Synopsis

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26 Νοε 2013 (πριν από 3 χρόνια και 6 μήνες)

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Total Design

Market
Assessment

Specification

Concept
Design

Detail
Design

Manufacture

Sell

is a systematic activity:

Identification of the market need
→ sale of product to
meet that need.

Product, Process, People, Organization, etc.


Design Core

Market Analysis

Specification

Concept Design

Detailed Design

Manufacturing

Sales


Product Design Specification (PDS)

Envelopes all stages of the design core


THE DESIGN CORE

The Design Core

Market
Assessment

Specification

Concept
Design

Detail
Design

Manufacture

Sell

DETAIL

DESIGN


A vast subject. We will concentrate on:


Materials Selection



Process Selection


Cost Breakdown


Materials Selection

Metals
and
Alloys

Polymers

Ceramics
and
Glasses

Steel
-
cord
tyres

CFRP

GFRP

Filled polymers

Wire
-
reinforced cement

Cermets

MMCs

Composites

Materials Properties

MATERIAL

Mechanical


tribology


fatigue


K
IC


σ
y


UTS


E

Thermal


α


K


H


T
m


T
Transition

Environmental


recycling


energy consumption


waste

Other


feel


look

Physical


optical


magnetic


electrical

Chemical


corrosion


oxidation

FUNCTIONAL

MATERIALS

STRUCTURAL MATERIALS

Young’s Modulus, E


Material


E

(GPa)


Material


E
(GPa)


Material


E
(GPa)

Diamond

Tungsten carbide, WC

Cobalt/WC cermets

Borides of Ti, Zr, Hf

Silicon carbide, SiC

Boron

Tungsten

Alumina, Al
2
O
3

Beryllia, BeO

Titanium carbide, TiC

Molybdenum and alloys

Tantalum carbide, TaC

Niobium carbide, TaC

Silicon nitride, Si
3
N
4

Chromium

Beryllium and alloys

Magnesia, MgO

Cobalt and alloys

Zirconia, Zr0

Nickel and alloys

CFRP

Iron

Iron based superalloys

Steels

1000

450
-
650

400
-
530

500

450

441

406

390

380

379

320
-
365




289

200
-
289

250

200
-
284

160
-
241

130
-
234

70
-
200

196

193
-
214

196
-
207

Cast irons

Tantalum and alloys

Platinum

Uranium

Boron/epoxy composites

Copper and alloys

Mullite

Vanadium

Titanium and alloys

Palladium

Brasses and bronzes

Niobium and alloys

Silicon

Zirconium and alloys

Silica glass, SiO
2

(quartz)

Zinc and alloys

Gold

Aluminium and alloys

Silver

Calcite (marble, limestone)

Soda glass

Granite

Tin and alloys

Concrete, cement

170
-
190

150
-
186

172

172

125

120
-
150

145

130

80
-
130

124

103
-
124

80
-
110

107

96

94

43
-
96

82

69
-
79

76

31
-
81

69

62

41
-
53

45
-
50

Magnesium and alloys

GFRP

Graphite

Alkyds

Common woods,
║ to grain

Lead and alloys

Ice, H
2
O

Melamines

Polyimides

Polyesters

Acrylics

Nylom

PMMA

Polystyrene

Epoxies

Polycarbonate

Common woods,


to grain

Polypropylene

Polyethylene (high density)

Polyethylene (low density)

Foamed polyurethane

Rubbers

PVC

Foamed polymers

41
-
45

7
-
45

27

20

9
-
16

14

9.1

6
-
7

3
-
5

1
-
5

1.6
-
3.4

2
-
4

3.4

3
-
3.4

3

2.6

0.6
-
1

0.9

0.7

0.2

0.01
-
0.06

0.01
-
0.1

0.003
-
0.01

0.001
-
0.01

Yield Strength (
σ
y
) & UTS (
σ
TS
)


Material

σ
y

(MPa)

σ
TS

(MPa)


Material

σy

(MPa)

σ
TS

(MPa)

