Surface finish, interferometry and alignment testing

Why it matters

Two parts can be within size limits and still fail because their surfaces are too rough, not flat enough, or their axes not aligned. Surface texture controls friction, wear, fatigue life, sealing and paint adhesion; optical flats and laser interferometers give the sub-micrometre references that calibrate every other instrument; and alignment tests decide whether a new machine tool can hold the tolerances it was bought for.

Key ideas

Surface texture

• A real surface carries three superimposed irregularities:
  • Roughness (primary texture): closely spaced marks left by the cutting process itself, e.g. feed marks and grit scratches.
  • Waviness (secondary texture): widely spaced undulations from machine vibration, chatter, spindle runout or heat treatment distortion.
  • Form error: the large-scale departure from the intended shape (flatness, roundness).
• Lay is the direction of the predominant surface pattern (parallel, perpendicular, crossed, circular, radial, multidirectional) and is shown by a symbol on the drawing.
• Roughness is separated from waviness by the cut-off (sampling) length, the filter wavelength. 0.8 mm is the usual default; 0.25 mm for very fine and 2.5 mm or 8 mm for coarse surfaces. The evaluation length is normally five sampling lengths.
• Mean line (M-system): a line through the profile such that the areas above and below it are equal. All parameters are measured from it. (The older E-system rolls a circle over the profile and is rarely used now.)

Roughness parameters

• Ra (centre-line average, CLA, AA): arithmetic mean of the absolute deviations from the mean line. The most quoted parameter, but it cannot tell peaks from valleys; very different surfaces can share the same Ra.
• Rq (RMS): root-mean-square deviation; more sensitive to occasional peaks and valleys. For a sine profile Rq ≈ 1.11 Ra.
• Rz: average peak-to-valley height over the sampling lengths (ISO: mean of the highest peak plus deepest valley in each sampling length). Rt / Rmax: the largest peak-to-valley height.
• Typical Ra: turning 0.8–6.3 μm, milling 0.8–6.3 μm, grinding 0.1–1.6 μm, honing and lapping 0.025–0.4 μm. Tighter Ra costs more process steps.

Measuring surface texture

• Stylus instruments (Talysurf, profilometer): a diamond stylus with tip radius about 2–10 μm traverses the surface; an LVDT or inductive transducer converts its vertical motion to a signal, which is filtered and processed. A skid-type head uses a skid as a local datum (removes waviness mechanically); a skidless head uses an accurate straight datum and can measure waviness and form. The stylus radius limits how narrow a valley it can follow.
• Non-contact methods: optical (white-light) interferometers, confocal microscopes and focus variation, for soft or delicate surfaces and areal (3D) parameters.
• Comparison specimens: quick visual and tactile check against standard samples from the same process.

Interferometry

• Light of wavelength λ splits into two paths and recombines. If the path difference is a whole number of wavelengths the waves reinforce (bright fringe); if it is an odd number of half-wavelengths they cancel (dark fringe).
• Optical flat: a flat quartz or glass disc laid on a lapped surface under monochromatic light (sodium, helium or mercury). The thin air wedge between them produces fringes. Because the light crosses the air gap twice, moving from one fringe to the next corresponds to a change of λ/2 in gap.
  • Straight, parallel, equally spaced fringes: the surface is flat (the wedge is plane).
  • Curved fringes: the surface is convex or concave. Pressing at the edge and watching which way fringes move tells which.
  • Flatness error ≈ (number of fringes of curvature) × λ/2.
• Comparing slip gauges: a gauge and a master are wrung on a base plate and covered by an optical flat; the different number of fringes across them gives the height difference.
• Instruments: NPL flatness interferometer, gauge-length interferometers, Michelson and Twyman-Green interferometers, and the laser (He-Ne, λ = 632.8 nm) interferometer, which counts fringes as a retroreflector moves. It is the standard for calibrating CNC axis positioning, and with angle and straightness optics it also measures pitch, yaw and straightness.

Alignment testing of machine tools

• Geometric (alignment) tests follow Schlesinger's charts and ISO 230 / the relevant IS acceptance codes. They check: levelling of the bed, straightness and flatness of guideways, parallelism of the spindle axis to the guideways, squareness of cross-slide motion to the spindle, true running (runout) of the spindle and its taper, axial float, and parallelism of the tailstock axis.
• Tools: precision spirit level (sensitivity in mm per m per division), test mandrels, dial indicators, straight edges, autocollimators, laser alignment systems.
• Straightness by autocollimator: a reflector on a carriage of base length L is stepped along the guideway. Each tilt reading θ gives a rise of L·θ for that step; the rises are accumulated to plot the profile, and a straight line through the end points gives the straightness error.
• Practical tests (machining a test piece and measuring it) follow the geometric tests and include the effect of load and heat.
• Shaft alignment of coupled machines (motor to pump or gearbox) uses rim-and-face dial readings or laser kits to remove parallel offset and angular misalignment.

