Mechanical Engineering 2023 Paper I 50 marks Calculate

Q8

(a) The following data represents the results of inspecting 50 units/day of personal computers produced by two processes A and B of a company for the past ten days. | Sample No. | Process A No. of Non-Conforming Units | Process B No. of Non-Conforming Units | |------------|----------------------------------------|----------------------------------------| | 1 | 5 | 8 | | 2 | 6 | 7 | | 3 | 7 | 8 | | 4 | 5 | 9 | | 5 | 4 | 10 | | 6 | 6 | 11 | | 7 | 5 | 15 | | 8 | 7 | 8 | | 9 | 9 | 9 | | 10 | 6 | 7 | Calculate control limits for both the processes A and B separately and also see if there is need for revision of control limits in any of the processes. The company claims that 5 PCs may be non-conforming at most out of 50 produced. Perform hypothesis tests for each process using Z-distribution to determine whether the claim of the company is valid for both or not. (Use Normal Distribution table) (20 marks) (b) A medium carbon steel cylindrical rod is being machined under orthogonal cutting condition with an HSS cutting tool having rake angle as 12°. While machining, following data were recorded : Vertical component of cutting force = 1600 N; Horizontal component of cutting force = 1250 N; Chip thickness ratio = 0·25. Calculate the following for the above mentioned machining condition : (i) Normal force on the rake face; (ii) Friction force along the rake face; (iii) Resultant cutting force; (iv) Coefficient of friction at chip tool interface; (v) Normal force on the shear plane; (vi) Shear force along the shear plane. (20 marks) (c) A manufacturing company wants to arrange work-centres A, B, C and D, so as to minimize inter-departmental parts handling costs. The flow of parts and existing work-centres layout are shown below : Parts moved between work-centres Existing layout with distances Suggest a modified layout. (10 marks)

हिंदी में प्रश्न पढ़ें

(a) निम्नलिखित आँकड़े पिछले 10 दिनों के हैं जो एक कंपनी की दो प्रक्रियाओं A और B द्वारा 50 इकाई प्रतिदिन उत्पादित निजी कंप्यूटर (पी.सी.) के निरीक्षण के परिणामों को दर्शाते हैं : | नमूना संख्या | प्रक्रिया A गैर-अनुकूलक इकाइयों की संख्या | प्रक्रिया B गैर-अनुकूलक इकाइयों की संख्या | |---|---|---| | 1 | 5 | 8 | | 2 | 6 | 7 | | 3 | 7 | 8 | | 4 | 5 | 9 | | 5 | 4 | 10 | | 6 | 6 | 11 | | 7 | 5 | 15 | | 8 | 7 | 8 | | 9 | 9 | 9 | | 10 | 6 | 7 | दोनों प्रक्रियाओं A और B के लिए अलग-अलग नियंत्रण सीमा परिकलित कीजिए तथा यह भी देखिए कि क्या किसी प्रक्रिया की नियंत्रण सीमा में बदलाव की ज़रूरत है । कंपनी यह भी दावा करती है कि ज़्यादा-से-ज़्यादा 50 उत्पादित पी.सी. में 5 गैर-अनुकूलक हो सकते हैं । Z-आबंटन का उपयोग करते हुए प्रत्येक प्रक्रिया के लिए परिकल्पना जाँच कीजिए यह ज्ञात करने के लिए कि कंपनी द्वारा दावा की गई दोनों प्रक्रियाओं के लिए यह सही है या नहीं । (सामान्य वितरण तालिका का प्रयोग कीजिए) (20 अंक) (b) मध्यम कार्बन इस्पात की बेलनाकार छड़ का मशीन लंबिक कतन अवस्था में HSS कतन औजार से किया गया है जिसका नति कोण 12° है। मशीन के दौरान निम्नलिखित आंकड़ों को अभिलेखबद्ध किया गया : कतन बल का उद्वर्धर घटक = 1600 N; कतन बल का क्षैतिज घटक = 1250 N; छीलन की मोटाई का अनुपात = 0·25। उपर्युक्त मशीन अवस्था के लिए निम्नलिखित को ज्ञात कीजिए : (i) नति (रैक) तल के लंबवत कार्यरत बल; (ii) नति (रैक) तल की दिशा में घर्षण बल; (iii) परिणामी कतन बल; (iv) छीलन तथा औजार के अंतराफलक का घर्षण गुणांक; (v) अपरूपण तल के लंबवत कार्यरत बल; (vi) अपरूपण तल के अनुदिश अपरूपण बल। (20 अंक) (c) एक विनिर्माण कंपनी कार्य-स्टेशन A, B, C तथा D को इस तरह व्यवस्थित करना चाहती है जिससे सामानों की अंतर्विभागीय हस्तांतरण लागत कम हो जाए । सामानों का प्रवाह और मौजूदा कार्य-स्टेशन का खाका नीचे दर्शाया गया है : सामानों का कार्य-स्टेशन के बीच प्रवाह मौजूदा खाका दूरियों के साथ संशोधित खाका का सुझाव दीजिए । (10 अंक)

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Directive word: Calculate

This question asks you to calculate. The directive word signals the depth of analysis expected, the structure of your answer, and the weight of evidence you must bring.

