QUESTIONS TO ANSWER:    Answer any FOUR (4) Questions

MARKING SCHEME:    All questions carry TWENTY FIVE (25) marks

MATERIALS PROVIDED:        None

MATERIALS ALLOWED:    Scientific Calculators; Graphical Calculators are NOT allowed

NOTES TO STUDENTS:    No further marks will be awarded for answers to a fourth question. Clearly cross out any answers to a question that you do not wish to be considered for marking.

Answer FOUR out of FIVE questions

Question 1

There are a number of various types of injection moulding machines. The most prominent in industry is that of the reciprocating-screw injection moulding machine.

(a)    Draw a schematic diagram of a thermoplastic reciprocating-screw injection moulding machine.

[6 marks]

(b)    Referring to your schematic diagram in (a) describe the process of thermoplastic reciprocating-screw injection moulding.

[11 marks]

(c)    Figure 1 below shows a graph of the pressure-volume-temperature path followed by a typical point within an amorphous polymer injection moulding.

Figure 1: Graph of the pressure-volume-temperature path.

Explain what occurs at the following stages:

(i)    Stage A-B

[2 marks]
(ii)    Stage B-C

[2 marks]
(iii)    Point C

[2 marks]
(iv)    Stage D-E

[2 marks]
Question 2

Laser technology is becoming more and more widely used within industries such as automotive and aerospace. This is due to the rapid development of commericially available techniques such as laser welding.

(a)    Describe the basic laser-setup to achieve an active medium to lase.

[7 marks]

(b)    Explain, with the use of a diagram, the process for effective laser welding

[10 marks]

(c)    A company is laser welding at a speed of 0.25 ms-1. The material they are welding has a thermal diffusivity of 9×10-5 m2s-1.

Calculate:

(i)    The interaction time for conduction.

[4 marks]

(ii)    The effective beam diameter on the weld pool required for the extent of the HAZ to be 0.9 mm.

[4 marks]

Question 3

Rapid/additive manufacturing is believed by many to be the next frontier of commercial industry and manufacturing. This is owed to the flexibility that this technology offers.

(a) State 3 advantages and 2 disadvantages of additive manufacturing.

[5 marks]

(b) Discuss the main areas of geometrical freedom which are afforded by additive manufacturing.

[6 marks]

(c) A company has received customer input on a design of a product they would like to manufacture with additive manufacturing. On account of the customer feedback received, 3 features have been identified for customisation. Details of the three features are:

•    Feature 1 – Cost to customise is £100, extra price paid by customer will be £200.

•    Feature 2 – Cost to customise is £200, extra price paid by customer will be £150.

•    Feature 3 – Cost to customise is £200, extra price paid by customer will be £300.

Show and explain which feature is most likely to be customised and which feature is less likely to be customised.

[6 marks]

(d) Explain the term infiltration and describe its importance in rapid manufacturing.

[8 marks]

Question 4

Six Sigma is a collection of techniques used to streamline and improve efficiency in bringing a product to market.

(a)
i.    What does sigma (S) refer to in the Six Sigma name?
ii.    What does six sigma imply with regard to the overarching aims of the Six Sigma strategy?
iii.    Which company first defined and introduced this strategy?

[3 marks]

(b)    The principle methodologies for the implementation of Six Sigma are DMAIC or DMADV.  Describe the meaning of each element of these acronyms

[10 marks]

(c)    You are to implement Six Sigma within your company (which produces gas turbine forged components).  QFD may be used in market testing for design.  Develop and describe a strategy to incorporate other techniques which may be used to improve:
•    Product manufacture
•    Fault analysis
•    Operational analysis
Briefly describe techniques proposed and their interaction to produce an overarching strategy.

[12 marks]

Question 5

Quality Function Deployment (QFD) is a Structured Product Planning and Development Methodology Established method of guiding design processes. Developed from concepts used in 1960’s during large ship production (Mitsubishi), it is has seen widespread use and enhancement by Toyota.

(a)
With reference to Figure 2 below, describe the purpose of the following matrices in a QFD House of Quality:

i.    Technical Correlations
ii.    Technical Response
iii.    Customer Needs
iv.    Relationships
v.    Planning Matrix
vi.    Technical Priorities
[18 marks]

(b)    Describe the flow(s) of information through these matrices.

