Milling calculator

When a cutter is only partly engaged, the chip comes out thinner than the feed per tooth. This tool computes the real chip thickness along the engagement arc, finds the feed you need, and takes the power from the mean chip thickness.

Live

Cutter diameter Dc mmEffective teeth zc

Which one is known? vc n

Cutting speed vc m/minSpindle speed n rpm

Feed input fz hex

Feed per tooth fz mmTarget max. chip thickness hex mm

Axial depth ap mmRadial engagement ae mm

Entering angle κr °Cut length L mm

Cutter positionCutting direction

Specific cutting force kc1.1 N/mm²Kienzle exponent mc

Take kc1.1 and mc from the material page or the tool maker’s catalogue. Power is computed from the mean chip thickness hm, as in the Sandvik Coromant method.

Kinematics

—rpmSpindle speed n

—m/minCutting speed vc

—mm/minTable feed vf

—cm³/minRemoval rate Q

—minCutting time tc

—mmFeed per tooth fz

Chip thickness

—°Engagement angle φe

—mmMax. chip thickness hex

—mmMean chip thickness hm

—Chip thinning factor fz / hex

Force and power (Kienzle, at hm)

—N/mm²Specific cutting force kc

—kWCutting power Pc

—N·mTorque Mc

Formulae

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

v_{f} = f_{z} \cdot z_{c} \cdot n

Q = \frac{a_{p} \cdot a_{e} \cdot v_{f}}{1000}

φ_{e} = \arccos (1 - \frac{2 a_{e}}{D_{c}})

h_{e x} = f_{z} \cdot \sin κ_{r} \cdot \sqrt{1 - {(1 - \frac{2 a_{e}}{D_{c}})}^{2}}

h_{m} = f_{z} \cdot \sin κ_{r} \cdot \frac{2 a_{e} / D_{c}}{φ_{e}}

k_{c} = k_{c 1.1} \cdot {h_{m}}^{- m_{c}}

P_{c} = \frac{a_{e} \cdot a_{p} \cdot v_{f} \cdot k_{c}}{60 \cdot 10^{6}}

M_{c} = \frac{P_{c} \cdot 30 \cdot 10^{3}}{π \cdot n}

Side-milling formulae. The hex formula applies for ae < Dc/2; otherwise hex = fz · sin κr. For centred face milling φe = 2 · arcsin(ae/Dc), hex = fz · sin κr and hm = fz · sin κr · (ae/Dc) / arcsin(ae/Dc). Angles in radians. Units: Dc mm, n rpm, vc m/min, fz mm, ap and ae mm, vf mm/min, Q cm³/min, kc N/mm², Pc kW, Mc N·m.

Notes

Chip thickness uses the standard model that treats the tooth path as a circle: h(φ) = fz · sin φ · sin κr. The model holds whenever fz is far smaller than the cutter radius, which covers every practical case.
In side milling with ae < Dc/2 the maximum chip thickness is smaller than fz, so the feed is raised by the chip thinning factor to reach the catalogue chip thickness. At ae ≥ Dc/2, hex = fz · sin κr.
In climb milling the chip starts thick and ends thin; in conventional milling the reverse. The mean chip thickness and the power are the same in both directions; tool life and surface are not.
Cutting time covers chip removal along L only; the extra travel of one cutter diameter to enter and leave the part, rapid moves and tool changes are not included.
Pc is the net cutting power. For the motor, divide by the spindle efficiency and check the machine’s power curve against the spindle speed.

Sources (4)

Sandvik Coromant — Formulas and definitions for milling (vf, Q, Pc, Mc)
Machining Doctor — Chip thinning calculator (radial chip thinning factor)
Y. Altintas, Manufacturing Automation, 2nd ed., Cambridge University Press, 2012 — chip thickness in milling, h(φ) = c · sin φ
O. Kienzle, VDI-Z 94 (1952) — specific cutting force kc = kc1.1 · h^−mc