Manufacturing and production systems: machining, forming, joining, metrology and quality
This section tests process calculations in machining, the logic of forming and joining processes, correct use of measuring instruments and statistical quality control. The numeric part is usually cutting speed, machining time or a capability index.
Machining
- Turning: v_c = π·D·n/1000 (m/min with D in mm and n in rpm); feed f (mm/rev); depth of cut a_p.
- Machining time t = L/(f·n).
- Drilling and milling use the same cutting-speed formula; feed is given in mm/min.
- Material removal rate ≈ v_c·a_p·f.
Forming and joining
- Plastic deformation: rolling, forging, extrusion, stamping, deep drawing; mass is conserved, no chips are produced.
- Joining: fusion welding (electrode, MIG, TIG), resistance welding, brazing and soldering, riveting, adhesives, threaded fasteners.
- Machining removes chips and improves surface finish without changing the material's core properties.
Metrology and quality
- Caliper (0.02 mm), micrometer (0.01 mm), dial gauge (0.01 mm), gauge blocks.
- Dimensional tolerance, clearance or interference fits, ISO fit system (e.g. H7/g6), measurement uncertainty.
- SPC: control charts with ±3σ limits; Cp = (USL − LSL)/6σ; Cpk = min[(USL − µ)/3σ, (µ − LSL)/3σ]. If µ = 10.02, σ = 0.01 and limits are 10.00 ± 0.05, then Cpk = min(0.03/0.03, 0.02/0.03) = 0.67, so the process is not capable.
Worked example
Turning a 60 mm shaft at n = 800 rpm, f = 0.2 mm/rev, a_p = 2 mm, over L = 150 mm. v_c = π·60·800/1000 = 150.8 m/min. Time = 150/(0.2·800) = 0.94 min ≈ 56 s. Removal rate ≈ 150 800 mm/min · 2 mm · 0.2 mm/rev ≈ 60 300 mm³/min ≈ 60 cm³/min.
Marks lost
- Using the radius instead of the diameter in v_c.
- Reporting time in minutes when the answer is asked in seconds.
- Confusing Cp with Cpk, which penalises off-centre processes.
- Reading the caliper without the vernier scale or the micrometer without the thimble.
- Confusing tolerance (admissible difference) with fit type.