[7 marks]

QUESTIONS TO ANSWER:    Answer any FOUR (4) Questions

MARKING SCHEME:    All questions carry TWENTY FIVE (25) marks

MATERIALS PROVIDED:        None

MATERIALS ALLOWED:    Scientific Calculators; Graphical Calculators are NOT allowed

NOTES TO STUDENTS:    No further marks will be awarded for answers to a fifth question. Clearly cross out any answers to a question that you do not wish to be considered for marking.

Answer FOUR out of FIVE questions

Question 1

(a)    Answer TRUE or FALSE to the following statements
a.    The LTI state equation   relates the system outputs to the system inputs.
[1 mark]
b.    A time invariant system is one where the parameters do not vary with time.
[1 mark]

(b)    Give two reasons for modelling a system in state space.
[2 marks]

(c)    How many state equations are needed to represent an eighth-order system?
[1 mark]

(d)    Consider the system shown in Figure 1. By setting the displacement of the mass  , show that the following mathematical model in state space form can be derived:

[10 marks]

Figure 1: A Mass, Spring and Damper

Question 1 continued on the next page…
….Question 1 continued

(e)        Assume that the mass M=10kg, spring stiffness K=275N/m and linear damping coefficient fv=300Nm/s. The measured output is x(t). Evaluate the transfer function of this system.
[10 marks]

Question 2

(a)    Consider a system with a mathematical model given by the differential equation:

Express this equation in state space form.
[5 Marks]

(b)        Find the roots of the system and sketch them on the s-plane. Is the system stable?
[7 marks]
(c)    The system is to be controlled as a regulator system with state variable feedback, as shown in Figure 2.

Figure 2: A Regulator System

a.    What is a Regulator System?
[1 mark]

Question 2 continued on the next page…
….Question 2 continued

b.     The closed-loop system should respond to an impulse with a settling time of 2s and a maximum overshoot of 10%. Show that these specifications mean the closed-loop poles occur at
-0.38 ± 0.52j
[5 marks]
c.    Find the state feedback gain necessary to give the desired system response
[7 marks]

Question 3

A CNC Milling Machine is shown in Figure 3.

Figure 3: A Computer Controlled CNC Machine (Open Loop)

(a)    How are the A/D and D/A operations of the computer usually modelled?
[2 marks]
(b)    Assume the microprocessor adds a unity gain. Using your answers to part a), draw a modified block diagram to describe the system in the s-domain.
[5 marks]
(c)    Let amplifier gain  . Show that the Pulse Transfer Function for the whole system is:

[8 marks]
(d)    Let  . Find the system poles and sketch their position on the z-plane. Is the system stable?
[5 marks]

Question 3 continued on the next page…
….Question 3 continued

Figure 4: A Computer Controlled CNC Machine with Feedback Control (Closed Loop)

(e)    Feedback Control is added to the system described in part a), as shown in Figure 4. Find the poles of the closed loop system and assess the effect on the system’s stability.
[5 marks]

Question 4
(a)    Consider a system described by Figure 5. Blocks denoted ‘T’ are Time Delays of 1s.

Figure 5: An Example System.

(i)    Is this system continuous or discrete?
[1 mark]

Question 4 continued on the next page…
….Question 4 continued

(ii)    Derive a state space representation of this system.
[7 marks]
(iii)    Assuming   and  , solve to find the output at k=1 and k=2.
[4 marks]

(b)    You are asked to design an observer for the system in Figure 5.
(i)    Show whether the system is observable.
[4 marks]
(ii)    Draw the system with an observer in block diagram form
[2 marks]
(iii)    Observer poles are typically chosen to be 2-5 times faster than the closed-loop system poles. Why is this?
[1 mark]
(iv)    Design an observer for the system, assuming that the observer will have a characteristic equation of

[6 marks]

Question 5

(a)    A robot leg can be modelled as a pendulum, with an applied torque as shown in Figure 6. Summing the torques in the free body diagram gives

(i)    Express this model in state space form.
[4 marks]
(ii)    Explain why this model is considered to be nonlinear.
[2 mark]
(iii)    At equilibrium, the leg hangs in a vertical position. Linearise the model about the equilibrium point.
[7 marks]

