(a) (i) A tube is to be drawn as per the dimensions given in the following Figure 7(a)(i) showing die, plug and tube. Assuming…

(a)(i) Drawing load and motor power for tube drawing over a plug

Use the slab-method result for tube drawing with a fixed plug. For die semi-angle α, plug semi-angle β and friction coefficients μ_d and μ_p: σ_d = Y[(1 + B)/B][1 − (A_f/A₀)^B], where B = (μ_d + μ_p)/(tanα − tanβ).

From the figure the initial tube is 20 mm outside diameter with 2.0 mm wall, and the drawn tube is 18 mm outside diameter with 1.5 mm wall (15 mm inside diameter). A₀ = (π/4)(20² − 16²) = 36π mm². A_f = (π/4)(18² − 15²) = 24.75π mm² = 77.75 mm². A_f/A₀ = 11/16 = 0.6875.

With Y = 1.40 kN/mm², μ_d = μ_p = 0.15, α = 15°, β = 10°: B = 0.30/(tan15° − tan10°) = 0.30/(0.2679 − 0.1763) = 3.274. (A_f/A₀)^B = 0.6875^3.274 = 0.2932. σ_d = 1.40 × (4.274/3.274) × (1 − 0.2932) = 1.292 kN/mm².

Drawing load F = σ_d A_f = 1.292 × 77.75 = 100.4 kN. Power = F × v = 100.4 × 0.50 = 50.2 kW.

This is for steady drawing with Coulomb friction, negligible redundant work and no back tension.

(a)(ii) Surface roughness symbol, centre line average and RMS value

Symbol: the basic roughness mark (a check-shaped tick on the surface line) carries the following entries. Ra 6.3 μm is placed above the tick, the production method "milling" beside it, the sampling length 3.0 mm below the horizontal bar, the lay symbol ⊥ (lay perpendicular to the surface) at the right end, and the machining allowance 2 mm at the left.

Profile ordinates at the eight stations: 70, 35, 75, 20, 65, 40, 80, 50 μm. Mean level: h̄ = 435/8 = 54.375 μm.

Deviations from the mean: 15.625, −19.375, 20.625, −34.375, 10.625, −14.375, 25.625, −4.375. Centre line average: CLA = Σ|h − h̄|/n = 145/8 = 18.13 μm. Root mean square: RMS = √[Σ(h − h̄)²/n] = √(3221.9/8) = √402.7 = 20.07 μm.

The RMS value is slightly larger than CLA, as it always is for a non-uniform profile.

(b) Economic order quantity with quantity-discount offers

D = 8000 units/year, C_o = ₹180/order, holding cost C_h = 10% of unit price. Q* = √(2DC_o/C_h), and an offer is feasible only if Q* lies inside its lot range; otherwise cost is evaluated at the nearest allowed lot size.

Price ₹22.00 (1–999): C_h = 2.20, Q* = 1144 lies outside the range. At Q = 999, TC = 176 000 + 1 441 + 1 099 = ₹1,78,540. Price ₹20.00 (1000–1499): C_h = 2.00, Q* = 1200 is feasible. TC = 160 000 + 1 200 + 1 200 = ₹1,62,400. Price ₹19.00 (1500–1999): C_h = 1.90, Q* = 1231 is below the range. At Q = 1500, TC = 152 000 + 960 + 1 425 = ₹1,54,385. Price ₹18.50 (2000 and above): C_h = 1.85, Q* = 1248 is below the range. At Q = 2000, TC = 148 000 + 720 + 1 850 = ₹1,50,570.

The total annual cost falls as the lot size rises, so the cheapest offer is the last one. Order 2000 units at ₹18.50, with a total annual cost of ₹1,50,570.

(c) Key features of Total Quality Management

TQM is an organisation-wide approach in which quality is built into design, manufacture and delivery to raise customer satisfaction. Its key features are:

1. Customer focus, treating internal customers (the next process) as well as external ones.
2. Leadership and commitment of top management, expressed through a quality policy.
3. Quality by design: design reviews, FMEA, robust design and reliability engineering.
4. Quality in manufacture: statistical process control, poka-yoke and a zero-defect aim, with prevention preferred to inspection.
5. Employee involvement: training, teamwork and empowerment.
6. Continuous improvement through Kaizen, Six Sigma and benchmarking.
7. Supplier partnership and fact-based decisions using quality data and cost of quality.
8. Delivery and service: on-time delivery, packaging, after-sales service and feedback, closing the loop to design.

Together these make customer satisfaction the outcome of a managed system rather than of final inspection.