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### Wave Washer Design Formula and Calculator

Spring Design and Engineering Equations and Calculators

Wave Washer Design Formula and Calculator

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 · EM · f · t · N2) / (D)2

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

Where:

S = Bending stress, lbs/in2, (N.mm2)
EM = 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

λSP = λSP,B · ( S / Ts )3 · Ccs · CR · CM

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

Eq. 3
λSP = λSP,B · CE · Ct · CD · CY · Cf · CNW · CCS · CR · CM

where:

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

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

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

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

CY = Multiplying factor which considers the effect of material tensile strength on the base failure rate
Eq. 7
CY = ( 190 x 103 / Ts )3

Ts = Tensile Strength, lbs/in2, (N/mm2)

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

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

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

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

CM = Multiplying factor which considers the effect of the manufacturing process on the base failure rate
Eq. 12
CM = 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

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