Exercises with Worked Solutions
Translating Requirements into Constraints and
Objectives
(To accompany Lecture Unit 6)
Professor Mike Ashby
Department of Engineering
University of Cambridge
© M. F. Ashby, 2013
For reproduction guidance see back page
This exercise unit is part of a set based on Mike Ashby’s books to help introduce students to materials, processes and rational
selection.
The Teaching Resources website aims to support teaching of materials-related courses in Design, Engineering and Science.
Resources come in various formats and are aimed primarily at undergraduate education.
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M.F. Ashby 2013
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1
Exercises With Worked Solutions – Unit 6
Exercises with Worked Solutions
This collection of exercises and solutions has been put together to help you as an
instructor choose or develop your own exercises for your students. You may simply
want to browse through them for inspiration, or you may use them with your class.
We are providing these in Word format so that you may pick and choose the
questions you find suitable for your course this year. We have also included
variations on a theme so that you can set different questions for different classes.
Most of the questions come from or are inspired by the exercises in the following
books by Professor Mike Ashby of the University of Cambridge Engineering
Department, co-founder of Granta Design.
•
•
•
Materials Selection for Mechanical Design by Michael F. Ashby (ISBN-13:
978-1-85617-663-7)
Materials: Engineering, Science, Processing and Design by Michael F.
Ashby, Hugh Shercliff, and David Cebon (ISBN-13: 978-1856178952)
Materials and the Environment by Michael F. Ashby (ISBN-13: 978-0-12385971-6)
(Reproduction and copyright information can be found on the last page. Please make
sure to credit Professor Mike Ashby and Granta Design if you use these questions.)
Most of the questions require the use of CES EduPack. However where a topic, such
as understanding how to translate design requirements into specific criteria for
selection, is important on courses that traditionally use CES EduPack, we have
included exercises on these topics too, even though they don’t directly use CES
EduPack. (CES EduPack is a materials teaching resource used at 800+ Universities
and Colleges worldwide. You can find out all about it here:
www.grantadesign.com/education.)
Topics on which there are Exercises with Worked Solutions are1:
Title
Associated Lecture Unit
Materials – classification and properties
Lecture Units 1 & 2
Elements
Lecture Unit 3
Design – translating requirements into constraints and Lecture Unit 6
objectives
Selecting Materials
Lecture Unit 7
Manufacturing Processes – classification and
Lecture Unit 10
properties
Eco Properties and the Eco Audit Tool
Lecture Unit 12
Low Carbon Power Systems
Lecture Unit 14
You can find the other units here: www.grantadesign.com/education/resources
If there are other topics upon which it would be good to have a collection of
questions, or if you have questions that you have used successfully with your
students that you would like to donate to the Materials Education Community,
attributed to you, then please contact Granta’s Materials Education Coordinator at
[email protected].
1
Exercise units follow the same numbering of the PowerPoint lectures for the same topic
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Exercises With Worked Solutions – Unit 6
Contents
The Design Process ............................................................................................................ 3
From Design Requirements to Constraints ...................................................................... 5
From Design Requirements to Constraints ...................................................................... 6
Design Limiting Properties ................................................................................................ 9
Case Studies in Translation ............................................................................................. 11
Longer Project-based Exercises – In-depth Design Analysis ...................................... 16
The Design Process
1. What are the steps in developing an original design?
Answer.
•
Identify market need, express as design requirements
•
Develop concepts: ideas for the ways in which the requirements might be met
•
Embodiment: a preliminary development of a concept to verify feasibility and
show layout
•
Detail design: the layout is translated into detailed drawings (usually as computer
files), stresses are analyzed and the design is optimized
•
Prototyping: a prototype is manufactured and tested to confirm viability
2. Concepts and embodiments for dust removers. The need for a “device to remove
household dust” has many established solutions. You can read about the various ways
this problem has been solved in the last 100 or more years by searching the Internet.
Now is the time for more creative thinking. Devise as many concepts to meet this need
as you can. Nothing, at the concept stage, is too far-fetched; decisions about practicality
and cost come later, at the detailed stage. List concepts and outline embodiments as
block diagrams like this:
Concept
Embodiment
Electric fan pulling air stream through
paper or cloth filter in portable unit
C1 Entrain in air stream
and filter
Central pump and filter linked to
rooms by ducting
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Exercises With Worked Solutions – Unit 6
Possible answers.
