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Stiffness of Helical Torsion Spring Formula

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Stiffness of helical torsion spring is the measure of resistance to twisting or torsion of a helical spring when a torque is applied to it. Check FAQs

k h = E \cdot \frac{d^{4}}{64 \cdot D \cdot N a}

k_h - Stiffness of helical torsion spring?E - Modulus of Elasticity of Spring?d - Diameter of spring wire?D - Mean Coil Diameter of Spring?N_a - Active Coils in Helical Torsion Spring?

Stiffness of Helical Torsion Spring Example

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Here is how the Stiffness of Helical Torsion Spring equation looks like with Values.

Here is how the Stiffness of Helical Torsion Spring equation looks like with Units.

Here is how the Stiffness of Helical Torsion Spring equation looks like.

88.5 = 207000 \cdot \frac{4^{4}}{64 \cdot 35.9844 \cdot 260}

88.5Nmm/rad = 207000N/mm² \cdot \frac{{4mm}^{4}}{64 \cdot 35.9844mm \cdot 260}

88.5 = 207000 \cdot \frac{4^{4}}{64 \cdot 35.9844 \cdot 260}

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Stiffness of Helical Torsion Spring Solution

Follow our step by step solution on how to calculate Stiffness of Helical Torsion Spring?

FIRST Step Consider the formula

k h = E \cdot \frac{d^{4}}{64 \cdot D \cdot N a}

Next Step Substitute values of Variables

∴

k h = 207000N/mm² \cdot \frac{{4mm}^{4}}{64 \cdot 35.9844mm \cdot 260}

Next Step Convert Units

∴

k h = 2.1E+11Pa \cdot \frac{{0.004m}^{4}}{64 \cdot 0.036m \cdot 260}

Next Step Prepare to Evaluate

∴

k h = 2.1E+11 \cdot \frac{{0.004}^{4}}{64 \cdot 0.036 \cdot 260}

Next Step Evaluate

∴

k h = 0.0885000113831537Nm/rad

Next Step Convert to Output's Unit

∴

k h = 88.5000113831536Nmm/rad

LAST Step Rounding Answer

∴

k h = 88.5Nmm/rad

Stiffness of Helical Torsion Spring Formula Elements

Variables

Stiffness of helical torsion spring

Stiffness of helical torsion spring is the measure of resistance to twisting or torsion of a helical spring when a torque is applied to it.

Symbol: k_h

Measurement: Roll StiffnessUnit: Nmm/rad

Note: Value should be greater than 0.

Formulas to find Stiffness of helical torsion spring

Modulus of Elasticity of Spring

Modulus of Elasticity of Spring is the measure of the spring's stiffness, representing the amount of stress it can withstand without deforming permanently.

Symbol: E

Measurement: PressureUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Modulus of Elasticity of Spring

Diameter of spring wire

Diameter of spring wire is the diameter of the wire used in a helical torsion spring, which affects the spring's stiffness and load-carrying capacity.

Symbol: d

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Diameter of spring wire

Mean Coil Diameter of Spring

Mean Coil Diameter of Spring is the average diameter of the coil in a helical torsion spring, which affects its stiffness and overall performance.

Symbol: D

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Mean Coil Diameter of Spring

Active Coils in Helical Torsion Spring

Active Coils in Helical Torsion Spring is the number of coils in a helical torsion spring that are actively participating in storing energy.

Symbol: N_a

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Active Coils in Helical Torsion Spring

Other formulas in Helical Torsion Springs category

Go Bending Stress in Spring

σb t = K \cdot 32 \cdot \frac{M b}{π \cdot d^{3}}

Go Bending Moment applied on Spring given Bending Stress

M b = σb t \cdot \frac{π \cdot d^{3}}{K \cdot 32}

Go Diameter of Spring Wire given Bending Stress in Spring

d = {(K \cdot 32 \cdot \frac{M b}{π \cdot σb t})}^{\frac{1}{3}}

Go Stress Concentration Factor given Bending Stress in Spring

K = σb t \cdot \frac{π \cdot d^{3}}{32 \cdot M b}

How to Evaluate Stiffness of Helical Torsion Spring?

Stiffness of Helical Torsion Spring evaluator uses Stiffness of helical torsion spring = Modulus of Elasticity of Spring*Diameter of spring wire^4/(64*Mean Coil Diameter of Spring*Active Coils in Helical Torsion Spring) to evaluate the Stiffness of helical torsion spring, Stiffness of Helical Torsion Spring formula is defined as a measure of the spring's resistance to twisting or torsional deformation, which is a critical parameter in the design and analysis of helical springs used in various mechanical systems. It characterizes the spring's ability to store energy and maintain its shape under torsional loads. Stiffness of helical torsion spring is denoted by k_h symbol.

How to evaluate Stiffness of Helical Torsion Spring using this online evaluator? To use this online evaluator for Stiffness of Helical Torsion Spring, enter Modulus of Elasticity of Spring (E), Diameter of spring wire (d), Mean Coil Diameter of Spring (D) & Active Coils in Helical Torsion Spring (N_a) and hit the calculate button.

FAQs on Stiffness of Helical Torsion Spring

What is the formula to find Stiffness of Helical Torsion Spring?

The formula of Stiffness of Helical Torsion Spring is expressed as Stiffness of helical torsion spring = Modulus of Elasticity of Spring*Diameter of spring wire^4/(64*Mean Coil Diameter of Spring*Active Coils in Helical Torsion Spring). Here is an example- 88500.01 = 207000000000*0.004^4/(64*0.03598435*260).

How to calculate Stiffness of Helical Torsion Spring?

With Modulus of Elasticity of Spring (E), Diameter of spring wire (d), Mean Coil Diameter of Spring (D) & Active Coils in Helical Torsion Spring (N_a) we can find Stiffness of Helical Torsion Spring using the formula - Stiffness of helical torsion spring = Modulus of Elasticity of Spring*Diameter of spring wire^4/(64*Mean Coil Diameter of Spring*Active Coils in Helical Torsion Spring).

Can the Stiffness of Helical Torsion Spring be negative?

No, the Stiffness of Helical Torsion Spring, measured in Roll Stiffness cannot be negative.

Which unit is used to measure Stiffness of Helical Torsion Spring?

Stiffness of Helical Torsion Spring is usually measured using the Newton Millimeter per Radian[Nmm/rad] for Roll Stiffness. Newton Meter per Radian[Nmm/rad], Newton Millimeter per Degree[Nmm/rad], Newton Meter per Degree[Nmm/rad] are the few other units in which Stiffness of Helical Torsion Spring can be measured.

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Stiffness of Helical Torsion Spring Formula

Stiffness of Helical Torsion Spring Example

Stiffness of Helical Torsion Spring Solution

Stiffness of Helical Torsion Spring Formula Elements

Other formulas in Helical Torsion Springs category

How to Evaluate Stiffness of Helical Torsion Spring?

FAQs on Stiffness of Helical Torsion Spring

Variable Name