Surface finish, interferometry and alignment testing

Why it matters

Cylinder bores are honed to a specific cross-hatch texture so they hold oil; crankpins and camshaft lobes are ground to fractions of a micrometre so the oil film is not broken; a gasket face that is too rough leaks. Surface finish controls friction, wear, fatigue life and sealing, while flatness checked with optical flats and the alignment of machine tools decide whether parts can be made accurately at all.

Key ideas

Surface texture has several components:

• Roughness – closely spaced irregularities left by the process (feed marks, grit scratches).
• Waviness – longer-wavelength undulations from vibration, deflection or heat.
• Lay – the dominant direction of the pattern (parallel, perpendicular, crossed, circular, radial, multidirectional).
• Flaws – isolated defects such as scratches and pits. Roughness is separated from waviness by the sampling (cut-off) length, commonly 0.8 mm for typical machined surfaces; the evaluation length usually covers several sampling lengths.

Roughness parameters (heights measured from the mean line, which divides the profile so that areas above and below are equal):

• Ra (arithmetic mean deviation, also called CLA) – the most widely specified value; turning gives roughly 0.8–6.3 µm, grinding 0.1–1.6 µm, lapping and superfinishing below 0.1 µm.
• Rq (root-mean-square) – weights peaks more heavily.
• Rt / Rmax – peak-to-valley height over the evaluation length.
• Rz – average peak-to-valley height over the sampling lengths (definitions vary between older and newer standards; check which one is quoted). Ra alone does not show the shape of the profile: surfaces with sharp peaks and with deep valleys can share the same Ra yet behave very differently in wear and lubrication.

Ideal roughness in turning. Feed marks form a regular pattern:

• With a sharp-pointed tool the profile is triangular, with height set by feed and the side and end cutting edge angles.
• With a nose radius R the profile is a series of arcs, and the height is about f²/(8R). Actual roughness is higher because of built-up edge, vibration, tool wear and side flow. Finer finish therefore comes from smaller feed, larger nose radius, higher speed (less BUE), sharp tools and rigid set-ups.

Measuring surface finish.

• Stylus instruments (profilometers such as the Talysurf): a diamond tip of a few micrometres radius traverses the surface; its vertical movement is amplified electrically and filtered to give Ra, Rq, Rz. The stylus radius limits how narrow a valley it can reach, and a skid acts as a mechanical filter.
• Optical methods – light-section microscope, white-light interferometry, confocal and focus-variation microscopes – non-contact.
• Comparison with standard roughness specimens by touch or eye for shop-floor checks. On drawings, roughness is indicated by the surface-texture symbol with the Ra value, process and lay direction.

Interferometry. When an optical flat (a transparent disc polished flat to a fraction of a wavelength) rests on a reflecting surface at a slight angle, monochromatic light reflected from the two surfaces interferes. Dark bands appear where the air gap equals a whole number of half-wavelengths, so each fringe represents a height change of λ/2.

• Straight, parallel, equally spaced fringes mean the surface is flat; curved fringes show convexity or concavity, and the fringe curvature, as a fraction of fringe spacing, gives the flatness error.
• Typical light sources: helium (λ ≈ 0.588 µm), mercury green (≈ 0.546 µm), sodium (≈ 0.589 µm).
• Interferometers (NPL flatness interferometer, gauge-length interferometers, laser interferometers) compare slip gauges and calibrate machine axes; a laser interferometer counts fringes to measure displacement in units of λ/2.

Alignment testing of machine tools. Acceptance tests (originated by Schlesinger, now in ISO 230 and machine-specific standards; take permissible deviations from the relevant standard) check the machine's geometric accuracy: levelling of the bed, straightness of guideways, run-out (true running) of the spindle, axial float, parallelism of the spindle axis to the carriage movement, alignment of the tailstock centre, and squareness of axes. Tools: precision spirit levels, dial indicators, test mandrels, straight edges, squares, autocollimators and laser alignment systems. Practical tests (machining a test piece) confirm performance under cutting conditions.

Formulas

Ra = (1/L)·∫|y| dx ≈ (1/n)·Σ|y_i| Arithmetic mean roughness (µm); y = height from the mean line (µm), L = sampling length (mm), n = number of equally spaced ordinates.

Rq = √((1/n)·Σ y_i²) RMS roughness (µm).

h_max = f / (tan C_s + cot C_e) Ra = h_max / 4 Sharp-pointed tool: peak-to-valley height (mm); f = feed (mm/rev), C_s = side cutting edge angle, C_e = end cutting edge angle (ASA).

h_max = f² / (8·R) Ra ≈ f² / (18√3·R) ≈ 0.0321·f² / R Nose-radius tool (f small compared with R); R = nose radius (mm).

Δh = N·λ / 2 Height difference (µm) across N fringes with an optical flat; λ = wavelength (µm).

Δφ = 2π·Δ / λ Phase difference (rad) for an optical path difference Δ.

Worked examples

Example 1 (standard) – ideal roughness in turning. (a) Nose radius R = 0.8 mm, feed f = 0.2 mm/rev:

1. h_max = f²/(8R) = 0.04/6.4 = 0.00625 mm = 6.25 µm.
2. Ra ≈ 0.0321·f²/R = 0.0321 × 0.04/0.8 = 0.0016 mm = 1.6 µm. (b) Sharp tool, C_s = 30°, C_e = 10°, same feed:
3. h_max = f/(tan C_s + cot C_e) = 0.2/(0.577 + 5.671) = 0.032 mm = 32 µm.
4. Ra = 32/4 = 8 µm – a nose radius improves finish fivefold here.

Example 2 (GATE level) – feed for a required finish, and an optical-flat reading. (a) A finishing pass must give Ra = 1.6 µm with a 1.2 mm nose radius. From Ra = f²/(18√3·R): f = √(18√3 × 1.2 × 0.0016) = √0.05986 = 0.245 mm/rev (round down to the nearest available feed). (b) A slip-gauge face viewed under an optical flat with helium light (λ = 0.5876 µm) shows 5 fringes across its width, curved in the same sense. The height difference across the face is Δh = 5 × 0.5876/2 = 1.469 µm ≈ 1.47 µm.

Example 3 – phase difference. For an optical path difference of 500 nm with 600 nm light: Δφ = 2π × 500/600 = 5π/3 rad (300°).

Common mistakes

• Reading Ra as peak-to-valley height; Ra is an average absolute deviation and is much smaller than Rt.
• Taking each fringe as λ instead of λ/2 of height.
• Squaring the nose radius instead of the feed in f²/(8R).
• Using tan for the end cutting edge angle instead of cot in the sharp-tool formula.
• Assuming the same Ra means the same functional surface.
• Measuring with a cut-off length that is too short, which filters out real roughness, or too long, which mixes in waviness.

For GATE ME

Expect ideal-roughness numericals for turning (sharp tool and nose radius), Ra and Rq from given ordinates, required feed for a target finish, optical-flat fringe counting, and conceptual questions on roughness vs waviness, lay, stylus instruments, and machine-tool alignment tests and instruments. Practise rearranging the nose-radius formula for feed.

Quick check

1. Height represented by 4 fringes with λ = 0.6 µm?
2. Peak-to-valley height for f = 0.1 mm/rev, R = 0.5 mm?
3. What is "lay"?
4. Ra of ordinates of magnitude 2, 4, 3, 3 µm?
5. Which instrument checks spindle run-out?

Answers: 1. 1.2 µm; 2. 2.5 µm; 3. The dominant direction of the surface pattern; 4. 3 µm; 5. A dial indicator with a test mandrel.