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.
Result
—
Equivalent Chip Thickness in Grinding (h_eq)
Anyone setting up a grinding cycle has three knobs pulling on the same problem: depth of cut, workpiece speed and wheel speed. Changing one of them rarely answers the question that matters — did the cycle get more aggressive or less? Equivalent chip thickness folds all three into a single number, the one a process engineer compares when switching wheels, moving from roughing to finishing, or investigating burn marks on a part. Two different machines running the same h_eq load every abrasive grain the same way.
The arithmetic is h_eq = a_e × v_w ÷ v_s: depth of cut times the ratio of workpiece speed to wheel peripheral speed. Because v_w goes in as m/min and v_s as m/s, the page divides v_w by 60 first and reports the answer in micrometres. With the default values — a_e of 0.02 mm, v_w of 15 m/min and v_s of 30 m/s — the result is 0.1667 µm. One check closes from outside the formula: specific removal rate equals both a_e × v_w (0.02 mm × 250 mm/s = 5 mm²/s) and h_eq × v_s (1.667e-4 mm × 30,000 mm/s = 5 mm²/s). Finishing sits in tenths of a micrometre; roughing runs above 1 µm.
h_eq treats the wheel as a single-point tool, and that is exactly where the model goes quiet. It knows nothing about grain density, grain protrusion, dressing condition or how blunt the wheel already got: two wheels at the same h_eq deliver very different roughness and forces. It also ignores contact length, which governs how much heat enters the part — conventional plunge grinding and creep-feed reach the same h_eq in opposite thermal regimes. Use the number to compare similar cycles, not to predict burn; that needs specific energy, coolant delivery and contact arc. The page returns h_eq alone, with no power and no temperature estimate.
Frequently asked questions
What is a typical equivalent chip thickness?
Does a high h_eq mean the part will burn?
Does the tool also give the specific removal rate?
Related Tools
Contact Length in Cylindrical Grinding
Computes the geometric contact arc length between wheel and workpiece in cylindrical grinding, l_c = √(a_e × d_e), where d_e = d_s × d_w ÷ (d_s + d_w) is the equivalent diameter that replaces the two real diameters with a single one. It is the stretch over which each abrasive grain stays cutting, and it governs how much heat enters the part: at constant work speed, doubling the contact length doubles how long the same area is exposed to the grinding zone. In external grinding the two diameters add up in the denominator and the contact shortens, whereas in surface grinding the part is flat and the contact tends to √(a_e × d_s), the largest value this formula reaches. Enter the depth of cut, the wheel diameter and the workpiece diameter.
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.
Equivalent Flow (PCE)
Calculate the equivalent flow in passenger car equivalents (PCE), q = Q_cars + Q_heavy × E, adding the car flow to the heavy-vehicle flow multiplied by the equivalence factor E (how many passenger cars each truck or bus equals in road occupancy — typically 1.5 to 3.0). The result, in PCE/h, converts a mixed traffic stream into an equivalent homogeneous one, allowing volumes to be compared and the capacity of roads with different traffic compositions to be computed. Heavy vehicles occupy more space and accelerate more slowly, especially on grades. Enter the car flow, the heavy-vehicle flow and the equivalence factor.
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.
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.
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.