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Machining & Turning formula solvers

Categories — 48 of them, 1269 solvers in all
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CMT

Cutting Power from Specific Cutting Energy

Pc=u QP_c = u \, Q

Machining & TurningThe power a cut demands: the volume of metal removed per second multiplied by the energy it takes to remove a unit volume of that material. The check that tells you whether the machine can actually take the cut you have planned.

Cutting Speed and Spindle Speed

V=π D NV = \pi \, D \, N

Machining & TurningThe bridge between the speed the cutting edge wants and the rpm the machine is set to: circumference times revolutions per minute. The single most confused pair of numbers in machining, and the reason a carbide grade rated at 250 gets run at 250 rpm and ruined.

Machining Time — Turning Pass

tm=Lf Nt_m = \frac{L}{f \, N}

Machining & TurningHow long one turning pass takes: the length to be travelled divided by how fast the tool advances, which is feed per revolution times revolutions per minute. The building block of every cycle time estimate and every quotation.

Material Removal Rate — Milling

Q=ae ap vfQ = a_e \, a_p \, v_f

Machining & TurningHow fast metal leaves the part under a milling cutter: the cross-section of the cut — width times depth — multiplied by how fast the table carries the work through it. A rectangle sweeping through a solid, and nothing more complicated than that.

Material Removal Rate — Turning

Q=V f apQ = V \, f \, a_p

Machining & TurningHow fast metal is leaving the part on a lathe: cutting speed times feed per revolution times depth of cut. Three numbers multiplied, and the product is the honest measure of how hard a roughing pass is working.

Merchant Shear Angle from Chip Thickness Ratio

tan⁡ϕ=rcos⁡α1−rsin⁡α\tan\phi = \frac{r \cos\alpha}{1 - r \sin\alpha}

Machining & TurningThe angle of the plane the chip shears along, recovered from two things you can measure with a micrometer: how thick the chip came out compared with how deep the cut was, and the rake angle of the tool. The foundation of the orthogonal cutting model Merchant published in 1945.

Milling Table Feed Rate

vf=N z fzv_f = N \, z \, f_z

Machining & TurningThe speed the table actually travels under a milling cutter: spindle speed times the number of teeth times the chip each tooth is asked to take. The one number a milling machine is programmed in, built from the one number the cutter cares about.

Taylor Tool Life Equation

V T n=CV \, T^{\,n} = C

Machining & TurningThe relation Frederick Taylor drew out of twenty-six years of cutting trials: cutting speed times tool life raised to a small exponent is a constant. It is why a modest increase in speed collapses tool life, and it is the arithmetic behind every decision about whether to run hard and change inserts often or run gently and leave them in.

Theoretical Surface Roughness — Turning

Rt=f28 rεR_t = \frac{f^{2}}{8 \, r_\varepsilon}

Machining & TurningThe peak-to-valley height a round tool nose leaves between one feed mark and the next: feed squared over eight times the nose radius. Pure geometry — the best a perfect tool on a perfect machine could do, and a floor the real surface never quite reaches.