Concept
Embodiment
Electric fan pulling air stream through
paper or cloth filter in portable unit
C1 Entrain in air stream
and filter
Central pump and filter linked to
rooms by ducting
Centrifugal turbo-fan with surrounding
dust collector, in portable unit
C2 Entrain in air
stream,
Central turbo-fan with centrifugal
dust collector linked to rooms by ducting
Centrifugal turbo-fan, injected water
spray to wash air stream, in portable unit
C3 Entrain in air
stream,
Central turbo-fan , water spray to wash
air stream, linked to rooms by ducting
Axial fan drawing air stream between
charged plates, in portable unit
C4 Entrain in air
stream, trap
C5 Trap dust on
adhesive strip
Central fan with electrostatic collector,
linked to rooms by ducting
Reel-to-reel single sided adhesive tape
running over flexible pressure-pad
3. Cooling power electronics. Microchips, particularly those for power electronics, get hot.
If they get too hot they cease to function. The need: a scheme for removing heat from
power microchips. Devise concepts to meet the need and sketch an embodiment of one
of them, laying out your ideas in the way suggested in the previous exercise.
Answer.
Four working principles are listed below: thermal conduction, convection by heat transfer
to a fluid medium, evaporation exploiting the latent heat of evaporation of a fluid, and
radiation, best achieved with a surface with high emissivity.
The best solutions may be found by combining two of these: conduction coupled with
convection (as in the sketch – an often-used combination) or radiation coupled with
evaporation (a possibility for short-life space structures).
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Exercises With Worked Solutions – Unit 6
Embodiment
Concept
Massive, with sufficient heat capacity to absorb heat
over work cycle without significant increase in
C1 Conduction
Compact, requiring back-up by coupling to convection,
evaporation or radiation
Free convection not requiring fan or pump.
C2 Convection
Forced convection with fan or pump
Unconfined, such as a continuous spray of volatile fluid
C3 Evaporation
Confined, utilising heat-pipe technology
Radiation to ambient, using high emissivity coatings
C4 Radiation
Radiation to cooled surface, from high emissivity
surface to highly absorbent surface
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Exercises With Worked Solutions – Unit 6
From Design Requirements to Constraints
4. Describe and illustrate the “Translation” step of the material selection strategy.
Answer.
Translation is the conversion of design requirements for a component into a statement of
function, constraints, objectives and free variables.
Function
What does the component do?
Constraints
What non-negotiable conditions must be met?
Objective
What is to be maximized or minimized?
Free variables
What parameters of the problem is the designer free to
change?
5. Materials are required to make safe, eco-friendly swings and climbing frames for a
children’s’ playground. How would you translate these design requirements into a
specification for selecting materials?
Answer.
The design requirements for a component of a product specify what it should do but not
what properties its materials should have. Translation is the step of converting the design
requirements into constraints and objectives that can be applied to a materials database.
Thus the design requirement “Materials are required to make safe, eco-friendly swings
and climbing frames for a children’s’ playground” might translate as shown in the table:
Design Requirements
Materials are required to make safe, ecofriendly swings and climbing frames for a
children’s’ playground
Translation
Constraints: seek materials that meet specified
levels of:
•
•
•
Stiffness
Strength
Fracture Toughness
Objective: minimize carbon footprint of material
6. What is meant by an objective and what by a constraint in the requirements for a design?
How do they differ?
Answer.
A constraint is an essential condition that must be met, usually expressed as a limit on a
material or process attribute. An objective is a quantity for which an extreme value (a
maximum or minimum) is sought, frequently cost, mass or volume, but there are others.
Constraints are used for screening to isolate candidates that are capable of doing the job
– if the constraint is not met, the material is rejected; objectives are used for ranking to
identify those among them that can do the job best: the one that minimizes the objective
is the best choice. The distinction is brought out by comparing common constraints and
objectives, as in the table below:
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Exercises With Worked Solutions – Unit 6
Common Constraints
Common Objectives
Must meet a target value of:
Minimize:
•
Stiffness
•
Cost
•
Strength
•
Mass
•
Fracture toughness
•
Volume
•
Thermal Conductivity
•
Energy Consumption
•
Service Temperature
•
Carbon Emissions
7. Formulate the constraints and objective you would associate with the choice of material to
make the forks of a racing bicycle.
Answer.
