Mechanical Engineering 2024 Paper I 50 marks Calculate

Q6

(a) A perfectly plastic material having yield strength of 300 MPa is subjected to extrusion at 400 °C. The extrusion speed is 300 mm/s. The extrusion process is done on billet of diameter 50 mm and length 300 mm. Extrusion reduces the diameter of billet from 50 mm to 20 mm. Assuming that the extrusion process is frictionless, determine the true strain, average true strain, ideal extrusion force and work done on billet during extrusion. The initial diameter of billet is significantly greater than the final diameter after extrusion. (20 marks) (b) The data for the number of dissatisfied customers in a department store observed for 20 samples of size 300 are shown in the table below. Construct a suitable control chart for the collected data. Any out-of-control situation may be treated as the presence of some assignable cause, accordingly revise the control limits: | Sample | No. of Dissatisfied Customers | Sample | No. of Dissatisfied Customers | |--------|-------------------------------|--------|-------------------------------| | 1 | 10 | 11 | 6 | | 2 | 12 | 12 | 19 | | 3 | 8 | 13 | 10 | | 4 | 9 | 14 | 7 | | 5 | 6 | 15 | 8 | | 6 | 11 | 16 | 4 | | 7 | 13 | 17 | 11 | | 8 | 10 | 18 | 10 | | 9 | 8 | 19 | 6 | | 10 | 9 | 20 | 7 | Management believes that the dissatisfaction rate is 2%, so establish control limits based on this value. Discuss whether the department can meet this goal. What actions would you recommend? (20 marks) (c) List down different types of wastes indicated in JIT system. How are they connected with flow layout? (10 marks)

हिंदी में प्रश्न पढ़ें

(a) एक पूरी तरह से पराप्रत्यास्थ (प्लास्टिक) सामग्री, जिसका प्रारंभ सामर्थ्य 300 MPa है, 400 °C पर बहिवेधन से गुजरती है। बहिवेधन गति 300 mm/s है। बहिवेधन प्रक्रिया 50 mm व्यास और 300 mm लंबाई के बिलेट पर की जाती है। बहिवेधन, बिलेट का व्यास 50 mm से 20 mm तक घटा देता है। यह मानते हुए कि बहिवेधन प्रक्रिया घर्षण रहित है, वास्तविक विकृति (स्ट्रेन), औसत वास्तविक विकृति, आदर्श बहिवेधन बल और बहिवेधन के दौरान बिलेट पर किया गया कार्य निर्धारित कीजिए। बिलेट का प्रारंभिक व्यास, बहिवेधन के बाद अंतिम व्यास से बहुत अधिक है। (20 अंक) (b) एक विभागीय स्टोर में असंतुष्ट ग्राहकों की संख्या के आँकड़े नीचे तालिका में दिखाए गए हैं, जो 300 आमाप (साइज़) के 20 नमूनों के लिए हैं। एकत्रित आँकड़ों के लिए एक उपयुक्त नियंत्रण चार्ट बनाइए। किसी भी नियंत्रण से बाहर की स्थिति को किसी निर्देश्य कारण की उपस्थिति के रूप में माना जा सकता है, तदनुसार नियंत्रण सीमाओं को संशोधित कीजिए: | नमूना | असंतुष्ट ग्राहकों की संख्या | नमूना | असंतुष्ट ग्राहकों की संख्या | |--------|---------------------------|--------|---------------------------| | 1 | 10 | 11 | 6 | | 2 | 12 | 12 | 19 | | 3 | 8 | 13 | 10 | | 4 | 9 | 14 | 7 | | 5 | 6 | 15 | 8 | | 6 | 11 | 16 | 4 | | 7 | 13 | 17 | 11 | | 8 | 10 | 18 | 10 | | 9 | 8 | 19 | 6 | | 10 | 9 | 20 | 7 | प्रबंधन का मानना है कि असंतोष दर 2% है, इसलिए इस मान के आधार पर नियंत्रण सीमाएँ स्थापित कीजिए। विवेचना कीजिए कि क्या विभाग इस लक्ष्य को पूरा कर सकता है। किन कार्यवाहियों की अनुशंसा आप कर सकते हैं? (20 अंक) (c) JIT प्रणाली में बताए गए विभिन्न प्रकार के कचरे की सूची बनाइए। ये सभी प्रवाह अभिन्यास से कैसे जुड़े हुए हैं? (10 अंक)

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Directive word: Calculate

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How this answer will be evaluated

Approach

Calculate the required parameters for part (a) using extrusion formulae for true strain, average strain, ideal force and work done. For part (b), construct a p-chart with given standard (2%), identify out-of-control points, revise limits after removing assignable causes, and interpret process capability. For part (c), enumerate the seven wastes of JIT and explain their connection to flow layout principles. Allocate approximately 40% time to (a), 40% to (b), and 20% to (c) based on marks distribution.

