Lathe and metal shop

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.

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

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 + a_c; 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.

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.

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.

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.

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%.

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.

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

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