Theoretical Turning Roughness
Calculate the theoretical mean roughness (Ra) generated in turning, Ra ≈ (f² ÷ (32·r_ε))·1000, from the feed f (mm/rev) and the tool nose radius r_ε (mm); the result is in micrometres (μm). In turning, the round-nosed tool leaves, each revolution, small crests and valleys — the feed advances the tool, and the nose radius 'copies' its profile onto the surface, creating a geometric roughness of microscopic threads. This formula predicts the IDEAL (theoretical) roughness from this geometry alone. The result reveals the two classic ways to improve turning finish: REDUCE the feed (Ra falls with f² — halving feed improves roughness fourfold) or INCREASE the tool nose radius (Ra is inversely proportional to r_ε). That is why finishing passes use small feeds and more rounded tools. REAL roughness is always worse than theoretical, due to vibration, built-up edge, tool wear and material deformation; but the theoretical is the lower bound and the starting point to pick finishing parameters. Enter the feed and the tool nose radius.
Resultado
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Rugosidade teórica de torneamento
A rugosidade média teórica (Ra) gerada no torneamento é Ra ≈ (f² ÷ (32·r_ε))·1000, a partir do avanço f e do raio de ponta da ferramenta r_ε; o resultado é em micrômetros (μm). No torneamento, a ferramenta com seu raio de ponta arredondado deixa, a cada volta da peça, pequenas cristas e vales — o avanço faz a ferramenta progredir, e o raio de ponta 'copia' seu perfil na superfície, gerando uma rugosidade geométrica em forma de roscas microscópicas. Esta fórmula prevê a rugosidade ideal (teórica) decorrente apenas dessa geometria. O resultado revela os dois caminhos clássicos para melhorar o acabamento: reduzir o avanço (Ra cai com o quadrado de f — reduzir o avanço pela metade melhora a rugosidade em quatro vezes) ou aumentar o raio de ponta da ferramenta (Ra é inversamente proporcional a r_ε). É por isso que as passadas de acabamento usam avanços pequenos e ferramentas de ponta mais arredondada. A rugosidade real é sempre pior que a teórica, por causa de vibração, aresta postiça, desgaste da ferramenta e deformação do material; mas a teórica é o limite inferior alcançável e o ponto de partida para escolher os parâmetros de acabamento que atendam à rugosidade especificada no desenho. Informe o avanço e o raio de ponta da ferramenta.
Related Tools
Turning Time
Calculate the cutting time of one turning pass, t = L ÷ (f·n), from the length to machine L (mm), the feed f (mm/rev) and the rotation n (rpm). The product f·n is the tool feed rate (mm/min); dividing the length by it gives the pass time. This is the PRODUCTIVE cutting time of a longitudinal turning operation (the tool traversing the part length), and the basis of total fabrication time and thus machining cost and production planning. Total time also includes non-productive times (tool approach and retract, part change, measuring, tool change) and the number of passes needed (depending on material to remove and depth per pass). Cutting time — by raising feed and rotation (and thus cutting speed) — is the path to productivity, always within tool life, machine power and required finish limits. This is essential to quote machined parts and size a machine shop's capacity. Enter the length, feed and rotation.
Machining Cutting Speed
Calculate the machining cutting speed, Vc = (π·D·n) ÷ 1000, from the diameter D (mm — of the workpiece in turning or the tool in milling) and the rotation n (rpm). The result, in m/min, is the relative tangential speed between the cutting edge and the workpiece — the MOST important machining parameter, governing cutting temperature, tool wear, finish and productivity. Each workpiece-tool material combination has an optimal cutting-speed range recommended by makers: too high overheats and wears the tool fast (shortening life per Taylor's equation); too low cuts productivity and can cause built-up edge (BUE) and poor finish. Cutting speed is the starting point of any machining plan: from it and the diameter, the machine rpm is computed; it depends on material (steel, aluminum, titanium have very different ranges), tool material (HSS, carbide, ceramic) and operation. Enter the diameter and the rotation.