Pressure
-
vessel steels

Low alloy steels

Molybdenum and alloys

Tungsten

Nickel alloys

Carbon steels

Titanium and alloys

Tantalum and alloys

CFRPs

Cobalt/WC cermets

Cast irons

Copper alloys

Concrete (steel reinforced)

Stainless steel (austenitic)

Aluminium alloys

Brasses and bronzes

Stainless steels (ferritic)

Zinc alloys

Zirconium alloys

Mild steel

GFRPs

Magnesium alloys

Beryllium and alloys

PMMA

1500
-
1900

500
-
1980

560
-
1450

1000

200
-
1600

260
-
1300

180
-
1320

330
-
1090

---

400
-
900

220
-
1030

60
-
960

---

286
-
500

100
-
627

70
-
640

240
-
400

160
-
421

100
-
365

220

---

80
-
300

34
-
276

60
-
110

1500
-
2000

680
-
2400

665
-
1650

1510

400
-
2000

500
-
1880

300
-
1400

400
-
1100

640
-
670

900

400
-
1200

250
-
1000

410

760
-
1280

300
-
700

230
-
890

500
-
800

200
-
500

240
-
440

430

100
-
300

125
-
380

380
-
620

110

Ice, H
2
O

Polyimides

Nickel

Nylons

Epoxies

Copper

Silver

ABS/polycarbonate

Polystyrene

Iron

Pure ductile metals

Acrylic/PVC

Aluminium

Gold

Lead and alloys

Polyurethane

Polypropylene

Tin and alloys

Polyethylene (high density)

Concrete (non
-
reinf’d, comp’n)

Polyethylene (low density)

Ultrapure fcc metals

Foamed polymers (rigid)

Polyurethane foam

85

52
-
90

70

49
-
87

30
-
100

60

55

55

34
-
70

50

20
-
80

45
-
48

40

40

11
-
55

26
-
31

19
-
36

7
-
45

20
-
30

20
-
30

6
-
20

1
-
10

0.2
-
10

1

---

---

400

100

30
-
120

400

300

60

40
-
70

200

200
-
400

---

200

220

14
-
70

58

33
-
36

14
-
60

37

---

20

200
-
400

0.2
-
10

1

Density,
ρ


Material

ρ

(Mgm
-
3
)


Material

ρ

(Mgm
-
3
)


Material

ρ

(Mgm
-
3
)

Osmium

Platinum

Tungsten and alloys

Gold

Uranium

Tungsten carbide, WC

Tantalum and alloys

Molybdenum and alloys

Cobalt/WC cermets

Lead and alloys

Silver

Niobium and alloys

Nickel and alloys

Cobalt and alloys

Copper and alloys

Brasses and bronzes

Iron

Iron
-
based superalloys

Steels

Tin and alloys

Cast irons

22.7

21.4

13.4
-
19.6

19.3

18.9

14.0
-
17.0

16.6
-
16.9

10.0
-
13.7

11.0
-
12.5

10.7
-
11.3

10.5

7.9
-
10.5

7.8
-
9.2

8.1
-
9.1

7.5
-
9.0

7.2
-
8.9

7.9

7.9
-
8.3

7.5
-
8.1

7.3
-
8.0

6.9
-
7.8

Titanium carbide, TiC

Zinc and alloys

Chromium

Zirconium carbide, ZrC

Zirconium and alloys

Titanium and alloys

Alumina, Al
2
O
3

Magnesia, MgO

Silicon carbide, SiC

Silicon nitride, Si
3
N
4

Mullite

Beryllia, BeO

Calcite (marble, limestone)

Aluminium and alloys

Silica glass, SiO
2

(quartz)

Soda glass

Concrete/cement

GFRPs

Carbon fibres

PTFE

Boron/epoxy composites

7.2

5.2
-
7.2

7.2

6.6

6.6

4.3
-
5.1

3.9

3.5

2.5
-
3.2

3.2

3.2

3.0

2.7

2.6
-
2.9

2.6

2.5

2.4
-
2.5

1.4
-
2.2

2.2

2.3

2.0

Beryllium and alloys

Graphite (high strength)

CFRPs

PVC

Polyesters

Polyimides

Epoxies

Polycarbonate

Polyurethane

PMMA

Nylon

Polystyrene

Polyethylene (high density)