Question 5 continued on the next page…
….Question 5 continued

Figure 6: Representation of a Robot Leg a) A Simple Pendulum; b) force components of Mg; c) free-body diagram

(iv)    Can this linearised model be used to assess the leg when it is ‘walking’ i.e. undergoing small motions of ± 5O from the equilibrium point? Explain your answer.
[3 marks]
(v)    Can this linearised model be used to assess the leg when it is ‘kicking’ at 90O from equilibrium point? Explain your answer.
[3 marks]

(b)    Describe Ackermann’s Method and how you would use it to design a controller
[6 marks]

Equations

Modelling
(Consequence of) Newton’s 2nd Law:
Hooke’s Law:
Linear damping characteristic:

Matrices
Matrix Inverse:
Determinant of a 2×2 Matrix

Time Response
Damping ratio:
Settling time:
Peak time:
2nd Order Transfer Function:

State Space
Transfer Function
Controllability Matrix
Observability Matrix
System with State Controller  ;
System with Full State Observer  ;
Ackermann’s Formula

Tables

QUESTIONS TO ANSWER:    Answer FOUR (4) out of six Questions: Answer any TWO (2) Questions in Section A, and Answer any TWO (2) Questions in Section B

MARKING SCHEME:    All questions carry TWENTY FIVE (25) marks

MATERIALS ALLOWED:    Scientific Calculators; Graphical Calculators are NOT allowed

NOTES TO STUDENTS:    No further marks will be awarded for answers to a third question in one section. Clearly cross out any answers to a question that you do not wish to be considered for marking.

Section A:
Answer TWO out of THREE questions

Question A1

(f)                         [4 marks]
Name the conditions for plastic deformation to take place in a material?

(g)                        [4 marks]
Why is it difficult to generate dislocation within ceramics in comparison to metals?

(h)                         [4 marks]
What should the microstructure of a material comprise of?

(i)                 [2 marks]
What is a ‘green body’ of a ceramic?

(j)                         [3 marks]
Explain what agglomerates are and how they influence the ceramics microstructure?
(k)                        [3 marks]
Why is surface preparation important prior to undergoing a Vickers hardness test and what effect could it have on the resulting hardness value?

(l)                         [2 marks]
Explain why ceramics are not manufactured by conventional processes?

(m)                         [3 marks]
How does porosity and microcracks pre-existing in a ceramic and what influence does it have upon characteristics such as K1c? Also what effect does the surface finish of the ceramic have upon the hardness of the material?

Question A2

(d)                         [4 marks]
What are the differences between a thermoplastic and a thermosetting plastic? List five advantages and disadvantages of plastics in general?

(e)                        [4 marks]
What is polymerization? How are polymers formed? Explain the process with an aid of a diagram.

Question A2 continued on the next page…
….Question A2 continued
(f)
Determine the average molecular weight and the degree of polymerization for polyethylene (PE) material? Assume that the molecular weight distribution shown below are for the given material (polyethylene (PE). For this, calculate (i), and (ii) using the values from Table 1:

Table 1 showing data for number-average molecular weight.
Molecular weight Range (g/mol)    xi    wi
2000 – 9000    0.05     0.02
8000 – 14000    0.16     0.10
13000 – 19000    0.24    0.20
18000 – 24000    0.28    0.30
23000 – 31000    0.20    0.27
30000 – 37000    0.27    0.11
36000 – 43000    0.29    0.14

(i)                                           [4 marks]
Number-average molecular weight (Mn = ? xi Mi)

(ii)                                             [4 marks]
The weight-average molecular weight (Mw = ?wi Mi)

(g)                          [5 marks]
Draw schematic of a linier polymer chain, a cross-linked rubber, a ladder polymer and regular polymer, and a block co-polymer. Explain how properties of polymers can be manipulated?
(h)                           [4 marks]
What is the influence of a high degree crystallinity on the polymer?

Question A3

(a)                          [2 marks]
Describe why it is beneficial to surfacace treat/engineer materials?
(b)                         [2 marks]
What are the differences between surface coating and surface modification?
(c)                           [3 marks]
Show with an aid of a diagram how fatigue occurs in a material and how it can be minimized?
(d)                         [3 marks]
Describe briefly three ways in which one can prevent corrosion?

(e)                          [2 marks]
Which reaction occurs at the anodic and cathodic site during corrosion?

