(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

Calculate the drawing load and power for part (a)(i) using Siebel's tube drawing formula with plug, accounting for work hardening and dual friction coefficients. For (a)(ii), construct the complete surface roughness symbol per IS/ISO standards and compute CLA and RMS from the given profile data. Solve part (b) by calculating EOQ for each price break, checking feasibility, and comparing total annual costs including purchase, ordering, and holding costs. For part (c), enumerate TQM features with specific linkage to customer satisfaction across design, manufacture, and delivery phases. Allocate time proportionally: ~25% each for (a)(i) and (a)(ii), ~35% for (b), and ~15% for (c).
- Part (a)(i): Apply Siebel's tube drawing formula F = π(D₀-t₀)t₀σ₀(1+μcotα+μ₁cotα₁)ln(D₀/D₁) with given σ₀=1.40 kN/mm², μ=μ₁=0.15; calculate drawing load and power P=F×v with v=0.50 m/s
- Part (a)(ii): Draw complete surface roughness symbol per IS 3073/ISO 1302 with milling process, 3.0 mm sampling length, perpendicular lay symbol (⊥), 2 mm machining allowance, and Ra=6.3 μm; calculate CLA = (Σ|yᵢ|)/n and RMS = √(Σyᵢ²/n) from profile measurements
- Part (b): Calculate EOQ = √(2DS/H) for each price break; check if EOQ falls within feasible lot size range; if not, use boundary quantity; compute total cost TC = DC + (D/Q)S + (Q/2)H for all feasible options and identify minimum
- Part (c): Identify key TQM features—customer focus, continuous improvement (Kaizen), total employee involvement, process approach, strategic quality planning, supplier quality integration, and fact-based decision making—linked to design (QFD), manufacture (SPC), and delivery (customer feedback loops)
- Part (b) specific: For D=8000, S=₹180, H=10% of unit price; EOQ at ₹22 gives EOQ₁≈1145 (infeasible, use 999), at ₹20 gives EOQ₂≈1200 (feasible), at ₹19 gives EOQ₃≈1231 (infeasible, use 1500), at ₹18.50 gives EOQ₄≈1249 (infeasible, use 2000); compare TC for feasible quantities
- Numerical precision: Maintain consistent units (kN, mm, m/s, kW for power; μm for roughness; ₹ for costs) and show 3-4 significant figures in final answers

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	20%	10	Correctly applies Siebel's tube drawing theory with plug for work-hardened material in (a)(i); uses proper ISO/IS surface roughness symbol conventions with all elements positioned correctly in (a)(ii); applies EOQ model with price breaks and total cost analysis in (b); comprehensively links TQM principles to customer satisfaction across product lifecycle in (c)	Uses correct basic formulas but misses work-hardening adjustment or confuses plug vs die friction; surface symbol mostly correct but omits one element (e.g., lay direction); EOQ calculated but feasibility check incomplete; TQM features listed but weak linkage to customer satisfaction	Applies solid rod drawing formula instead of tube drawing; surface symbol unrecognizable or uses obsolete conventions; ignores price breaks and calculates single EOQ; generic management jargon without TQM-specific content
Numerical accuracy	25%	12.5	Drawing load within 2% of expected value (~calculated using proper Siebel formula with given parameters), power correctly converted to kW; CLA and RMS computed accurately from profile data with proper sign handling; EOQ values precise, feasibility correctly determined, total costs accurate to ₹10, optimal choice justified with numerical evidence	Drawing load correct order of magnitude but arithmetic slip in logarithmic term or friction component; CLA/RMS with minor calculation error or n value; EOQ formula correct but rounding errors in H or final TC comparison; one part completely correct, others approximate	Order of magnitude errors in drawing load (e.g., missing π or area term); CLA/RMS confused or negative values squared incorrectly; EOQ formula wrong (e.g., omits √ or uses H as absolute not percentage); no numerical work shown for TQM part when examples expected
Diagram quality	15%	7.5	Clear schematic of tube drawing setup in (a)(i) showing die angle, plug position, and dimensional annotations; surface roughness symbol in (a)(ii) drawn precisely per ISO 1302 with all five elements (basic symbol, machining allowance, manufacturing method, sampling length, lay direction) correctly positioned and proportioned	Sketch of drawing process present but missing key labels (die angle, plug type); surface symbol recognizable but elements misplaced or proportions poor; diagrams support answer but require interpretation	No diagram for drawing process despite figure reference; surface symbol completely wrong (e.g., uses old √ symbol without extensions) or omitted; diagrams confuse rather than clarify
Step-by-step derivation	25%	12.5	Full derivation of Siebel formula application with substitution of all parameters shown; explicit calculation of area reduction ratio and logarithmic strain; surface roughness calculations with tabulated yᵢ values and explicit Σ\|yᵢ\|, Σyᵢ²; complete EOQ working for all price breaks with feasibility table and TC breakdown (purchase + ordering + holding)	Key formulas stated with partial substitution; some intermediate steps skipped but critical values shown; EOQ calculated for 2-3 price breaks with abbreviated comparison; calculations readable but condensed	Final answers stated without derivation; jumps from given data to result; no working for CLA/RMS or EOQ; illegible or disorganized calculations; TQM part has no structured response
Practical interpretation	15%	7.5	Interprets drawing load relative to machine capacity and comments on power efficiency; relates Ra=6.3 μm to typical milling capability and functional suitability; explains why optimal lot size may deviate from EOQ due to price discounts; connects TQM features to Indian manufacturing context (e.g., ISI certification, Make in India quality initiatives) with specific customer satisfaction metrics	Brief comment on each part's practical significance without depth; mentions that surface finish affects assembly or that bulk buying saves money; generic statement on TQM importance	No interpretation of numerical results; treats all parts as pure calculation exercises; TQM response purely theoretical without application to product lifecycle or customer satisfaction

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