Table of Contents
What Is Spring Rate?
Spring rate (also called spring constant or stiffness) is the force required to deflect a spring by one unit of length. For a helical compression or extension spring, the rate depends on four key parameters: wire diameter, coil diameter, number of active coils, and the material's shear modulus. Engineers calculate spring rate during the design phase to ensure springs meet load and deflection requirements.
The spring index C = D/d (ratio of mean coil diameter to wire diameter) is a critical design parameter. Values between 4 and 12 are typical; below 4, the spring is difficult to manufacture, and above 12, it tends to tangle and buckle.
Design Formula
Where k is the spring rate (N/mm), G is the shear modulus (MPa), d is wire diameter (mm), D is mean coil diameter (mm), and N is the number of active coils. The Wahl correction factor K_w = (4C-1)/(4C-4) + 0.615/C accounts for stress concentration due to curvature.
Material Properties
| Material | G (GPa) | Max Temp (°C) |
|---|---|---|
| Music Wire (ASTM A228) | 79.3 | 120 |
| Chrome Vanadium | 79.3 | 220 |
| Stainless Steel 302/304 | 69.0 | 260 |
| Stainless Steel 17-7PH | 77.2 | 315 |
| Phosphor Bronze | 44.8 | 95 |
| Inconel X-750 | 79.3 | 590 |
Design Considerations
- Spring index (C = D/d): Keep between 4 and 12 for manufacturability.
- Wire diameter: Increasing d by 10% increases stiffness by 46% (d^4 dependency).
- Coil diameter: Increasing D by 10% decreases stiffness by 33% (D^3 dependency).
- Active coils: More coils = softer spring (inversely proportional).
- Buckling: Free length should not exceed 4x mean diameter for compression springs.
Frequently Asked Questions
What are active coils?
Active coils are the coils that actually deflect under load. End coils that are ground flat or closed are inactive. For a spring with N_total coils: closed and ground ends have N_active = N_total - 2; closed unground ends have N_active = N_total - 1.5.
How do I measure mean coil diameter?
Mean coil diameter D = OD - d = ID + d, where OD is the outer diameter, ID is the inner diameter, and d is the wire diameter. Measure the OD with calipers and subtract one wire diameter.
Why does the d^4 term dominate spring rate?
Wire diameter appears to the fourth power because spring deflection involves torsion of the wire. Torsional stiffness scales with the polar moment of inertia (proportional to d^4). Even small changes in wire diameter dramatically affect spring rate, making wire diameter the most sensitive design variable.