The important constraints are those of meeting target values of stiffness (for control and
comfort) and strength (for safety). Cost, in highly competitive sport, is irrelevant. Mass,
however, carries a heavy performance penalty. The central objective is to minimize mass.
8. You are asked to design a fuel-saving cooking pan with the goal of wasting as little heat
as possible while cooking. What objective would you choose, and what constraints would
you think must be met?
Answer.
Constraints:
•
Material of the pan must be non-toxic
•
Meet constraints of formability
•
Maximum service temperature > 400ºC
•
Corrosion resistance in fresh and salt water, weak acids (e.g. vinegar)
•
Sufficient stiffness to prevent flexing if lifted when full
•
Sufficient strength to survive handling
•
Sufficient toughness to survive a drop
•
Able to be manufactured at a competitive price
•
Meet legal standards for contact with food
Objective: Maximize heat-transfer to the contents of the pan; thus maximize thermal
conductivity of the material of the pan while making it thick enough to spread the heat.
9. Bikes come in many forms, each aimed at a particular sector of the market:
•
Sprint bikes
•
Touring bikes
•
Mountain bikes
•
Shopping bikes
•
Children’s bikes
•
Folding bikes
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Exercises With Worked Solutions – Unit 6
Use your judgment to identify the primary objective and the constraints that must be met
for each of these.
Answer.
Take the example of a bicycle frame. It must have a certain stiffness and strength. If it is
not stiff and strong enough it will not work, but it is never required to have infinite stiffness
or strength. Stiffness and strength are therefore constraints that become limits on
modulus, elastic limit and shape.
If the bicycle is for sprint racing, it should be as light as possible – if you could make it
infinitely light that would be the best of all. Minimizing mass, here, is the objective,
perhaps with an upper limit (a constraint) on cost. If instead it is a shopping bike to be
sold through supermarkets it should be as cheap as possible – the cheaper it is, the more
will be sold. This time minimizing cost is the objective, possibly with an upper limit (a
constraint) on mass.
For most bikes, of course, minimizing mass and cost are both objectives: you would like
the bike to be both as light and as cheap as possible. Then trade-off methods are
needed. They come later. For now use judgment to choose the single most important
objective and make all others into constraints.
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Exercises With Worked Solutions – Unit 6
Design Limiting Properties
10. What is meant by the design-limiting properties of a material in a given application?
Answer.
A design limiting property in a given application is one that limits the performance of the
application. To meet a required level of performance, the design-limiting properties must
meet or exceed target values.
11. A material is needed for a tube to carry fuel from the fuel tank to the carburetor of a motor
mower. The design requires that the tube can bend and that the fuel be visible. List what
you would think to be the design-limiting properties.
Answer.
Flexible (meaning low modulus E); transparency (to allow fuel to be visible); very good
resistance to organic solvents (gasoline and oil); ability to be formed to tube.
12. A material is required as the magnet for a magnetic soap holder. Soap is mildly alkaline.
List what you would judge to be the design-limiting properties.
Answer.
Ferromagnetic; very good resistance to fresh water and mild alkali.
13. What, in your judgment, are the design-limiting properties for the material for the blade of
a knife that will be used to gut fish?
Answer.
Hardness (to give a wear resistant, sharp edge); ability to be shaped to a blade;
resistance to corrosion in fresh and salt water; stiffness (meaning modulus) to ensure that
the thin blade does not bend or buckle during use.
14. What, in your judgment, are the design-limiting properties for the material of an oven
glove?
Answer.
Flexibility (to allow weaving or shaping, and motion in use); low thermal conductivity (to
insulate); maximum operating temperature > 200ºC (high oven setting); and ability to be
washed, meaning tolerance of water.
15. What, in your judgment, are the design-limiting properties for the material of an electric
lamp filament?
Answer.
The filament must be a good electrical conductor; maximum operating temperature >
2000ºC (or a temperature of that order); ductility to enable it to be drawn to fine wire.
16. There have been many attempts to manufacture and market plastic bicycles. All have
been too flexible. Which design-limiting property is insufficiently large?
Answer.
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Exercises With Worked Solutions – Unit 6
Flexibility is lack of stiffness. The stiffness of a structure depends on its shape and size,
and on the value of Young’s modulus E of the material of which it is made. In design for
stiffness E is a design-limiting property. In bicycle design the values of E offered by
plastics are insufficiently large. However if the plastic is reinforced with carbon or glass
fiber the stiffness can be increased to a useful level – high performance bicycles are
made of carbon-reinforced plastic.
