Torsion Spring Conversion Calculator

Torsion Spring Formula:

\[ k = \frac{G \times d^4}{8 \times D^3 \times N} \]

Shear Modulus (G):

Wire Diameter (d):

Mean Coil Diameter (D):

Number of Coils (N):

coils

Spring Rate (k):

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1. What is the Torsion Spring Formula?

The torsion spring formula calculates the spring rate (k) from material properties and geometric parameters. It provides a measure of the spring's resistance to twisting or torsion, expressed in newton-meters per radian (Nm/rad).

2. How Does the Calculator Work?

The calculator uses the torsion spring formula:

\[ k = \frac{G \times d^4}{8 \times D^3 \times N} \]

Where:

\( k \) — Spring rate (Nm/rad)
\( G \) — Shear modulus (Pa)
\( d \) — Wire diameter (m)
\( D \) — Mean coil diameter (m)
\( N \) — Number of active coils

Explanation: The formula demonstrates how spring rate increases with the fourth power of wire diameter, but decreases with the cube of coil diameter and linearly with number of coils.

3. Importance of Spring Rate Calculation

Details: Accurate spring rate calculation is crucial for designing mechanical systems, predicting spring behavior under load, and ensuring proper functioning in applications ranging from automotive suspensions to precision instruments.

4. Using the Calculator

Tips: Enter all values in the specified units. Ensure consistent units (meters for length, Pascals for shear modulus). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is shear modulus (G)?
A: Shear modulus is a material property that measures its resistance to shear deformation. Common values are ~79 GPa for steel and ~26 GPa for aluminum.

Q2: How does wire diameter affect spring rate?
A: Spring rate increases with the fourth power of wire diameter, making it the most influential parameter in the formula.

Q3: What is meant by "active coils"?
A: Active coils are those that contribute to deflection. End coils that are pressed together or used for attachment typically don't count as active coils.

Q4: Can this formula be used for all torsion springs?
A: This formula works well for helical torsion springs with round wire. Special considerations may be needed for rectangular wire or unusual geometries.

Q5: How accurate is this calculation?
A: The formula provides a theoretical spring rate. Actual performance may vary due to manufacturing tolerances, material variations, and end conditions.