§1What a surface really is
A real surface carries texture at three wavelengths stacked on top of each other, plus its direction and its accidents.
Roughness is the fine, closely spaced texture the cutting process leaves — the tool’s fingerprint. Waviness is the longer-wave undulation from machine vibration, deflection and heat. Lay is the dominant direction of the pattern — along the feed on a turned part, crossed arcs on a milled face, multidirectional on a lapped one. Flaws are the accidents: scratches, pits, tears. Measurement separates roughness from waviness with a wavelength filter (§4), because they come from different causes and cure by different means — a rougher insert is a feed problem; waviness is a machine problem.
Contents§2Ra — the arithmetic average
Draw the mean line through the profile; Ra is the average distance of the surface from it, valleys counted as positively as peaks.
Heights from the mean line: +2, −3, +1, −2, +3, −1, +2, −2 µm. Sum of magnitudes 16, so Ra = 16/8 = 2.0 µm — a healthy general-machining finish. The hero trace above carries the same arithmetic done over 800 samples, its Ra and Rz printed from the computation.
Ra’s virtues are stability and universality — averaging tames measurement noise, and everyone quotes it. Its vice is the averaging itself: §3.
Contents§3Rz and the peaks Ra hides
Rz averages the peak-to-valley height over five sampling lengths — a measure that notices the scratch Ra shrugs off.
Surface A alternates ±2 µm: Ra = 2.0, total height 4 µm. Surface B runs gently at ±1 µm but carries one 6 µm scratch pair per length: Ra = (8×1 + 6 + 6)/10 = 2.0 µm — identical — yet its peak-to-valley is 12 µm, three times A’s. A seal, a plated coat or a fatigue-loaded fillet meets the 12 µm, not the average. Where extremes matter, specify Rz (or Rt, the single worst) alongside Ra; as working texture, Rz commonly runs 4–7 × Ra, and a ratio far outside that band is itself a diagnosis — isolated scratches or tears.
§4Measuring texture
The standard instrument drags a fine diamond stylus across the surface and filters what it feels.
The stylus (tip a few microns) rides the profile; electronics remove the long waves above the cutoff wavelength λc — 0.8 mm is the common default — so that only roughness remains, and evaluate over five cutoffs (a 4 mm traverse) for a stable average. Quoting a roughness number without its cutoff is quoting half a number: a wavy surface can grade “smooth” at a short cutoff and “rough” at a long one. Trace across the lay — the reading along the lay flatters. Non-contact optical instruments map whole areas without touching soft or delicate surfaces; the parameters and cutoffs carry over.
Contents§5Typical roughness by process
| Process | Typical Ra | Process | Typical Ra |
|---|---|---|---|
| Sawing, flame cutting | 12.5 – 25 | Grinding | 0.2 – 1.6 |
| Rough turning / milling | 3.2 – 12.5 | Honing | 0.1 – 0.8 |
| Finish turning / milling | 0.8 – 3.2 | Lapping / polishing | 0.025 – 0.4 |
| Reaming | 0.8 – 3.2 | Die casting / injection moulding | 0.4 – 3.2 (as-formed) |
| Each halving of Ra roughly means another operation or a slower one — the cost curve behind §7’s advice to specify only what the function needs. | |||
§6The N-grade series
The roughness grades N1–N12 are a doubling ladder of Ra values, rounded to preferred numbers — one label per rung.
| Grade | Ra | Grade | Ra |
|---|---|---|---|
| N1 | 0.025 | N7 | 1.6 |
| N2 | 0.05 | N8 | 3.2 |
| N3 | 0.1 | N9 | 6.3 |
| N4 | 0.2 | N10 | 12.5 |
| N5 | 0.4 | N11 | 25 |
| N6 | 0.8 | N12 | 50 |
| Each grade doubles the Ra of the one below, rounded to the preferred-number series — so N7 (1.6 µm) is a typical finish-machined face and N1 (0.025 µm) a lapped one. The grade is shorthand; the Ra value is the requirement. | |||
§7Specifying finish on drawings
The tick symbol carries the whole requirement: the value, and only where the function pays for it.
The basic check-mark on a surface means “machined”; the Ra value (or grade) sits on the symbol’s long arm; a bar across the top means no material removal permitted (an as-cast or as-rolled face must stay); additions call the process, the lay direction and the sampling where they matter. Discipline mirrors dimensioning: a general note (“machined surfaces 3.2 Ra unless stated”) covers the bulk, and explicit ticks mark only the working faces — the bearing seat at 0.4, the seal land at 0.2, the gasket face at 1.6. Every unnecessary 0.4 on a drawing is a grinding operation bought for nothing.
Contents§8Function and finish
Finish is not cosmetics; each function reads the mountain range differently.
Fatigue starts cracks in valleys — smoother fillets live longer, and a ground-then-polished radius on a cycled shaft is cheap life insurance. Sealing needs peaks low enough for the elastomer to follow: dynamic seal lands typically want Ra around 0.2–0.4, and Rz watched, because one scratch is one leak path. Bearings and slides want an apparent paradox: too rough tears the oil film, but a mirror finish holds no oil at all — the classic answer is the plateau surface (honed cylinder bores): flat load-bearing lands with deliberate valleys left as oil reservoirs, a surface two roughness parameters describe better than one. Coating and bonding want controlled roughness as a key. State the function; the number follows.
Contents§9Quick reference
The working core of the page on one card rack.
Ra
mean of |z| from the mean line
the universal number
Rz
mean peak-to-valley, 5 lengths
≈ 4–7 × Ra when healthy
Measurement
stylus · cutoff λc 0.8 mm
trace across the lay
Processes
turn 0.8–3.2 · grind 0.2–1.6
lap 0.025–0.4
Specify
general note + ticks where it pays
halving Ra ≈ one more operation