Modulus Of Elasticity Given Angle Of Rotation Of Arbor Calculator

Formula Used:

\[ E = \frac{12 \times M \times l}{\theta \times b \times (t^3)} \]

Bending Moment in Spiral Spring (M):

Newton Meter

Length of Spiral Spring Strip (l):

Meter

Angle of Rotation of Arbor (θ):

Radian

Width of Strip of Spiral Spring (b):

Meter

Thickness of Strip of Spring (t):

Meter

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.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ E = \frac{12 \times M \times l}{\theta \times b \times (t^3)} \]

Where:

\( E \) — Modulus of elasticity of spiral spring (Pascal)
\( M \) — Bending moment in spiral spring (Newton Meter)
\( l \) — Length of Spiral Spring Strip (Meter)
\( \theta \) — Angle of rotation of arbor (Radian)
\( b \) — Width of Strip of Spiral Spring (Meter)
\( t \) — Thickness of Strip of Spring (Meter)

Explanation: This formula calculates the modulus of elasticity based on the bending moment, geometric properties of the spring strip, and the angle of rotation of the arbor.

3. Importance of Modulus of Elasticity Calculation

Details: Accurate calculation of modulus of elasticity is crucial for designing spiral springs with specific mechanical properties, ensuring proper performance, and predicting spring behavior under various loading conditions.

4. Using the Calculator

Tips: Enter all values in the specified units. Bending moment, length, angle, width, and thickness must be positive values greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range of modulus of elasticity for spring materials?
A: The modulus of elasticity for common spring materials like steel typically ranges from 190-210 GPa, while for other materials it can vary significantly.

Q2: How does thickness affect the modulus of elasticity calculation?
A: Thickness has a cubic relationship in the denominator, meaning small changes in thickness can significantly affect the calculated modulus of elasticity.

Q3: What factors can affect the accuracy of this calculation?
A: Measurement accuracy of all input parameters, material homogeneity, and proper unit conversion can affect the calculation accuracy.

Q4: Can this formula be used for all types of spiral springs?
A: This formula is specifically designed for spiral springs with the described geometry and may not be applicable to other spring configurations.

Q5: How does temperature affect the modulus of elasticity?
A: The modulus of elasticity typically decreases with increasing temperature for most materials, though the rate of change varies between materials.