Bending Moment Due To Force Given Angle Of Rotation Of Arbor With Respect To Drum Calculator

Formula Used:

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

Angle of Rotation of Arbor (θ):

rad

Modulus of Elasticity of Spiral Spring (E):

Width of Strip of Spiral Spring (b):

Thickness of Strip of Spring (t):

Length of Spiral Spring Strip (l):

Bending Moment in Spiral Spring (M):

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1. What is Bending Moment in Spiral Spring?

Bending moment in spiral spring is the reaction induced in a spiral spring when an external force or moment is applied to the element, causing the element to bend. It represents the internal moment that resists the bending deformation.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( M \) — Bending moment in spiral spring (N·m)
\( \theta \) — Angle of rotation of arbor (rad)
\( E \) — Modulus of elasticity of spiral spring (Pa)
\( b \) — Width of strip of spiral spring (m)
\( t \) — Thickness of strip of spring (m)
\( l \) — Length of spiral spring strip (m)

Explanation: This formula calculates the bending moment in a spiral spring based on the angle of rotation, material properties, and geometric dimensions of the spring.

3. Importance of Bending Moment Calculation

Details: Accurate calculation of bending moment is crucial for designing spiral springs, ensuring they can withstand applied loads without permanent deformation, and predicting their performance in various applications.

4. Using the Calculator

Tips: Enter all values in appropriate units (radians for angle, Pascals for modulus, meters for dimensions). All values must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the angle of rotation?
A: The angle of rotation determines how much the arbor has turned relative to the drum, which directly affects the bending moment in the spring.

Q2: How does modulus of elasticity affect the bending moment?
A: Higher modulus of elasticity means the material is stiffer, resulting in higher bending moment for the same angle of rotation.

Q3: Why is thickness raised to the third power in the formula?
A: The thickness appears as t³ because bending stiffness is proportional to the cube of the thickness in beam bending theory.

Q4: What are typical applications of spiral springs?
A: Spiral springs are commonly used in mechanical watches, clocks, toys, and various precision instruments where rotational energy storage is required.

Q5: How does length affect the bending moment?
A: Longer spring length reduces the bending moment, as the deformation is distributed over a greater length, reducing stress concentration.