Modulus Of Elasticity Given Deflection Of One End Of Spring With Respect To Other End Calculator

Formula Used:

\[ E = \frac{12 \times M \times l \times r}{\delta \times b \times t^3} \]

Bending Moment in Spiral Spring (M):

N·m

Length of Spiral Spring Strip (l):

Distance of CG of Spiral Spring (r):

Deflection of Spiral Spring (δ):

Width of Strip of Spiral Spring (b):

Thickness of Strip of Spring (t):

Modulus of Elasticity of Spiral Spring (E):

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1. What is the Modulus of Elasticity of Spiral Spring?

The Modulus of Elasticity of Spiral Spring is a quantity that measures the spring's resistance to being deformed elastically when stress is applied to it. It represents the stiffness of the spring material and is a fundamental property in spring design and analysis.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ E = \frac{12 \times M \times l \times r}{\delta \times b \times t^3} \]

Where:

\( E \) — Modulus of elasticity of spiral spring (Pa)
\( M \) — Bending moment in spiral spring (N·m)
\( l \) — Length of spiral spring strip (m)
\( r \) — Distance of CG of spiral spring from outer end (m)
\( \delta \) — Deflection of spiral spring (m)
\( b \) — Width of strip of spiral spring (m)
\( t \) — Thickness of strip of spring (m)

Explanation: This formula calculates the modulus of elasticity based on the spring's geometric properties and the applied bending moment and resulting deflection.

3. Importance of Modulus of Elasticity Calculation

Details: Accurate calculation of modulus of elasticity is crucial for spring design, performance prediction, and ensuring the spring will function properly under specified loads without permanent deformation.

4. Using the Calculator

Tips: Enter all values in the specified units. Ensure all values are positive and valid. The calculator will compute the modulus of elasticity in Pascals (Pa).

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range of modulus of elasticity for spring materials?
A: For most spring steels, the modulus of elasticity typically ranges from 190-210 GPa (gigapascals).

Q2: How does temperature affect the modulus of elasticity?
A: The modulus of elasticity generally decreases with increasing temperature, which should be considered in high-temperature applications.

Q3: What factors can affect the accuracy of this calculation?
A: Measurement errors in geometric dimensions, material inhomogeneity, and non-linear behavior at large deflections can affect accuracy.

Q4: Can this formula be used for all types of springs?
A: This specific formula is designed for spiral springs. Different formulas apply to other spring types like helical or leaf springs.

Q5: How does the modulus of elasticity relate to spring rate?
A: The modulus of elasticity is directly proportional to the spring rate - higher modulus materials produce stiffer springs.