Measurement and Workshop Calculations
Measurement and Workshop Calculations
This domain tests instruments, least count, reading scales, tolerances, fits and basic workshop mathematics. Expect questions on vernier and micrometer readings, torque, pressure, volume and Ohm's law.
Core rules
- Vernier caliper: least count = 1 main-scale division − 1 vernier division; for a 0.02 mm caliper, read the main scale before the vernier zero, then add the coinciding vernier division × 0.02 mm.
- Micrometer: least count 0.01 mm; read the sleeve, then the thimble. Check zero before use.
- Other instruments: dial gauge (0.01 mm), bore gauge, feeler gauge, steel rule, torque wrench, pressure gauge, multimeter.
- Fits: clearance fit (shaft smaller than hole), interference fit (shaft larger), transition fit (either). Tolerance is the permitted variation.
- Calculations: torque = force × radius; pressure = force ÷ area; Ohm's law V = I × R; power P = V × I; compression ratio = (swept + clearance) ÷ clearance.
Worked example
A vernier caliper with least count 0.02 mm is used to measure a shaft. The main-scale zero of the vernier lies past the 12 mm mark, and the 24th vernier division coincides with a main-scale line. Reading = 12 mm + (24 × 0.02) = 12 + 0.48 = 12.48 mm. If the instrument shows a zero error of +0.03 mm (it reads 0.03 mm when closed), the true size is 12.48 − 0.03 = 12.45 mm. A shaft specified as 12.50 ± 0.05 mm is therefore within tolerance.
Traps
- Reading the vernier scale from the wrong end.
- Forgetting to apply zero error.
- Parallax error from viewing the scale at an angle.
- Mixing millimetres and centimetres in one calculation.