Chris Collins

Tools · metalworking

Lathe and metal shop

Change gears for screw cutting on any lathe — simple and compound trains from your own gear set, the 127-tooth gear for metric on an inch leadscrew, and the error in ppm — thread-cutting passes and the 29.5° compound, clean knurling diameters, taper turning and Morse tapers, hardening and tempering O1, A2, D2, W1, 1045 and 4140 with temper colours, and a casting calculator for shrinkage, metal to melt and crucible size.

Added

How to use it

Pick Metric or Imperial at the top (remembered); each tab works in either.

Change gears

The leadscrew turns at (drivers ÷ driven) times the spindle speed, so the pitch you cut is leadscrew pitch × fixed ratio × (A × C) ÷ (B × D). Choose a gear set (or type your own: 40x2 means two 40-tooth gears), the leadscrew (TPI or mm) and the thread you want. The tool searches every simple train (A on the stud drives D on the leadscrew, through any idler, which does not change the ratio) and every compound train (A drives B; C, keyed to B on the banjo stud, drives D), and lists the best eight with their error in parts per million. Tap one to draw it.

  • Metric on an inch leadscrew is only exact with a 127-tooth gear, because 25.4 mm = 127 ÷ 5: 1.5 mm on an 8 TPI leadscrew is 60 driving 127. Without one the search finds the nearest approximation; 63/160 for 1/2.54 (125 ppm) is the classic one. A 127/120 pair does the same job on a compound stud.

  • Banjo clearance rejects compound trains that would foul: A + B ≥ C + k (C clears the stud that carries A) and C + D ≥ B + k (B clears the leadscrew). 15 teeth is a fair start; 0 turns it off.

  • Fixed ratio covers any gearing already between spindle and stud (tumbler reverse, a 2:1 stud).

  • What this set can cut lists the best train for every common metric pitch and TPI.

For a reduction from any gear sizes, see the gear-train search.

Thread passes

Choose the form (ISO metric, Unified, Whitworth, ISO trapezoidal, ACME), external or internal, and the pitch. Depths: ISO 68-1 / ASME B1.1 external h3 = 0.61343P and internal H1 = 0.54127P; Whitworth (BS 84) 0.640327P; ISO 2904 trapezoidal 0.5P + ac; ACME 0.5P + 0.010″ (0.020″ at 10 TPI and coarser). The passes follow Sandvik Coromant’s degressive, constant-area infeed: depth after pass x = depth × √φ ÷ √(n − 1), with φ = 0.3 for the first pass and x − 1 after it. Leave Passes blank for Sandvik’s typical count for the pitch (these are carbide figures; with HSS on a light lathe, take more).

The table gives the compound-dial reading for each pass with the compound set at 29.5° from the cross-slide (27° for 55° Whitworth, 14.5° for trapezoidal, 14° for ACME): compound feed = radial depth ÷ cos(angle). If your compound’s scale reads from the lathe axis, set 60.5° instead. Check the fit before the last passes with a nut, a gauge or three wires.

Knurling

A knurl tracks cleanly when the circumference holds a whole number of teeth. For ASME B94.6 knurls, specified by diametral pitch (64, 80, 96, 128, 160 DP), the work gets DP × D teeth, so clean diameters are multiples of 1/DP inch. For knurls specified by pitch (DIN 82, or TPI), D = teeth × pitch ÷ π; a 30° diamond wheel whose pitch is measured square to its teeth repeats every pitch ÷ cos 30° around the work. The tool shows the clean diameters either side of the one you want.

Tapers

From the large and small diameters and the taper length, the compound (top-slide) angle is the half-angle atan((D − d) ÷ 2l); the tailstock set-over for work of length L between centres is (D − d) × L ÷ 2l; and taper per foot is 12 (D − d) ÷ l in inches. Choose a Morse taper (MT0–MT7) for its standard angle and dimensions (ANSI/ASME B5.10, via Machinery’s Handbook). The tool warns when the set-over is more than about 2.5% of the work length.

Heat treatment

Hardening, quench and tempering ranges for O1, A2, D2, W1, 1045 and 4140, from the ASM Heat Treater’s Guide, manufacturers' datasheets (Uddeholm Arne, Rigor and Sverker 21; Crucible A2 and D2; Böhler K305) and EN 10083-2/-3 for C45 and 42CrMo4. They are typical published ranges, so check them against your supplier’s datasheet. Temper (oxide) colours on bright steel run from pale straw at about 220 °C to grey–blue at 330 °C; incandescent heat colours run from faint red at about 525 °C to white above 1200 °C. Oxide colour depends on time as well as temperature, so use it as a check on a thermometer. The tab lists the safety points for quench oil, fumes and handling.

