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.
Result
—
Kienzle Equation for Cutting Force in Machining
The main cutting force closes three process calculations: the power the spindle has to deliver, the reaction the fixture has to hold, and the deflection a slender part will suffer. Machining programmers usually estimate it by multiplying a specific pressure by the chip area, and that estimate goes wrong at fine feeds — exactly the condition you end up in when the surface finish requirement tightens. The Kienzle equation fixes that by building the chip size effect into the exponent.
The form is F_c = k_c1.1 · b · h^(1 − m_c). The k_c1.1 term is the tabulated specific cutting force of the material, measured on a chip section of 1 mm by 1 mm; b is the chip width and h the chip thickness; m_c measures how much specific pressure climbs as the chip thins, because the edge radius stops being negligible next to h. With the defaults, k_c1.1 = 1500 N/mm², m_c = 0.26, b = 3 mm and h = 0.2 mm, 0.2^0.74 gives 0.3039, and F_c = 1500 × 3 × 0.3039 = 1367.6 N. Divide by the chip area, 0.6 mm², and the effective pressure reads 2279 N/mm², 52 % above the tabulated value. Test the definition: at h = 1 mm the output has to be 4500.0 N for any m_c, since 1 raised to anything equals 1.
The equation is dimensionally impure: k_c1.1 hides a millimetre raised to m_c inside it, so b and h have to be entered in millimetres, no exceptions. Tabulated k_c1.1 and m_c pairs hold for test conditions — sharp tool, rake angle near 6°, a narrow speed band — and shop practice still multiplies the result by corrections for rake, flank wear, cutting speed and chip form, together worth 30 to 50 %, which appear nowhere on this page. The power law also blows up as h approaches zero: below roughly the edge radius the tool ploughs instead of cutting and the model loses meaning. And the output covers the main component only: no feed force, no passive force, no power.
Frequently asked questions
How do I turn feed and depth of cut into b and h?
Does the tool give the cutting power?
Where do I find k_c1.1 and m_c for my material?
Related Tools
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 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.
Machining Cutting Power
Calculate the cutting power in machining, P_c = (F_c·Vc) ÷ 60000, from the main cutting force F_c (N) and the cutting speed Vc (m/min); the result is in kW (60000 converts N·m/min to kW). Cutting power is the mechanical power the operation consumes to remove material, decisive for machine selection: the spindle motor must supply this power (plus losses, dividing by drive efficiency, typically 0.7-0.9) without stalling in the cut. If the required power exceeds the available, the machine loses speed, the cut jams or the tool breaks — so heavy roughing needs robust machines. Cutting power also relates to MRR by the specific cutting energy (P_c = u·Q, where u is energy per unit volume removed) — a practical alternative to estimate it directly from removed volume. Computing power is essential for planning (choosing the right machine), optimizing parameters (extracting the most from available power) and estimating energy use and heating. Enter the cutting force and the cutting speed.
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.
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.
Machining Cutting Force
Calculate the main cutting force in machining, F_c = k_s·a_p·f, from the specific cutting pressure k_s (N/mm², a workpiece-material property) and the cut section area (depth a_p × feed f, both mm). Cutting force is the main component of the force the tool exerts on the part (along the cutting-speed direction), and it sets the POWER required, the loads on the tool, holder, spindle and machine structure, and the part deflection. The specific cutting pressure k_s is the force per unit chip-section area, varying with material (steels ~1500-3000 N/mm², aluminum ~500-900, titanium and stainless much more), with feed (k_s drops at larger feeds — size effect) and with tool geometry. Knowing the cutting force is essential to: size the machine motor power, check that the fixturing (chuck, vise) holds, predict deflection of slender parts (causing dimensional error) and avoid tool breakage. It is a central machining process-planning calculation. Enter the specific cutting pressure, depth of cut and feed.
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.