 # Formulas: Wave Springs

It all begins with engineering, tap our decades of spring design expertise when designing wave springs into an application

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### Wave Spring Design

Rotor Clip engineers have designed wave springs for nearly every industry. Please use the following information as a reference, our team of experts is available to consult you on your project to see how a wave spring could save valuable space and weight in an application.

NOMENCLATURE

 T = Thickness of Material OD = Outside Diameter SW = Radial Width of Material ID = Inside Diameter F = Load Dm = Mean Diameter* W.H. = Work Height B = Deflection H = Free Height σ = Operating Stress N = Number of Turns E = Modules of Elasticity Z = Number of Wave per Turn K = Wave Factor**

*Mean Diameter Dm = [(OD + ID) / 2]
** Wave Factor K:

 Number of Waves per Turn [Z]: 2.0 – 4.0 4.5 – 6.5 7.0 – 9.5 ≥10.0 Wave Factor [K]: 3.88 2.90 2.30 2.13

###### Single-Turn Wave Spring WIth Gap or Overlap

The operating stress of a single turn wave spring should never exceed the minimum tensile strength of the flat wire material. Keep deflection between 30 and 70%. ###### Multi-Turn Wave Spring

The operating stress of a single turn wave spring should never exceed the minimum tensile strength of the flat wire material. Keep deflection between 20 and 80%. ###### Nested Wave Wave Spring

The operating stress of a single turn wave spring should never exceed the minimum tensile strength of the flat wire material. Keep deflection between 30 and 70%. ###### Wave Spring Diametric Expansion

The diameter of a flat wire wave spring increases when compressed in the axial direction. The following formula is an example of its maximum achievable outside diameter when compressed at the block level.

Variables:
Z = Number of Waves per turn
Df = Free (uncompressed) Diameter
Dc = Compressed Diameter
FH = Per turn Free Height
WH = Per turn Work Height (per turn compressed height)  ###### Fatigue Stress Ratio

Calculating the ratio between Work Height 1 and Work Height 2 can determine the required number of load cycles. The results are then compared to the guideline table values to figure out final number.

 δ Fatigue Stress Ratio σ1 Calculated operating stress at lower work height σMat Material tensile strength σ² Calculated operating stress at upper work height FATIGUE GUIDELINES Fatigue Stress Ratio δ Estimated Cycle Life < 0.40 < 30.000 0.40 – 0.49 30.000 – 50.000 0.50 – 0.55 50.000 – 75.000 0.56 – 0.60 75.000 – 100.000 0.61 – 0.67 100.000 – 200.000 0.68 – 0.70 200.000 – 1.000.000 > 0.70 > 1.000.000