spring 2001isat 430 dr. ken lewis1 things to know review isat 430

Spring 2001 ISAT 430 Dr. Ken Lewis 1

Things to KnowThings to Know

Review

ISAT 430

Spring 2001 ISAT 430 Dr. Ken Lewis 2review

Process-Property-Product-Performance Continuum

Process-Property-Product-Performance Continuum

Understand howProduct performanceComposition and structureSynthesis and processingAssumed behavior

– interact


Manufacturing ProcessesManufacturing Processes

Know what the processes are doingChanging the state, geometry, physical properties, appearance,…. Changing the value of the material

Know that (in principle) manufacturing adds value to the material.


HistoryHistory

For millennia, stuff was madeOne of a kindLabor intensiveA person was a jack of all trades

Material discovery drove manufacturing processesWoodFibersClaymetals


HistoryHistory

Industrial revolution (1760 – 1845)The steam engineMachine toolsTextile machineryThe factory system

Other forcesEli Whitney – interchangeable partsHenry Ford – the assembly line


ConversionConversion

ExtractionBring it from the earth

Cast or formBring it to use


Manufacturing ProcessesManufacturing Processes

ConversionRaw or natural to a more useful finished form

ProcessingTransform a material

AssembleMany parts into one.


Process SelectionProcess Selection

If you can find or discover a process, there are bases for the choiceTechnical

– Do not violate the laws of physics in our area of the known UniverseEconomical

– Can I do it and make a profit? Compatibility

Know obvious incompatibilities– Forging a plastic– Blow mold aluminum


Process SelectionProcess Selection

EconomicsNumbers –vs- cost

– Inspection– Reduction in versatility

Capital investmentConversion costs

EnvironmentalWaste production, release, and conversion costs

MiscellaneousMaterial availabilityTime linesAnd all others,… supply, labor, deadlines…


The Effect of Numbers On Process SelectionThe Effect of Numbers On Process Selection understand

The total cost of a batch of a given number of pieces is:

P T xn Where:

P = total cost of a batch

T = cost of tools and equipment

n = number of pieces in a batch

x = the costs associated with each individual piece


Processing of PolymersProcessing of Polymers

Know the three types of economic importanceThermoplasticThermosettingElastomeric

Know their assetsLight weightCorrosion resistantElectrically insulatingThermally insulating


Fluid Mechanics 201Fluid Mechanics 201 Understand viscosity and shear

rate for a polymeric fluid

The shear force per unit area is proportional to the local velocity gradient.

The constant of proportionality is

called the viscosityxv y

Y

x

zy

0v

xyx

dvdy

This is Newton’s law of viscosity


Shear Flow in a Cylinder Fluid velocity is zero at the wall. Fluid velocity remains constant on

concentric cylindrical surfaces. The flow is purely axial The fluid velocity reaches a

maximum at the center. This is called:

Laminar Flow


Velocity Distribution in a Cylindrical Tube

There is friction, both at the wall of the tubeWithin the fluid itself

Thus, the fluid is:Accelerated by the pressure gradientRetarded by the frictional shearing stressPressure gradient

• The fluid moves under the influence of a pressure gradient.


Shear Rates4

Shear rate 0 at the center (r = 0)Max at the wall (r = R)

Shear rate is an indication of the stress being seen by the fluid, and how fast it sees it!

The shear rate at the wall for a Newtonian fluid is:

r

L

PP

dr

dv ambientpumpz

2

3

32QD

Q = volumetric flow rate

D = diameter


Volumetric Newtonian Flow in a Tube

The laminar flow of a Newtonian fluid in a pipe or tube may be expressed:

4

8PR

QL

Where:

Q = the volumetric flow rate [=] m3/s or gal/min

P = the pressure drop or driving force [=] kg/m2 or Pa

R = the radius of the tube [=] m or cm

L = the length of the pipe [=] m or cm

= the Newtonian viscosity [=] Pa s


Fluid mechanics -- viscosityFluid mechanics -- viscosity

Understand the effect of viscosity on pressure drop through a cylindrical pipe.

