacement of a spring from its original position when a load is applied, providing a way to calculate the spring's stiffness and deformation under various loads and stresses. Deflection of Spring is denoted by δ symbol.

How to calculate Deflection of Spring using this online calculator? To use this online calculator for Deflection of Spring, enter Axial Spring Force (P), Mean Coil Diameter of Spring (D), Active Coils in Spring (N_a), Modulus of Rigidity of Spring Wire (G) & Diameter of Spring Wire (d) and hit the calculate button. Here is how the Deflection of Spring calculation can be explained with given input values -> 23321.25 = (8*138.2*(0.036^3)*10)/(86400000000*0.004^4).

FAQ

What is Deflection of Spring?

Deflection of Spring formula is defined as a measure of the maximum displacement of a spring from its original position when a load is applied, providing a way to calculate the spring's stiffness and deformation under various loads and stresses and is represented as δ = (8*P*(D^3)*N_a)/(G*d^4) or Deflection of Spring = (8*Axial Spring Force*(Mean Coil Diameter of Spring^3)*Active Coils in Spring)/(Modulus of Rigidity of Spring Wire*Diameter of Spring Wire^4). Axial Spring Force is the force acting at the ends of a spring trying to compress or expand it in axial direction, The Mean Coil Diameter of Spring is defined as the average of the inner and the outer diameters of a spring, Active Coils in Spring is the number of coils or turns of a spring that actually contributes to the load-bearing capacity of the spring. All of the coils that aren't on the ends of a spring, Modulus of rigidity of spring wire is the elastic coefficient when a shear force is applied resulting in lateral deformation. It gives us a measure of how rigid a body is & Diameter of Spring Wire is the diameter of the wire of which a spring is made.

How to calculate Deflection of Spring?

Deflection of Spring formula is defined as a measure of the maximum displacement of a spring from its original position when a load is applied, providing a way to calculate the spring's stiffness and deformation under various loads and stresses is calculated using Deflection of Spring = (8*Axial Spring Force*(Mean Coil Diameter of Spring^3)*Active Coils in Spring)/(Modulus of Rigidity of Spring Wire*Diameter of Spring Wire^4). To calculate Deflection of Spring, you need Axial Spring Force (P), Mean Coil Diameter of Spring (D), Active Coils in Spring (N_a), Modulus of Rigidity of Spring Wire (G) & Diameter of Spring Wire (d). With our tool, you need to enter the respective value for Axial Spring Force, Mean Coil Diameter of Spring, Active Coils in Spring, Modulus of Rigidity of Spring Wire & Diameter of Spring Wire and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Deflection of Spring?

In this formula, Deflection of Spring uses Axial Spring Force, Mean Coil Diameter of Spring, Active Coils in Spring, Modulus of Rigidity of Spring Wire & Diameter of Spring Wire. We can use 1 other way(s) to calculate the same, which is/are as follows -

Deflection of Spring = 2*Strain Energy in Spring/Axial Spring Force

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