Machining & Turning formula solvers

Categories — 73 of them, 1787 solvers in all

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B C D L M P T

Bend Allowance

BA = \theta \left( R + K t \right)

Machining & TurningThe length of material consumed by a bend: the arc the neutral axis travels through, from where the bend starts to where it ends. The K-factor says where inside the thickness that neutral axis actually lies, and it is the only part of this equation that is not pure geometry.

Bend Deduction

BD = 2 \left( R + t \right) \tan\!\left( \frac{\theta}{2} \right) - BA

Machining & TurningThe number a flat pattern is actually laid out from. Add the two flange lengths as if the part had a perfectly sharp corner, subtract this deduction, and you have the flat blank. It is twice the outside setback less the bend allowance, and it exists because drawings dimension flanges to the outside of the part while material follows the neutral axis.

Blank Diameter for a Cylindrical Cup

D = \sqrt{d^{2} + 4 d h}

Machining & TurningThe diameter of the flat disc that becomes a flat-bottomed cylindrical cup, taken from surface-area equivalence: the blank has the same area as the bottom disc plus the wall it unrolls into. A starting point for a trial blank, not a finished answer.

Cutting Power from Specific Cutting Energy

P_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 = \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.

Deep Drawing Force (Swift)

F = \pi d t \, UTS \left( \frac{D}{d} - 0.7 \right)

Machining & TurningThe peak force the punch has to pull to draw a flat blank into a cylindrical cup, in the form Swift published in 1952. The circumference of the cup times the thickness times the tensile strength, scaled by how much material has to be dragged in — the term in brackets, whose 0.7 is empirical rather than derived.

Limiting Drawing Ratio

LDR = \frac{D_{max}}{d}

Machining & TurningThe largest blank a material will draw into a cup in one operation, divided by the cup diameter. The standard measure of drawability, determined by experiment rather than by calculation, and governed by the sheet's plastic strain ratio r — the quantity Lankford and his colleagues introduced in 1950.

Machining Time — Turning Pass

t_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 = 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 \, 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\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

v_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.

Press Brake Bending Force — Air Bending

F = \frac{K_b \, UTS \, L \, t^{2}}{V}

Machining & TurningThe force an air bend takes: the bending factor times the tensile strength, times the length of the bend, times the square of the thickness, all divided by the die opening. The thickness is squared, which is why a small increase in gauge doubles the tonnage, and the die opening is in the denominator, which is why opening the die is the cheapest way to get a bend a small press can make.

Taylor Tool Life Equation

V \, 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

R_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.