Processable Surface Formula for Smooth Finish

• 1
  The processable surface formula for smooth finish, term by term
• 2
  Which inputs move Ra, and which ones barely matter
• 3
  How material sets the ceiling on a smooth finish
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  Feature geometry decides whether the finish is even possible
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  How to check the finish before the parts ship
• 6
  Realistic Ra by material and operation

Every milling cut leaves a row of scallops. The peaks come from the tool tip, the valleys from the step between passes. The processable surface formula for smooth finish predicts the height of those scallops from three numbers you already control: feed per tooth, tool corner radius, and the stepover between passes.

For a ball or bull nose tool the theoretical peak-to-valley height is fz² / (8 × r), where fz is feed per tooth in mm and r is the corner radius in mm. A 6 mm radius cutter at 0.10 mm per tooth gives 0.0001 / 0.048 = about 2.1 μm. That is the floor. Nothing on the machine can beat it at those settings.

Turn the formula around and it becomes a design tool. If the print calls for Ra 0.8 μm, the cutter radius has to be large enough, or the feed per tooth small enough, that the scallop height stays under roughly half of that value. Half is a practical margin, because tool wear, vibration, and built-up edge all add roughness on top of the theoretical number.

The same arithmetic applies to turning, with feed per revolution in place of feed per tooth and the tool nose radius in place of the corner radius. The formula is the same shape. Only the units change.

What the formula does not include is deflection, chatter, and material smearing. Those are real, and on thin walls they can double the measured Ra. Treat the number as the best case your geometry allows, then check it against the cut.

Feed per tooth is the strongest lever. Halve it and the scallop height drops by a factor of four, because the term is squared. That is why finishing passes run slow and shallow. It is also why a light finishing pass after a heavy roughing pass does more for finish than any change in spindle speed.

Corner radius is the second lever, and it moves linearly. Going from a 0.4 mm corner to a 6 mm corner is a fifteen-fold reduction in scallop height at the same feed. The trade is reach. A large radius tool cannot get into a tight internal corner, so the corner either needs a smaller tool or a different strategy such as a trochoidal path.

Cutting speed matters far less than most people assume, as long as you stay inside the window for the material. Run too slow in aluminium and you get built-up edge, which tears the surface and adds roughness you cannot calculate. Run too fast in titanium and the tool edge breaks down, which does the same thing from the other direction.

Depth of cut barely touches Ra in finishing, but it does change cutting forces. A 0.2 mm finishing pass deflects the tool and the part less than a 1 mm pass, so the wall stays straighter and the finish stays even along the length of the cut.

Coolant choice is not in the formula, but it shows up in the result. Misting aluminium with the wrong fluid leaves residue that reads as roughness on a profilometer. Flood coolant on deep pockets is easier to control.

Aluminium 6061 and 7075 machine to Ra 0.4–0.8 μm without much effort. The chips clear well, the material cuts cleanly, and a sharp carbide tool with polished flutes will hold that finish across a long run. Free-machining grades are not always better here; some contain inclusions that tear the surface.

Stainless 304 and 316 work-harden at the cut. If the tool rubs instead of shearing, the surface hardens a few micrometres deep and the next pass cuts into harder metal. The fix is a positive rake tool, constant feed, and never letting the cutter dwell in the cut. Done right, 316L holds Ra 0.8 μm. Done wrong, it tears.

Titanium Ti-6Al-4V and Inconel sit at the other end. Both hold heat at the cutting edge, and both are chemically reactive at temperature. A sharp edge and a generous flow of high-pressure coolant are not optional. Expect Ra 0.8–1.6 μm as a realistic production target, with 0.4 μm only on short, well-supported features.

Plastics behave differently again. POM and PEEK cut cleanly with sharp, high-rake tools. ABS and PC soften with heat and smear, so a light finishing pass with air blast beats a heavy cut with coolant.

Hardened tool steel above 45 HRC needs a different plan. Cut it with carbide at the hardness it is, or finish it soft and then heat treat. Grinding after hardening is often the only route to Ra 0.4 μm on a hardened feature.

A flat face is easy. The tool runs a constant stepover across the surface, and the scallop pattern stays uniform from edge to edge. Any Ra you can reach on a test coupon, you can reach on a flat face.

A deep pocket with a 3:1 depth-to-width ratio is harder. The tool has to reach the floor with a long, thin shank, and that shank deflects under load. The finish at the top of the wall will not match the finish at the bottom. Splitting the pocket into a roughing cycle and a light finishing cycle with a stubby tool helps, but it costs setup time.

Internal corners are the classic problem. A 6 mm radius cutter cannot leave a sharp internal corner, and no amount of polishing will fix a corner that was never cut. Either the drawing calls for a corner radius the tool can produce, or the operation moves to EDM or to a smaller cutter with a slower stepover.

Thin walls below 1 mm move under cutting force. The wall springs away from the tool, the effective depth of cut drops, and the surface shows chatter marks. Support the wall with fixturing or leave material and take it off in two light passes.

Features that need Ra 0.4 μm or better over a large area are usually a sign the drawing should specify a ground or lapped surface, not a milled one. We flag that during DFM review rather than at final inspection.

The theoretical formula gives you a target. Measurement tells you whether you hit it. On the shop floor we compare a machined surface to a certified roughness comparator, and we confirm with a profilometer on the features the drawing actually calls out.

Where you measure matters. Ra on a curved surface reads differently from Ra on a flat one, and Ra across the feed direction differs from Ra along it. The drawing should say which direction and which feature, or the inspection report will not match what the customer expected.

Cutting parameters drift over a run. A tool that starts at Ra 0.4 μm may be at Ra 0.8 μm after two hours of aluminium. We monitor in process and change the insert on a count or a finish trigger, not on a fixed schedule.

For parts that go into medical or automotive assemblies, the finish callout is often tied to a function: seal face, bearing bore, sliding surface. Those features get measured 100 percent. Cosmetic surfaces get a visual standard agreed with the customer.

GreatLight holds ISO 9001:2015, IATF 16949:2016, ISO 13485:2016 and ISO 27001:2022, and inspection reports are available on request with every shipment.