## Design of Machine Elements I - Dec 2014

### Mechanical Engg (Semester 5)

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.

### Answer any one question from Q1 and Q2

**1 (a)** Explain various types of failure to be considered in designing a cotter joint. Write down strength equation for each failure along with necessary sketches.(6 marks)
**1 (b)** A solid circular shaft a diameter 'd' is subjected to a torsional moment of M_{t} over a length of 'L'. The permissible angle of twist is 'θ' prove that the shaft diameter is given by $$ d= \left [ \dfrac {584 MtL}{Ge} \right ]^{1/4} $$(4 marks)
**10 (a)** Derive an expression for the shear stress induced in a helical compression spring with usual notations.(6 marks)
**10 (b)** Design a concentric spring for an air craft engine valve to exert a maximum force of 5000N under deflection of 40mm. Both the springs have same free length, solid length and are subjected to equal maximum shear stress of 0.85 GPa, spring index for both spring is 6. Assume G=80 GPa and diametral clearance to be equal to difference between wire diameter.(12 marks)
**2 (a)** The section of the crane hook is circular in shape whose diameter is 60 mm. The centre of the curvature of the section is at a distance of 125 mm from the inside section and the load line is 100 mm from the same point. Find the capacity of the hook if the allowable stress in tension is 75 MPa.
(6 marks)
**2 (b)** Prove that square key is equally strong in crushing and shearing. State the assumptions you make.(4 marks)

### Answer any one question from Q3 and Q4

**3 (a)** Why coupling are located as near as possible to the bearings?(2 marks)
**3 (b)** A circular bar of 500 mm length is supported freely at its two ends. It is acted upon by a central concentrated cyclic load having a minimum value of 50 KN. Determine the diameter of the bar by taking a factor of safety of 1.5 size effect of 0.85, surface finish factor of 0.9. The material properties of bar are given by Ultimate strength of 650 MN/m^{2}, yield strength of 500 MN/m^{2} and endurance strength of 350 MN/m^{2}.(8 marks)
**4 (a)** Suggest suitable coupling in the following cases:

i) Shaft having parallel axes with small distance apart.

ii) Shaft having intersecting axis.(2 marks)
**4 (b)** A machine part is subjected to biaxial stress system. The stress in the X direction varies from +30 to 110 MN/m^{2} while the stress in Y direction varies from +10 to 80MN/m^{2}. The frequency of vibration of these stresses is equal. The endurance limit of the machine part is 260 MPa. The ultimate tensile strength of the material is 0.66 GPa. Determine the factor of safety used by the designer.(8 marks)

### Answer any one question from Q5 and Q6

**5 (a)** How does the helix angle influence on the efficiency of square threaded screw?(4 marks)
**5 (b)** A triple threaded power screw used in a screw jack has nominal diameter 50 mm and a pitch of a 8mm. The threads are square and length of nut 48mm. The screw jack is used to lift a load of 8KN. The coefficient of friction at the threads is 0.12. Calculate

i) the principal shear stress in the screw body

ii) the transverse shear stresses in the screw and the nut and

iii) the unit bearing pressure. State the condition of screw with statement.(12 marks)
**6 (a)** What is recirculating ball screw? Explain with neat sketch.(4 marks)
**6 (b)** A C Clamp as shown in fig (2) has a trapezoidal threads of 12 mm outside diameter and 2mm pitch. The coefficients of friction for screw is 0.12 and for the collar is 0.25. The mean radius of the collar is 6mm. If the force exerted by the operator at the end of the handle is 80 N. Find

i) the length of the handle

ii) the maximum shear stress in the body of the screw and where does this exit

iii) the bearing pressure on the threads

iv) efficiency of the mechanism.
(12 marks)

### Answer any one question from Q7 and Q8

**7 (a)** Explain the method of determining the size of bolt when the bracket carriers an eccentric load perpendicular to the axis of the bolt.(6 marks)
**7 (b)** Determine the size of the bolt for the joint as shown in figure (3). The bracket is made of steel τ_{y}=254 MPa, factor of safety 2
(10 marks)
**8 (a)** What are the assumptions made in the design of welded joint? Also discuss the procedure for designing an eccentric loaded welded joint.(6 marks)
**8 (b)** A welded joint as shown in figure (4) is subjected to an eccentric load. A bracket is welded to the side of a column and carries a vertical load P as shown in figure. Calculate the value of 'P' so that the maximum shear stress is 80MPa when the size of weld is 12 mm.
(10 marks)

### Answer any one question from Q9 and Q10

**9 (a)** Explain what do you understand by AM Wahl's factor and state its importance in the design of helical springs?(6 marks)
**9 (b)** The valve spring of a gasolina engine is 40 mm long when the valve is open and 48 mm long when the valve is closed. The spring loads are 250 N when the valve is closed and 400 N when the valve is open. The inside diameter of the spring is not to be less than 25 mm and shear stress of the spring material is 345 MN/m^{2}, modulus of rigidity of material is 84 GPa. Design the spring.(12 marks)