Cutting force, power and machining time by Kienzle
Calculate the cutting force Fc, the specific cutting force kc, the cutting power Pc and the machining time when turning, using the Kienzle model. Pick a material or enter kc1.1 and mc directly, provide the uncut chip width and thickness directly or derive them from depth of cut, feed and lead angle – live with every keystroke.
Cutting Force & Power (Kienzle)
Model: cutting force by Kienzle (straight main cutting edge, approximation) without correction factors for rake angle, wear and chip compression. Real forces are typically 20 to 50 % higher due to wear; kc1.1 and mc scatter between sources and batches. For kinematics, material removal rate and guideline values per operation use the cutting-data calculator.
Results
Calculating …
Formulas and fundamentals
The basis is the Kienzle model (Kienzle/Victor, VDI-Z 94, 1952): the specific cutting force kc follows a power law of the uncut chip thickness h, kc = kc1.1·h^(−mc). Here kc1.1 is the main value of the specific cutting force (referred to b = 1 mm, h = 1 mm) and mc is the slope of the line kc(h) on a log-log scale. The cutting force follows from the uncut chip section A = b·h as Fc = b·h·kc = kc1.1·b·h^(1−mc).
The chip dimensions follow from the kinematics: the uncut chip thickness is h = f·sin κ, the width b = ap/sin κ, with feed f, depth of cut ap and lead angle κ. Their product b·h = ap·f (the uncut chip section) is independent of κ – the lead angle only redistributes the same section between width and thickness and influences the specific cutting force through h.
The cutting power is Pc = Fc·vc; with vc in m/min and Fc in N, Pc = Fc·vc/60000 gives the power in kW. The required drive power of the machine is P_M = Pc/η with the efficiency η. The machining time for longitudinal turning is t_h = (l + approach + overtravel)·i/(n·f) with spindle speed n, feed f, workpiece length l and number of cuts i.
Worked example
For 16MnCr5 the Kienzle parameters are kc1.1 = 2020 N/mm² and mc = 0.17. With an uncut chip width b = 3 mm and thickness h = 0.2 mm this gives kc = 2020·0.2^(−0.17) = 2655.7 N/mm².
The cutting force is Fc = b·h·kc = 3·0.2·2655.7 = 1593.4 N. The check via Fc = kc1.1·b·h^(1−mc) = 2020·3·0.2^0.83 yields the same value.
At a cutting speed vc = 200 m/min the cutting power is Pc = 1593.4·200/60000 = 5.31 kW. With an efficiency η = 0.8 the spindle must deliver P_M = 5.31/0.8 = 6.64 kW.
Frequently asked questions
What do kc1.1 and mc mean?
kc1.1 is the main value of the specific cutting force, referred to an uncut chip section of b = 1 mm and h = 1 mm. mc is the slope of the line kc(h) on a log-log scale. Both are material dependent and scatter by roughly 10 to 20 percent between sources and batches. A direct kc1.1 comparison between materials is not valid because mc differs.
Why does the specific cutting force drop with larger chip thickness?
Because for a thin chip the cutting-edge rounding, friction and chip compression carry relatively more weight (size effect). Through kc = kc1.1·h^(−mc), kc decreases as h grows – cutting becomes specifically more efficient. The total cutting force Fc still rises with h, because the section A = b·h grows over-proportionally.
What role does the lead angle κ play?
κ distributes the fixed uncut chip section A = ap·f over the width b = ap/sin κ and the thickness h = f·sin κ. A smaller κ makes the chip thinner and wider, slightly lowers the specific cutting force through h, but lengthens the engaged cutting edge. The effect on Fc is weak; the influence on passive force and tool life, which this calculator does not cover, is more pronounced.
How accurate are the calculated forces?
This is a design approximation for the straight main cutting edge without correction factors for rake angle, tool wear, cutting speed and chip compression. Real forces are typically 20 to 50 percent higher due to wear. A margin should therefore be allowed for drive sizing.
How does this differ from the cutting-data calculator?
This calculator focuses on cutting force and power by Kienzle plus the machining time for turning. The cutting-data calculator additionally covers turning, milling and drilling with speed, feed and material-removal-rate calculation as well as guideline ranges per material group. Both use the same Kienzle model.
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