Transcript Lecture 10

Design Realization
lecture 10
John Canny
9/25/03
Last Time
 Introduction to prototyping processes
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CNC machining
PC board manufacture
Laser cutters, plasma, water cutters
3D printing: SLA, SLS, LOM, FDM
Modular 3D printing
 Design review next Tuesday: bring your
prototypes!
Materials: Physical constants: Length
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1 m (meter) = 39.37 inches
1 dm (decimeter) = 0.1 m
1 cm (centimeter) = 0.01m
1 mm = 10-3 m = 0.03937 inches
1 mil = 10-3 inches = 0.0254 mm
 Surface finish tolerances of this order
 Human hair diameter 1 to 4 mils
 1 liter = 1 cubic decimeter = 0.001 cubic m
Physical constants: Length
 1  (micron) = 10-6 m = 0.0394 mils
 Dust particles, smoke, yeast cell
 Particles ≤ 1  float in air, adhere to surfaces
 Infra-red light wavelength
 1 nm (nano-meter) = 10-9 m
 Visible light 400-700 nm
 Nano-particles (1-100s of nm)
 Large molecules
 1 Å (Angstrom unit) = 10-10 m = 0.1 nm
 Most atom diameters are a few Å
Mass, Force
 1 kg (kilogram) = mass of 1 liter of water
(about 2.2 lbs)
 1 N (Newton) = force required to accelerate 1
kg mass to 1 m s-2
 From Newton’s law F = ma
 Gravitational force on 1 kg = 9.81 N
 Objects in free fall accelerate at 9.81 m s-2
 1 amu (atomic mass unit) 1.66 x 10-27 kg
 Average mass of 1 neutron/proton
 Approximate mass of hydrogen atom
Density of common materials
 Mass/volume
Material
Density, kg/liter
Steel
7.87
Titanium
4.7
Aluminum
2.7
Carbon Fiber
1.75
Low-Grade Plastic
1.2
Pressure
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Pressure = force per unit area
1 Pa (Pascal) = 1N per sq meter
1 psi (pound per sq. inch) = 6,895 Pa
1 atmosphere = 101,300 Pascals = 14.7 psi
 Blood pressure is about 300 kPa
 Hydraulic pressure 10 – 1000 MPa
Strength and Stiffness
 When pressure is applied to a material, it
deforms in the direction of the pressure:
L
P
L
 The pressure is called stress .
 The displacement L/L is strain . It is
dimensionless.
Stiffness
 Material stiffness is stress/strain and it is in
units of pressure.
 aka Young’s modulus E = /
 Defined for stretching a cylindrical rod, it must
always be > 0.
Stiffness and Compressibility
 When the rod stretches, its area normally
decreases (to minimize volume change).
 Poisson’s ratio  = - axial strain/ linear strain
 It must lie between -1 and 0.5
 An incompressible material has  = 0.5.
 Most materials have  between 0 and 0.5
Shear modulus
 G is the ratio of shear strain to shear stress:
 G is always positive and satisfies:
E
G
2(1  )
Strength and Stiffness
 Strength is the stress at which the material fails:
Stiffness of Common Materials
Material
Young Modulus (in GPa)
Steel
210
Iron
209
Carbon Fiber
231
Aluminum
69
Titanium
117
Diamond
1035
Nylon
3
Strength of Common Materials
 Yield to plastic region & final breaking strength.
Material
Yield Strength (MPa) Tensile Strength (Mpa)
Cast Iron
275
275
Steel
500
700
Carbon Fiber
4000
Titanium
800
900
Aluminum
175
350
Nylon
90
90
Kevlar
3600
Spider Silk
3000
Temperature
 Heat is kinetic (motion) energy of atoms.
 Temperature measures the energy per
molecule in a gas, or energy per degree of
freedom in a solid.
