Rate of Spring Calculator

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Stress and Deflections in Springs

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✖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%
✖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%

✖Stiffness of Spring is a measure of the resistance offered by an elastic body to deformation, every object in this universe has some stiffness.ⓘ Rate of Spring [k]

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Formula

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Rate of Spring

Formula

`"k" = "G"*"d"^4/(8*"D"^3*"N"_{"a"})`

Example

`"5.925926N/mm"="86400N/mm²"*("4mm")^4/(8*("36mm")^3*"10")`

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Rate of Spring Solution

STEP 0: Pre-Calculation Summary

Formula Used

Stiffness of Spring = Modulus of rigidity of spring wire*Diameter of spring wire^4/(8*Mean Coil Diameter of Spring^3*Active Coils in Spring)
k = G*d^4/(8*D^3*N_a)
This formula uses 5 Variables

Variables Used

Stiffness of Spring - (Measured in Newton per Meter) - Stiffness of Spring is a measure of the resistance offered by an elastic body to deformation, every object in this universe has some stiffness.
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.
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.

STEP 1: Convert Input(s) to Base Unit

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)
Mean Coil Diameter of Spring: 36 Millimeter --> 0.036 Meter (Check conversion here)
Active Coils in Spring: 10 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

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

Evaluating ... ...

k = 5925.92592592593

STEP 3: Convert Result to Output's Unit

5925.92592592593 Newton per Meter -->5.92592592592593 Newton per Millimeter (Check conversion here)

FINAL ANSWER

5.92592592592593 ≈ 5.925926 Newton per Millimeter <-- Stiffness of Spring

(Calculation completed in 00.004 seconds)

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

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Osmania University (OU), Hyderabad

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< 24 Stress and Deflections in Springs Calculators

Diameter of Spring Wire given Deflection in Spring

Go Diameter of spring wire = ((8*Axial Spring Force*(Mean Coil Diameter of Spring^3)*Active Coils in Spring)/(Modulus of rigidity of spring wire*Deflection of Spring))^(1/4)

Mean Coil Diameter given Deflection in Spring

Go Mean Coil Diameter of Spring = (Deflection of Spring*Modulus of rigidity of spring wire*Diameter of spring wire^4/(8*Axial Spring Force*Active Coils in Spring))^(1/3)

Number of Active Coils given Deflection in Spring

Go Active Coils in Spring = (Deflection of Spring*Modulus of rigidity of spring wire*Diameter of spring wire^4)/(8*Axial Spring Force*(Mean Coil Diameter of Spring^3))

Modulus of Rigidity given Deflection in Spring

Go Modulus of rigidity of spring wire = (8*Axial Spring Force*(Mean Coil Diameter of Spring^3)*Active Coils in Spring)/(Deflection of Spring*Diameter of spring wire^4)

Deflection of Spring

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)

Force Applied on Spring given Deflection in Spring

Go Axial Spring Force = Deflection of Spring*Modulus of rigidity of spring wire*Diameter of spring wire^4/(8*(Mean Coil Diameter of Spring^3)*Active Coils in Spring)

Diameter of Spring Wire given Resultant Stress in Spring

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

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

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

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

Diameter of Spring Wire given Rate of Spring

Go Diameter of spring wire = ((Stiffness of Spring*8*Mean Coil Diameter of Spring^3*Active Coils in Spring)/(Modulus of rigidity of spring wire))^(1/4)

Mean Coil Diameter given Rate of Spring

Go Mean Coil Diameter of Spring = (Modulus of rigidity of spring wire*Diameter of spring wire^4/(8*Stiffness of Spring*Active Coils in Spring))^(1/3)

Modulus of Rigidity given Rate of Spring

Go Modulus of rigidity of spring wire = Stiffness of Spring*(8*Mean Coil Diameter of Spring^3*Active Coils in Spring)/Diameter of spring wire^4

Rate of Spring

Go Stiffness of Spring = Modulus of rigidity of spring wire*Diameter of spring wire^4/(8*Mean Coil Diameter of Spring^3*Active Coils in Spring)

