Surface finish
How to use the roughness calculator
The calculator operates in two modes. In the “Ra / Rz from feed” mode, specify the process, insert nose radius (rε), feed (f) and coefficient k - get the calculated roughness Ra and Rz. In the “Feed from Ra” mode, specify the target Ra - the calculator will calculate the maximum allowable feed. A visual scale shows which zone the result is in.
Why is roughness determined by feed and radius?
When turning, the cutting edge leaves microridges on the surface - their height (h) depends on two parameters: feed per revolution (f) and the radius at the tip of the insert (rε). Formula: h = f² / (8·rε). This is a geometric dependence - it always works, regardless of the material and speed.
The actual roughness Ra is obtained by multiplying the theoretical ridge height by a factor k (usually 0.25–0.35 for good conditions). This coefficient takes into account everything that degrades the surface beyond the geometry: vibrations, edge wear, built-up edge (BUE), feed instability. The worse the conditions, the higher k, the rougher the surface under the same conditions.
What affects roughness
Feed (f).Main lever. Roughness is proportional to the square of the feed: if f was reduced by half, Ra decreased by four times. Typical range for fine turning: 0.05–0.20 mm/rev. Below 0.04 mm/rev, “rubbing” begins - the tool does not cut, but rubs, and the surface deteriorates.
Nose radius (rε). A larger radius gives a smoother surface at the same feed. A plate with rε = 1.2 mm at f = 0.15 mm/rev will give Ra approximately half as low as a plate with rε = 0.4 mm. But a large radius increases cutting forces and the tendency to vibration - balance is needed.
K-factor: 0.25–0.35 is typical for a new tool with good clamping. As the edge wears, k increases to 0.4–0.6. During vibrations, k can exceed 0.6 - in this case, the formula underestimates the real roughness. If Ra on a part is significantly worse than calculated, look for vibrations or wear.
Machining process: The formula is accurate for fine turning. For milling and grinding, the calculator gives an estimate - the actual result depends on runout, number of teeth, processing strategy and abrasive grain. For these processes, use the calculator as a guide rather than as an accurate prediction.
Cutting speed (Vc). It is not directly included in the formula, but it affects through k: if Vc is too low, a built-up edge (BUE) is formed, which spoils the surface. At optimal Vc the surface is smooth. If it is too high, accelerated edge wear increases k over time.
Frequently Asked Questions
How are Ra and Rz related? Approximate relationship: Rz ≈ 4–6 × Ra. The calculator uses Rz ≈ 5.5 × Ra - this is the average value for turning. For grinding the ratio is closer to 4, for rough operations - to 6–7. If Rz is indicated on the drawing, and you are used to working with Ra, divide Rz by 5.5 to estimate.
Which Ra corresponds to which cleanliness class? Compliance (GOST / ISO): Ra 12.5 = N10, Ra 6.3 = N9, Ra 3.2 = N8, Ra 1.6 = N7, Ra 0.8 = N6, Ra 0.4 = N5. Soviet cleanliness classes (∇): 4th class ≈ Ra 12.5, 5th class ≈ Ra 6.3, 6th class ≈ Ra 3.2, 7th class ≈ Ra 1.6. The calculator shows Ra - convert to classes using this table.
Why is the real roughness worse than the calculated one? Three reasons: 1) Vibrations - even imperceptible ones, they leave marks on the surface and increase k. 2) Edge Wear – A worn edge “smudges” instead of cutting. 3) Built-up edge (BUE) - at low speed on stainless steel and aluminum, the material sticks to the edge and tears out fragments of the surface.
At what feed rate is Ra 1.6 µm achieved? Depends on rε and k. For a typical insert with rε = 0.8 mm and k = 0.32: f ≈ 0.10 mm/rev. For rε = 0.4 mm you need f ≈ 0.07 mm/rev. The calculator in the “Feed from Ra” mode will calculate the exact value for your parameters.
Is it possible to obtain Ra 0.4 μm by turning? Theoretically, yes, with a very low feed (f ≈ 0.03–0.04 mm/rev) and large rε (1.2+ mm) with wiper geometry. In practice, this is the limit of turning capabilities. Needed: ideal system rigidity, new tools, absence of vibrations and BUE. For a stable Ra 0.4, grinding or superfinishing is usually used.
Need help selecting a finishing insert or achieving the desired finish? Contact our specialists - we will select the geometry and modes to suit your tolerance.