Wave Springs • Calculator

Single-Turn Wave Spring Force & Fatigue Calculator

Enter geometry, material and two working heights. The calculator returns spring rate, load, stress and a provisional Fatigue Stress Ratio life band (Smalley). Defaults match our worked example.

Open the calculator → Intro to Wave Springs Worked Example

Force & Fatigue Calculator

Geometry

Outside diameter D_e [mm] Must clear the bore when loaded.

Inside diameter D_i [mm] Must clear the shaft.

Thickness t [mm] Strip thickness.

Number of waves N Whole number for single-turn parts.

Free height L₀ [mm] Overall height with no load.

Mean diameter D [mm] D = (D_e + D_i) / 2

Radial width b [mm] b = (D_e − D_i) / 2

Wave factor K From N: ≤4 → 3.88; ≤6.5 → 2.90; ≤9.5 → 2.30; else 2.13

Material

Material Default R_m = 1 650 MPa.

Young’s modulus E [MPa] Room-temperature modulus before temperature correction.

Tensile strength R_m [MPa] Minimum tensile used in X and the 80% peak gate.

Operating temperature T [°C] Optional. E is reduced for |T − 20| (capped at 18%).

Cycle heights (deflection s = L₀ − H)

Lower working height H₁ [mm] Most compressed height in the cycle → S₁.

Upper working height H₂ [mm] Least compressed height → S₂. Use free height when the spring returns to free.

Returns to free each cycle (sets S₂ = 0; H₂ is ignored for fatigue)

248Spring rate k [N/mm]

496Load at H₁ [N]

706Stress S₁ [MPa]

0.57Fatigue Stress Ratio X

E used (after temperature): 207 000 MPa
Deflection s₁ at H₁: 2.00 mm
Deflection s₂ / stress S₂: 0 mm / 0 MPa
Load at H₂: 0 N
Peak vs R_m: 43% of R_m
Dynamic gate (≤ 80% R_m): Pass
Estimated cycle life: 75 000 – 100 000
D′_e at H₁: 79.60 mm

Provisional life band from published guidance — not Reliable Pressings test data.

Results update as you change the inputs. Theory versus test on load is typically within about ±15%.

Disclaimer

Estimated cycle life from published wave-spring Fatigue Stress Ratio bands. Approximate only. Not a warranty. Critical applications need Reliable Pressings fatigue testing on the actual part, material and cycle. Life bands are labelled provisional, from published guidance until we have our own SAE 1075 S–N data.

FORCE, STRESS AND X

Method and Equations

Single-turn rate and stress (wave factor K from N):

k = \frac{E \cdot b \cdot t^{3} \cdot N^{4} \cdot D_{e}}{K \cdot D^{3} \cdot D_{i}}, P = k \cdot s, σ = \frac{3 π P D}{4 b t^{2} N^{2}}

Deflection uses the standard convention s = L₀ − H. Optional temperature correction: E_T = E × (1 − min(0.18, |T − 20| × 0.00018)).

Fatigue Stress Ratio (not classical R = σ_min/σ_max):

X = \frac{R_{m} - S_{1}}{R_{m} - S_{2}}

Default material assumption: SAE 1075 quench and double tempered to HRC 46–48 with R_m = 1 650 MPa (same as the worked example). A Goodman / SMI overlay is planned for version 2 and is not calculated here.

PROVISIONAL, FROM PUBLISHED GUIDANCE

Life Bands

Smalley / Rotor Clip Fatigue Stress Ratio bands (provisional)
Fatigue Stress Ratio X	Estimated cycle life
0.00 < X < 0.40	Under 30 000
0.40 ≤ X < 0.49	30 000 – 50 000
0.50 ≤ X < 0.55	50 000 – 75 000
0.56 ≤ X < 0.60	75 000 – 100 000
0.61 ≤ X < 0.67	100 000 – 200 000
0.68 ≤ X ≤ 0.70	200 000 – 1 000 000
X > 0.70	Over 1 000 000

For dynamic claims keep peak stress S₁ ≤ 80% of R_m. Static designs on our pages often use a tighter 75–80% ceiling.

Notes and Limits

Single-turn wave springs only. Multi-turn and stacked packs are not covered yet.
Linear rate is a useful estimate mainly in the mid-travel band; near solid height the load/deflection curve becomes digressive.
To raise X: narrow the stroke (raise S₂), raise R_m, or lower S₁ (more waves, thicker strip, or less peak deflection).
Reproduce the worked example with the defaults: D_e 79.5, D_i 61.5, t 1.2, N 3, E 207 000, H₁ 4.5 → k ≈ 248 N/mm, P ≈ 496 N, S₁ ≈ 706 MPa.

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