Ice, H
2
O

Polyethylene (low density)

Polypropylene

Rubber

Common woods

Foamed polymers

Foamed polyurethane

1.8
-
2.1

1.8

1.5
-
1.6

1.3
-
1.6

1.1
-
1.5

1.4

1.1
-
1.4

1.2
-
1.3

1.1
-
1.3

1.2

1.1
-
1.2

1.0
-
1.1

0.94
-
0.97

0.92

0.91

0.88
-
0.91

0.83
-
0.91

0.4
-
0.8

0.01
-
0.6

0.06
-
0.2


Specific Properties


Material

E

(GPa)

σ

(MPa)

ρ

(Mgm
-
3
)

E
/
ρ
mean

(10
6

m
2
s
-
2
)

σ
/
ρ
mean

(10
3

m
2
s
-
2
)

Cobalt/WC cermets

Beryllium and alloys

Low
-
alloy steels

CFRP

Aluminium alloys

Common woods,
║ to grain

Lead and alloys

Polypropylene

Foamed polymers

400
-
530

200
-
289

200
-
207

70
-
200

69
-
79

9
-
16

14

0.9

0.001
-
0.1

400
-
900

34
-
276

500
-
1980

640
-
670

100
-
627

35
-
55

11
-
55

19
-
36

0.2
-
10

11
-
12.5

1.8
-
2.1

7.8

1.5
-
1.6

2.6
-
2.9

0.4
-
0.6

10.7
-
11.3

0.88
-
0.91

0.01
-
0.6

34
-
45

103
-
148

26
-
27

45
-
129

25
-
45

15
-
27

1.3

1.0

0.003
-
0.03

34
-
77

17
-
141

64
-
253

413
-
432

36
-
228

58
-
92

1.0
-
5.0

21
-
40

0.66
-
33

E

E
/
ρ
mean

σ

σ
/
ρ
mean

Cobalt/WC cermets

Beryllium and alloys

Low
-
alloy steels

CFRP

Aluminium alloys

Common woods,
║ to grain

Lead and alloys

Polypropylene

Foamed polymers

Beryllium and alloys

CFRP

Cobalt/WC cermets

Aluminium alloys

Low
-
alloy steels

Common woods,
║ to grain

Lead and alloys

Polypropylene

Foamed polymers

Low
-
alloy steels

Cobalt/WC cermets

CFRP

Aluminium alloys

Beryllium and alloys

Common woods,
║ to grain

Lead and alloys

Polypropylene

Foamed polymers

CFRP

Low
-
alloy steels

Aluminium alloys

Beryllium and alloys

Common woods,
║ to grain

Cobalt/WC cermets

Polypropylene

Lead and alloys

Foamed polymers

Materials Selection without Shape


Generic materials selection



Problem statement


Model


Function, Objective,
Constraints


Selection



Examples



Oars


Mirrors for large telescopes


Low cost building materials


Flywheels


Springs


Safe pressure vessels


Precision devices


Generic Materials Selection

p:

Performance of component;

f(F,G,M)

F: Functional requirement, e.g. withstanding a force

G:

Geometry, e.g. diameter, length etc.

M:

Materials properties, e.g. E, K
IC
,
ρ


Separable function if:

P = f
1
(F)


f
2
(G)


f
3
(M)


TASK:

Maximize f
3
(M) where M is the “performance index”

Procedure for Deriving “M”

(a)
Identify the
attribute

to be maximized or minimized (weight, cost, energy, stiffness,
strength, safety, environmental damage, etc.).

(b)
Develop an equation for this attribute in terms of the functional requirements, the
geometry, and the material properties ( the
objective function
).

(c)
Identify the
free

(unspecified)
variables.

(d)
Identify the
constraints
; rank them in order of importance.

(e)
Develop
equations

for the constraints (no yield, no fracture, no buckling, maximum
heat capacity, cost below target, etc.).

(f)
S
ubstitute

for the free variables from the constraints into the objective function.

(g)
G
roup the variables

into three groups: functional requirements, F, geometry, G, and
materials properties, M.