Realize that for a Newtonian fluid, the viscosity is independent of shear rate

But….Most polymeric fluids are not NewtonianThus, the viscosity is NOT constant

There is an important family of fluids called POWER LAW FLUIDS


Newton’s Law of Viscosity

xyx

dvdy

or

constantyx


Power Law Fluids The deviation of n from unity

indicates the degree of Non-Newtonian behavior.

If n < 1, material behavior is pseudoplasticIf n> 1, material behavior is dilatant.

1n

x xyx

dv dvm

dy dy

xyx

dvdy


Power Law Viscosity

For most polymers, the isothermal viscosity decreases with increasing shear rate.

Effect of shear on the entangled polymer chains

Usually, in the literature, the viscosity is not shown as “”,

but rather “”

So:1n

x xyx

dv dvm

dy dy

xyx

dvdy


Viscosity

Velocity Gradient

Non-NewtonianPower Law Flow

NewtonianFlow

Newtonian FluidViscosity (slope) constant

Non-Newtonian FluidViscosity is not constantProfound affect on processing


The Effect of Shear Rate on Viscosity

The effect can be enormous

In this case the zero shear viscosity is about 1000 Pa s.

At a shear rate of 1000 sec-1, the viscosity has dropped to about 5 Pa s

0.1

1

10

100

1000

10000

0.1 1 10 100 1000 10000 100000

Shear Rate (sec-1)

Zero Shear Viscosity

Slope = n - 1


Shear RatesShear Rates

3

3 1n Qn r

3

4Qr

Power Law n = 1Newtonian Law


Volumetric Flow RatesVolumetric Flow Rates

3 1 1

3 1 2

nn nr P

Qn mLn

4

8PR

QmL

Power Law Fluid N = 1Newtonian Fluid


Synthetic FibersSynthetic Fibers

Predates recorded history Early fibers were plant or animal

WoolSilkCottonLinen

1910 – first commercial rayon 1938 – nylon 1959 – Lycra® spandex 1974 – Kevlar® aramid


DenierDenier

Measure of the fineness of a yarn

Denier = weight in grams of 9,000 meters of yarn

Essentially a linear density


SpinningSpinning

Things common to all spinning systemsMetering pump

– Precise volumetric flow control

Spinneret– Extrusion of the filaments

Spin cell– Manipulation and protection of the forming filaments


Methods of Spinning fibersMethods of Spinning fibers

There are three main methods of spinning fibers

Melt spinning

Wet spinning

Dry spinning


Melt Spinning

Not the oldest spinning method More straight forward

removal of heatno solvents to worry about.

Example -- nylon


Nylon Either cross flow or radial gas flow.

staple yarn uses radial

filament yarn uses crossflow

Uniformity of the air flow is critical

Minimum air necessary is used to reduce

turbulence. Three forces resist the feed roll

Resistive inertial

Rheological stresses

Aerodynamic or drag forces (important

for spinning speeds > 5000 m/min


Wet Spinning

If a polymerdoes not meltdissolves only in non-volatile or thermally unstable solvents

We wet spin Polymer solution is extruded into a liquid bath

miscible with the solventdoes not solvate the polymer.

Example: Kevlar®


Kevlar® Air Gap Spinning

4 ºC water

SpinneretMetering pump

Neutralization & Washing bath

To drying and constant tension winder


Solution is extruded into a hot gas As the filaments pass down the cell, the hot gas causes the

solvent to vaporize This process is complex

Heat transferMass transfer

– through the filament– into the gas

Gas - solvent management Example: Lycra®

Dry SpinningDry Spinning


Polymer is dissolved in dimethylacetamide (DMAc) and

then pumped to the top of the cell

Hot Nitrogen (300 - 450 ºC)inserted

Gas is made uniform andPasses into the filaments

And Down The cell

Gas heats the solvent, drivingIt from the filaments.


Vacuum Box

Near the bottom of the cell there is a vacuum box.

The solvent rich gas is extracted.The solvent is recovered.

Just at the cell exitRecycle gas is inserted into the cell– DMAc >15% flammable– Keeps solvent/gas from the

room– Acts as a curtain

The fibers exit the cell and pass to the winders.Recycle

Long cell


Cell limits

Drying rate limitationsHow fast we can transfer heat into the filaments and mass out of the filaments.

