Manufacturing, machining models and metrology
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).
- The diameter-speed relation also applies to appropriate drilling and milling models. Feed per revolution, feed per tooth and table feed are distinct quantities and must be converted with the specified tooth count and speed.
- For an ideal turning model, removal rate can be estimated as cutting speed times depth times feed after converting units consistently.
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 material, but finish and near-surface integrity depend on tool, heat, loading and process conditions; improvement is not automatic.
Metrology and quality
- Caliper, micrometer, dial gauge and gauge blocks have instrument-specific ranges, resolutions, calibration and uncertainty; example resolutions are not universal accuracy guarantees.
- Dimensional tolerance, clearance or interference fits, ISO fit system (e.g. H 7/g 6), measurement uncertainty.
- SPC control limits depend on chart type, subgrouping and estimated process variation; specification limits are separate engineering requirements. 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((10.05−10.02)/0.03,(10.02−9.95)/0.03) = min(1,2.33) =1.00. The lower distance is 0.07, not 0.02. Whether this meets an acceptance requirement depends on a stated criterion and a stable, appropriate process model.
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 ≈ 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.