(h)
R
ead off

the performance index, expressed as a quantity, M, to be maximized.

(i)
N
ote

that a full solution is not necessary in order to identify the material property
group.

The Materials Selection Map

1
10
100
1000
0.1
1
10
100
MATERIALS PROPERTY 1
MATERIALS PROPERTY 2
Guidelines for

M = Prop2/Prop1

Search

Region

M = 40

Example I: A light strong tie

So, to minimize mass m,

maximise



f
M



L
m
A
AL
m



:
Mass
m
FL
A
F
f




:
Stress
f
L
F
m






f
1
(F)

f
2
(G)

f
3
(M)

Search

Region

M = 100Nm/g

Example II: A light stiff column (circular)

2
2
L
EI
n
F
buckling




4
/
4
/
2
4
A
r
I



AL
m

2
4
2
2
2
2
4
4




L
Em
n
L
EA
n
F
buckling


E
n
L
F
m






4
2
f
1
(F)

f
2
(G)

f
3
(M)

So, to minimize mass m,

maximise


2
/
1
E
M

Search

Region

Example III: Pressure Vessel

So, to minimize mass m,

maximise



f
M

f
1
(F)

f
2
(G)

f
3
(M)








L
R
p
m
2
2
RL
m
dR


2

m
RL
pR



2

RLdR
m
dR
pR



2
,


Light weight cylindrical

vessel of fixed radius

Search

Region

Performance Indices: Elastic Design

Component and design goal

Maximise

Springs:

Specified energy storage, volume to be minimized

Springs:

Specified energy storage, mass to be minimized

Elastic hinges:

Radius of bend to be minimized

Knife edges, pivots:

Minimum contact area, maximum bearing load

Compression seals and gaskets:

Maximum contact area with specified
maximum contact pressure

Diaphragms:

Maximum deflection under specified pressure of force

Rotating drives, centrifuges:

Maximum angular velocity, radius specified,
wall thickness free

Ties, columns:

Maximum longitudinal vibration frequencies

Beams:

Maximum flexural vibration frequencies

Plates:

Maximum flexural vibrationfrequencies

Ties, columns, beams, plates:

Maximum self
-
damping

σ
f
2
/E

σ
f
2
/E
ρ

σ
f
/E

σ
f
3
/E
2

& E

σ
f
/E & 1/
σ
f



σ
f
3/2
/E

σ
f
/
ρ


E/
ρ

E
1/2
/
ρ

E
1/3
/
ρ

η

Note:

σ
f

= failure strength;
E

= Young’s modulus;
ρ

= density;
η

= loss coefficient

Performance Indices: Min. Weight

Component and loading

Stiffness:

Maximize

Strength:

Maximize

Tie (tensile strut):

Load, stiffness, length specified, section area free

Torsion bar or tube:

Torque, stiffness, length specified, section area free

Beam:

Loaded externally or by self
-
weight in bending; stiffness, length specified,
section area free

Column (compression strut):

Failure by elastic buckling or plastic compression;
collapse load and length specified, section area free

Plate:

Loaded externally or by self
-
weight in bending; stiffness, length, width
specified, thickness free

Plate:

Loaded in
-
plane; failure by elastic buckling or plastic compression; collapse
load, length and width specified, thickness free

Rotating disks, flywheels:

Energy storage specified

Cylinder with internal pressure:

Elastic distortion, pressure and radius
specified, wall thickness free

Spherical shell with internal pressure:

Elastic distortion, pressure and radius
specified, wall thickness free

E/
ρ

G
1/2
/
ρ

E
1/2
/
ρ


E
1/2
/
ρ


E
1/3
/
ρ


E
1/3
/
ρ


-

E/
ρ


E/(1
-
ν
)
ρ

σ
f
/
ρ

σ
f
2
/3
/
ρ

σ
f
2
/3
/
ρ


σ
f
/
ρ


σ
f
1/2
/
ρ


σ
f
/
ρ


σ
f
/
ρ

σ
f
/
ρ


σ
f
/
ρ

Note:

σ
f

= failure strength;
E

= Young’s modulus;
G

= shear modulus;
ρ

= density

Performance Indices: Min. Weight

Component and loading

Crack length

fixed:

Maximize

≈ min section:
Maximize

Tie (tensile strut):

Load, length specified, section area free

Torsion bar or tube:

Torque, length specified, section area free

Beam:

Loaded externally or by self
-
weight in bending; stiffness,
length specified, section area free

Column (compression strut):

Failure by elastic buckling or plastic
compression; collapse load and length specified, section area free

Plate:

Loaded externally or by self
-
weight in bending; load, length,
width specified, thickness free

Plate:

Loaded in
-
plane in tension; collapse load, length and width
specified, thickness free

Rotating disks, flywheels:

Energy storage specified

Cylinder with internal pressure:

Elastic distortion, pressure and
radius specified, wall thickness free

Spherical shell with internal pressure:

Elastic distortion,
pressure and radius specified, wall thickness free

K
IC
/
ρ

K
IC
2/3
/
ρ

K
IC
2/3
/
ρ


K
IC
2/3
/
ρ


K
IC
1/2
/
ρ


K
IC
/
ρ


K
IC
/
ρ

K
IC
/
ρ


K
IC
/(1
-
ν
)
ρ

K
IC
4/3
/
ρ

K
IC
4/5
/
ρ

K
IC
4/5
/
ρ


K
IC
4/5
/
ρ


K
IC
2/3
/
ρ


K
IC
2
/
ρ


K
IC
/
ρ

K
IC
2
/
ρ


K
IC
2
/(1
-
ν
)
ρ

Note:

K
IC

= fracture toughness
ρ

= density

Nomenclature

a,R,r

a
C

A

C,C
1
,n

C
R

E

F

F
buckling

g

G

I

J

K

K
IC

L

m

M

p

Q

S
B

S
T

t

Radius

Half crack length

Cross
-
sectional area

Constant dependent upon loading system

Relative cost

Young’s modulus

Force

Critical force for the onset of buckling

Acceleration due to gravity

Shear modulus

Second moment of area

Polar moment

Resistance to twisting of section

Fracture toughness

Beam, shaft etc. length

Mass

Performance index; Bending moment

Pressure

Section modulus in torsion

Bending stiffness

Torsional stiffness

Thickness

T

T
o

U

V

y
m

W
V

x

Z

α

δ

ε

η

θ

λ

ν

ρ

σ

σ
f



φ

ψ

ω

Temperature; Torque

Initial temperature

Kinetic energy

Volume

Distance from neutral axis to highest stressed surface

Stored energy

Distance

Section modulus in bending

Linear coefficient of thermal expansion

Deflection

Strain

Loss coefficient

Angle of twist

Thermal conductivity

Poisson’s ratio

Density

Stress

Failure stress

Maximum surface shear stress

Macro
-
shape factor

Micro
-
shape factor

Angular velocity

Materials for Large Telescopes

DESIGN REQUIREMENTS

Function

Precision mirror

Objective

Minimize mass

Constraints

(a)
Radius
a

specified

(b)
Must not distort more
than
δ

under its own
weight

(c)
High dimensional
stability: no creep, no
moisture absorbtion, low
thermal expansion



t
a
m
Mass
2
:

3
2
4
3
:
Et
mga
Deflection



2
/
3
3
/
1
2
2
/
1
4
3
















E
a
g
m



f1(F)

f2(G)

f3(M)


3
/
1
E
M

So, to minimize mass m,

maximise

Materials for Large Telescopes

Search

Region


3
/
1
E
M

M = 2
(GPa)
1/3
m
3
/Mg

Material

M

Comment

Steel

Concrete


Al alloys

Glass

GFRP

Mg alloys


Wood

Beryllium


Foamed polystyrene


CFRP

0.7

1.4


1.5

1.6

1.7

2.1


3.6

3.65


3.9


4.3

Very heavy. The original choice.

Heavy. Creep, thermal distortion
problems.

Heavy. High thermal expansion.

The present choice.

Not dimensionally stable enough.

Lighter than glass, but high thermal
expansion.

Dimensionally unstable.

Very expensive. Good for small
mirrors.

Very light, but not dimensionally
stable.