How fast solvent can diffuse through the filament and across the surface

DMAcNu Dk

hDN and , • Is the limitation

The persistence of the solvent / gas boundary layer.


Fiber Tenacities


Fiber Elongation


Polymer Processing

Processing Methods and OperationsChoice is dictated by the product desired and the quantity desired.

– Fiber, film, sheet, tube– Cup, bucket, car bumper, chair.

Fiber manufacture is different, it is continuous.Large quantities usually use extrusion or injection moldingSmaller quantities use compression molding or transfer molding


ExtrusionExtrusion

Used mostly for thermoplastics Products

Piping, tubes, hosesWindow and door moldingsSheet and filmContinuous filament (spinning)Coated electrical wire and cable

ElementsA hopperA barrelA screw


Extruder

The die is not part of the extruder

Usually ~ 1 – 6 in. dia.

Up to 60 rpm

Flight clearance of only 0.002 in.


Screw details

Helical flights with space between them

Carries the polymer.Flight land is hardened and barely clears the barrel.The Pitch (distance the flight travels in one complete rotation) is usually about equal to the diameter.

pitchtan

DA


Extruder detailsExtruder details

Understand melt flow in the extruderFlow forward occurs because of friction between the fluid and the screw flights.Axial flow (z – direction) provides the pumpingCross flow provides the mixing


Extruder transport – back pressure.

This is the maximum possible output for an extruder. Conveyance of the polymer through

Smaller and smaller cross sectionsthe screen pack and die…

Creates a back pressure, Qbp.

2 20.5 sin cosdr cQ D Nd A A

3 2sin12c

bp

Dd A dpQ

dl


net dr bpQ Q Q

3 22 2 sin

0.5 sin cos12

cnet c

p Dd AQ D Nd A A

L

Qnet is what finally comes out of the die!


Net flowNet flow

Some parameters we control (design parameters) Some we can’t control (operating parameters)

3 22 2 sin

0.5 sin cos12

cnet c

p Dd AQ D Nd A A

L


Design Parameters

These we control at conception time and are fixed thereafter.

Barrel diameterFlight or Helix angleChannel depth dc

Barrel length L


Operating Parameters

These we can fiddle with to optimize the process.Rotational speed, NThe head pressure (change the die, slow the screw, change the temperature)The hidden variable … TEMPERATURE.The viscosity

– But only to the extent that the shear rate and temperature will allow!


Extruder characteristicsExtruder characteristics

A given extruder will have known operating characteristics.

2 20.5 sin coscdrQ D Nd A A N

3 2sin

12c

bp

p Dd A pQ

L

or

e

pQ N


Extruder Characteristics

Extrusion PressurePmax

Extruder CharacteristicCurve

Increasing N orincreasing viscosityE

xtruder Flow Rate

Flow up withIncreasing NDecreasing pIncreasing

Ignores non-Newtonian flow behavior

Ignores friction

e

pQ N


Die Characteristics

Flow through a die generates back pressure For a simple cylindrical flow channel the flow rate is given

by the famous Hagen – Poiseuille equation:

4

128d

cl

p DQ

L

D = diameter

= melt viscosity [=]


Die characteristics

So flow increases with p Look at the power of the die diameter! This gives the linear die characteristic curve. Note: some people write the above equation as:

4

128d

cl

p DQ

L

c sQ K p


Extrusion PressurePmax

Extruder CharacteristicCurve

Die characteristiccurve

IncreassingL, n,decreasingD

Increasing N orincreasing viscosityE

xtruder Flow Rate

OperatingPoint

Extrusion Curve


Go to page 78


Stress StrainStress Strain

Curves obtained from tensile tests Information obtained

StrengthDuctilityToughnessElastic modulusStiffnessRange of workable properties


Stress -- StrainStress -- Strain

Know a lot about the material just from a glance at the S – S curve

Know the elastic region Understand strain hardening

Grain boundary movement and blockage Understand the effect of temperature on the stress strain

properties.


