Design Realization lecture 10

John Canny

9/25/03

Last Time

Introduction to prototyping processes 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

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 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:

The pressure is called stress . The displacement L/L is strain . It is

dimensionless.

L

P

L

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:

)1(2

EG

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

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

Yield to plastic region & final breaking strength.

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) andk 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

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 holdthe liquid in an invertedcontainer.

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”.

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!).