 E per molecule = 3/2 kT, per dof = ½ kT
 T is absolute temperature (C + 273) and
k is Boltzmann’s constant k = 1.38 x 10-23 J/
Brownian motion
 At normal temperature (300 K), each particle
has average energy 3/2 kT = 6.3 x 10-21 J
 Particle energy is given by ½ mv2
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0.1 mm particle, mass 10-9 kg, v is 3 x 10-7 m/s
10 micron particle, mass 10-12 kg, v is 1 x 10-5 m/s
1 micron particle, mass 10-15 kg, v is 3 x 10-4 m/s
Molecule of atomic wt 100, v is 250 m/s
Thermal conduction
 Thermal conductivity = heat flow/temp. gradient
Material
Thermal conductivity k(W/m C)
Air
0.025
Paper
0.04
Polyester
0.05
Steel
50
Aluminum
237
Copper
401
Diamond
895
Electrical conduction
 Resistivity, Electric field/(current per unit area)
Material
Resistivity, Ω-m
Steel (conductor)
70.0 x 10-8
Brass (conductor)
3.5 x 10-8
Aluminum (conductor)
4.0 x 10-8
Gold (conductor)
2.4 x 10-8
Copper (conductor)
1.7 x 10-8
Silver (conductor)
1.6 x 10-8
Silicon (semiconductor)
1.0 x 103
Rubber (insulator)
1.0 x 1012
Metals
 Metals: strong atomic bonds (high strength and
melting point), but also high thermal and
electrical conduction.
 Structure can be characterized as “positive ions
in a sea of electrons”.
 Conductivity also implies strong reflection of
light (shininess).
Ferro-Metal Chemistry
 Metal properties can be enhanced by mixing in
other materials.
 Steel is an alloy of iron and carbon (< 2%). First
producing in China around 300 BC.
 High-carbon steels are stiffer, stronger, more brittle.
 Stainless steel adds chromium, which forms a
tightly packed oxide layer on the metal’s surface,
protecting it from corrosion.
Ferro-magnetism
 Iron is an important material for its magnetic
properties, which depend on crystal structure
 Ferritic and Martensitic steels are magnetic
 Austenitic steels are not
 The boundaries are not clear: non-magnetic
(including most common stainless) steels can be
worked into a magnetic state.
Flavors of Magnets
 The current killer magnet material is NIB
(Neodymium-Iron-Boron), which is about 4x
stronger than the strongest ferrite.
 Actually NIB is Nd2Fe14B, so its mostly iron
 Very stiff and brittle (safety glasses!), flammable!
 Refrigerator magnets use ferrite particles (e.g.
Strontium Ferrite SrFe12O19) in an elastomer
(flexible plastic).
 The magnetic field is actually periodic.
Liquid Magnets
 There are magnetic liquids: ferro-fluids, which
contain simple ferrite (Fe3O4) with fatty acid
molecules attached to them.
 The fatty acid chains are attracted to an oil
medium and help the
magnetic particles
“dissolve” in the oil.
 A magnet will also hold
the liquid in an inverted
container.
Shape-Memory Alloy
 Two main metal phases are shown below:
Shape-Memory Alloy
 In steel, the martensite/austenite transition is
influenced by alloying, cold-working etc.
 In shape memory allow, the transition is
caused by a small change in temperature.
 The best-known shape memory allow is Nitinol
NiTi (Nickel Titanium).
Shape-Memory Alloy
 The austenite is stiffer and has lower volume.
 Heating SMA wire causes it to contract with
some force. Strains of 3-5% are typical.
Shape-Memory Alloy
 Nitinol has the following attributes:
Martensite
Austenite
Stiffness GPa
28
75
Resistivity
76
82
Transition T
62-72
88-98
Aluminum and Alloys
 Aluminum is a versatile metal that is light, has
very good thermal and electrical conduction.
 Easy to machine (mill or drill).
 Tricky to weld (need to remove oxygen).
 Strength is not high, but can be improved by
alloying with many other metals.
 Titanium-aluminum alloys offer excellent
strength/weight, and dominate the aircraft
industry.
Brass
 Brass is an alloy of Copper and Zinc.
 It has good corrosion resistance, electrical
conduction, and is easy to machine.
 A close relative is bronze, which includes some
other metal like tin or phosphor.
 It offers a range of attractive shades and is
polishes well.
Surface treatments
 Plain metals are often susceptible to corrosion
in water or air. Treatments include:
 Galvanizing: coating ferrous metal with zinc, or
zinc-based paint.
 Electroplating: deposit a variety of metals on
another metal surface.
 Anodizing: for Aluminum, creates a thicker oxide
layer on the surface,
possibly with other
metals.
Metals limitations
 Material properties are not “programmable”.
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Very high melting point
Structure-dependent properties
Complex manufacturing processes
Small vocabulary of basic materials (periodic
table!), and compatible combinations
Metals summary
 Metals are essential for strength, cost and
electrical, magnetic and thermal properties.
 Aluminum is a very easy material to work with,
and has good finishing properties.
 Customization cost is moderate, e.g. custom
extrusions.
 Steel: workhorse for maximum strength.
 Needs heavier tooling (or outsource your CAD
model!).