17. List three applications that, in your judgment, need high stiffness and low weight.
Possible answers.
Racing bicycle frames; aircraft wing spars; car wheels, sports equipment, precision
machine tools; radio-telescope dishes; high-speed printing presses.
18. List three applications that, in your judgment, need optical quality glass.
Possible answers.
Binoculars, cameras, contact lenses, microscopes, telescopes, fiber-optic cables.
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Exercises With Worked Solutions – Unit 6
Case Studies in Translation
19. A material is required for the windings of an electric air-furnace capable of temperatures
up to 1000ºC. Think out what attributes a material must have if it is to be made into
windings and function properly in the furnace. List the function and the constraints; set the
objective to “minimize material price” and the free variables to “choice of material”.
Answer.
Function
Constraints
Windings for 1000ºC electric air furnace
•
•
•
•
Good electrical conductor
Capable of being rolled or drawn to wire
Maximum service temperature > 1200ºC (allowing 200ºC over operating
temperature of the furnace itself)
Resistance to oxidation at elevated temperature: excellent
Objective
Minimize material price
Free variables
Choice of material
20. A material is required to manufacture office scissors. Paper is an abrasive material, and
scissors sometimes encounter hard obstacles like staples. List function and constraints;
set the objective to “minimize material price” and the free variables to “choice of material”.
Answer.
Function
Constraints
Blades for office scissors
•
•
•
•
High hardness (for wear resistance)
Adequate toughness (to avoid chipping the blade edge)
High stiffness to ensure that the blades do not bend in service
Able to be forged
Objective
Minimize material price
Free variables
Choice of material
21. A material is required for a heat exchanger to extract heat from geo-thermally heated,
saline, water at 120ºC (and thus under pressure). List function and constraints; set the
objective to “minimize material price” and the free variables to “choice of material”.
Answer.
Function
Constraints
Geothermal heat exchanger
• Good thermal conductivity
• Durability in hot salt water: very good/excellent
• Maximum service temperature > 120ºC
• Sufficient strength to carry the pressure of the super-heated water
• Ability to be rolled into sheet or tube
• Sufficient ductility to allow shaping to form tubes
Objective
Minimize material price
Free variables
Choice of material
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Exercises With Worked Solutions – Unit 6
22. A material is required for a disposable fork for a fast-food chain. List the objective and the
constraints that you would see as important in this application.
Answer.
Function
Constraints
Disposable cutlery
•
•
•
•
•
Easy (and thus cheap) to mold
Non-toxic
Sufficient strength and stiffness (modulus) to withstand loads in use
Recyclable or renewable (e.g. wooden cutlery)
Ability to be colored (?)
Objective
Minimize material price
Free variables
Choice of material
23. Formulate the constraints and objective you would associate with the choice of material to
make the forks of a racing bicycle.
Answer.
Both stiffness and strength are important in bicycle design. But the first consideration in
the design of the forks is strength – it is essential that they do not fail in normal use –
which includes riding over curbs and other irregularities. The loading on the forks is
predominantly bending. If the bicycle is for racing, then the mass is a primary
consideration: the forks should be as light as possible.
Function
Constraints
Forks for racing bike
• Must not fail under design loads – a constraint bending strength
• Dimensions specified
Objective
Minimize weight
Free variables
Choice of material
24. A C-clamp is required for the processing of electronic components at temperatures up to
450ºC. It is essential that the clamp has as low a thermal inertia as possible so that it
reaches that temperature quickly, and it must not charge-up when exposed to an electron
beam. The time t it takes a component of thickness x to reach thermal equilibrium when
the temperature is suddenly changed (a transient heat flow problem) is
t ≈
x2
2a
where the thermal diffusivity a = λ/ρCp and a is the thermal conductivity, ρ the density and
Cp the specific heat. List the function, constraints and objective; set the free variables to
“choice of material”.
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Exercises With Worked Solutions – Unit 6
Answer.
If the C-clamp is to reach temperature quickly it must, according to the equation given in
the question, be made of a material with as high a thermal diffusivity, a as possible. It
carries loads, so it must have adequate strength, and it must not charge up, so it must be
an electrical conductor.