Very light, but not dimensionally
stable: use for radio telescopes.

Materials for Oars

DESIGN REQUIREMENTS

Function

Light, stiff beam

Objective

Minimize mass

Constraints

(a)
Length specified

(b)
Bending stiffness
specified

(c)
Toughness > 1 kJ/m
2

(d)
Cost <$100/kg

2
/
1
2
/
5
2
/
1
1
4
E
L
C
F
m















So, to minimize mass m,

maximise


2
/
1
E
M



AL
r
m
Mass


2
:
3
1
:
L
EI
C
F
S
Stiffness





2
4
4
A
r
I


Second

moment of area:

Materials for Oars

Material

M

Comment

Woods


CFRP


GFRP


Ceramics

5
-
8


4
-
8


2
-
3.5


4
-
8

Cheap, traditional, but with
natural variability.

As good as wood, more control
of properties.

Cheaper than CFRP, but lower
M
, thus heavier.

Good
M
, but toughness low and
cost high.

Search

Region


2
/
1
E
M

M = 6
(GPa)
1/2
m
3
/Mg

Materials for Buildings

DESIGN REQUIREMENTS

Function

Floor beams

Objective

Minimize cost

Constraints

(a)
Length specified

(b)
Stiffness: must not
deflect too much
under design loads

(c)
Strength: must not fail
under design loads

σ
=
σ
y

y

F

b

b

R
y
R
C
M
C
E
M



3
/
2
2
2
/
1
1


Floor Beam

Materials for Buildings

M
2

= 6.8

Search

Region

M
1

= 1.6

Search

Region

Materials for Safe Pressure Vessels

DESIGN REQUIREMENTS

Function

Pressure vessel =contain
pressure
p

Objective

Maximum safety

Constraints

(a)
Must yield before break

(b)
Must leak before break

(c)
Wall thickness small to
reduce mass and cost

Yield before break

2
2
,










f
IC
C
C
IC
K
C
a
a
CK




f
IC
K
M


1

Leak before break

f
IC
IC
C
f
K
pR
C
t
CK
t
a
pR
t
t
pR






2
2
4
2
/
2
2
,
2






f
IC
K
M

2
2


Minimum strength

f
M


3
Materials for Safe Pressure Vessels

Search

Region

M
3
= 100 MPa

M
1

= 0.6 m
1/2

f
IC
K
M


1
f
IC
K
M

2
2

f
M


3
Material

M
1

(m
1/2
)

M
3

(MPa)

Comment

Tough steels

Tough Cu alloys

Tough Al alloys


Ti
-
alloys

High strength Al
alloys

GFRP/CFRP

>0.6

>0.6

>0.6


0.2

0.1

0.1

300

120

80


700

500

500

Standard.

OFHC Cu.

1xxx & 3xxx


High strength,
but low safety
margin. Good
for light
vessels.

Materials for Springs

DESIGN REQUIREMENTS

Function

Elastic spring

Objective

(a)
Maximum stored elastic energy
per unit volume

(b)
Maximum stored elastic energy
per unit mass

Constraints

(a)
No failure by yield, fracture or
fatigue, i.e.
σ

<
σ
f

everywhere

(b)
Adequate toughness: G
C
>1
kJ/m
2

σ
f

σ

ε

σ
f
/E

Energy
Stored

E
W
Leaf
E
W
Torsion
E
W
Tie
f
V
f
V
f
V
2
2
2
4
1
:
3
1
:
2
1
:









E
M
E
M
f
f
2
2
2
1


Materials for Springs

E
M
f
2
1


M
1

= 6 MJ/m
3

Search

Region

Material

M
1

(MJ/m
3
)

Comment

Ceramics

Spring steel


Ti alloys

CFRP


GFRP

Glass (fibres)


Nylon


Rubber

10
-
100

15
-
25


15
-
20

15
-
20


10
-
12

30
-
60


1.5
-
2.5


20
-
50

Brittle in tension; good only in compression.

The traditional choice: easily formed and heat
treated.

Expensive, corrosion resistant.

Comparable in performance with steel;
expensive.

Almost as good as CFRP and much cheaper.

