Workshop Calculation and Science
What this domain tests
Cutting-speed and feed calculations, taper and sine-bar trigonometry, gear and pulley ratios, and basic applied science.
Core rules
- Cutting speed V (m/min) = πDN/1000, so N = 1000V/(πD). Turning mild steel with HSS uses about 25–30 m/min; carbide is several times faster.
- Feed is in mm/rev; machining time for turning = L/(f × N); for drilling, time = depth/(feed per rev × N).
- Taper: tan (α/2) = (D − d)/(2L), where α is the included angle. Sine bar: sin θ = h/L, so h = L sin θ.
- Gear and pulley trains: overall ratio = product of driven teeth ÷ product of driver teeth.
- Mechanics: stress = force ÷ area, strain = extension ÷ original length, and Young's modulus = stress ÷ strain. Torque = force × radius; power = 2πNT/60.
- Electrical: V = IR, power P = VI, efficiency = output ÷ input × 100 %.
Worked example
A 20 mm diameter hole is drilled in mild steel with an HSS drill at a cutting speed of 25 m/min. N = 1000 × 25 / (π × 20) = 25 000 / 62.83 ≈ 398 rpm, so set the machine at the nearest speed, 400 rpm. If the feed is 0.2 mm/rev, the time to drill a 40 mm deep hole (ignoring approach) = 40/(0.2 × 400) = 0.5 min = 30 s.
Traps that cost marks
- Using radius instead of diameter in πDN/1000.
- Forgetting the factor 2 in the taper formula when calculating the included angle.
- Using degrees in a calculator set to radians.
- Mixing units – mm with metres, or minutes with seconds.