(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 the metal in work hardened condition with yield stress 1·40 kN/mm², coefficient of friction for die as well as for plug is

Question

(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 the metal in work hardened condition with yield stress 1·40 kN/mm², coefficient of friction for die as well as for plug is 0·15, calculate the drawing load and power of the motor required for drawing the tube with the speed of drawing 0·50 m/s. (All dimensions are in 'mm') Figure 7(a)(i) (10 marks)

(ii) Draw and label the surface roughness symbol, if the method of machining was milling, sample length 3·0 mm, direction of lay is perpendicular to the surface, machining allowance is 2 mm with roughness Rₐ as 6·3 μm. Also, calculate the centre line average and root mean square values of surface roughness for the following measurements {figure 7(a)(ii)} taken over a sample length of 20 mm. (10 marks)

(b) The following information is given for the items procured and sold by a shopkeeper : Annual Demand : 8000 units; Ordering Cost : ₹ 180/order; Holding Cost : 10% of the item cost. Following offers are given to the shopkeeper for different lot sizes : Lot Size 1 – 999: Unit Price ₹ 22.00; Lot Size 1000 – 1499: Unit Price ₹ 20.00; Lot Size 1500 – 1999: Unit Price ₹ 19.00; Lot Size 2000 and above: Unit Price ₹ 18.50. Check the feasibility of different offers using Economic Order Quantity and compare the total annual costs of the feasible offers. (20 marks)

(c) What are the key features of Total Quality Management to improve customer satisfaction through design, manufacture and delivery of quality products ? (10 marks)

UPSC Answer Check · Accepted Answer

(a)(i)

Use the slab-method result for tube drawing over a stationary plug. For die semi-angle α and plug semi-angle β:
σ_d = Y (1+B)/B [1 - (A_f/A₀)^B], where B = μ(cot α + cot β).

Initial tube area:
A₀ = π/4 (20² - 16²) = 36π mm².
Final tube area:
A_f = π/4 (18² - 15²) = 99π/4 = 24.75π mm².
Area ratio:
A_f/A₀ = (99π/4)/(36π) = 11/16 = 0.6875.

Given Y = 1.40 kN/mm², μ = 0.15, α = 15°, β = 10°:
B = 0.15(cot15° + cot10°) = 0.15(3.7321 + 5.6713) = 1.4105.
Then
0.6875^1.4105 = 0.5895.
σ_d = 1.40 × (2.4105/1.4105) × (1 - 0.5895)
= 1.40 × 1.7090 × 0.4105
= 0.9822 kN/mm².

Drawing load:
F = σ_d A_f = 0.9822 × 24.75π = 76.37 kN.
Power:
P = F v = 76.37 × 0.50 = 38.18 kW.

Final drawing load = 76.37 kN; motor power = 38.18 kW.
Valid for steady-state drawing, Coulomb friction, negligible redundant work, and no back tension.

(a)(ii)

Standard surface roughness symbol (schematic):
```
 2 mm milling Ra 6.3
 /---------------- ⊥
 /
 / 3.0
```
Here: milling = machining method; Ra 6.3 μm = roughness value; ⊥ = lay perpendicular to surface; 2 mm = machining allowance; 3.0 = sample length in mm.

For the roughness profile, mean ordinate:
h̄ = (70+35+75+20+65+40+80+50)/8 = 435/8 = 54.375 μm.

CLA:
CLA = Σ|h_i - h̄|/n = (15.625+19.375+20.625+34.375+10.625+14.375+25.625+4.375)/8
= 145/8 = 18.125 μm.

RMS:
RMS = √[Σ(h_i - h̄)²/n]
= √(3221.875/8)
= √402.734375
= 20.068 μm.

Final CLA = 18.125 μm; RMS = 20.068 μm.

(b)

Economic Order Quantity:
Q* = √(2D C_o / C_h), where C_h = 0.10C.
D = 8000 units/year, C_o = ₹180/order.

For C = ₹22.00, C_h = ₹2.20:
Q* = √(2×8000×180/2.20) = 1144.16.
Not feasible in 1–999, so use Q = 999.
TC = 8000×22 + (8000/999)×180 + (999/2)×2.20
= 176000 + 1441.44 + 1098.90 = ₹178540.34.

For C = ₹20.00, C_h = ₹2.00:
Q* = √(2×8000×180/2.00) = 1200.
Feasible in 1000–1499, so Q = 1200.
TC = 8000×20 + (8000/1200)×180 + (1200/2)×2.00
= 160000 + 1200 + 1200 = ₹162400.

For C = ₹19.00, C_h = ₹1.90:
Q* = √(2×8000×180/1.90) = 1231.17.
Not feasible in 1500–1999, so use Q = 1500.
TC = 8000×19 + (8000/1500)×180 + (1500/2)×1.90
= 152000 + 960 + 1425 = ₹154385.

For C = ₹18.50, C_h = ₹1.85:
Q* = √(2×8000×180/1.85) = 1247.70.
Not feasible in 2000 and above, so use Q = 2000.
TC = 8000×18.50 + (8000/2000)×180 + (2000/2)×1.85
= 148000 + 720 + 1850 = ₹150570.

Comparing feasible total annual costs:
₹178540.34 > ₹162400 > ₹154385 > ₹150570.
The minimum total annual cost occurs for lot size 2000 and above.

Final: order 2000 units per order at unit price ₹18.50; total annual cost = ₹150570.

(c)

Key features of Total Quality Management for improving customer satisfaction through design, manufacture and delivery are:
Strong customer focus, covering both external and internal customers.
Top-management commitment, leadership and quality policy deployment.
Continuous improvement through Kaizen, Six Sigma and benchmarking.
Employee involvement, training, teamwork and empowerment.
Process approach and system management rather than inspection alone.
Quality by design: design reviews, FMEA, robust design and reliability.
Quality in manufacture: SPC, poka-yoke, process control and zero-defect approach.
Supplier partnership and incoming quality assurance.
Fact-based decision making using quality data and cost of quality.
Timely delivery, proper packaging, after-sales service and customer feedback.
Elimination of waste, lean practices and preventive maintenance.

These features ensure quality is built into design, manufacture and delivery, thereby raising customer satisfaction.

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