Brittle in torsion, but excellent if protected
against damage; very low loss factor.

The least good; but cheap and easily shaped,
but high loss factor.

Better than spring steel, but high loss factor.

Materials for Springs



E
M
f
2
2

M
2

= 2 kJ/kg

Search

Region

Material

M
2

(kJ/kg)

Comment

Ceramics

Spring steel

Ti alloys


CFRP

GFRP

Glass (fibres)


Wood


Nylon

Rubber

5
-
40

2
-
3

2
-
3


4
-
8

3
-
5

10
-
30


1
-
2


1.5
-
2

20
-
50

Brittle in tension; good only in compression.

Poor because of high density.

Better than steel; corrosion resistant,
expensive.

Better than steel; expensive.

Better than steel; less expensive than CFRP.

Brittle in torsion, but excellent if protected
against damage; very low loss factor.

On a weight basis, wood makes good
springs.

As good as steel; but has a high loss factor.

Outstanding;10 times better than steel, but
has a high loss factor.

Materials for Flywheels

DESIGN REQUIREMENTS

Function

Flywheel for energy storage

Objective

Maximize kinetic energy per
unit mass

Constraints

(a)
Must not burst

(b)
Adequate toughness to
give crack tolerance

DESIGN REQUIREMENTS

Function

Flywheel for child’s toy

Objective

Maximize kinetic energy per
unit volume

Constraints

Outer radius fixed



Kinetic energy:

Polar moment of inertia:

Mass:

Stress:

2
/
2

J
U

2
/
4


t
R
J

t
R
m
2


2
/
2



R

Materials for Flywheels

Search

Region

M
1

= 100 kJ/kg

2
4
4
2
4
2
,
2
1






t
R
U
t
R
J
J
U




2
2
2
4
1



R
m
U
t
R
m










f
m
U
R

















3
2
8
3
2
max


f
M

1
2
2
4
1


R
V
U



2
M
Maximizing energy/volume

Maximizing energy/mass

Materials for Flywheels

Material

M

(kJ/kg)

Comment

Ceramics


Composites:


CFRP


GFRP


Beryllium


High strength steel

High strength Al alloys

High strength Mg alloys

Ti alloys

200
-
2000

(Compression only)


200
-
500

100
-
400


300


100
-
200

100
-
200

100
-
200

100
-
200

Brittle and weak in tension


eliminate.



The best performance


a good choice.

Almost as good as CFRP and cheaper


an excellent choice.


Good, but expensive, difficult to work and toxic.



All about equal performance. Steel and Al alloys cheaper
than Mg and Ti alloys.


Pb alloys

Cast iron

3

8
-
10

High density makes these a good (and traditional) selection
when performance is velocity limited, not strength limited.

Materials for Precision Devices

DESIGN REQUIREMENTS

Function

Force loop (frame)

Objective

Maximize positional
accuracy (minimize
distortion)

Constraints

(a)
Must tolerate heat flux

(b)
Must tolerate vibration




2
/
1
2
1
E
M
M


Heat flow :

Thermal strain :



)
d
/
d
(
x
T
q



)
(
T
T
o








/
)
d
/
d
(
)
d
/
d
(
q
x
T
x


Materials for Precision Devices

Material

M
1

M
2

Comment

Diamond


5x10
8


8.6


Oustanding M
1

and M
2
;
expensive

Si

4x10
7

6.0

Excellent M
1

and M
2
; cheap

SiC


2x10
7


6.2


Excellent M
1

and M
2
; potentially
cheap

Be

10
7

9

Less good than Si or SiC

Al

10
7

3.1

Poor M
1
, but very cheap

Ag

Cu

Au

2x10
7

2x10
7

2x10
7

1.0

1.3

0.6


High density gives poor M
2


W

Mo

Invar

3x10
7

2x10
7

3x10
7

1.1

1.3

1.4

Better than Cu, Ag or Au, but
less good than Si, SiC or
diamond




2
/
1
2
1
E
M
M


M
1
= 10
7

W/m

Search

Region

Diamond

Si

SiC

Al

Ag

Au

Be

Cu

Mo

W