**Related Resources: calculators**

### Helical Spring Fatigue Loading and Factor of Safety Formulas and Calculator

Helical Spring Fatigue Loading and Factor of Safety Formula and Calculator

Rarely are helical springs not subjected to fatigue loading. The number of cycles may only be in hundreds or thousands, but usually they must be designed for millions and millions of cycles such that an infinite life is desired.

Helical springs may be subjected to completely reversed loading, where the mean shear
stress (τ_{m}) is zero; however, as this type of spring is installed with a preload, the spring
is usually subjected to fluctuating loading. The fluctuating loading may be compressive or
tensile, but never both.

If the maximum force on the spring is denoted as (Fmax) and the minimum force is
denoted as (F_{min}), whether they are compressive or tensile, then the mean force (F_{m}) and
alternating force (F_{a}) are given by the relationships in Eqs. 1 and 2.

Helical Compression Spring

Preview Helical Spring Fatigue Loading and Factor of Safety Calculator

Mean spring force

Eq 1

F_{m} = ( F_{max} + F_{min} ) / 2

Alternating spring force

Eq. 2

F_{a} = ( F_{max} - F_{min} ) / 2

Stress-concentration factors are applied only to the
alternating stresses the mean shear stress (τ_{m}) is given by:

Eq. 3

τ_{m} = K_{s} ( 8 F_{m} D ) / ( π d^{3 )}

where is the shear-stress correction factor

Eq. 4

K_{s} = 1 / ( 2 C ) + 1 = ( 1 + 2 C ) / ( 2 C )

and

C = D / d ≤ C ≤ 12

Using the Bergstrasser factor ( K_{B} ) in place of the shear-stress correction factor ( K_{s} ), the alternating shear stress ( τ_{a} ) is:

Eq. 5

τ_{a} = K_{B} ( 8 F_{a} D ) / ( π d^{3} )

and

K_{B} = ( 4C + 2 ) / ( 4C -3)

Also, the Goodman theory for fluctuating torsional loading is applicable where the factor of safety (n) for a safe design was given by:

Eq. 6

(Goodman Theory)

τ_{a} / S_{e} + τ_{a} / S_{us} = 1 / n

where the endurance limit (S_{e}) is calculated as usual using the Marin formula with the load type factor (k_{c}) equal to (0.577), and the ultimate shear stress ( S_{us} ) found
from the relationship:

Eq. 7

S_{us} = ( 0.67 ) S_{ut}

The Goodman theory given in Eq. (6) can be represented graphically as:

The perpendicular distance (d) to the Goodman line in Fig. 2 represents how close the factor-of-safety (n) is to the value of 1.

Once the mean shear stress (τ_{m}), the alternating shear stress (τ_{a}), the endurance limit
(S_{e}), and the ultimate shear strength (S_{us}) are known, the factor-of-safety (n) for the design
can be determined either mathematically using Eq. 8) or graphically using figure 2.

Factor of safety

Eq. 8

τ_{a} / S_{e} + τ_{m} / S_{us} = 1 / n

Where:

F_{min} = minimum force on the spring (lb, N)

F_{max}max = maximum force on the spring (lb, N)

D = spring coil mean diameter ( in, m )

d = section diameter ( in, m )

S_{e} = endurance limit (kpsi, MPa)

S_{us} = ultimate shear stress(kpsi, MPa)

Related:

- Helical Compression Spring Critical Frequency Formula and Calculator
- Spring Terminology and Definitions
- Belleville Spring Washer Equation and Calculator
- Spring Types and Materials Review
- Morrison's Spring Tables Design Reference
- Leaf Spring Design and Engineering Strength of Materials
- Coil Spring Engineering Design Application
- Helical Compression Spring Design Equations and Calculator
- Compression Spring Assembly Operating Life and Reliability Equations and Calculator
- Shock Loading Helical Springs Formulas and Calculator

Source:

Mark's Calculations for Machine Design

Thomas H. Brown, Jr.

Faculty Associate

Institute for Transportation Research and Education

NC State University

Raleigh, North Carolina

* Link to this Webpage*:

**© Copyright 2000 - 2021, by Engineers Edge, LLC www.engineersedge.com All rights reserved
Disclaimer
| Feedback | Advertising
| Contact **