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UNCERTAINTY

FACTOR OF SAFETY

SAFETY MARGIN

Namik CIBLAK Department of Mechanical Engineering Yeditepe University Fall 2021

UNCERTAINTY IN MANUFACTURING

• All physical quantities are uncertain up to varying degrees.
• Manufacturing techniques, regardless of how precise, always yield properties (dimensions, relations, material, …) that are inherently uncertain.
• You can never produce a shaft with a perfect diameter of 10-mm.
• You cannot even produce a perfect circle or cylinder.
• You cannot order a steel with exactly 207 GPa elastic modulus or 500 MPa yield strength.
• You cannot make two planes exactly parallel.
• You cannot have perfectly straight lines or planes.
• A shaft will never fit exactly in a hole.
• There is no perfect bearing (rulman) or gear (dişli).

DISTRIBUTIONS

• If you order 100 shafts to be manufactured from the same drawing,

you will get 100 different diameters (straightness, cylindricity, …).

• How are these diameters distributed if there is no other factors

affecting the outcome (unbiased)?

• Answer:
  • Gaussian or Normal distribution
  • Imagine the zero points as the expected value (say, 500 MPA)
  • You may know this curve as the “Çan Eğrisi”.
  • Note the 6-sigma interval
  • 𝜎: Standard deviation.

SAFETY FACTOR AND SAFETY MARGIN

• We use safety factor (load factor, design factor, …) in order take

precautions against uncertainties and variations in design parameters,

including the environmental factors.

Stress Safe Unsafe Max 500 Allowed 300 Safety Margin Safety Factor: 500/300 = 1. Safety Margin: 500 – 300 = 200 MPa Strength