Wave Washer Design Formula and Calculator

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Wave Washer Design Formula and Calculator

Spring Design and Engineering Equations and Calculators

Wave washers are used to apply moderate thrust loads when radial space is limited. A typical wave washer is shown in Figure 1.

Figure 1 - Typical Wave Washer

Preview: Wave Washer Design Calculator

The stress on a curved washer is:

Eq. 1
S = (0.3 · π · E_M · f · t · N²) / (D)²

Eq. 1a
D = ( OD + ID ) / 2, in (mm)

Where:

S = Bending stress, lbs/in², (N.mm²)
E_M = Modulus of Elasticity, lbs/in², (N.mm²)
f = washer deflection, in (mm)
t = washer thickness, in (mm)
N = Number of waves
D = Mean diameter, = ( OD + ID )/2 , in (mm)
OD = outside diameter, in (mm)
ID = Inside diiameter, , in (mm)

The failure rate of a curved washer is determined using the following equation:

Eq. 2

λ_SP = λ_SP,B · ( S / T_s )³ · C_cs · C_R · C_M

A generalized equation that adjusts the base failure rate of a curved washer considering anticipated operating conditions can be established:

Eq. 3
λ_SP = λ_SP,B · C_E · C_t · C_D · C_Y · C_f · C_NW · C_CS · C_R · C_M

where:

λ_SP = Failure rate of torsion spring, failures/million hours
λ_SP,B = Base failure rate for torsion spring, 14.3 failures/million hours

C_E = Multiplying factor which considers the effect of the material elasticity modulus on the base failure rate
Eq. 4
C_E = ( E_M / 28.5 x 10⁶ )³

C_t = Multiplying factor which considers the effect of the material thickness on the base failure rate
Eq. 5
C_t = ( t / 0.025 )³

C_D = Multiplying factor which considers the effect of washer diameter on the base failure rate
Eq. 6
C_D = ( 1.20 / OD )⁶

C_Y = Multiplying factor which considers the effect of material tensile strength on the base failure rate
Eq. 7
C_Y = ( 190 x 10³ / T_s )³
T_s = Tensile Strength, lbs/in², (N/mm²)

C_f = Multiplying factor which considers the effect of washer deflection on the base failure rate
Eq. 8
C_f = ( f / 0.055 )³

C_NW = Multiplying Factor which considers the number of waves on the base failure rate
Eq. 9
C_NW = ( 5 / NW )²

C_CS = Multiplying factor which considers the effect of a corrosive environment on the base failure rate
Eq. 10a
C_CS = 0.100 If C_R ≤ cycles/min
Eq. 10b
C_CS = C_R / 300 ) For 30 cycles/min < CR ≤ 300 cycles min,
Eq. 10c
C_CS = ( C_R / 300 )³ ForC_R > 300 cycles/min,

C_R = Multiplying factor which considers the effect of a corrosive environment on the base failure rate
Eq. 11
C_R = 1.0 unless or greater than 1.0 with user's experience with the spring and the operating environment.

C_M = Multiplying factor which considers the effect of the manufacturing process on the base failure rate
Eq. 12
C_M = 1.0 a higher value for the multiplying factor is used based on previous experience with the manufacturer.

Reference:

Handbook of of Reliability Predictions Procedure for Mechanical Equipment
Logistics Technology Support
CARDEROCKDIV, NSWC-11
2011