Stress Factor of Spring

Go Wahl Factor of Spring = ((4*Spring Index-1)/(4*Spring Index-4))+(0.615/Spring Index)

Shear Stress Correction Factor given Diameter of Spring Wire

Go Shear Stress Correction Factor of Spring = (1+(.5*Diameter of spring wire/Mean Coil Diameter of Spring))

Mean Coil diameter given Shear Stress Correction Factor

Go Mean Coil Diameter of Spring = 0.5*Diameter of spring wire/(Shear Stress Correction Factor of Spring-1)

Diameter of Spring Wire given Shear Stress Correction Factor

Go Diameter of spring wire = (Shear Stress Correction Factor of Spring-1)*Mean Coil Diameter of Spring/.5

Strain Energy Stored in Spring

Go Strain energy in spring = .5*Axial Spring Force*Deflection of Spring

Force Applied on Spring given Strain Energy Stored in Spring

Go Axial Spring Force = 2*Strain energy in spring/Deflection of Spring

Deflection of Spring given Strain Energy Stored

Go Deflection of Spring = 2*Strain energy in spring/Axial Spring Force

Rate of Spring given Deflection

Go Stiffness of Spring = Axial Spring Force/Deflection of Spring

Spring Index given Shear Stress Correction Factor

Go Spring Index = (0.5)/(Shear Stress Correction Factor of Spring-1)

Shear Stress Correction Factor

Go Shear Stress Correction Factor of Spring = (1+(.5/Spring Index))

Rate of Spring Formula

Stiffness of Spring = Modulus of rigidity of spring wire*Diameter of spring wire^4/(8*Mean Coil Diameter of Spring^3*Active Coils in Spring)
k = G*d^4/(8*D^3*N_a)

Define 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 Rate of Spring?

Rate of Spring calculator uses Stiffness of Spring = Modulus of rigidity of spring wire*Diameter of spring wire^4/(8*Mean Coil Diameter of Spring^3*Active Coils in Spring) to calculate the Stiffness of Spring, The Rate of Spring formula is defined as the amount of weight that is needed to compress a spring one inch. If the rate of the spring is linear, its rate is not affected by the load that is put on the spring. Stiffness of Spring is denoted by k symbol.

How to calculate Rate of Spring using this online calculator? To use this online calculator for Rate of Spring, enter Modulus of rigidity of spring wire (G), Diameter of spring wire (d), Mean Coil Diameter of Spring (D) & Active Coils in Spring (N_a) and hit the calculate button. Here is how the Rate of Spring calculation can be explained with given input values -> 0.005926 = 86400000000*0.004^4/(8*0.036^3*10).

FAQ

What is Rate of Spring?

The Rate of Spring formula is defined as the amount of weight that is needed to compress a spring one inch. If the rate of the spring is linear, its rate is not affected by the load that is put on the spring and is represented as k = G*d^4/(8*D^3*N_a) or Stiffness of Spring = Modulus of rigidity of spring wire*Diameter of spring wire^4/(8*Mean Coil Diameter of Spring^3*Active Coils in 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, 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.

How to calculate Rate of Spring?

The Rate of Spring formula is defined as the amount of weight that is needed to compress a spring one inch. If the rate of the spring is linear, its rate is not affected by the load that is put on the spring is calculated using Stiffness of Spring = Modulus of rigidity of spring wire*Diameter of spring wire^4/(8*Mean Coil Diameter of Spring^3*Active Coils in Spring). To calculate Rate of Spring, you need Modulus of rigidity of spring wire (G), Diameter of spring wire (d), Mean Coil Diameter of Spring (D) & Active Coils in Spring (N_a). With our tool, you need to enter the respective value for Modulus of rigidity of spring wire, Diameter of spring wire, Mean Coil Diameter of Spring & Active Coils in Spring 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 Stiffness of Spring?

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

Stiffness of Spring = Axial Spring Force/Deflection of Spring

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