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.
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Material removal rate (turning)
The material removal rate (MRR) in turning is Q = Vc·a_p·f, from the cutting speed Vc, the depth of cut a_p and the feed f. The result, in cm³/min, is the volume of material the operation removes per unit of time — the direct measure of machining productivity. Maximising the removal rate, which cuts manufacturing time and cost per part, is the central goal in roughing, and it comes from raising any of the three factors: speed, depth or feed. But there are limits and trade-offs: raising the cutting speed shortens tool life (Taylor); raising depth and feed increases the cutting force and power required, which may exceed the machine capacity or trigger vibration — chatter — and worsens the surface finish. The usual strategy therefore applies high removal rates in roughing, favouring productivity, and low ones in finishing, favouring accuracy and roughness. The removal rate, multiplied by the specific cutting energy of the material, gives the required power directly — a practical way to size the machine. Enter the cutting speed, the depth of cut and the feed.
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.
Weld Deposition Rate
Compute a weld's deposition rate by dividing the mass of deposited metal by the arc-on time, giving kg/h. It is a central indicator of process productivity: processes like submerged arc and MIG/MAG have far higher rates than stick electrode. Combined with the operating factor (actual arc time), it estimates a joint's output. Enter the deposited mass and the arc time.
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.
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.
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.
Vasicek Bond Price
Computes the price of a zero-coupon bond with the Vasicek model, the first short-rate interest-rate model with mean reversion. It describes the short rate oscillating around a long-run mean and yields a closed form for the bond price from four parameters: reversion speed, mean, volatility and current rate. Despite allowing negative rates, it's the foundation of the whole family of term-structure models. Enter the parameters and the maturity, and see the price and implied yield.
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.