Length of Strip from Outer End to Inner End given Deflection of one End of Spring Calculator

Formula Used:

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

Deflection of Spiral Spring (δ):

Modulus of Elasticity of Spiral Spring (E):

Width of Strip of Spiral Spring (b):

Thickness of Strip of Spring (t):

Bending Moment in Spiral Spring (M):

N·m

Distance of CG of Spiral Spring (r):

Length of Spiral Spring Strip (l):

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1. What is the Length of Spiral Spring Strip Formula?

The formula calculates the length of spiral spring strip based on deflection, material properties, and geometric parameters. It's essential for designing spiral springs with specific deflection characteristics.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( l \) — Length of Spiral Spring Strip (m)
\( \delta \) — Deflection of Spiral Spring (m)
\( E \) — Modulus of Elasticity of Spiral Spring (Pa)
\( b \) — Width of Strip of Spiral Spring (m)
\( t \) — Thickness of Strip of Spring (m)
\( M \) — Bending Moment in Spiral Spring (N·m)
\( r \) — Distance of CG of Spiral Spring (m)

Explanation: The formula relates the spring's length to its deflection characteristics and material properties, accounting for bending moment and geometric parameters.

3. Importance of Length Calculation

Details: Accurate length calculation is crucial for designing spiral springs with specific deflection requirements, ensuring proper functionality in mechanical systems.

4. Using the Calculator

Tips: Enter all values in appropriate SI units. Ensure all input values are positive and within reasonable physical limits for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is a spiral spring?
A: A spiral spring is a flat strip of material wound in a spiral shape that stores mechanical energy when twisted.

Q2: Why is thickness raised to the third power in the formula?
A: The thickness appears as t³ because the bending stiffness of a rectangular beam is proportional to the cube of its thickness.

Q3: What is the center of gravity distance in this context?
A: The distance of CG refers to the distance from the outer end of the spiral to its center of gravity, which affects the bending characteristics.

Q4: Can this formula be used for all types of spiral springs?
A: This formula is specifically for spiral springs with uniform cross-section and material properties throughout the length.

Q5: What are typical applications of spiral springs?
A: Spiral springs are commonly used in mechanical watches, clocks, retractable cords, and various precision instruments.