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Mechanical System Design (April 2010)

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Total No. of Questions : 12] [Total No. of Pages : 6 P1393 [3764]-131 B.E. (Mechanical) MECHANICAL SYSTEM DESIGN (2003 Course) Time : 4 Hours] [Max. Marks : 100 Instructions to the candidate: 1) Answer three questions from Section I and three questions from Section II. 2) Answers to the two sections should be written in separate answer book. 3) Neat diagrams must be drawn wherever necessary. 4) Use of logarithmic tables slide rule, Mollier charts, electronic pocket calculator and steam tables is allowed. 5) Assume suitable data, if necessary. SECTION - I Q1) a) Derive the equation for the thickness of a thick cylinder subjected to internal pressure by maximum shear stress theory. [6] b) A cylindrical pressure vessel shell of inside diameter 1500 mm is subjected to an internal pressure of 2 MPa. The shell as well as the heads are made of low alloy steel with sult = 450 MPa. Double welded butt joints which are spot radiographed are used to fabricate the vessel. Corrosion allowance is 3 mm. Determine the thickness of the cylindrical shell and thickness of head if the heads are i) Flat ii) Plain formed iii) Torispherical with crown radius of 1125 mm. [12] OR Q2) a) Describe with sketch different types of supports used in horizontal pressure vessels. [6] P.T.O. 1 b) Design a skirt support for a vertical pressure vessel with following specifications. Diameter of vessel = 3 m. Height of vessel = 40 m. Mass of vessel and its contents = 200 tons. Diameter of skirt = 3 m. Height of skirt = 4 m. Wind pressure upto 20 m = 1.2 KPa. Wind pressure above 20 m = 1.5 KPa. Allowable tensile stress of skirt = 65 MPa. Allowable compressive stress of skirt = 98 MPa. [12] Q3) A cantilever beam of circular cross section is subjected to the specified constant vertical force F and Torque T at its free end. The factor of safety based on tensile yield strength is N. Due to space limitations, the length and diameter of the beam should not exceed Lmax and dmax respectively. Outline the procedure for the design of the beam with the objective of maximising the strain energy absorption capacity using following materials. a) Steel b) Aluminium alloy c) Titanium alloy. Use maximum shear stress theory of failure. [16] OR Q4) A tensile bar of circular cross section and made of plain carbon steel (Sult = 580 MPa, Syp = 330 MPa, E = 207 GPa and = 7750 MPa) is subjected to cyclic tensile force which varies from zero to 90 kN. The required stiffness of the bar is 3.5 105 N/mm. The surface finish and size factors are 0.76 and 0.6 respectively. Using the Soderberg equation, design the bar with the objective of optimising the factor of safety. Following limitations are used in design. d 30 mm 350 mm M 500 mm. 3 kg. [3764]-131 2 l [16] -2- Q5) Torque produced by a 4 stroke diesel engine is given by T = 4000 + 1500 Sin + 4000 Sin2 Nm. Where is the angle turned through by the crank shaft. Speed of the engine is to remain between 200 rpm and 210 rpm as it is loaded with a negligible moment of inertia and uniform torque device. Design a suitable flywheel of CI having tensile strength of 160 MPa. Maximum size of the flywheel is limited to 2 m. Neglecting the effect of [16] spokes find the stress in the rim, = 7200 kg/m3, b = 2t. OR Q6) A mechanical press is designed to punch 20 mm diameter holes in 15 mm thick plates. The material of plate has an Sult = 380 MPa. The press is designed to punch 60 holes/min and punching 1 hole in each stroke. The hole is punched during 75o of the eccentric travel. The eccentric shaft is connected to a flywheel through a gear train of ratio 6:1. The overall efficiency of the press is 75%. The speed fluctuation and the mean diameter of the flywheel rim are limited to 16% and 1.1 m