Thickness Of Strip When Angle Of Rotation Of Arbor With Respect To Drum Calculator

Formula Used:

\[ t = \left( \frac{12 \times M \times l}{E \times b \times \theta} \right)^{1/3} \]

Bending Moment In Spiral Spring (M):

N·m

Length Of Spiral Spring Strip (l):

Modulus Of Elasticity Of Spiral Spring (E):

Width Of Strip Of Spiral Spring (b):

Angle Of Rotation Of Arbor (θ):

rad

Thickness Of Strip Of Spring (t):

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1. What is the Thickness Calculation Formula?

The thickness calculation formula determines the required thickness of a spiral spring strip based on bending moment, length, modulus of elasticity, width, and angle of rotation. This calculation is essential for designing spiral springs with specific mechanical properties.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ t = \left( \frac{12 \times M \times l}{E \times b \times \theta} \right)^{1/3} \]

Where:

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

Explanation: The formula calculates the cube root of the ratio between the product of bending moment and length, and the product of modulus of elasticity, width, and angle of rotation.

3. Importance of Thickness Calculation

Details: Accurate thickness calculation is crucial for ensuring the spiral spring can withstand the required bending moments while maintaining proper elasticity and rotational characteristics.

4. Using the Calculator

Tips: Enter all values in the specified units. Bending moment in N·m, length in meters, modulus of elasticity in Pascals, width in meters, and angle of rotation in radians. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the cube root in the formula?
A: The cube root relationship indicates that thickness increases proportionally to the cube root of the ratio between bending moment/length and modulus/width/angle.

Q2: How does modulus of elasticity affect thickness?
A: Higher modulus materials (stiffer materials) require less thickness to achieve the same bending characteristics.

Q3: What happens if the angle of rotation increases?
A: For a given bending moment, larger rotation angles require thinner strips to achieve the desired flexibility.

Q4: Are there limitations to this formula?
A: This formula assumes linear elastic behavior and may not account for extreme deformations or material non-linearities.

Q5: How does width affect thickness calculation?
A: Wider strips can be thinner to achieve the same bending characteristics, as width and thickness both contribute to the moment of inertia.