(a) Explain the principle of electric discharge machining (EDM) using suitable diagram. Describe the effect of process parameters…

Part (a) Electric discharge machining removes material by controlled thermal erosion, not by mechanical cutting. A conductive tool electrode and workpiece are held apart by a small dielectric-filled gap; a pulse generator applies short high-voltage pulses across the gap. When the dielectric breaks down, a spark discharge occurs, locally heating the workpiece to melting/vapourisation temperature. A tiny volume of metal is ejected, and the dielectric flushes debris, cools the zone and re-insulates the gap. A servo system maintains the gap by feeding the tool according to discharge conditions. In a suitable diagram, the tank contains dielectric, a pump circulates it, the pulse-generator circuit connects the tool and workpiece, and the tool-workpiece gap is shown. The tool is generally made cathode and workpiece anode for many materials, though polarity can be changed to control wear.

Process parameters control energy per spark and gap stability. Increasing pulse on-time or peak current raises energy per discharge, so material removal rate increases, but larger craters, deeper recast layer, higher surface roughness, more electrode wear and poorer tolerance follow. Higher gap voltage also increases spark energy and MRR, but excessive voltage causes arcing, irregular craters and worse finish. Longer pulse off-time improves flushing and dielectric recovery, reducing arcing and improving surface finish and dimensional tolerance, but it lowers MRR. Adequate flushing pressure and dielectric properties remove eroded particles, maintain a stable gap, and improve surface characteristics; poor flushing causes short circuits and rough surface. Thus EDM involves a trade-off: high MRR is obtained with high current and long on-time, while fine finish, tight tolerance and low wear require low current, short on-time, longer off-time and good flushing.

Part (b) Current capacity is 100,000 units and unutilised capacity is 10,000 units, so current sales volume is 90,000 units. Margin of safety (MOS) is given as 50% of break-even point (BEP). Since MOS = Sales − BEP, let BEP = x. Then 0.5x = 90,000 − x, giving 1.5x = 90,000 and x = 60,000 units. Hence BEP in sales volume is 60,000 units and MOS is 90,000 − 60,000 = 30,000 units. The P/V ratio is 25%, so contribution per unit is 25% of selling price ₹40, i.e. ₹10 per unit. Variable cost per unit is therefore ₹40 − ₹10 = ₹30. At break-even, total contribution equals fixed cost; fixed cost = 60,000 × ₹10 = ₹6,00,000. Thus fixed costs are ₹6,00,000, variable cost is ₹30 per unit, BEP is 60,000 units and MOS is 30,000 units.

Part (c) The centre of gravity model chooses the facility location that minimises weighted transportation distance by using supply quantities as weights. The coordinates and weights are: A (125,550) with 200 t; B (350,400) with 450 t; C (450,125) with 175 t; D (700,300) with 350 t. Total supply W = 200 + 450 + 175 + 350 = 1,175 tons. The weighted x-coordinate is X̄ = (200×125 + 450×350 + 175×450 + 350×700)/1,175 = (25,000 + 1,57,500 + 78,750 + 2,45,000)/1,175 = 5,06,250/1,175 = 430.85 units. The weighted y-coordinate is Ȳ = (200×550 + 450×400 + 175×125 + 350×300)/1,175 = (1,10,000 + 1,80,000 + 21,875 + 1,05,000)/1,175 = 4,16,875/1,175 = 354.79 units. Therefore the most appropriate point on the grid is approximately (431, 355). This point lies nearer to the high-supply points B and D, showing that the solution is sensitive to the weight distribution; if supplies change, the centre of gravity should be recalculated.