Turning calculator

Enter the diameter and the cutting speed (or spindle speed); spindle speed, feed speed, removal rate and cutting time follow at once. Add the material’s Kienzle constants and force, power and torque are computed too.

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Diameter D mm

Which one is known? vc n

Cutting speed vc m/minSpindle speed n rpm

Feed f mm/revDepth of cut ap mm

Cut length L mmEntering angle κr °

Specific cutting force kc1.1 N/mm²Kienzle exponent mc

Take kc1.1 and mc from the material page or the tool maker’s catalogue. For orientation: unalloyed and low-alloy steels run about 1500–2100 N/mm² with mc around 0.2–0.3.

Kinematics

—m/minCutting speed vc

—rpmSpindle speed n

—mm/minFeed speed vf

—cm³/minRemoval rate Q

—minCutting time tc

—mmChip thickness h

Force and power (Kienzle)

—N/mm²Specific cutting force kc

—NCutting force Fc

—kWCutting power Pc

—N·mCutting torque Mc

Formulae

v_{c} = \frac{π \cdot D \cdot n}{1000}

n = \frac{v_{c} \cdot 1000}{π \cdot D}

v_{f} = f \cdot n

Q = v_{c} \cdot a_{p} \cdot f

t_{c} = \frac{L}{f \cdot n}

h = f \cdot \sin κ_{r}

k_{c} = k_{c 1.1} \cdot h^{- m_{c}}

F_{c} = k_{c} \cdot a_{p} \cdot f

P_{c} = \frac{F_{c} \cdot v_{c}}{60000}

M_{c} = \frac{F_{c} \cdot D}{2000}

Units: D mm, n rpm, vc m/min, f mm/rev, ap mm, L mm, kc N/mm², Fc N, Pc kW, Mc N·m.

Notes

vc is the speed at the uncut diameter D; at the machined diameter D − 2ap it is proportionally lower. In facing the diameter changes continuously, which is why constant surface speed (G96) exists.
Pc is the net cutting power. For the machine motor divide by the spindle efficiency (typically 0.7–0.9) and check the power curve against the spindle speed in the machine catalogue.
The Kienzle model rests on the chip thickness h = f·sin κr; at very small h (below about 0.05 mm) edge rounding makes the model drift.
Cutting time covers chip removal only; approach, overrun, rapid moves and tool changes are not included.

Sources (3)

Sandvik Coromant — General turning formulas and definitions
O. Kienzle, Die Bestimmung von Kräften und Leistungen an spanenden Werkzeugen und Werkzeugmaschinen, VDI-Z 94 (1952)
Machinery’s Handbook, 31st ed., Industrial Press — Speeds and feeds, cutting power