Function
Constraints
C-clamp of low thermal inertia
• Maximum service temperature, Tmax > 450ºC
• Sufficient strength to carry clamping loads without failure
• Electrical conductor (to prevent charging)
Objective
Maximize the thermal diffusivity, a of the material
Free variables
Choice of material
o
25. A furnace is required to sinter powder-metal parts. It operates continuously at 650 C
while the parts are fed through on a moving belt. You are asked to select a material for
furnace insulation to minimize heat loss and thus to make the furnace as energy-efficient
as possible. For reasons of space the insulation is limited to a maximum thickness of
x = 0.2 m. List the function, constraints, objective and free variable
Answer.
This is a problem involving steady-state heat flow. The heat lost by conduction per unit
∆T
area of insulation per second, q, is q = λ
x
where λ is the thermal conductivity, x the insulation thickness and ∆T the temperature
difference between the interior of the furnace and its surroundings. The aim is to
minimize q, leading (via the equation) to the objective of minimizing the thermal
conductivity of the insulation material. There are two constraints: one on thickness, the
other on service temperature.
Function
Constraints
Insulation for energy-efficient furnace
• Maximum service temperature, Tmax > 650ºC
• Insulation thickness x ≤ 0.2 m
Objective
Maximize the thermal conductivity λ of the material
Free variables
Choice of material
26. Ultra-precise bearings that allow a rocking motion make use of knife-edges or pivots. As
the bearing rocks, it rolls, translating sideways by a distance that depends on the radius
of contact. The further it rolls, the less precise is its positioning, so the smaller the radius
of contact R the better. But the smaller the radius of contact, the greater is the contact
pressure (F/A). If this exceeds the hardness H of either face of the bearing, it will be
damaged. Elastic deformation is bad too: it flattens the contact, increasing the contact
area and the roll.
A rocking bearing is required to operate in a micro-chip fabrication unit using fluorine gas
o
at 100 C, followed by e-beam processing requiring that all structural parts of the
equipment can be earthed to prevent stray charges. Translate the requirements into
material selection criteria, listing function, constraints, objective and free variable.
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Exercises With Worked Solutions – Unit 6
Answer.
The objective is to minimize the radius of curvature at the contact. This is limited by the
hardness H and modulus E of the materials. The objective is met by seeking materials
with: maximum hardness H to enable the smallest possible area of contact without
damage, and maximum modulus E to minimize elastic flattening of the contact. In a later
exercise we return to this problem of two objectives, treating it by trade-off methods.
Here we choose maximizing hardness as the primary objective, since deficiency here
results in a damaged bearing. We then treat modulus as a constraint, together with the
other obvious constraints suggested by the design requirements.
Function
Constraints
Rocking bearing
•
•
•
•
Maximum service temperature, Tmax > 100ºC
Good electrical conductor
Good resistance to fluorine gas
High modulus, E
Objective
Maximize hardness H of bearing faces
Free variables
Choice of material
27. The standard CD (“Jewel” case) cracks easily and, if broken, can scratch the CD. Jewel
cases are made of injection molded polystyrene, chosen because it is transparent, cheap
and easy to mold. A material is sought to make CD cases that do not crack so easily.
The case must still be transparent, able to be injection molded, and able to compete with
polystyrene in cost.
Answer.
The question expresses constraints on transparency, moldablity and fracture toughness
(it must be greater than that of polystyrene). Given these, the cheapest material is the
best choice.
Function
Constraints
Improved CD case
• Optically transparent
• Fracture toughness greater than that of polystyrene
• Able to be injection molded
Objective
Minimize material cost
Free variables
Choice of material
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Exercises With Worked Solutions – Unit 6
28. A storage heater captures heat over a period of time, then releases it, usually to an air
stream, when required. Those for domestic heating store solar energy or energy from
cheap off-peak electricity and release it slowly during the cold part of the day. Those for
research release the heat to a supersonic air stream to test system behavior in
supersonic flight. What is a good material for the core of a compact storage material
capable of temperatures up to 120ºC?
Answer.
When a material is heated from room temperature To to a working temperature T, it
absorbs heat Q per unit volume where Q = C p ρ ( T − To )
and Cp is the specific heat of the material of the core (in J/kg.C) and ρ is its density (in
3
kg/m ). Thus the most compact storage heater is one made from a material with a high
C p ρ . Even a small storage heater contains a considerable quantity of core (that is why
they are heavy), so it is probable that an objective will be to minimize its cost per unit
volume. If, however, space were critical, maximizing C p ρ might become the objective.
