What Is a Torsional Spring?
A torsional spring is a mechanical device that stores energy when it is twisted. Unlike compression or extension springs that resist linear forces, torsional springs resist rotational forces (torque). They are used in clothespins, clipboard mechanisms, garage doors, mouse traps, and automotive suspension systems.
The spring exerts a restoring torque proportional to the angular displacement from its equilibrium position, following Hooke's law in the rotational domain. The proportionality constant is the torsional spring rate, measured in units of torque per radian (or degree) of rotation.
Torsional Spring Rate Formula
Where E is Young's modulus, d is wire diameter, D is mean coil diameter, Na is the number of active coils, and θ is the angular deflection in radians. The bending stress in the wire can be computed as σ = (32 × Torque) / (π × d³).
Spring Wire Materials
| Material | E (GPa) | Typical Use |
|---|---|---|
| Music Wire (ASTM A228) | 207 | High-stress springs |
| Stainless Steel 302 | 193 | Corrosion-resistant springs |
| Phosphor Bronze | 103 | Electrical contacts |
| Beryllium Copper | 128 | Low-fatigue springs |
Frequently Asked Questions
What is the spring index and why does it matter?
The spring index C = D/d is the ratio of mean coil diameter to wire diameter. An index between 4 and 12 is considered practical. Too low (tight coils) causes manufacturing difficulty, and too high (loose coils) makes the spring prone to tangling.
How do I increase the torque of a torsional spring?
You can increase torque by using thicker wire (increases as d^4), reducing the coil diameter, reducing the number of active coils, or choosing a material with a higher Young's modulus. Increasing the deflection angle also increases torque proportionally.
What is the difference between torsion spring rate in N-mm/deg and N-mm/rad?
They differ by a factor of 180/pi (approximately 57.3). To convert from N-mm/rad to N-mm/deg, divide by 57.296. Always check which unit convention is being used in your design specifications.