C. S. (MAIN) 2009

MECHANICAL ENGINEERING

Paper-I

Time Allowed Three Hours Maximum Marks 300

INSTRUCTIONS

Each question is printed both m Hindi and in English.

Answers must be written in the medium specified in the Admission Certificate issued to you, which must be stated clearly on the cover of the answer-book in the space provided for the purpose. No marks will be given for the answers written in a medium other than that specified in the Admission Certificate.

Candidates should attempt Question Nos. 1 and 5 which are compulsory, and any three of the remaining questions selecting at least one question from each Section.

The number of marks carried by each question is indicated at the end of the question. Symbols/ notations carry their usual meanings, unless othen..uise indkated. If any data is considered insufficient, assume suitable value and indicate the same clearly. Newton may be converted to kg using the equality 1 kilo newton 1 kN) 100 kg, if found necessary.

Section-A

1. Attempt any three of the following

Define a general case of forces acting on a rigid body. State clearly and precisely the equations of equilibrium for this body. How do these equations change when applied to a particle? 8

A smooth hollow cylinder of radius r open at both ends rests on a smooth horizontal plane. Two smooth spheres of weights W1 and W2, and radii r1 and r2 respectively are placed inside the cylinder, with the larger sphere (radius r2 resting on the horizontal plane as shown in Fig. 1. Determine the minimum weight W of the cylinder that will prevent the cylinder from tipping over. <img src='./qimages/40-1a2.jpg'> 12

A beam is of square section with diagonals 60 mm long, vertical and horizontal, as shown in Fig. 2. Shear force at a particular section is 5 kN. What is the shear stress at layer AB as shown?
<img src='./qimages/40-1b1.jpg'> 15

A beam ABCD, 6 m long, hinged at both ends A and is subjected to moments 6 kN-m at B and 3 kN-m at C as shown in Fig. 3. Sketch the bending moment diagram of the beam. How many points of contraflexure are there in the beam? <img src='./qimages/40-1b2.jpg'> 5

In an orthogonal crystal structure with lattice parameters a ¢ b ¢ draw the direction T 2}. 10

Show that in a hexagonal closepacked structure, atomic packing factor is 0·74. Take dimension C 1 · 633 a. 10

What is meant by 'whirling or critical speed of shaft? 4

Calculate the whirling speed in case of a rotating steel tube simply supported in short bearings 2 m centre-to-centre. The external and internal diameters of the tube are 35 mm and 25 mm, respectively. The weight of steel may be taken as 78 kN/m 3 and Young's modulus of elasticity for steel is 200 GPa. 16

2.a(i) State why gear teeth have to be undercut. 4

The following data refers to two 2 0° involute spur gears in mesh externally Velocity ratio 3 Module 3 mm Addendum 1· 1 module If the pinion rotates at 120 r.p.m., find- the minimum number of teeth on each gear wheel to avoid interference; the number of pairs of teeth in contact. 16
A plate is riveted to a channel section in a structure as shown in Fig. 4. An eccentric load of 12·5 kN acts as shown on the plate. Determine the rivet diameter so that the maximum shear stress in any rivet is not to exceed 40 MPa. Diameter of the rivet should be chosen from preferred series. <img src='./qimages/40-2b.jpg'> 40

3. A homogeneous ball of weight Q and radius a as well as a weight P are suspended by cords from a point O as shown in Fig. 5. The distance OM is b. Find the inclination of OM with the vertical when the system is in equilibrium. <img src='./qimages/40-3a.jpg'> 8
A body A of weight IO kN is connected to an another body B of weight 50 kN, resting on a smooth table of weight 200 kN through an inextensible thread, passing over a fr eely rotating pulley mounted on a comer of the table. Find the vertical component of the reaction of the ground on the table when the bodies A and B are in motion. Does the reaction change with time? The system is shown in Fig. 6. <img src='./qimages/40-3a2.jpg'> 12

Stresses on two perpendicular planes, at a point, are given in Fig. 7. What are the directions of principal planes with respect to plane BC What are the principal strains on principal planes, if <img src='./qimages/40-3b.jpg'> 20

A beam ABCD, 5 m long, is supported at A and C as shown in Fig. 8. It carries a point load of 2 kN at end and a moment of 2 cw) at B. What is the flexural rigidity of the beam, if deflection at Dis not to exceed 1 mm? <img src='./qimages/40-3c.jpg'> 20
4. State the function of a flywheel. 4
A punching machine carries out 5 holes per minute. Each hole of 40 mm diameter in 40 mm thick plate 10 N-m of energy/ mm 2 of the sheared area. The punch has a stroke of 100 mm. Find the power of the motor required, if the mean speed of the flywheel is 25 s. If the total fluctuation of speed is not to exceed of the mean speed, determine the mass of the flY'-vheel. 16

A shaft carries four rotating masses C and Din sequence along its axis. The masses C and D are assumed to be concentrated at radii of 12 cm, 16 cm, 8 cm and 10 cm, respectively. The masses of C and D are 30 kg, 50 kg and 40 kg, respectively. The planes containing B and C are 30 cm apart. The angular spacing of the planes containing C and D are 90° and 210°, respectively relative to B measured in the same sense. If the system is to be in complete dynamic balance, find- .the mass and angular position of mass the spacing positions of the planes containing A and B. 20

Give chemical reactions and temperature ranges in the cases of cyaniding, carbonitriding and nitriding processes. What is the serious problem encountered in nitriding process? In which process is case hardened thickness maximum? 20

Section-B

5. Attempt any three of the following

Describe the properties of tungsten carbide as a cutting tool material and its applications. 5
<img src='./qimages/40-5a2.jpg'> 8
Explain 'sudden-death mechanism' of tool fa ilure. 4
What are extreme-pressure lubricants?


