A compression spring that failed after 200,000 cycles. It was used as a return spring on a pneumatic cylinder. The spring was music wire, 1 mm diameter, 10 mm OD. The customer thought the wire diameter was too small. It was the right size — but the spring was working near its solid height, and the fatigue stress was above the limit. This is about selecting compression springs for cyclic life.
The spring rate
The spring rate (N/mm) tells you how much force per mm of compression:
k = G · d⁴ / (8 · D³ · n)
Where G is the shear modulus (79,000 MPa for steel), d is wire diameter (mm), D is mean coil diameter (mm), n is active coils. For our spring: d=1 mm, D=9 mm, n=10. k = 79,000 × 1 / (8 × 729 × 10) = 79,000 / 58,320 = 1.35 N/mm. At 10 mm compression: F = 1.35 × 10 = 13.5 N. That’s the return force needed for the cylinder.
The fatigue stress
The spring fails in fatigue if the torsional stress exceeds the fatigue limit. The torsional stress:
τ = 8 · F · D / (π · d³) × K_w
Where K_w is the Wahl curvature factor (~1.15 for spring index C=D/d=9). At maximum compression (10 mm): τ = 8 × 13.5 × 9 / (π × 1) × 1.15 = 972 / 3.14 × 1.15 = 310 × 1.15 = 357 MPa. The fatigue limit for music wire at 1 mm diameter is about 45% of tensile strength. Tensile strength for 1 mm music wire is about 2200 MPa. Fatigue limit = 0.45 × 2200 = 990 MPa. Wait — that’s way above 357 MPa. So why did it fail?
Because the spring was compressed to near its solid height. At solid height, the coils close. The stress at solid height is much higher. For our spring, solid height = n × d = 10 × 1 = 10 mm. The working compression was 9 mm (nearly solid). At solid height, the stress is about 800-1000 MPa — above the fatigue limit. The spring coils grind together at near-solid height. Micro-cracks form. After 200,000 cycles, the spring breaks.
What I changed
1. Increased the free length. I increased the free length from 25 to 40 mm. The same 10 mm working compression now goes from 40 to 30 mm. The solid height is still 10 mm. The spring never gets within 20 mm of solid. The working stress stays at 357 MPa (well below fatigue limit). The spring life extends to millions of cycles.
2. Increased wire diameter. For a higher load application, I increase d. But increasing d by 0.2 mm (to 1.2 mm) changes the rate by (1.2/1)^4 = 2.07x. The spring rate doubles. I’d need to adjust the number of coils to keep the same rate. Easier to just increase free length.
3. Specified shot-peened wire. For cyclic applications, I spec shot-peened music wire (or chrome-silicon valve spring wire). Shot peening introduces compressive residual stress on the coil surface. The fatigue limit increases by 30-40%. The spring lasts 3x longer for the same stress. Shot-peened costs 20% more — worth it for a 200,000-cycle application that should last 10 million cycles.
The working range rule
I always keep the working compression between 20% and 80% of the available travel (free length minus solid height). At 20% compression, the spring isn’t preloaded enough. At 80%, it’s near solid and fatigue-stressed. The sweet spot is 30-70%. For our spring: available travel = 40 – 10 = 30 mm. Working compression = 10 mm (33%). That’s in the sweet spot.
Spring materials
| Material | Max temp | Fatigue life | Cost |
|---|---|---|---|
| Music wire | 120°C | Medium (10⁶ cycles) | Low |
| Chrome-silicon | 220°C | High (10⁷ cycles) | Medium |
| Stainless 302 | 250°C | Medium | Medium |
| Inconel X750 | 400°C | High | Very high |
The working range I enforce: 30-70% of available travel. The broken spring wasn’t undersized — it was working at 90% of solid height. Increase free length so the working compression is in the middle of the travel range. For high-cycle applications, use shot-peened chrome-silicon wire.