Function
Constraints
Core for compact storage heater
• Maximum service temperature, Tmax > 120ºC
• High heat capacity per unit volume C p ρ
Objective
Minimize material cost per unit volume
Free variables
Choice of material
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Exercises With Worked Solutions – Unit 6
Longer Project-based Exercises – In-depth Design Analysis
29. Cheap coat hangers used to be made of wood – now it is only expensive ones that use
this material. Most coat hangers are now metal or plastic, and both differ in shape from
the wooden ones, and from each other. Examine wood, metal and plastic coat hangers,
comparing the designs, and comment on the ways in which the choice of material has
influenced them.
Answer.
Coat hangers often have three components: the hook, the ‘shoulders’ and the ‘trouser
bar’. To make this structure entirely from wood is not practical: it is difficult to make the
thin curved shape of the hook from wood. So wooden hangers normally have steel wire
hooks. This has the added advantage that the hooks can be made to rotate about a
vertical axis in the shoulders, making it easier to hook the hanger over the rail.
Joining the trouser bar to the shoulders requires machining and gluing, or additional wire
joining pieces and surface has to be shaped, sanded and varnished for aesthetic
reasons. The whole process is expensive: wooden hangars typically cost $1 or more.
Many different types of plastic hangers are available, in a wide variety of different
polymers, shapes, sizes and colors. The cheapest are molded in one piece.
Consequently their hooks do not rotate. More expensive ones have metal wire hooks that
can rotate. Some are adjustable, some have additional garment hooks or textured
shoulders to make them more versatile.
Simple plastic hangers cost about 40c each. If you are a drycleaner even this is too
much. The cheapest hangers are made of bent steel wire. Steel wire is cheap and the
manufacturing operations – cutting the wire, bending it into a triangular shape and
twisting the two ends together – are fast and inexpensive. The hooks don’t rotate, but at
10c each, you can’t be too choosy!
30. Cyclists carry water in bottles that slot into bottle holders on their bicycles. Examine metal
and plastic bottle holders, comparing the designs, and comment on the ways in which the
choice of material has influenced them.
Answer.
The main criteria for ‘bottle cages’ are to hold the bottle securely, while being lightweight
and aesthetically pleasing. The importance of each of these factors varies, depending on
the application. Mountain bikes have an emphasis on ‘secure’. They traverse rough
terrain, and the riders occasionally fall off at high speed – the resulting impact can test
even the most robust bottle holder. Aluminum alloy and stainless steel wire are the
favored materials: aluminum for its lower weight, stainless steel for its aesthetic appeal.
The designs often make use of the ‘springiness’ of the metal wire to clamp the bottle in
place. Racing cyclists need the lightest possible accessories – their bottle cages are often
made of carbon-fiber reinforced plastics (CFRP). These come in a variety of shapes that
tend to surround the bottle, rather than clamping it. They are significantly more expensive
than their aluminum counterparts – about a factor of 5 to 10 times more.
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Exercises With Worked Solutions – Unit 6
Using Translation Criteria to Justify the Use of Certain
Materials
The next few questions involve products that had translation on them done earlier in the
chapter explored earlier in this Unit. First you have to find out what materials are used for
the product in real life. Then, return to the earlier question, examine the translation table
you created, noting the constraints and objectives you identified. Then, use these
constraints and objectives as criteria for comparison between the materials used, and
provide a case for the material you would use if you were in the hot seat. No answer is
absolutely correct; that is why all are materials used for the actual function in real life.
31. Use the “Search” facility in CES EduPack Level 2 to find materials for furnace windings.
(see Question 19)
Answer.
•
Nickel-chromium alloys
•
Tungsten alloys
Function
Windings for 1000ºC electric
air furnace
Nickel-chromium
Alloys
Tungsten Alloys
Constraints
Good electrical conductor
Good Conductor
Good Conductor
Capable of being rolled or
drawn to wire
Elongation = 20-35 %
strain
Elongation = 1-17 %
strain
Maximum service temperature
> 1200ºC (allowing 200ºC over
operating temperature of the
furnace itself)
No
Yes
Resistance to oxidation at
elevated temperature: very
good
Resistance to O2:
excellent (Tolerance
above 850ºC:
unacceptable)
Resistance to O2:
excellent (Tolerance
above 850ºC:
excellent)
Objective
Minimize material price
24.5 – 26.9 $/kg
54.2 – 59.6 $/kg
Free variables
Choice of material
In terms of performance, tungsten alloys are better than nickel-chromium alloys for
furnace windings at higher temperatures. However, if you read the datasheet for tungsten
alloys, you will learn that tungsten is difficult to process – a comparison by clicking the
“ProcessUniverse” links of the two materials will let you see that there is a much wider
range of shaping processes that can be applied to nickel-chromium alloys.
