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Spring Index given Torsional Stress Amplitude Formula

GoSpring Index given Mean Stress on spring Formula

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Spring Index is defined as the ratio of mean coil diameter of the spring to the diameter of the spring Wire. Check FAQs

C = τ a \cdot \frac{π \cdot d^{2}}{8 \cdot K s \cdot P a}

C - Spring Index?τ_a - Torsional Stress Amplitude in Spring?d - Diameter of Spring Wire?K_s - Shear Stress Correction Factor of Spring?P_a - Spring Force Amplitude?π - Archimedes' constant?

Spring Index given Torsional Stress Amplitude Example

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Here is how the Spring Index given Torsional Stress Amplitude equation looks like with Values.

Here is how the Spring Index given Torsional Stress Amplitude equation looks like with Units.

Here is how the Spring Index given Torsional Stress Amplitude equation looks like.

8.9448 = 77 \cdot \frac{3.1416 \cdot {4.0047}^{2}}{8 \cdot 1.08 \cdot 50.2}

8.9448 = 77N/mm² \cdot \frac{3.1416 \cdot {4.0047mm}^{2}}{8 \cdot 1.08 \cdot 50.2N}

8.9448 = 77 \cdot \frac{3.1416 \cdot {4.0047}^{2}}{8 \cdot 1.08 \cdot 50.2}

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Spring Index given Torsional Stress Amplitude Solution

Follow our step by step solution on how to calculate Spring Index given Torsional Stress Amplitude?

FIRST Step Consider the formula

C = τ a \cdot \frac{π \cdot d^{2}}{8 \cdot K s \cdot P a}

Next Step Substitute values of Variables

∴

C = 77N/mm² \cdot \frac{π \cdot {4.0047mm}^{2}}{8 \cdot 1.08 \cdot 50.2N}

Next Step Substitute values of Constants

∴

C = 77N/mm² \cdot \frac{3.1416 \cdot {4.0047mm}^{2}}{8 \cdot 1.08 \cdot 50.2N}

Next Step Convert Units

∴

C = 7.7E+7Pa \cdot \frac{3.1416 \cdot {0.004m}^{2}}{8 \cdot 1.08 \cdot 50.2N}

Next Step Prepare to Evaluate

∴

C = 7.7E+7 \cdot \frac{3.1416 \cdot {0.004}^{2}}{8 \cdot 1.08 \cdot 50.2}

Next Step Evaluate

∴

C = 8.94481485414881

LAST Step Rounding Answer

∴

C = 8.9448

Spring Index given Torsional Stress Amplitude Formula Elements

Variables

Constants

Spring Index

Spring Index is defined as the ratio of mean coil diameter of the spring to the diameter of the spring Wire.

Symbol: C

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Spring Index

Torsional Stress Amplitude in Spring

Torsional Stress Amplitude in Spring is defined as the effect of stress concentration due to curvature in addition to direct shear stress in the spring.

Symbol: τ_a

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Torsional Stress Amplitude in Spring

Diameter of Spring Wire

Diameter of Spring Wire is the diameter of the wire of which a spring is made.

Symbol: d

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Diameter of Spring Wire

Shear Stress Correction Factor of Spring

Shear Stress Correction Factor of Spring is for comparing the strain energies of the average shear stresses with those obtained from the equilibrium.

Symbol: K_s

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Shear Stress Correction Factor of Spring

Spring Force Amplitude

The Spring Force Amplitude is defined as the amount of force deviation from the mean force and is also called the alternating component of force in fluctuating loads.

Symbol: P_a

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Spring Force Amplitude

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other Formulas to find Spring Index

Go Spring Index given Mean Stress on spring

C = σ m \cdot \frac{π \cdot d^{2}}{8 \cdot K s \cdot P m}

Other formulas in Design Against Fluctuating Load category

Go Mean Force on spring

P m = \frac{P min + P max}{2}

Go Maximum Force on Spring given Mean Force

P max = 2 \cdot P m - P min

Go Minimum Force on Spring given Mean Force

P min = 2 \cdot P m - P max

Go Force Amplitude of Spring

P a = .5 \cdot (P max - P min)

How to Evaluate Spring Index given Torsional Stress Amplitude?

Spring Index given Torsional Stress Amplitude evaluator uses Spring Index = Torsional Stress Amplitude in Spring*(pi*Diameter of Spring Wire^2)/(8*Shear Stress Correction Factor of Spring*Spring Force Amplitude) to evaluate the Spring Index, Spring Index given Torsional Stress Amplitude formula is defined as a dimensionless parameter that characterizes the spring's behavior under fluctuating loads, providing a measure of the spring's ability to withstand torsional stress amplitude, which is essential in design against fluctuating load applications. Spring Index is denoted by C symbol.

How to evaluate Spring Index given Torsional Stress Amplitude using this online evaluator? To use this online evaluator for Spring Index given Torsional Stress Amplitude, enter Torsional Stress Amplitude in Spring (τ_a), Diameter of Spring Wire (d), Shear Stress Correction Factor of Spring (K_s) & Spring Force Amplitude (P_a) and hit the calculate button.

FAQs on Spring Index given Torsional Stress Amplitude

What is the formula to find Spring Index given Torsional Stress Amplitude?

The formula of Spring Index given Torsional Stress Amplitude is expressed as Spring Index = Torsional Stress Amplitude in Spring*(pi*Diameter of Spring Wire^2)/(8*Shear Stress Correction Factor of Spring*Spring Force Amplitude). Here is an example- 8.944815 = 77000000*(pi*0.004004738^2)/(8*1.08*49.95129).

How to calculate Spring Index given Torsional Stress Amplitude?

With Torsional Stress Amplitude in Spring (τ_a), Diameter of Spring Wire (d), Shear Stress Correction Factor of Spring (K_s) & Spring Force Amplitude (P_a) we can find Spring Index given Torsional Stress Amplitude using the formula - Spring Index = Torsional Stress Amplitude in Spring*(pi*Diameter of Spring Wire^2)/(8*Shear Stress Correction Factor of Spring*Spring Force Amplitude). This formula also uses Archimedes' constant .

What are the other ways to Calculate Spring Index?

Here are the different ways to Calculate Spring Index-

Spring Index=Mean Shear Stress in Spring*(pi*Diameter of Spring Wire^2)/(8*Shear Stress Correction Factor of Spring*Mean Spring Force)

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: Value
: Unit

Spring Index given Torsional Stress Amplitude Formula

​GoSpring Index given Mean Stress on spring Formula

Spring Index given Torsional Stress Amplitude Example

Spring Index given Torsional Stress Amplitude Solution

Spring Index given Torsional Stress Amplitude Formula Elements

Other Formulas to find Spring Index

Other formulas in Design Against Fluctuating Load category

How to Evaluate Spring Index given Torsional Stress Amplitude?

FAQs on Spring Index given Torsional Stress Amplitude

Variable Name

GoSpring Index given Mean Stress on spring Formula