Workshop calculation and science
Workshop calculation and science tests numerical fluency needed in the tool room: units, speeds and feeds, tapers, gears, trigonometry, areas, volumes, force and simple material calculations.
Core rules
- Keep units consistent. Convert mm to m when using speed in m per minute, and minutes to hours when calculating production time.
- Cutting speed S = pi times D times N divided by 1000, so N = 1000S divided by pi times D. Feed per revolution and feed per tooth are different; for a milling cutter with z teeth, table feed = feed per tooth times z times N.
- Taper turning by tailstock offset: offset = (D minus d) divided by 2, multiplied by L divided by l, where L is total work length and l is taper length.
- Trigonometric ratios apply to right triangles: sin = opposite divided by hypotenuse, cos = adjacent divided by hypotenuse, tan = opposite divided by adjacent.
- Percentage, ratio and proportion are used for allowances, mixtures and gear ratios. Gear ratio = driven teeth divided by driving teeth.
Worked example
A taper is 30 mm at the large end and 25 mm at the small end over 100 mm. The work is 200 mm long. Tailstock offset = (30 minus 25) divided by 2, times 200 divided by 100 = 2.5 times 2 = 5 mm. The tailstock is set over 5 mm toward the operator or away according to the lathe and taper direction.
Traps
Using diameter difference instead of half the difference doubles the offset; mixing taper length with total length gives a wrong setting; and using the wrong trigonometric side is a common exam error.