## Design of Machine Elements 2 - May 2016

### Mechanical Engg. (Semester 6)

TOTAL MARKS: 100

TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.

(2) Attempt any **four** from the remaining questions.

(3) Assume data wherever required.

(4) Figures to the right indicate full marks.
**1(a)** Determine the dimensions of the curved bar shown in Fig.Q1(a) Assume σ_{yt}=400M/Nm^{2} and FOS=3.5.

!mage(10 marks)
**1(b)** A circular plate made of steel and of diameter 200 mm with thickness 10 mm is subjected to a load inducing a pressure of 4 MN/m^{2}. Taking E = 201 kN/mm^{2} Poisson?s ratio 0.3, Determine

(i) Maximum stress, its location and maximum deflection when the edges of the plate are supported.

(ii) Maximum stress, its location and maximum deflection when the edges ofthe plate is fixed.

**2(a)**A flat belt 200 mm wide weighting 20N/m connecting a 300 mm diameter pulleyto a 900 mm diameter driven pulley at a shaft spacing of 6 m, transmits 55.2kW at a belt speed of 25m/sec

i) Calculate the belt length and the a angles of wrap

ii) Compute the belt tensions based in a coefficient of friction 0.38.(10 marks)

**2(b)**A V-belt drive is required to transmit 15 kW at 210 mm sheave running at 750 rpm to another pulley to run at 375 rpm. The belt used is 30 mm wide at top, 21 mm thick with V-angle 40°. The allowable stress for belt material is Mpa. Center distance is 1.2m. Specific weight of belt material is 1.1 gm/cc. Coefficient of friction of smaller pulley is 0.3 and for large pulley is 0.25. Find the number of bnelt of given cross-section required for this application.(10 marks)

**3(a)**Derive the expression for the stress induced in a helical spring with usual notations.(7 marks)

**3(b)**Write a note on Wahl stress correction factor.(3 marks)

**3(c)**A semi-elliptical leaf spring has a span of 1.8m. The spring carriers a helical spring upon which is imposed an impact of 3kN-m. The laminated spring has 8 graduated and 3 full length leaves each 60mm wide and 6mm thick. The coil spring has coil of 12.5 mm write diameter and a spring index of 7. Find the stresses induced in each spring. Take G=80×10

^{3}MPa,

E=206×10

^{3}MPa.(10 marks)

**4(a)**State any four advantages of gear drive over other types of drives.(4 marks)

**4(b)**A pair of spur gears with 20° full depth involute teeth consists of a 20 teeth pinion meshing with a 41 teeth gear. The module is 3 mm while the face width is 40mm. The material for the pinion as well as the gear is steel with an ultimate tensile strength of 600 MN/M

^{2}. The gears are heat treated to a surface hardness of 400BHN. The pinion rotates at 140 rpm and the service factor for the application is 1.75. Assume that the velocity factor accounts for the dynamic load and the factor of safety is 1.5.Determine the rated power that the gears can transmit.(16 marks)

**5(a)**A two teeth right hand worm transmits 2 k W at 1500 rpm to 36 teeth wheel. The module is 5 mm and pitch diameter of worm is 60mm. The pressure angle is 14.5°. The co-efficient of friction is found to be 0.06 Find :

i) The center distance, lead and lead angle

ii) The efficiency of the derive

iii) The forces.(10 marks)

**5(b)**A pair of bevel gear wheels with 20° pressure angle consist of 20 teeth pinion meshing with 30 teeth gear. The module is 4 mm while the face width is 20 mm. Surface hardness for both pinion and gear is 400BHN. The pinion rotates at 500 rpm and receives power from an electric motor. The starting torque of the motor is 30% greater than the mean torque, Determine the safe power that can be transmitted. Considering dynamic load, wear strength and blending strength. The allowable bending stress may be taken as 240MPa.(10 marks)

**6(a)**Determine the dimensions of a simple cone clutch to transmit 20kW at 1000 rpm. The minimum diameter is to be 300 mm and the cone angle 20° Assume μ=0.2 and permissible pressure=0.1 MN/m

^{2}. Also determine the axial force required to engage the clutch.(10 marks)

**6(b)**A differential band break as shown in Fig.Q6(b), has an angle of contact of 225° . The band has a compressed woven lining and bears against a cast iron drum of 350 mm diameter. The brake is to sustain a torque of 350N-m and the coefficient of friction between the band and the drum is to 0.3. Find

i) the necessary force P for the clockwise and anticlockwise rotation of the drum.

ii) The value of 'OA' for the brake to be self locking when the drum rotates clockwise.

(10 marks)
**7(a)** Derive Pertoff's equation for coefficient of friction for hydrodynamic bearing.(8 marks)
**7(b)** The trust of a propeller shaft in a ship engine is taken by a number of collars integral with the shaft which is 300mm/diameter. The trust on the shaft is 200kN and speed is 75 rpm. Bearing pressure id 0.3MN/m^{2}. Find

i) the number of collar required if the outside diameter is 500 mm

ii) Power lost in friction assuming uniform wear

iii) Heat generated in the bearing.(12 marks)
**8(a)** Design a connecting rod for a petrol engine from the following data :

Cylinder bore or diameter of piston = 100 mm.

Length of connecting rod = 350 mm

Maximum gas pressure = 3N/mm^{2}

Length of stroke = 150mm

Engine speed=1500 rpm

Weight of reciprocating parts = 25N

Compression ratio=4:1

Compression rod is made of steel and assume 'I' section. Assume any further data required for the design.(20 marks)