Material Removal Rate (Turning)
Calculate the material removal rate (MRR) in turning, Q = Vc·a_p·f, from the cutting speed Vc (m/min), the depth of cut a_p (mm) and the feed f (mm/rev). The result, in cm³/min, is the material volume removed per unit time — the direct measure of machining PRODUCTIVITY. Maximizing MRR (cutting fabrication time and cost per part) is the core goal in roughing, achieved by increasing any of the three factors: cutting speed, depth or feed. But there are limits and trade-offs: higher speed shortens tool life (Taylor); higher depth and feed raise the cutting force and power required (which may exceed machine capacity or cause chatter) and worsen finish. So the typical strategy uses high MRR in ROUGHING (productivity) and low in FINISHING (precision and roughness). MRR times the material's specific cutting energy gives the required power. Enter the cutting speed, depth of cut and feed.
Cutting Force by the Kienzle Equation
Computes the main cutting force with the Kienzle equation, F_c = k_c1.1 · b · h^(1 − m_c), where k_c1.1 is the tabulated specific cutting force of the workpiece material for a reference chip section of 1 mm × 1 mm, b is the chip width and h the chip thickness, and m_c is the exponent describing the size effect. That is exactly where it differs from the direct calculation F_c = k_s·b·h: the latter treats specific pressure as a material constant, while Kienzle embeds the experimental fact that thin chips cost far more force per unit area, because the cutting edge radius stops being negligible next to the chip thickness. With k_c1.1 = 1500 N/mm² and m_c = 0.26, a 0.2 mm thick chip works at 2279 N/mm², 52 % above the tabulated value — which is why very low feeds raise the power spent per cubic millimetre removed, and the tool wear with it, instead of saving them — even though the absolute force falls. Since k_c1.1 carries a hidden millimetre raised to m_c, the equation is not dimensionally pure: thickness and width have to be entered in millimetres, and switching units is off by orders of magnitude. Enter the specific force k_c1.1, the exponent m_c, the chip width and the chip thickness.
Feed per Tooth (Milling)
Calculate the feed per tooth in milling, f_z = v_f ÷ (z·n), from the table feed rate v_f (mm/min), the number of cutter teeth (cutting edges) z and the rotation n (rpm). Feed per tooth is the material thickness EACH cutter tooth removes per pass through the part, and it directly controls chip thickness, the load on each edge and thus tool life and finish. Makers specify a recommended feed per tooth for each tool-material pair: too HIGH overloads and chips the teeth (chip too thick); too LOW makes the edge rub instead of cut, causing friction, heat and premature wear, plus low productivity. The relation shows how the table feed rate (programmed by the operator) connects to feed per tooth (the cutting physics): v_f = f_z·z·n. So cutters with more teeth allow higher feed rates at the same feed per tooth — the basis of high-productivity milling. Enter the feed rate, the number of teeth and the rotation.
Mean Friction Radius (Clutch)
Calculate the mean friction radius of a disc clutch or brake by uniform-wear theory, r_m = (D + d) ÷ 4, from the outer D and inner d diameters (m) of the friction annulus. The mean radius is the EFFECTIVE radius at which the resultant friction force is taken to act for torque calculation (T = μ·F·N·r_m). There are two classic assumptions for this radius: UNIFORM WEAR (assuming the disc has 'bedded in' and wears evenly, concentrating pressure at the inner radius; gives r_m = (D+d)/4, the simple mean of radii) and UNIFORM PRESSURE (new disc, constant pressure; gives r_m = (2/3)·(D³−d³)/(D²−d²), slightly larger). Uniform wear is most used in DESIGN, being conservative (slightly lower torque) and representing the run-in steady state. The mean radius shows an interesting design point: discs with a narrow friction annulus (D close to d, thin ring at large radius) have a high mean radius, transmitting more torque per unit force — so high-performance disc brakes use calipers acting near the disc edge (large radius). Enter the outer and inner diameters.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.