Question A3 continued on the next page…
….Question A3 continued

(f)                  [4 marks]
Differentiate the two given micrographs and state how the grain morphology and hardness of aluminium-silicon alloy (AlSi) differ between a laser melted microstructure and a cast iron microstructure?

Figure 1                                   Figure 2
(g)                  [3 marks]
Explain the different factors which lead to deterioration of polymers, ceramics and metals?
(h)                         [6 marks]
Designers and manufacturers are making increased use of smart materials to enhance the performance of products. For the two of the following areas, describe specific examples of where smart materials are used to enhance the performance of the product:
–    Kitchen products, e.g. kettles, plastic spoons, etc;
–    Any children’s toys which you know of that employs smart material system;
–    Biomedical products.

Section B continued on the next page…

Section B:
Answer TWO out of THREE questions

Question B1

(a)                                                                                          [4 marks]
In elasticity theory, what are the 15 unknown parameters and the 15 equations to solve them at a point in a material body? Where are boundary conditions needed?

(b)                                                                                                        [6 marks]
Draw sketches and explain anisotropic, orthotropic and isotropic materials.

(c)                                                                                                         [10 marks]
Draw sketches and derive the reduction of the stiffness matrix for an anisotropic material to that of a monoclinic material according to the material symmetry. The stiffness matrix for an anisotropic material is
,
and the stiffness matrix for a monoclinic material is
.
Note: assume direction 3 is the principal direction.

(d)                                                                                                           [5 marks]
The compliance matrix can be written in terms of the engineering constants. The compliance matrix for an orthotropic material is
.
Derive that  ,   and  .

Question B2

(a)                                                                                                        [4 marks]
Explain ‘mechanics of materials models’ and ‘semi-empirical models’ for micromechanics of a composite lamina, and compare their pros and cons.

(b)                                                                                                           [6 marks]
Draw sketches and derive the ‘rule of mixtures’ for the longitudinal Young’s modulus,  , of a composite lamina based on the mechanics of materials model, in terms of the elastic properties of fibres and matrix ( and  ) and the volume fractions of fibres and matrix ( and  ).

(c)
The properties of a unidirectional composite lamina are:
the volume fractions of fibres and matrix are   and  ;
the Young’s moduli of fibres and matrix are   and  ; and the tensile strengths of fibres and matrix are   and  .
(i)    Determine the longitudinal Young’s modulus,  , based on the mechanics of materials model;                               [1 mark]
(ii)    Determine the transverse Young’s modulus,  , using Halpin-Tsai equations;                                                                                [3 marks]
(iii)    Determine the longitudinal tensile strength,  .                     [3 marks]

Note:
The Halpin-Tsai equation is  ,  , and   for calculating  .

(d)                                                                                                           [8 marks]
A   composite lamina is under uniaxial compression and shear of equal magnitude,  ,  , ( ), see Fig. 3. The strength properties of the unidirectional lamina are  . Determine the stress level  at failure of the lamina according to the modified Tsai-Hill failure theory.

Question B2 continued on the next page…
….Question B2 continued

Figure 3

Note:

The transformation matrix   for local axes (1,2) and global axes (x,y) is

, where  ,  .

The modified Tsai-Hill failure theory is

,      ,  ,        .

Question B3

(a)
(i)           Draw the stacking sequence for a   laminate.
[2 marks]
(ii)    Classify a   laminate (e.g. symmetric, balanced, antisymmetric, cross-ply or angle-ply), and indicate which terms in the laminate stiffness matrices  ,   and   are zero for the laminate.                                                                               [2 marks]

Question B3 continued on the next page…

….Question B3 continued

(b)                                                                                                           [4 marks]
Draw sketches and explain how the stresses and strains vary through the thickness of a composite laminate.

(c)                                                                                                           [8 marks]
Derive the expressions for the laminate stiffness matrices  ,   and   of a   cross-ply laminate in terms of the basic lamina properties ( ,  ,   and  ) and the lamina thickness  .

Note:

Both laminas have the same thickness  .

The stiffness matrix for the unidierectional lamina is
,
and the relation holds that
.

(d)                          [9 marks]
Draw the flowchart for the first ply failure analysis of a symmetric composite laminate based on the modified Tsai-Hill failure theory, and explain each of the steps.