Distance Of Centre Of Gravity Of Spiral From Outer End Given Deflection Of One End Of Spring Calculator

Formula Used:

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

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

Length of Spiral Spring Strip (l):

Distance of CG of Spiral Spring from Outer End (r):

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1. What is the Distance of CG of Spiral Spring?

The Distance of CG of Spiral Spring from Outer End is the distance between the spiral's outer end strip and the center of gravity of the spiral. This measurement is crucial in understanding the mechanical properties and behavior of spiral springs under various loads.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( r \) — Distance of CG of Spiral Spring from Outer End (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)
\( l \) — Length of Spiral Spring Strip (m)

Explanation: This formula calculates the distance from the outer end to the center of gravity based on the spring's material properties, dimensions, and applied bending moment.

3. Importance of Distance Calculation

Details: Accurate calculation of the center of gravity distance is essential for designing spiral springs with optimal performance characteristics, ensuring proper load distribution, and predicting spring behavior under various operating conditions.

4. Using the Calculator

Tips: Enter all values in appropriate SI units. Ensure all input values are positive numbers. The deflection, modulus of elasticity, width, thickness, bending moment, and length must all be greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: Why is the center of gravity important in spiral springs?
A: The center of gravity affects the spring's balance, stability, and how it responds to external forces and moments during operation.

Q2: What factors influence the distance of CG from the outer end?
A: The distance is influenced by the spring's material properties (modulus of elasticity), physical dimensions (width, thickness, length), and the applied bending moment.

Q3: How does deflection affect the center of gravity distance?
A: Greater deflection typically results in a larger calculated distance to the center of gravity, as the formula shows a direct proportional relationship.

Q4: Are there limitations to this calculation?
A: This calculation assumes ideal material behavior and may need adjustment for extreme conditions or non-linear material properties.

Q5: What units should be used for input values?
A: All input values should be in SI units: meters for length dimensions, Pascals for modulus of elasticity, and Newton-meters for bending moment.