Define the terms 'rose reamer' and 'feed in milling'. 2+2
Name four independent variables and three dependent variables 1n metal cutting. 5
What 1s the function of stepper motor? 2
With a sketch, explain the principle of working and variations of bed-type milling machine. 9

Name the fa ctors to be considered while choosing a good fo recasting system. 5

The quarterly demand of a company product for past six years is given in the table below. The four-quarter moving average is also given. Find the seasonality index for 3rd quarter. 15 Quarter Demand Four-Quarter <img src='./qimages/40-5c2.jpg'> 15


Explain briefly the MTM. Which basic motions does it recognize? Suggest its applications and also describe the sequence of steps of procedure to implement the same. 1 2
The following costs were incurred in a year in a company. Classify them into various quality costs. <img src='./qimages/40-5d2.jpg'> 8
6.a(i) What do you mean by 'interchangeable manufacture' and combination set? 8
What is the difference between a plug gauge and a ring gauge? 4
Discuss, with figure(s), pneumatic gauges and their applications. 8


How does inventory level depend on service level?5
4000 spare parts are required annually. A set-up cost of Rs 100 and a carrying cost of 25°/o per year 1s charged on the item cost of Rs 320. The production fa cility is open for 5 days per week and 50 weeks per year. The lead time of this product 1s 9 days and the standard deviation of the demand is 2 units per day. The company wants to have a 95% service level for this spare part. If the company were using continuous review sy stem (Q-system) of inventory control, compute the order quantity and reorder level. Interpret the results. If the company were using periodic review system (P-system) of inventory control, give the 5 specific decision rule. 15
Briefly state the intermittent process layout problem. 5
Five departments are currently arranged in the followin.g manner <img src='./qimages/40-6c2.jpg'> New products have been added and the movements between the departmen ts have changed substantially.since the existing arrangement was made. The movement between the departments is on rectangular path. The monthly number of trips, cost/trip and distance of each trip are given below: <img src='./qimages/40-6c3.jpg'> 1 Calculate the monthly cost of travel between the departinents. How much is the saving in monthly cost of travel between the departments, if departments 1 and 3 are interchanged? A one-time cost of Rs 2 2 500 is associated with interchanging the positions of departments 1 and and if this cost is to be recovered within two months, should the change be made? 1 5
Na.me the various alloying elements used with tungsten for GTAW. Give the approximate content of any two used in GTAW process. Enumerate applications of GTAW process. 4
Define the term 'keyholing1 used in laser welding. 3
What 1s 'dip transfer' in GMAW? 3
Write the differences between coining and embossing. 4
What are the advantages of isothermal forging? 3
What 1s the difference between extrusion and drawing? 3
Define 'slack'. 5
A project consists of six activities. The precedence relationship of activities and the three time estimates of completion of activities in days are tabulated below <img src='./qimages/40-7b2.jpg'> 1 Draw the arrow diagram. Which of the six activities 1s most uncertain? What is the probability that the project will be completed within 1 0 days? Refer the SND-chart (Cumulative Distribution Function for the Standard Normal Distribution) attached at the end. 1 5

A company uses a decision rule to determine production level in t-th period, as under Pt Pt 1 (Ft Pt i where Pt Ft denote production and forecast for t-th period and A is smoothing constant. 1 Given the information in the table below, find the appropriate production level for period 2 using a smoothing constant of <img src='./qimages/40-7c1.jpg'> Assuming that actual production for period 2 will be equal to the value as determined in case above, determine the prod uction levels for period 3 using chase, level and intermediate strategies. 1 0
A company manufactures two products A and B. The manufacturing and marketing data for the two products is given below <img src='./qimages/40-7c2.jpg'> 1 Formulate the problem . Find the product mix that will maximize the profit. 1 0

8. Describe the applications of abrasive-jet machining. 5
What are the differences between electrolyte and dielectric? 5
What is wire EDM process? Explain the reasons for its popularity. 1 0
With a figure, explain 1 method of location. 1 0
Draw leaf jig and mention its advantages. 10
Give the steps for sequencing n jobs through 2 machines for minimum elapsed time. 5
A foreman wants to process four different jobs on three machines B and C in his shop. The order of machining for all the jobs is fixed> i.e., B and C. The processing time for all the jobs are given in the table below <img src='./qimages/40-8c2.jpg'> Decide the optimal sequence for the jobs to minimize the elapsed time between start of the first job to completion of the last job. 15


Note English version of the Instructions is printed on the front cover of this question paper.