MEGHANICAL ENGINEERING, PAPER- I – 2003,SECTION A

                   Time Allowed: three Hours                  Maximum Marks: 200

Candidates should attempt Questions 1 and 5 which are compulsory, and any THREE of the remaining questions selecting at least ONE question from each Section. Assume suitable data, if considered necessary, and indicate the same clearly. Newton may be converted to kg using the relation 1 kilonewton (1 kN) = 100 kg if found necessary.

SECTION A

1.       Answer any four of the following (each answer should conform to a limit  of around 150 words): 
             (a)                 (i) Distinguish between the laws of friction for dry and film lubricated surfaces.

What conditions must be satisfied in order that film lubrication may be obtained

  (ii) Explain the difference between oiliness and viscosity of a lubricant.

Discuss the conditions under which friction between two lubricated surfaces is influenced by the two properties respectively.

           (b)   Explain briefly the role of factors that influence the change in the sum of tensions on the slack and tight side of a belt transmission, as power transmitted is increased.

Why is a horizontal drive capable of transmitting more power than a similar vertical drive?

          (c)    Explain clearly the meanings of terms:

Elastic solid, nonelastic solid, inelastic solid, linearly elastic solid and nonlinearly elastic solid.

Illustrate your answer using a diagram showing the load deformation relationship for the above solides.

          (d)                          (i) Define allotropy. Give an example of different allotropic  forms of a material

   (ii) What is edge dislocation?

   (iii) Prove that the atomic packing factor of a HCP (Hexagonally. Close –Packed) structure is 0.74.

          (e)   (i) What are solubility limits? 
               (ii) Describe a eutectic structure.

(iii) Why does the cooling curve for a pure meal show a isothermal hold at the freezing point?

2.       (a)  (i) Explain briefly. Why the static deflection curve of a loaded shaff may be used as a whirling form.

(ii) Establish the relationship of critical speed with loads and load point deflections.

(b) a shaft Y is driven by a coaxial shaff X through the epicy click gear train as shown in the above figure . The wheel A is keyed to X, and E to Y. the compound wheel BD s carried on the arm F which can rotate freely about the common axis of X and Y. The wheel C is fixed.

The number of teeth on the gears A, B, C, D and E are respectively 20, 64, 80, 30 and 50. The shaff X rotates at 600rpm clockwise looking from A.

Determine the speed (in RPM) of Y and the direction of rotation, looking from E.

3.       (a) A beam has a cross-section in the form of an isosceles triangle of base b and height h. Derive an expression for the magnitude of the maximum horizontal shearing stress under a vertical shear force V. What will be the location of the plane of this stress?

If the beam has b = 10 cm, and h = 30 cm find the magnitude of maximum shear stress, and the shear stress at neutral axis when V= 10, 000 kgf.

     (b) Two springs, outside diameters a45 mm and 65 mm respectively are made with a steel wire of diameter 5 mm and are placed coaxially. Both the springs have 25 active coils but the outer spring is 27 mm longer than the inner one.

Find the compression of the inner spring when a load of 15 kgf is placed on a plate supported initially by the outer spring.

G for spring wire = 8 x 10⁵ kgf/ cm².

4.       (a) state the theories of failure based on the following criteria:

(i)                  Maximum stress

(ii)                Maximum shear stress

(iii)                Maximum strain Energy

(iv)              Maximum distortion energy

Compare the safe domains based on the above criteria illustrating your answer with a σ₁, σ₂ safe domain plot for a two dimensional stress state. Compare the safe values based on each of the above theories for the specific case σ₁ = - σ₂

     (b) Determine the width of 9.5 mm thick leather belt required to transmit 10 kW from a motor running at 750 rpm. The motor pull is 300 mm distance between the pully runs at 250 rpm and the centre distance between the pulleys is 3 m. 

Assume an open belt drive with no slip and Relative Density of Leather = 1.0

Maximum Permissible Stress for leather belt = 2.46 N/ mm²

Friction between belt and pulley = 0.3

Neglect the sag of belt, and the effect of thickness of belt on velocity.