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How this answer will be evaluated

Approach

Calculate requires systematic numerical working across all three sub-parts. For (a), construct p-charts for both processes, test for control, then perform Z-tests for hypothesis testing—allocate ~40% time. For (b), apply Merchant's circle analysis using given force components and chip thickness ratio to find all six required quantities—allocate ~35% time. For (c), use load-distance method or systematic pairwise interchange to optimize facility layout—allocate ~25% time. Present each sub-part with clear headings, formulae stated before substitution, and final answers boxed.

Key points expected

  • For (a): p-bar_A = 0.12, p-bar_B = 0.184; UCL_A = 0.258, LCL_A = 0; UCL_B = 0.348, LCL_B = 0.02; Process B needs revision (points 7,8,9 out of control)
  • For (a): Z-test for Process A: Z = 1.414 < 1.96, claim valid; Process B: Z = 4.743 > 1.96, claim invalid at 5% significance
  • For (b): Shear angle φ = 28.61°, friction angle β = 38.05°; Normal force on rake face = 2538 N; Friction force = 1986 N
  • For (b): Resultant force = 2031 N; μ = 0.781; Normal force on shear plane = 1789 N; Shear force = 1421 N
  • For (c): Current layout cost calculation; improved layout by placing A-C and B-D adjacent (high flow pairs); cost reduction demonstrated
  • Merchant's circle diagram sketched for part (b) showing force relationships; p-chart drawn for part (a) with control limits marked

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Correctly applies p-chart formulae (UCL = p̄ + 3√[p̄(1-p̄)/n]) for attribute control in (a); uses Merchant's circle and Ernst-Merchant shear angle relation for (b); applies load-distance formula or CRAFT heuristic for (c); identifies when process is out of statistical control.Uses correct formulae but with minor errors in identifying sample size n=50; recognizes out-of-control points but misses one; applies correct cutting mechanics concepts but confuses force component directions.Confuses p-chart with c-chart or X̄-R chart; uses wrong shear angle formula (treats as 45°-γ/2 without derivation); applies random assignment for layout without systematic method.
Numerical accuracy20%10All calculations precise to 2-3 decimal places: p̄_A = 0.12, p̄_B = 0.184; Z_A ≈ 1.41, Z_B ≈ 4.74; shear angle φ = 28.61°, friction coefficient μ = 0.781; layout cost computed correctly with measurable improvement shown.Correct final answers for most quantities but arithmetic slips in one sub-part (e.g., wrong standard deviation calculation in Z-test); shear angle correct but friction angle off by 2-3 degrees.Major computational errors: wrong p̄ values, incorrect Z-formula (uses σ instead of SE), shear angle completely wrong; layout cost not calculated or arbitrary arrangement proposed.
Diagram quality20%10Clean p-charts for both processes with center line, UCL, LCL, and all 10 points plotted—out-of-control points clearly marked; Merchant's circle for (b) with all forces (F, F_s, F_n, N, F_f) labelled with correct angular relationships; facility layout diagrams for (c) showing before/after with distance matrix.Charts present but missing labels or scale; Merchant's circle drawn but forces not clearly distinguished; layout sketch present but without distance annotations.No diagrams despite requirement; or diagrams drawn without any labels, wrong shapes (e.g., triangular p-chart), completely wrong force polygon.
Step-by-step derivation20%10Every formula stated before substitution: p̄ = Σnp/Σn, SE = √[p̄(1-p̄)/n], Z = (p̄ - p₀)/SE; shear angle from tanφ = rcosγ/(1-rsinγ); all force components derived from F_c, F_t using transformation equations; layout cost computed stepwise with pairwise exchange logic shown.Formulae stated but some intermediate steps skipped (e.g., jumps from given data to final answer); working present but disorganized across sub-parts.Final answers only with no working; or incorrect formulae stated; no derivation of shear angle from chip thickness ratio; layout solution asserted without method.
Practical interpretation20%10For (a): explains that Process B requires immediate investigation (special causes present) and Process A is stable but company claim only valid for A; suggests corrective action for B. For (b): interprets high μ (0.78) as indicating poor lubrication/built-up edge; comments on tool life implications. For (c): quantifies percentage cost reduction and discusses implementation constraints.States which process is in control but limited insight on corrective actions; notes friction coefficient value without interpreting machining implications; mentions layout improvement without cost quantification.No interpretation of results; treats all calculations as abstract exercises; no comment on why Process B fails company standards or what high friction means for HSS tool performance.

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