SME
Machine Design · Problem type
Endurance limit from Marin factors
Use this for “A machined 30 mm steel shaft has Sᵤₜ = 600 MPa. Find kₐ, kb and its endurance limit in rotating bending.”
Diagram
The polished test bar holds Sₑ′ = 0.5 × Sᵤₜ = 300 MPa.
Each Marin factor cuts it down: Sₑ = kₐ kb Sₑ′ = 0.8279 × 0.8617 × 300 MPa = 214 MPa.
This is an example. Type your own values to start a new problem.
Sᵤₜ
Ultimate tensile strength
example
a
Surface coefficient
example
b
Surface exponent
example
kₐ
Surface factor
calculated
d
Diameter
example · mm
kb
Size factor
calculated
Sₑ′
Test bar endurance limit
calculated
Sₑ
Part endurance limit
calculated
Formulas
Sₑ′ = 0.5 × Sᵤₜ
300 = 0.5 × 600
kₐ
=
a
×
Sᵤₜ
b
0.8279
=
4.51
×
600
−0.265
kb
=
1.24
×
d
−0.107
0.8617
=
1.24
×
30
−0.107
Sₑ = kₐ × kb × Sₑ′
214.0215 = 0.8279 × 0.8617 × 300
Assumptions
•
Steel in rotating bending at room temperature; Sₑ′ = 0.5Sᵤₜ (Sᵤₜ up to 1400 MPa).
•
Surface constants a and b are typed from their table (machined: a = 4.51, b = −0.265, Sᵤₜ in MPa).
•
kb = 1.24d−0.107 holds for diameters from 2.79 to 51 mm; the other factors are 1.
Step-by-step
WE KNOW
Sᵤₜ = 600 MPa, a = 4.51, b = −0.265, d = 30 mm
FIND
test bar endurance limit (Sₑ′), surface factor (kₐ), size factor (kb), part endurance limit (Sₑ)
Step 1 · Find test bar endurance limit (Sₑ′)
Use Sₑ′ = 0.5 × Sᵤₜ
A polished steel test bar survives endlessly below about half its ultimate strength.
Sₑ′ = 0.5 × 600
Sₑ′ = 300 MPa
Step 2 · Find surface factor (kₐ)
Use kₐ = a × Sutᵇ
The surface fit: rougher finishes and stronger steels lose more, with Sᵤₜ in MPa.
kₐ
=
4.51
×
600
−0.265
kₐ = 4.51 × 0.1836
kₐ = 0.8278782
Step 3 · Find size factor (kb)
Use kb = 1.24 × d−0.107
The size fit: a thicker part holds more flaws in its stressed skin, so it is weaker.
kb
=
1.24
×
30
−0.107
kb = 1.24 × 0.6949
kb = 0.861727
Step 4 · Find part endurance limit (Sₑ)
Use Sₑ = kₐ × kb × Sₑ′
Each Marin factor takes the real part further below the polished test bar.
Sₑ = 0.8278782 × 0.861727 × 300
Sₑ = 0.7134 × 300
Sₑ = 214.0215 MPa
Check
Put the numbers back in. Both sides should match.
300 = 0.5 × 600 ✓
0.8278782
=
4.51
×
600
−0.265
✓
0.861727
=
1.24
×
30
−0.107
✓
214.0215 = 0.8278782 × 0.861727 × 300 ✓
Topic check
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