Casting

Choose the metal, then give the pattern’s weight and material (a printed pattern only at 100% infill) or the casting’s volume from CAD. The tool gives the casting’s weight; the metal to melt, allowing for sprue, runners and risers plus melt loss; and the smallest A-shape crucible that holds it. The rule of thumb is that an A-number holds about that many pounds of aluminium, or about three times as many pounds of brass. Shrinkage is applied the way a patternmaker’s shrink rule reads: pattern = casting × (1 + s). Typical figures are cast iron ⅛″/ft ≈ 1%, steel ¼″/ft ≈ 2%, aluminium 5⁄32″/ft ≈ 1.3% and brass 3⁄16″/ft ≈ 1.5%.

Limits

  • The gear search assumes every gear meshes with its neighbour. It cannot tell whether your banjo reaches, whether the gears' modules match, or whether a quick-change gearbox is in the drive (put its ratio in Fixed ratio).

  • Thread depths are the basic profile depths. Cutting with a sharp-nosed tool, or to a class of fit, needs a little more or less, so finish to a gauge. The pass counts are a starting point for carbide inserts.

  • Knurled diameters grow by roughly half the tooth depth, and knurl makers state pitch in different ways.

  • Heat-treatment figures are typical ranges for annealed stock, not a specification. Section size, furnace atmosphere and soak time change the result, and a home forge will not hold D2’s temperature evenly.

  • Shrinkage varies with the shape and the mould, and the crucible rule is approximate. Molten metal is dangerous; read the safety notes.

Related: speeds and feeds (lathe turning speeds), taps, drills and threads (tap drills, pitch diameter, three-wire), gears, belts and chains (gear-train search), metal weight, welding settings, bolt torque.

Linking to an example

Links can be written by hand. Add the tab after #: gears, infeed, knurl, taper, heat or casting.

Parameter Meaning Example

units

mm (metric) or in (imperial)

units=in

gset

Gear set: mini, mini-us, myford, myford-127, generic or custom

gset=generic

glist

Your gears, comma-separated (40x2 = two)

glist=20,30,40,60,127

ls

Leadscrew pitch (TPI or mm)

ls=8

lsu

Leadscrew unit: tpi or mm

lsu=tpi

tp

Thread to cut

tp=1.25

tpu

Its unit: mm or tpi

tpu=mm

fixed

Fixed ratio between spindle and stud

fixed=0.5

comp

Allow compound trains: true or false

comp=false

clr

Banjo clearance in teeth (0 = ignore)

clr=10

form

Thread form: iso, un, bsw, tr, acme

form=un

side

ext or int

side=int

ip

Pitch to cut

ip=13

ipu

Its unit: mm or tpi

ipu=tpi

passes

Number of cutting passes

passes=10

spring

Spring passes at full depth (0–3)

spring=2

kmode

Knurl spec: dp (diametral pitch) or pitch

kmode=dp

dp

Diametral pitch: 64, 80, 96, 128, 160

dp=128

kp

Knurl pitch

kp=0.8

kpu

Its unit: mm or tpi

kpu=tpi

kform

straight or diamond

kform=diamond

kmeas

Diamond pitch measured circ (around the work) or normal (square to the teeth)

kmeas=normal

kd

Diameter you want (in the current units)

kd=25

tmode

Taper from dims or a morse taper

tmode=morse

mt

Morse taper MT0…MT7

mt=MT3

tD, td

Large and small diameter

tD=30&td=25

tl

Taper length

tl=80

tL

Work length between centres

tL=200

steel

o1, a2, d2, w1, c1045, c4140

steel=a2

alloy

al, brass, bronze, iron, steel, zinc, pewter

alloy=brass

cmode

Volume from the pattern weight or the casting volume

cmode=volume

pmat

Pattern: pine, mahogany, mdf, pla, petg, abs, wax, eps

pmat=mdf

pw

Pattern weight (g, or oz in imperial)

pw=250

cvol

Casting volume (cm³, or in³ in imperial)

cvol=180

gate

Sprue, runners and risers, % of the casting

gate=60

loss

Melt loss, %

loss=8

cdim

A casting dimension to scale for the pattern

cdim=150

example

One of the presets below; parameters given with it override the preset’s

example=mt2

Presets:

example= Shows

metric-on-8tpi

1.5 mm pitch on an 8 TPI leadscrew: 60 driving 127 is exact (open)

imperial-on-mini

20 TPI on a 1.5 mm mini-lathe leadscrew with the stock gears, no 127 (open)

m10-thread

M10 × 1.5 external: 0.92 mm deep in 6 passes, compound at 29.5° (open)

bsw-half

½″ BSW, 12 TPI: the 55° form with the compound at 27° (open)

knurl-96dp

96 DP diamond knurl on a 1″ handle (open)

knurl-1mm

1 mm straight knurl on a 20 mm knob (open)

mt2

Morse taper 2: the compound at 1° 25′ 50″ (open)

tailstock-offset

1″ to 0.8″ over 4″ on 10″ work: set the tailstock over 0.25″ (open)

o1

O1 gauge plate: harden at about 800 °C, quench in oil, temper at 200 °C (open)

al-casting

A 120 g PLA pattern cast in aluminium: about 250 g of casting, 0.39 kg to melt, an A1 crucible (open)

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