Mechanical Engineering 2023 Paper I 50 marks Calculate

Paper I — Q8

(a) The following data represents the results of inspecting 50 units/day of personal computers produced by two processes A and B…

(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 UnitsProcess B No. of Non-Conforming Units
158
267
378
459
5410
6611
7515
878
999
1067

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 संख्याप्रक्रिया A गैर-अनुकूलक इकाइयों की संख्याप्रक्रिया B गैर-अनुकूलक इकाइयों की संख्या
158
267
378
459
5410
6611
7515
878
999
1067

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)

Q8 of the 2023 UPSC Mains Mechanical Engineering Paper I, as printed
The question as printed in the 2023 Mechanical Engineering paper

The figure this question refers to, in words

The question paper is a scan and the diagram did not survive as text. This is the figure as read from the original page — every component, value and label — so the question can be worked from the text below.

(a) Table with columns: Sample No., Process A No. of Non-Conforming Units, Process B No. of Non-Conforming Units. Rows: 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.

(b) Text data: Rake angle = 12 degrees. Vertical component of cutting force = 1600 N. Horizontal component of cutting force = 1250 N. Chip thickness ratio = 0.25.

(c) Diagram titled 'Existing layout with distances'. It shows four rectangular blocks arranged in a horizontal line, labeled from left to right as A, B, C, D. Below the blocks, dimension lines indicate the distance between the center of A and B is 30 m, between B and C is 30 m, and between C and D is 30 m.

What "Calculate" is asking you to do

Apply the standard formula or schedule to data the question has already supplied — a table of readings, cost records, a balance sheet — and produce the number. The method is rarely in doubt; the marks sit in the named intermediate quantities, each of which has to appear as a labelled line.

Structure that answers it

Data as given → formula or standard treatment, named → substitution → each intermediate, labelled → result with units

Where marks are lost

Omitting an intermediate the marking scheme pays for separately, or rounding at an intermediate line so the final figure drifts. In commerce and accountancy, any figure in a statement that no numbered working note supports is treated as unearned.

All UPSC directive words, compared →

How this answer will be evaluated

Approach

Framework: null. (a) calculate: given > formula > substitution > result with units > interpretation | (b) calculate: given > formula > substitution > result with units > interpretation | (c) suggest: the problem in one line > implementable measures > who acts > conclusion Full marks: All calculations correct, clear reasoning, and well-justified layout.

Key points expected

  • Calculate p-bar for each process
  • Compute UCL and LCL using 3-sigma limits
  • Identify out-of-control points for revision
  • Formulate H0 and H1 for Z-test
  • Resolve forces into rake face components
  • Calculate resultant cutting force
  • Determine coefficient of friction
  • Calculate shear plane angle

Evaluation rubric

Each sub-part is marked on its own, against the marks and word limit printed on the paper.

  1. (a) Determine p-chart control limits and perform Z-tests for non-conforming proportions. 20 marks

    calculate— given → formula → substitution → result with units → interpretation

    Must cover

    • Calculate p-bar for each process
    • Compute UCL and LCL using 3-sigma limits
    • Identify out-of-control points for revision
    • Formulate H0 and H1 for Z-test

    Loses marks

    • Fails to check for out-of-control points
    • Incorrect calculation of p-bar
    • Missing hypothesis statement

    Earns more

    • Correctly identifies sample 7 for Process B
    • Recalculates limits excluding out-of-control points
    • Uses correct standard error formula
    • States conclusion clearly for both processes

    Extra mark

    • Provides a clear p-chart visual
    • Explicitly states the significance level used
  2. (b) Compute cutting forces, friction coefficient, and shear plane parameters. 20 marks

    calculate— given → formula → substitution → result with units → interpretation

    Must cover

    • Resolve forces into rake face components
    • Calculate resultant cutting force
    • Determine coefficient of friction
    • Calculate shear plane angle

    Loses marks

    • Incorrect force resolution
    • Missing shear plane angle calculation
    • Confusion between rake and shear planes

    Earns more

    • Correctly applies rake angle in force resolution
    • Accurate calculation of shear force
    • Clear force diagram or vector representation
    • Consistent units throughout

    Extra mark

    • Includes a labelled force vector diagram
    • Verifies results using alternative method
  3. (c) Propose a modified layout to minimize inter-departmental handling costs. 10 marks

    suggest— the problem in one line → implementable measures → who acts → conclusion

    Must cover

    • Analyze current flow matrix
    • Identify high-flow pairs
    • Propose a new layout arrangement
    • Justify the proposed layout

    Loses marks

    • No justification for the new layout
    • Ignores high-flow pairs
    • Layout is not feasible

    Earns more

    • Uses a systematic layout planning method
    • Calculates cost reduction
    • Provides a clear diagram of new layout
    • Conserves existing constraints

    Extra mark

    • Includes a cost comparison table
    • Mentions specific layout planning software

Model answer coming soon

Every evaluation on this site is marked against a verified model answer. This question's answer is still being written; evaluation opens the moment it lands.

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