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M.F. Ashby 2013
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Exercises With Worked Solutions – Unit 6
32. Use the “Search” facility in CES EduPack Level 2 to find materials for scissors. (see
Question 20)
Answer.
•
Stainless steel
•
High carbon steel
•
Medium carbon steel
•
Low alloy steel
Function
Blades for office scissors
Constraints
High hardness (for wear resistance)
Adequate toughness (to avoid chipping the blade edge)
High stiffness to ensure that the blades do not bend in service
Able to be forged
Objective
Minimize material price
Free variables
Choice of material
From the Toolbar select “Tools > Options > Numbers” and tick “Display data ranges as
average values”
Property
High carbon
steel
Low alloy
steel
Medium
carbon steel
Stainless
steel
Hardness (HV)
322
311
260
272
Toughness (MPa.m^0.5)
49.8
52.9
33.2
96.4
Young’s Modulus (GPa)
207
211
208
199
Can be forged
Yes
Yes
Yes
Yes
0.589
0.629
0.589
6.05
Price ($/kg)
Low alloy steel, medium carbon steel and high carbon steel do not differ greatly. Stainless
steel is the odd one out; it is THE toughest material at Level 2, however, you will also
notice that it is about 10 times more expensive than any of the other steel variants, yet it
is in the stainless steel datasheet which you find a picture of a pair of office scissors.
The reason why stainless steel is the material of choice is that it is extremely corrosion
resistant, whereas carbon steels oxidize, and no one wants to keep having to polish their
scissors every now and then. This relates to the convenience of the user, a factor which
surfaces more in product design than the translation process.
In any case, the material price can be somewhat offset by efficient design and the fact
that a pair of scissors uses only somewhere in the order of 50g of material. Thus the
objective to ‘Minimize material cost’ should be taken into context.
Scissors which oxidise are still being produced though, as there are always people looking for
cheaper options. For office purposes, rather than culinary purposes it does not matter if the
scissors get rusty so the cheaper materials are equally viable. There is also always the option
of buying a new pair each time the old one gets rusty, which since the other 3 materials are
significantly cheaper than stainless steel, might work out to be more cost efficient.
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M.F. Ashby 2013
18
Exercises With Worked Solutions – Unit 6
33. Use the “Search” facility in CES EduPack Level 2 to find materials for heat exchangers.
(see Question 21)
Answer.
•
Metal foam
•
Nickel
•
Commercially pure titanium
•
Nickel-chromium alloys
•
Copper
•
Titanium alloys
•
Brass
•
Bronze
Function
Geothermal heat exchanger
•
•
•
•
•
•
Constraints
Good thermal conductivity
Durability in hot salt water: very good/excellent
Maximum service temperature > 120ºC
Sufficient strength to carry the pressure of the super-heated water
Ability to be rolled into sheet or tube
Sufficient ductility to allow shaping to form tubes
Objective
Minimize material price
Free variables
Choice of material
Metal
Foam
Nickel
Comm.
pure Ti
Nickelchromium
alloys
Copper*
Titanium
alloys
Brass
Bronze
Thermal
Conductivity
(W/m.ºC)
3.8 - 7
67 - 91
16 - 18
9 - 15
160 - 390
7 - 14
100 - 130
50 - 63
Durability in
salt water
Acceptable
Excellent
Excellent
Excellent
Excellent
Excellent
Excellent
Excellent
Max service
temp (ºC)
140 - 190
240 - 370
400 - 450
900 - 1000
180 - 300
450 - 500
210
170 - 200
0.7 - 2
70 - 900
270 - 600
365 - 460
30 - 350
750 - 1200
95 - 500
100 - 500
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
1-4
2 - 60
5 - 25
20 - 35
3 - 50
5 - 10
5 - 60
2 - 40
11.5 – 12.6
18.2 - 20
11.9 – 13.1
24.5 – 26.9
8.81 – 9.69
25 – 27.6
6.54 – 7.19
9.64 – 10.6
Property
Strength (MPa)
Can be rolled
to sheet/tube
Ductility
strain)
Price ($/kg)
(%
*Copper alloys have similar properties to copper, except that they are stronger (due to the
alloying)
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M.F. Ashby 2013
19
Exercises With Worked Solutions – Unit 6
Of the 8 candidate materials, we shall discuss the odd one out first. Metal foam has only
Acceptable durability in salt water, cannot be rolled into sheet or tube, and has very poor
strength and ductility compared with the rest. Yet it is still used as a heat exchanger.
