GALWAY-MAYO INSTITUTE OF TECHNOLOGY

GMIT EXAMINATIONS

SESSION: AUTUMN 2012

PROGRAMME: Bachelor of Engineering in Energy Engineering

(Level 7 Ordinary)

YEAR: 3

SEM: 6

MODULE: Machine Design

Internal Examiner(s): Mr. Gerard ODonnell

External Examiner(s): Dr. Philip C Griffin

Time Allowed: 3 Hours

Instructions to Candidates:

Note: Answer 5 Questions - All Questions Carry Equal Marks

Special Requirements:

Attachments: Yes x No If yes, please list details: Formulae Sheet Supplied

Special Requirements: Yes No If yes, please list details:

Calculators permitted: Yes x No Not applicable

Q1. (a) Given the following expression for the normal stress (n) and shear stress (n) as shown in Figure 1,

222

)(

2

)(SinCos xy

yxyx

n

222

)(CosSin xy

yx

n

Prove that when the shear stresses are at a maximum, normal stresses are given by:

2

)( yxn

(15 Marks)

(b) Explain the following terms as applied to fatigue analysis of materials.

(i) Uncorrected endurance strength. (ii) Finite and infinite life. (iii) Modifying factors. (iv) S-N diagram.

(5 Marks)

Q2. (a) For the stress element shown in Figure 2, sketch Mohrs circle of stress. Clearly label this sketch. Draw the stress elements indicating the maximum principal

stresses and the maximum shear stresses. Clearly label these sketches and label the

magnitude of stress levels in correct units. (NOTE: You are not required to calculate

exact values for 1, 2 etc, it is sufficient to read values from Mohrs circle)

(10 Marks)

(b) Explain why the maximum shear is calculated by:

222max

1221

max

(10 Marks)

Q3. The bar shown in Figure 3 is loaded by completely reversed axial load of 4450N. Based on

an infinite life calculate the factor of safety for this part. Sut = 1000MPa and Syt = 750MPa.

The surface is machine finished and the reliability is 99.9%

(20 Marks)

Q4. Figure 4 shows a shaft A made from a material with Sut = 1000MPa and Syt = 750MPa.

The shaft is loaded, via shaft B, by a load F that varies between 0.5kN to 2.0kN. A

theoretical stress concentration factor of Kts = 1.6 is induced by the fillet radius of 3mm.

The length of Shaft A from the support to shaft B is 1.0m. All surfaces are machined. Find

the factor of safety based on an infinite life.

(20 Marks)

Q5. In Figure 5, let A=0.9m, B=1.0m, C=1.1m, D=20mm and E=20mm. The cylinder is made

from BS260 cast iron steel (E=120GPa), and the head is of low carbon steel (E=210GPa).

There are 36 M10 x 1.5 bolts of metric grade 10.9 steel. These bolts are tightened so that

the preload is 75% of the proof load. During use, the cylinder pressure will vary between 0

and 550 kPa. Find the factor of safety guarding against a fatigue failure on a 99.9%

reliability.

(20 Marks)

Q6. Determine a suitable diameter for the rotating shaft shown in Figure 6, based on an infinite

life using a factor of safety of 2.5. The uniform diameter, cold drawn steel shaft has Sut =

386 MPa, Syt = 324 MPa. The factor of safety is 2. The counter shaft shown in Figure has

two spur gears mounted on it with a 20 degree pressure angle. The force vectors at A and

B are:

FA = -4.1j + 11.3k kN

FB = -8.2j -22.6k kN

(20 Marks)

Q7. (a) Prove that the maximum shear stress in the body of a spring, subjected to an applied axial

force F, is given by the formula:

Cd

FD 5.01

83max

Where:

d

DC

D is the mean diameter of the spring, d is the diameter of the wire from which the spring

is fabricated.

(8 Marks)

(b) An extension spring is made of 0.55mm music wire and has an outside diameter of

4.7mm. The spring is wound with a pretension of 1.15N and the load fluctuates

between this value and 7.8N. Since the spring may fail statically or in fatigue, find

the factor of safety for both types of failure.

(12 Marks)

Figure 1

Figure 2

x

y

xy

n

n

y = 75 MPa

xy = 150 MPa

x = 75 MPa

Figure 3

Figure 4

50 mm

Figure 5

Figure 6