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.
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Feed per Tooth (Milling)
In milling, the feed per tooth is f_z = v_f ÷ (z·n), computed from the table feed rate v_f, the number of teeth (cutting edges) on the cutter z and the spindle speed n. Feed per tooth is the thickness of material each tooth of the cutter removes on every pass through the workpiece, and it is the parameter that directly governs chip thickness, the load carried by each edge and, through them, tool life and surface finish. Tooling manufacturers publish a recommended feed per tooth for every cutter-material combination: a value that is too high overloads and chips the teeth (the chip comes out too thick); one that is too low makes the edge rub instead of cut, generating friction, heat and premature wear on top of poor productivity. The relationship also shows how the table feed rate the operator programs into the machine ties back to the feed per tooth that sets the physics of the cut: v_f = f_z·z·n. That is why cutters with more teeth can run at a higher feed rate while holding the same feed per tooth — the basis of high-productivity milling, where cutters carrying many inserts advance fast without overloading any single edge. Enter the feed rate, the number of teeth and the spindle speed.
Related Tools
Chip Thinning Corrected Feed per Tooth (Milling)
Computes the feed per tooth corrected for radial chip thinning in milling, f_z,corr = f_z / sin(φ_max), where sin(φ_max) = √(1 − (1 − 2·a_e/D)²) as long as the radial depth of cut a_e is less than half the cutter diameter D, and equals 1 above that. When the cutter engages little material sideways, each tooth enters and leaves the cut before reaching the point of maximum thickness, and the chip actually formed is THINNER than the programmed feed — the edge starts rubbing instead of cutting, generates heat, work-hardens the surface and wears fast, which is why light finishing passes often destroy tools quicker than heavy roughing. Correcting the feed restores the catalogue chip thickness: with a 12 mm cutter engaging only 1.2 mm, or 10 % of the diameter, the feed must rise 67 % for the tooth to cut at the intended thickness. Above half the diameter there is no thinning and the correction is neutral. Enter the target feed per tooth, the cutter diameter and the radial depth of cut.
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.
Equivalent Chip Thickness (Grinding)
Computes the equivalent chip thickness in grinding, h_eq = a_e × v_w ÷ v_s, that is, the depth of cut times the workpiece speed divided by the wheel peripheral speed, with the m/min to m/s conversion built in and the answer given in micrometres. It is the thickness of the continuous layer that would be removed if the wheel cut like a single-point tool running at the same speed, so it condenses the aggressiveness of the whole cycle into one number. A high value means more material per grain, more tangential force and more risk of burn; a low value means fine finish but also more rubbing and faster wheel wear. Enter the depth of cut, the workpiece speed and the wheel speed.
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.
Chip Shear Angle
Calculate the shear-plane angle in chip formation, φ = arctan[(r_c·cos α) ÷ (1 − r_c·sin α)], from the cutting ratio r_c (undeformed chip thickness ÷ deformed chip thickness, always < 1) and the tool rake angle α (degrees). In the orthogonal cutting model (the basis of machining theory), material is not 'scraped': it undergoes intense SHEAR deformation along an inclined plane — the shear plane — where it turns from part to chip almost instantly. That plane's angle, φ, is a central measure of cutting mechanics: LARGER shear angles mean thinner chips, less deformation, lower cutting force and energy and less heat — all desirable. The angle depends on the cutting ratio (measured by comparing chip thickness to feed) and the tool rake angle: tools with more positive rake give larger shear angles and cut with less effort (but have a more fragile edge). Merchant's theory relates φ to chip-tool friction and rake angle, and predicts the angle that minimizes energy. From chip measurements, this calculation lets you analyze cutting efficiency and the influence of tool geometry and lubrication. Enter the cutting ratio and the rake angle.
Lead Screw Lead
Compute the lead of a ball screw or power screw, Lead = pitch · number of starts, the linear distance the nut travels per full turn of the screw. On a single-start screw the lead equals the pitch; with multiple starts the lead increases proportionally, allowing more linear speed at the same rotation. The basis of rotation-to-displacement conversion in CNC and linear actuators. Enter the pitch and the number of starts.
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