Arc Beam Spring Design Formulae and Calculator

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Arc Beam Spring Design Formulae and Calculator

Spring Design and Engineering Equations and Calculators

Arc Beam Spring Design Formula and Calculator

Beam springs are usually rectangular in shape and formed into an arc as shown in Figure 1.

Figure 1 - Typical Arc Beam Spring
Typical arc Spring

Preview: Arc Beam Spring Design Calculator

The bending stress for Arc Beam Spring can be determined as follows:

Eq. 1
S = ( 6 · E_M · f · t ) / ( L² )

Where:

S = Bending stress, lbs/in², (N.mm²)
E_M = Modulus of Elasticity, lbs/in², (N.mm²)
f = deflection, in (mm)
t = thickness, in (mm)
L = Active spring length, in (mm)

The failure rate of a Arc Beam Spring 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 beam spring considering anticipated operating conditions can be established:

Eq. 3
λ_SP = λ_SP,B · C_E · C_t · C_L · C_f · C_Y · 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_L = Multiplying factor which considers the effect of washer diameter on the base failure rate
Eq. 6
C_L = ( 1.20 / L )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_CS = Multiplying factor which considers the effect of a corrosive environment on the base failure rate
Eq. 9a
C_CS = 0.100 If C_R ≤ cycles/min
Eq. 9b
C_CS = C_R / 300 ) For 30 cycles/min < CR ≤ 300 cycles min,
Eq. 9c
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. 10
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. 11
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