(a) (i) If the power source characteristic in a Metal Inert Arc welding process is V_P = 38 - I/60, and the arc characteristic is V_a = 3L_a + 27, where V_P and V_a is voltage, I is current and L_a is arc length in mm. Calculate the change in power o

Question

(a) (i) If the power source characteristic in a Metal Inert Arc welding process is V_P = 38 - I/60, and the arc characteristic is V_a = 3L_a + 27, where V_P and V_a is voltage, I is current and L_a is arc length in mm. Calculate the change in power of the arc if the arc length is changed from 1 mm to 3 mm.

If the maximum current capacity of the power source is 300 Amps, then determine the maximum arc length that can be sustained. 10 marks

(ii) An electro-discharge machining process is used for cutting a 6 mm deep cavity in a high carbon steel workpiece using the following:

(I) Copper-tungsten electrode, and

(II) Copper electrode.

Assuming the wear ratio for copper-tungsten electrode as 9 : 1 and for copper electrode as 3 : 1, determine the required spindle movement for cutting this cavity. 10 marks

(b) (i) A long hole having 15 mm diameter and 125 mm depth is required to be drilled in high carbon steel using electro-chemical machining process. Calculate the time required to drill this hole if the supplied current magnitude is 45 Amp and electrolyte used is 15% NaCl. Consider that the valency of iron is 2, atomic weight of iron is 56 and density of steel is 7·8 gm/cm³. 10 marks

(ii) An electro-chemical machining process is used for machining of Nimonic 75 alloy. The composition (% by weight) of Nimonic 75 alloy is given here:

| Ni | Cr | Fe | Si | Mn | Cu | Ti |
|----|----|----|----|----|----|----|
| 72·5 | 19·5 | 5·0 | 1·0 | 1·0 | 0·6 | 0·4 |

Consider the following data:

| Metal | Gram atomic weight | Valency of dissolution | Density gm/cm³ |
|-------|-------------------|------------------------|----------------|
| Nickel | 58·71 | 2/3 | 8·90 |
| Chromium | 51·99 | 2/3/6 | 7·19 |
| Iron | 55·85 | 2/3 | 7·86 |
| Silicon | 28·09 | 4 | 2·33 |
| Manganese | 54·94 | 2/4/6/7 | 7·43 |
| Copper | 63·57 | 1/2 | 8·96 |
| Titanium | 47·9 | 3/4 | 4·51 |

Using the lowest valency of dissolution for each element, determine the material removal rate, when a current of 1050 Amp is applied. 10 marks

(c) With the help of a line diagram, explain the different types of flow patterns used in plant layouts. What are the conditions to be satisfied by an ideal flow pattern ? 10 marks

UPSC Answer Check · Accepted Answer

Calculate numerical solutions for all five sub-parts with systematic derivations. For (a)(i)-(ii), solve MIG arc power equations and EDM spindle movement using wear ratios. For (b)(i)-(ii), apply Faraday's laws of electrolysis for ECM material removal rates. For (c), sketch line diagrams showing straight-line, L-shaped, U-shaped, S-shaped, and circular flow patterns with ideal conditions. Allocate approximately 15 minutes per 10-mark sub-part, ensuring unit consistency throughout.
- (a)(i) Equate V_P = V_a to find operating point; calculate power P = VI at L_a = 1 mm and 3 mm; find ΔP = P_3 - P_1; determine max L_a at I = 300 A using V_P(300) = V_a(L_a,max)
- (a)(ii) Apply EDM wear ratio definition: tool wear/workpiece removal; for 6 mm depth cavity, spindle movement = depth × (1 + wear ratio) for each electrode material
- (b)(i) Apply Faraday's law: MRR = (A × I)/(ρ × Z × F); calculate volume of hole = π×(1.5)²×12.5 cm³; time = volume/MRR using given NaCl electrolyte data
- (b)(ii) Calculate equivalent gram equivalent weight for Nimonic 75 alloy using lowest valencies; apply weighted average based on composition percentages; MRR_total = (I × Σ(w_i × A_i/Z_i))/(F × ρ_eff)
- (c) Draw line diagrams for: straight-line (product layout), L-shaped (medium variety), U-shaped (cellular manufacturing), S-shaped (process layout), circular (robotic/FMS); state ideal conditions: minimum backtracking, shortest distance, smooth flow, flexibility, safety

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	20%	10	Correctly applies power source-arc characteristic intersection for MIG welding; uses proper wear ratio interpretation for EDM spindle movement; applies Faraday's laws with correct valency selection for ECM; identifies all five flow pattern types with appropriate industrial examples (e.g., U-shaped for Maruti Suzuki assembly)	Correct basic formulas but minor errors in valency selection or wear ratio application; identifies 3-4 flow patterns with generic descriptions	Confuses MIG with TIG characteristics; treats EDM wear ratio as simple subtraction; applies incorrect valency or ignores alloy composition weighting; describes only 2 flow patterns or confuses with plant layout types
Numerical accuracy	20%	10	All five sub-parts yield correct numerical answers with proper significant figures: (a)(i) ΔP and L_a,max exact; (a)(ii) spindle movements for both electrodes correct; (b)(i) drilling time accurate to 2 decimal places; (b)(ii) MRR with proper alloy calculation; units consistent (mm, cm³, min, g/min)	Correct approach but arithmetic slips in 1-2 sub-parts (e.g., decimal error in Faraday constant or density conversion); final answers within 10% of correct value	Major calculation errors in multiple sub-parts; wrong formula substitutions (e.g., using thermal conductivity instead of electrochemical constants); inconsistent or missing units
Diagram quality	20%	10	Clear line diagrams for all five flow patterns with arrows showing material movement direction; labelled workstations/departments; (c) includes comparison table or integrated sketch showing when each pattern suits Indian manufacturing contexts (e.g., S-shaped for HAL aircraft component flow)	Diagrams present but missing directional arrows or labels; 3-4 flow patterns shown instead of five; rough freehand sketches without scale	No diagrams for flow patterns; or diagrams confused with plant layout types (product vs process); illegible sketches without any labels
Step-by-step derivation	20%	10	Shows complete derivation: (a)(i) equating linear equations, solving simultaneous equations for I and V; (a)(ii) explicit wear ratio formula; (b)(i) volume calculation → MRR formula → time; (b)(ii) weighted equivalent weight calculation with tabular presentation; all algebraic steps visible	Key steps shown but skips intermediate algebra (e.g., jumps to final MRR without showing alloy composition calculation); some substitution steps implied rather than explicit	Final answers only with no derivation; or incorrect formula stated without justification; missing essential steps like unit conversions or simultaneous equation setup
Practical interpretation	20%	10	Interprets (a)(i) arc length effect on heat input and penetration; (a)(ii) explains why Cu-W preferred for precision vs Cu for economy; (b) comments on ECM advantages for hard alloys vs conventional drilling; (c) relates flow patterns to lean manufacturing principles and Indian SME applicability; suggests improvements for each pattern's limitations	Brief practical comment on 2-3 sub-parts (e.g., ECM good for hard materials) but superficial; generic statements without process-specific insight	No practical interpretation; treats all problems as pure mathematics; or makes incorrect practical claims (e.g., EDM suitable for soft materials)

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