Cantilever Beam Spring Design Formula and Calculator

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Cantilever Beam Spring Design Formula and Calculator

Spring Design and Engineering Equations and Calculators

Cantilever springs are fabricated from flat strip material which stores and releases energy upon being deflected by an external load. A typical cantilever spring is shown in Figure 1. In complex designs, only a small part of the device may be functioning as a spring, and for analytical purposes, that portion which is active during operation may be considered as an independent device.

Figure 1 - Typical Cantilever Spring

Preview: Cantilever Spring Design Calculator

The bending stress for cantilever springs can be determined as follows:

Eq. 1
S = ( 3 · E_M · f · t ) / ( 2 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 = Length, in (mm)

The failure rate of a cantilever 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 curved washer 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