What the search term didn’t define was what type of heat exchanger. If you refer to the
‘Typical uses’ section of metal foam, you will see that metal foams are used as heat
exchangers for power electronics (water shouldn’t be passing through there). They are
used because their foam structure greatly increases the surface area for heat dissipation,
and being metallic-based, have higher conductivity than other foams.
Considering the other 7 materials, titanium alloys prove the most expensive. The plus
side with titanium is that you can use it at higher temperatures, but for the purposes of the
application stated in Q21, any of the materials would qualify. Hence in this case study
commercially pure titanium and titanium alloys would be lowly-ranked based on the
objective, to minimize cost, though if the situation were different (higher temperature fluid,
bigger budget), titanium might be preferable.
For heat exchanging, thermal conductivity has to be one of the most important criteria
and if we compare the materials based on it, we will again have a case for not using
titanium or its alloys (high cost, low performance!). On the other hand, though, there is
one material that catches the eye and that is copper. Copper has one of the highest
thermal conductivities of all materials (plot a bar chart of thermal conductivity to convince
yourself of this), which is why in the past, entire pans and kettles were made of copper
(however it is poisonous, so it has to be lined), but it is also a notoriously soft material.
Hence the solution is to produce copper alloys, which strengthen copper (why alloys are
stronger is a story best saved for another unit while allowing the use of its thermal
properties. Copper, when now alloyed, has a strength similar to bronze, making bronze a
material which is dominated by it in all properties. The choice between copper and brass
would depend on whether brass can meet the requirements of the design, in which case it
is a better choice as it is cheaper.
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M.F. Ashby 2013
20
Exercises With Worked Solutions – Unit 6
34. Use the “Search” facility in CES EduPack Level 2 to find materials for cutlery. (see
Question 22)
Answer.
Candidates from CES EduPack Level 2 are:
•
Cellulose polymers
•
Starch-based thermoplastics (TPS)
•
Stainless steel
•
Polystyrene (PS)
Function
Disposable cutlery
•
•
•
•
•
Constraints
Easy (and thus cheap) to mold
Non-toxic
Sufficient strength and stiffness (modulus) to withstand loads in use
Recyclable or renewable (e.g. wooden cutlery)
Ability to be colored (?)
Objective
Minimize material price
Free variables
Choice of material
Property
Cellulose
polymers
TPS
Stainless
steel
Polystyrene
3-4
4-5
3-4
4-5
Toxicity rating
Non-toxic
Non-toxic
Non-toxic
Non-toxic
Strength (MPa)
25-45
16-22
170-1000
28.7-56.2
Young’s Modulus (GPa)
1.6-2
0.24-1.5
189-210
1.2-2.6
Recyclable?
Yes
Yes
Yes
Yes
Colorable?
Yes
Yes
Yes
Yes
4644.3
7035.8
68295
2277.6
Castability / Moldability
Approximate Price
($/volume)
Note that we have used the price per volume because cutlery tends to be of a certain size
(one that the average hand can grasp) thus making it easier to compare across the
materials.
Purely based on the exorbitant rates of stainless steel it can be excluded from our
selection on the basis of cost. It comes up in the search for cutlery because it is used to
make non-disposable cutlery.
Although disposable cutlery tends to be associated with polymers, aluminum alloys (not
shown in search) turn out to not be as ridiculous as you think; due to their high strength
and modulus, cutlery made of aluminum alloys can be made thinner than one made of
polymer, making them a relatively cheap option, and you will probably find them in
relatively cheap restaurants.
TPS and cellulose polymers are solutions that are more or less dominated by
Polystyrene, the former mainly because it is rather weak and flimsy (think about using a
TPS fork to eat steak), the latter because it is less moldable, and both are more
expensive than Polystyrene.
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M.F. Ashby 2013
21
Author
Professor Mike Ashby
University of Cambridge, Granta Design Ltd.
www.grantadesign.com
www.eng.cam.ac.uk
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