gearboxes, pumps, electric motors, and industrial machinery.
During operation, shafts experience repeated cyclic stresses caused by
rotating loads, torque fluctuations, and mechanical imbalance.
Over time, these repeated stresses can initiate fatigue cracks that
eventually lead to shaft failure if not properly analyzed during design.
1. Engineering Question
If a rotating shaft in a gearbox experiences fluctuating bending stresses
during operation, how much fatigue damage will accumulate after millions
of load cycles, and will the shaft survive its expected service life?
Engineers use fatigue analysis to determine whether rotating components
can safely operate under repeated loading conditions over long periods
of time.
2. Stress Calculation Formula
In many rotating shafts, cyclic bending stresses occur due to rotating
loads and shaft deflection. The bending stress in the shaft can be
estimated using the bending stress formula:
σ = (M × c) / I
- σ = bending stress in the shaft (MPa)
- M = bending moment applied to the shaft (N·m)
- c = distance from neutral axis to outer surface of the shaft (m)
- I = second moment of area of the shaft cross-section (m⁴)
As the shaft rotates, the bending moment acting on the shaft changes
continuously due to load variations and mechanical forces.
Using this formula, engineers calculate the resulting stress values
and record them over time.
These calculated stress values form a stress time history
which can be exported as a CSV file for fatigue analysis.
3. Example Stress History (CSV Data)
A simplified example of stress values recorded in a rotating shaft
may look like the following:
95 120 140 135 150 125 110 145 130 100
Each value represents the stress level in MPa at a specific
moment during shaft rotation. These values may be obtained from
simulation software, finite element analysis (FEA), or experimental
strain gauge measurements.
When exported as a CSV file, this stress sequence can be used for
fatigue analysis to evaluate how repeated stress cycles affect the
component’s lifespan.
4. Fatigue Analysis Workflow
Engineers typically follow these steps when performing fatigue
analysis on rotating shafts:
- Obtain stress history data from simulation software or sensors.
- Export the stress sequence as a CSV file.
- Upload the CSV file into a fatigue analysis tool.
- Apply rainflow cycle counting to identify stress cycles.
- Use the material S–N curve to estimate fatigue life for each cycle.
- Calculate cumulative fatigue damage using Miner’s Rule.
This process allows engineers to estimate how long a component can
operate before fatigue failure becomes likely.
5. Try This Example
You can upload similar stress history data and estimate fatigue damage
using the FatigueLab Fatigue Damage Calculator
This tool allows engineers and students to evaluate fatigue damage
for rotating shafts, gears, bearings, and other mechanical components
subjected to cyclic loading.