Know what’sGoing on here


CompositesComposites

Know what a composite is. Know the benefits of a composite

Using different materials to affect the bulk propertiesWeightStrength…



Know the function of the matrix Know the function of the reinforcement Know the various types of reinforcement and why you would

choose eachContinuousDiscontinuousparticulate



Have a knowledge of the various fibers used in most composites

GlassAramidCarbon and graphite

– Know difference

Boron…



Understand the effect on properties that occurs using different types of reinforcements

Understand the importance of the reinforcement / matrix interface / bond

Understand anisotropy in composites and why it occurs



The rule of MixturesKnow that it uses the volume fractionKnow why

Other types of compositesSandwichesFoam cores


FRPs…..MMCs…..& CMCs….FRPs…..MMCs…..& CMCs….

Know the differencesAdvantages and disadvantages of eachApplications for eachGeneral material used in each


Composite ProcessingComposite Processing

Understand preforms Know the various ways of laying up a composite FRP’s

By hand Spray moldingFilament winding

– Mandrels– Helical, polar, braid

pultrusion


Composite ProcessingComposite Processing

MMC’sCermetsCemented carbides

CMC’sMixingCompactionsintering


Metal CastingMetal Casting

Know history (in general) Sand casting

Know the process steps Investment casting

Know the process steps Know the advantages of each


Phase DiagramsPhase Diagrams

Understand phases Understand solutions and compounds

InterstitialSubstitutional

Understand how phase diagrams are made Know what they are good for



Know what phases are present Function of compositionFunction of temperature



Understand and be able to use the inverse lever rule

Ends of the line give the compositionRatios of the line tell how much of each


Heat TreatmentHeat Treatment

Know the principal ways of heat treating Know why heat treating is done For the Fe – C system

Know where iron, steels, and cast irons existKnow what the various important phases of Fe—C are; ferrite, iron, iron, austenite, bainite, Pearlite, and

cementite



AnnealingKnow the principals

MartensiteKnow what it is,How it is formedWhat is its structure



Understand the TTT curvesTheir usesHow they work

QuenchingWhy quenchWhy different fluids are used



Surface hardeningKnow the common proceduresKnow the different uses


Extra CreditExtra Credit

Be able to derive the matter – energy relationship first proposed by Albert Einstein

Oh Yeah!!!!!!!!!!!!

E = ma2 E = mb2

E = mc2


Dies Dies

The die determines the extruded shape Two important factors

Die swellbambooing


Effect of Die Swell

Knowing that die swell will occur is importantAfter the polymer leaves the die it is rapidly cooling and becoming fixed in shapeFor each polymer, if we know

– Viscosity– Temperature– Shear rate

We can account for the die swell in the shape of our die


Die shapes

The dies The finished shapes


Pipe extrusion

The central mandrel is supported by spider legs

These disrupt the flow of polymerThe polymer rejoins itself because

– the flow rate is low – The conditions haven’t

changed (temperature)To minimize the effect of the spiders, the mandrel is tapered.


Tubing Die

Note the expansion to the spider legs and the reduction afterwards.

If the extrusion is too rapid, the spider leg openings will not heal.


Wire Coating Die

The wire runs straight through Polymer comes in vertically into

a distribution cavity Used for wire diameters of 1

mm up to submarine cables with diameters of 150 mm.

Wire helps to draw the melt through the die

Coated wire speeds up to 10,000 ft/min


Injection Molding

Polymer is heated, mixed, the then forced to flow into a mold cavity

Similar to extrusionHopper, barrel, screw

Screw rotation is the principal motion only in one part of the cycle

Mixes, compacts, plasticizes, and heatsPressures may reach 10 – 20 MPa (1450 – 2900 psi)

In the injecting stage, the screw is driven axially by a piston to generate the working pressure 150 – 250 MPa (21,756 – 36,260 psi)


Injection Molding Sequences

(1) Close the mold (2) Inject the melt

(3) Retract the screw (4) Open mold – eject part


Thermoforming

A flat thermoplastic sheet is softened and deformed into the desired shape.

Used for large items– Bathtubs– Skylights– Freezer interior walls– Bumpers

Two steps– Heating– Deforming / forming


Three major types of thermoforming

Vacuum

»Pressure limit of 1 atmosphere

Pressure

»Higher allowable pressures

Mechanical


General plastic considerationsGeneral plastic considerations


Product design Considerations In general

Strength– Plastics are not metals– Should not be used in strength or creep critical applications.