Key points expected

  • Part (a): True strain ε = 2ln(D₀/Df) = 2ln(50/20) = 1.832; average true strain ε̄ = ε/2 = 0.916 for frictionless extrusion
  • Part (a): Ideal extrusion force F = σ₀ × A₀ × ln(A₀/Af) = 300 × π×25² × 1.832 = 1.079 MN; work done W = F × L₀ × ln(A₀/Af) or σ₀ × V × ε = 300×10⁶ × π×0.025²×0.3 × 1.832 = 323.7 kJ
  • Part (b): Calculate p̄ from data, establish p-chart with UCL/LCL using 2% standard; identify samples 12 (p=0.063) and 16 (p=0.013) as potentially out-of-control
  • Part (b): Revise control limits after removing assignable causes; compare revised process average with 2% target; conclude on process capability and recommend actions
  • Part (c): List seven JIT wastes: overproduction, waiting, transport, over-processing, inventory, motion, defects (TIMWOOD); explain how flow layout (cellular/line) minimizes transport, inventory and motion wastes
  • Part (c): Connect flow layout to JIT principles: single-piece flow reduces WIP, U-shaped cells minimize walking, pull system eliminates overproduction waste

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Correctly applies frictionless extrusion theory with area reduction ratio for true strain; uses p-chart (not c-chart) for attribute data with variable sample size justification; identifies all seven JIT wastes accurately and links each to flow layout benefits.Uses correct extrusion strain formula but confuses average strain calculation; chooses p-chart correctly but with minor formula errors; lists most JIT wastes but connections to flow layout are superficial.Uses engineering strain instead of true strain for extrusion; applies x̄-R chart or c-chart incorrectly for proportion data; misses key JIT wastes or fails to connect to layout.
Numerical accuracy20%10All calculations precise: ε=1.832, ε̄=0.916, F=1.079 MN, W=324 kJ; p-chart with correct control limits (e.g., UCL≈0.041, LCL≈0 for n=300), proper revision after removing samples 12, 16; revised limits and process capability assessment accurate.Correct final values for extrusion but minor arithmetic slips in intermediate steps; p-chart structure correct but control limit calculation errors; revised limits attempted but incorrect removal of points.Major errors in extrusion force (forgetting area or using diameter instead of radius); wrong chart type or control limits off by factor >2; no numerical work shown for JIT part.
Diagram quality15%7.5Clear p-chart with center line, UCL, LCL, all 20 points plotted with sample numbers, out-of-control points circled; revised chart shown separately; extrusion process sketch with billet, die, extrudate labeled; flow layout diagram showing U-cell or line layout.p-chart drawn but missing labels or scale; extrusion mentioned but no diagram; flow layout described verbally without visual.No charts or diagrams; or incorrect chart type drawn (e.g., histogram instead of control chart).
Step-by-step derivation25%12.5Full derivation: ε = ln(A₀/Af) = 2ln(D₀/Df) shown; F = σ₀A₀ln(A₀/Af) derived from work-energy; p-chart formulas stated (p̄, σp, UCL/LCL); clear stepwise removal of out-of-control points with recalculation; JIT waste definitions systematic.Key formulas stated but derivation abbreviated; p-chart construction steps present but revision process unclear; JIT wastes listed without systematic approach.Final answers only with no derivation; no working for control limits; no logical structure in JIT response.
Practical interpretation20%10Interprets extrusion results: notes ideal vs actual force difference due to friction/die angle; assesses process capability (Cp, Cpk) for customer satisfaction; specific actionable recommendations for department store (training, service redesign); relates JIT-flow layout to Indian manufacturing examples (e.g., Maruti Suzuki lean cells).Brief comment on friction ignored in ideal analysis; states process is/is not capable without quantitative Cpk; generic recommendations; mentions flow layout benefits without Indian context.No interpretation of results; no recommendations; treats all parts as purely theoretical exercises.

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