Engineering metrology = measuring dimensions (length, thickness, diameter, taper, angle, flatness, profiles).

• Post-process inspection (after making) vs in-process / real-time inspection (the modern trend).
• Dimensional tolerance = permissible variation; smaller tolerance → higher cost.

Linear-Measurement Instruments

• Vernier calipers — beam + sliding jaw with a vernier; read at matching graduations.
• Micrometers — thickness and inside/outside dimensions.

Fixed Gages

Replicas of the part shape — cheap and easy, but only tell too small / too large (no actual reading).

• Plug gages (holes): GO (smaller) enters; NOT GO (larger) must not. Two gages (or a step-type).
• Ring gages (shafts): GO / NOT GO marked by knurling.
• Snap gages (external): one-unit GO–NOT GO.

Optical Instruments

• Toolmaker’s microscope — movable stage, reads to ~2.5 µm.
• Scanning electron microscope (SEM) — excellent depth of field at >100,000×; great for surface texture & fracture, but not for metrology.

Automated Measurement

On-line sensor systems monitor dimensions during production and feed back corrections — reduces rejects.

Dimensional Tolerance

• Permissible variation in a dimension; unavoidable (no two parts are identical).
• Close tolerances raise cost → use only where needed (hydraulic pistons, aircraft-engine bearings).
• Tolerances matter only for assembled/mated parts; free surfaces don’t need tight control (e.g. a connecting-rod’s hole spacing is more critical than its width).
• The ISO tolerance system standardizes these; tolerances depend on part size and process (tabulated for a 25-mm dimension).

Fit Definitions

• Bilateral tolerance: deviation ± from the basic size (e.g. $40.00 pm 0.05$).
• Unilateral tolerance: deviation in one direction only.
• Limit dimensions: the maximum and minimum dimensions of a part.
• Clearance: space between mating parts.
• Clearance fit: allows rotation/sliding.
• Interference: negative clearance.
• Interference fit: an interference always results on assembly.
• Transition fit: small clearance or interference for accurate location.

Appendix — Electron Microscopes

Electrons have a far shorter wavelength than light (~0.5 Å vs ~4000 Å), resolving much finer structure; magnetic “lenses” focus the beam in a high vacuum.

• TEM (transmission): beam passes through a very thin sample → magnified image (up to ~1,000,000×).
• SEM (scanning): a focused beam scans the surface; scattered/secondary electrons are counted per point → 3-D-like surface images (100,000×+); samples need dehydration, not thinning.
• STEM combines both (resolves single atoms); the electron-probe microanalyzer adds X-ray analysis for composition.

Notes

GO / NOT-GO gages are simple and easy but give no numerical reading → no statistical process control. Tolerance generally increases with surface roughness (a roughing cut has large force variation and rough surfaces).