Formulas

Ra = (1/L)·∫₀ᴸ |y(x)| dx ≈ (1/n)·Σ|yᵢ|

• yᵢ = profile ordinate measured from the mean line (μm), n = number of equally spaced ordinates, L = sampling length (mm).

Rq = √((1/n)·Σ yᵢ²)

• Same symbols, μm.

Mean line: ȳ = (1/n)·Σ hᵢ ; yᵢ = hᵢ − ȳ

• hᵢ = ordinates read from an arbitrary datum. Use when the given values are not already about the mean line.

Bright fringe: path difference = m·λ ; dark fringe: path difference = (m + ½)·λ

• m = integer order, λ = wavelength (nm or μm).

Height change per fringe (optical flat, laser interferometer) = λ / 2 Displacement = N·λ / 2

• N = number of fringes counted.

Rise per step (autocollimator straightness) = L·θ

• L = reflector base length (mm), θ = tilt (rad).

Ideal turned surface: Rmax = f² / (8·r) ; Ra ≈ f² / (32·r)

• f = feed (mm/rev), r = tool nose radius (mm). Geometric, ignores built-up edge and vibration.

Worked examples

Example 1 (standard): Ra and Rq from a profile. Given: six equally spaced ordinates from an arbitrary datum, h = 12, 8, 15, 6, 10, 9 μm.

1. Mean line: ȳ = (12 + 8 + 15 + 6 + 10 + 9)/6 = 60/6 = 10 μm.
2. Deviations yᵢ = hᵢ − 10: +2, −2, +5, −4, 0, −1 μm.
3. Ra = (2 + 2 + 5 + 4 + 0 + 1)/6 = 14/6 = 2.33 μm.
4. Rq = √((4 + 4 + 25 + 16 + 0 + 1)/6) = √(50/6) = √8.333 = 2.89 μm.

Example 2 (GATE level): optical flat and laser interferometer. (a) A lapped face viewed under an optical flat with helium light (λ = 0.5876 μm) shows fringes curved by 4 fringe spacings across the face.

1. Height change per fringe = λ/2 = 0.5876/2 = 0.2938 μm.
2. Flatness error = 4 × 0.2938 = 1.175 μm. (b) A He-Ne laser interferometer (λ = 632.8 nm) counts 1000 fringes as the CNC table moves.
3. Displacement = N·λ/2 = 1000 × 632.8 × 10⁻⁶ mm / 2.
4. Displacement = 0.3164 mm.

Example 3 (link to machining). Turning with feed f = 0.2 mm/rev and nose radius r = 0.8 mm.

1. Rmax = f²/(8r) = 0.04/6.4 = 0.00625 mm = 6.25 μm.
2. Ra ≈ f²/(32r) = 0.04/25.6 = 0.00156 mm ≈ 1.56 μm. Halving the feed cuts both by a factor of four.

Common mistakes

• Taking absolute values of ordinates that are not measured from the mean line. Find the mean line first.
• Using λ instead of λ/2 per fringe for an optical flat or a reflecting interferometer.
• Treating Ra as a complete description; two surfaces with equal Ra can behave very differently in wear and sealing.
• Choosing a cut-off length that is too short, which filters out real roughness wavelengths and under-reports Ra.
• Confusing roughness with waviness, or lay with the direction of measurement (measure across the lay).
• Doing practical machining tests before the geometric alignment tests.

For GATE ME

Expect Ra or Rq from a set of ordinates or a simple triangular profile, peak-to-valley height from feed and nose radius, fringe counting with optical flats (height = n·λ/2), and conceptual MCQs on roughness, waviness, lay, cut-off length, and which instrument suits which alignment test. Practise finding the mean line before averaging.

Quick check

1. Which texture component comes from machine vibration rather than the tool mark?
2. An optical flat on a surface shows 3 fringes of curvature in sodium light (λ = 0.589 μm). What is the flatness error?
3. Ordinates about the mean line are +3, −1, −2 μm. What is Ra?
4. What is the usual default roughness cut-off length?
5. Why is a test mandrel used in a spindle alignment test?

Answers: 1. Waviness. 2. 3 × 0.2945 ≈ 0.88 μm. 3. 2 μm. 4. 0.8 mm. 5. It extends the spindle axis so runout and parallelism can be measured with a dial indicator along its length.