respectively. Design the rim type CI flywheel with 8 spokes of elliptical cross section. The permissible tensile stress for CI may be taken as 10 MPa. Assume flywheel rim width to depth ratio as 1.5:1. Determine also the kW rating of the electric motor required to drive the press. = 7200 kg/m3. Rim contributes 90% of total inertia. [16] SECTION - II Q7) a) A shaft and hole assembly have the following dimensions. Shaft diameter = 40 0.18 mm. Hole diameter = 40.2 0.24 mm. Assuming the shaft and hole diameters are normally distributed, determine the probability of interference fit between the shaft and hole area from 0 to Z is as given below. Z 1.6 Area 0.4452 b) 2.0 2.2 2.4 0.4641 0.4772 0.4861 0.4918 Explain with sketch design principles in machining. [3764]-131 3 1.8 -3- [10] [8] OR Q8) a) A mechanical component is subjected to a mean stress of 207 MPa with a standard deviation of 55.2 MPa. The material has a mean strength of 276 MPa with a standard deviation of 41.4 MPa. i) Find the probability of failure. ii) If the material is changed such that its mean strength is 380 MPa find the probability of failure. Area from 0 to Z is as Z 1.0 Area 0.3413 b) 2.5 3.0 0.4938 0.4987 Explain with sketch design considerations in controls. [12] [6] Q9) a) Establish the structure equations for a 4 speed gear box and draw their structure diagrams. [6] b) Draw the ray and speed diagram for a six speed gear box. State the necessary assumptions made. [6] c) Derive the relation for difference between number of teeth of successive gears in a change gear block. [4] OR Q10)a) b) Q11)a) b) A 2 2 drive is required for transmitting speeds starting from 400 rpm with a geometric progression ratio of 1.4. Draw a suitable structure and speed diagram. Also draw the layout of the gear box and determine the number of teeth on each gear. Assume that a belt drive is used to get the desired speed at input from motor shaft. [12] Explain nodal method of optimisation with example. [4] State the advantages of a belt conveyor over other conveyors. [6] A flat horizontal belt conveyor is used for transporting crushed rock having a mass density of 2 t/m3. The belt is 800 mm wide and has a speed of 1.75 m/s. Determine the capacity of conveyor in t/hr. [10] OR Q12)a) Describe in brief various resistances offered on belt conveyor. [3764]-131 4 -4- [4] Plow b) Tail pulley Drive pulley 1.5 m Snub pulley Snub pulley Rotary cleaner A horizontal conveyor is used in transporting mineral ore. Maximum capacity of the conveyor is 225 tph at belt speed of 2 m/s. The mineral ore has a density of 800 kg/m3. A three ply belt is used for which surcharge factor is 0.08. The mass of each idler is 20 kg. The centre to centre distance between drive pulley and tail pulley is 300 m while that between snub pulleys is 299 m. Friction factor for idlers = 0.025. Snub factor for both snub pulleys = 0.02. Snub factor for drive and fail pulleys = 0.06. Velocity of rotary brush cleaner = 2 m/s. Kclean, Cleaning factor = 5 Vclean. Cleaning force = KcleangB. Unloading resistance = 3.5 mmgB. B: belt width in m, mm - mass of material/unit length (kg/m). Angle of lap on drive pulley = 210o. Coefficient of friction between belt and drive pulley = 0.4. Ultimate tensile strength per width of ply = 60 N/mm. Drive efficiency = 93%. Motor speed = 1440 rpm. Carrying idler pitch, Pc = 1.5 m. Approximate return idler pitch = 2 Pc. Assume pulley diameter as 125 times number of ply. Standard pulley diameter : 315, 400, 500, 630, 800, 1000 mm. Standard motor rating : 5, 5.5, 7.5, 10, 11, 12.5, 15, 20, 22 kW. [3764]-131 5 -5- Standard belt width B mm mb (kg/m) 400 500 650 800 1000 5 6.5 9 12 16 Find :i) Standard belt width. ii) Standard diameter pulley. iii) Number of carrying and return side idler pulleys. iv) Standard electric motor. [3764]-131 6 -6- [12]

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