Engineering & Technology · Mechanisms, Machine Elements & Mechanical Design

Fatigue-aware design, tolerances and maintainability

A shaft surface can experience repeated stress even under an apparently steady external load. Meanwhile, a small change in fit can affect alignment and service access. Mechanical design life therefore combines loading history, material evidence, geometry and the ability to inspect or restore the assembly.

Use Statics, Stress & Deformation; Dynamics, Vibration & Mechanical Response; and Materials Selection, Durability & Degradation. Retain force and moment balances, small elastic models, torque-speed power and units. The slider case supplies elementary trigonometry and a square-root geometry relation. All numbers, records, coefficients and efficiencies are constructed teaching inputs, not hardware selections, permissible loads, maintenance intervals or operating instructions.

Back to the chapter

After reading, you can

Describe cyclic stress, fit variation and maintenance consequences without turning a static pass into a life prediction.

A maximum value does not describe the cycle

Let σmax and σmin be the largest and smallest normal stress in a repeating cycle. Mean stress is(σmax+σmin)/2; alternating amplitude is(σmax−σmin)/2. Stress range is twice that amplitude. Where σmax is nonzero, the ratio R=σmin/σmax is another compact description. Preserve the stress sign and reference location.

Fatigue is progressive damage associated with repeated loading and can occur when peak nominal stress is below a simple yield comparison. Local stress concentration, surface condition, environment, mean stress and the sequence of loads can affect life. A stress-life curve is empirical evidence for stated material/specimen conditions, with scatter; it is not a universal number transferable to every notched component.

A steady bending field can create a repeating material history

The beam lesson placed the upper material in compression and the lower material in tension under its stated sagging moment. Now consider one section of a circular shaft with a bending moment that stays fixed in space while the shaft rotates about its own axis. Track one small marked surface region as part of the material, rather than keeping your attention at a fixed location above the shaft.

When the mark is at the top, its local bending normal stress is compressive. After a quarter turn it passes the neutral-axis level and this bending component is zero. After half a turn the same material is at the bottom in tension. A full revolution returns it to compression. The external transverse load did not need to reverse; rotation moved the material through the fixed bending field. This is why a steady-looking load can produce fatigue-relevant cycles.

For a constructed pure-bending example, assume the outer-surface stress amplitude is 60 MPa. A mark starting at the top follows −60, 0, +60, 0, −60 MPa at zero, quarter, half, three-quarter and full turns. Its mean is zero, alternating amplitude 60 MPa and range 120 MPa. The figure uses σ=−60 cosθ MPa, with θ measured from that top position; it represents small linear elastic bending of a homogeneous circular shaft with no other stress component in the example.

If a separate steady axial tensile stress of 20 MPa is included in the same simple elastic normal-stress account, the history shifts to −40 through +80 MPa. Mean becomes 20 MPa, amplitude remains 60 MPa and R=−40/80=−0.5. A steady transmitted torque instead adds a shear-stress component and needs an appropriate combined assessment; it is not just another number to add to this normal-stress maximum. Neither history by itself supplies a fatigue life.

Without shaft rotation, a fixed material point under this same steady bending field would have a constant bending stress after loading. That does not rule out other cyclic sources in a real assembly, such as varying loads or vibration. Identify the material location, coordinate reference and actual changes before counting cycles or borrowing specimen fatigue evidence.

One marked material region begins at the top in a stationary bending field with −60 MPa normal stress. After quarter, half, three-quarter and full turns its bending stress is 0, +60, 0, −60 MPa. The circle marks successive locations of the same region, not four simultaneous material histories. The right graph uses σ=−60cos(2πn) MPa for revolutions n from 0 to 1. This is a constructed pure-bending model with mean 0, amplitude 60 MPa and range 120 MPa. It is not stress-life data.

Tolerances govern the assembled relationship

A nominal fit can change through manufacturing variation, thermal movement, deformation or wear. Clearance is a relationship between mating dimensions, not a property of either part alone. Worst-case dimension bounds describe possible combinations; they do not by themselves say which clearance is most probable.

An appropriate clearance may be needed for motion, lubrication or alignment, while too much movement can create impact or positioning errors. The functional requirement and environment decide which relationship needs control. A tighter nominal fit can raise assembly or service difficulty, so it should be connected to a demonstrated need rather than treated as automatically superior.

Inspection and replacement belong in the life model

A maintainable arrangement gives access to the features that need inspection or replacement and preserves the required location afterward. Consider disassembly sequence, identification, tool approach and replacement-part availability. A replaceable wear element helps only if the surrounding components can be restored to the intended condition.

Keep load cycles, operating conditions, inspection findings and component versions linked. A changed material, process, fit or repair can invalidate part of the previous life evidence. The plan may require appropriate inspection or replacement criteria, but those must come from qualified evidence for the actual assembly; they cannot be supplied by an illustrative stress history alone.

Case A σ=50−30cos(2πt)MPa has min 20, max 80, mean 50, amplitude 30, range 60MPa, R.25. Case B σ=−80cos(2πt)MPa has min−80, max 80, mean 0, amplitude 80, range 160MPa, R−1. Both are 1Hz constructed histories, not stress-life data or survival predictions.

Compare cycles and an elementary clearance

Case A varies from 20 to 80 MPa. Its mean is 50 MPa, amplitude 30 MPa, range 60 MPa and R=0.25. Case B varies from−80 to+80 MPa, so its mean is 0, amplitude 80 MPa, range 160 MPa and R=−1. Both have the same maximum 80 MPa, but they cannot be described as the same fatigue condition or assigned a life without additional evidence.

Separately, a constructed pin is 6.00±0.02 mm and its hole 6.10±0.03 mm. Minimum diametral clearance is 6.07−6.02=0.05 mm; maximum is 6.13−5.98=0.15 mm. This interval is a geometric result, not a recommended fit. Temperature, shape, lubrication and the actual positioning requirement can change whether it is acceptable.

Try the reasoning

Are stress range and alternating amplitude equal?
Show the answer and reasoning
No. Range is maximum minus minimum; amplitude is half that range.
Does a maximum stress below yield establish indefinite life?
Show the answer and reasoning
No. Cyclic damage and other modes require appropriate evidence beyond a static yield comparison.
Why keep a replacement’s version and fit record?
Show the answer and reasoning
A replacement or repair can change geometry, material or load transfer and therefore the evidence supporting earlier decisions.
A shaft rotates under a bending moment fixed in space. Why is the stress of a marked surface region not necessarily constant, and what changes if the shaft stops rotating under that same ideal steady load?
Show the answer and reasoning
Rotation takes the material region from the compression side through the neutral level to the tension side and back. Without rotation, that region stays at one location in the fixed bending field and its bending stress is constant after loading in this model. Other varying loads or vibration would need a separate account.
For the constructed bending amplitude 60 MPa plus steady axial tension 20 MPa, find maximum, minimum, mean, alternating amplitude and R. Does the 80 MPa maximum alone describe the cycle?
Show the answer and reasoning
Maximum is +80 MPa, minimum −40 MPa, mean (80−40)/2=20 MPa, alternating amplitude (80−(−40))/2=60 MPa, and R=−40/80=−0.5. The maximum alone hides both mean and reversal, so it cannot replace the history or establish a life.

What to carry forward

Evaluate loading history, assembled geometry and restoration together when reasoning about design life.

References

Teaching resources and research supporting this lesson’s explanations and examples.

Massachusetts Institute of Technology3 sources