Impact resistance– Good, better than many ceramics

Service temperature– Much less than metals or ceramics

Degradation– Radiation– Oxygen or ozone– Solvents

Corrosion resistance– Better than metals


Extrusion Considerations

Desirable product traitsWall thickness should be uniformHollow sections seriously complicate the extrusion processCorners

– Avoid as they cause uneven polymer flow and are stress concentrators


Forming and ShapingForming and Shaping


Forming and ShapingForming and Shaping

Forming – changing the shape of an existing solid body

Shaping – usually is creating a desired shape by casting or molding


FormingForming Rolling flat

Plate, sheet, and foilGood surface finishHigh capital

Rolling shapedStructural shapes, bar, I – beams, t – beamsShaped rolls, high capital

ForgingProduction of discrete parts with a set of dies.Material is stampedUsually at elevated temperaturesSome finishing is neededHigh capital


FormingForming Extrusion

Long lengthsConstant cross section (solid or hollow)Not real high costs

DrawingLong rod and wire of some cross sectionSmaller cross section than extrusionGood finishModerate costs


FormingForming Sheet metal forming

Variety of thin shapes and sizesModerate to high costsCan be complex


Shaping Shaping Powder metallurgy

Compact SinterUsed to make pellets for diamond shots (except no sintering)

Plastics and compositesInvolves molding, shaping, extruding, spinning

CeramicsSimilar to powder metallurgyShaping and sintering (firing)


Rolling Rolling is a process to reduce the thickness of a long workpiece

by compressive forces applied through a set of rolls.First developed in the late 1500’s

A steel ingot is cast into a rectangular mold Placed in a furnace while just solidified and held for many hours

(36) until the temperature is uniform. This process is called soaking

Furnaces are called soaking pits. Implies that properties will be uniform throughout the ingot and

process that way. The rolling temperature for steel is about 1200°C From here the ingot goes to the rolling mill.


Rolling Starting material depends upon what you are producing.

Bloom– Square cross section 6 x 6 in or larger

Slab– Rolled from an ingot or a bloom– Rectangular cross section 10 x 1.5 in or more

Billet– Rolled from a bloom– Square cross section 1.5 x 1.5 in or larger.


review


review

Metal Behavior in formingMetal Behavior in forming

As metal deforms, its strength increases (strain hardening) The strain rate is important

Higher the rate, the higher the average metal stressThe higher the temperature, the less the effect


review

Working temperaturesWorking temperatures

Cold working – room temperatureAdvantages

– Accuracy, good surface, some strain hardening, no heating

Disadvantages– High force and power needed, part must be clean, crazing or

stress fracture is a concern


review


Warm working – 0.3 – 0.5 Tm

Advantages– Low force and power, material is more ductile, annealing may

not be needed

Disadvantages– Surface finish not as good, energy needed to heat


review


Hot working – 0.5 – 0.7 Tm

Advantages– Low force and power, brittle material may be worked, properties

are isotropic

Disadvantages– Localized melting (maybe), scale formation, lower dimensional

stability, poorer surface, shorter tool life


review

Ring Rolling

Ring is placed between two rolls, of which one is driven

Volume of the ring is constant to the diameter increases during the process

Ring blanksCut from a plateCutting a thick walled pipe.


review

Thread Rolling

No loss in material Good strength (cold working) Surface finish is very good Process induces residual

compressive stresses on surface which improves fatigue life.


review

Thread properties Machining cuts through the

grains Rolling compresses them


JoiningJoining


review

Joining Technologies Joining is a many splendored thing.

Welding– Arc or melting– Resistance or other

Soldering & brazingMechanical fastening (bolts & nuts).Seaming and crimpingAdhesive bonding

All are important for different reasons.


review

Fusion Welding Oxyfuel gas welding

Uses a fuel gas and oxygen to produce the heat. Arc welding

Heating is accomplished by an electric arc Resistance welding

Heating is accomplished by the passage of an electric current Others

Electron beam and laser welding


review

Oxyfuel weldingOxyfuel welding

Most common fuel is acetylene, C2H2

Flame temperature can reach 3,300°C Flame heats the material

Low efficiencies .1 -- .3 Must control the fuel/oxygen mixture to protect the workpiece

CheapGood for repair jobsLow volume stuff


review

Fuel Temperatures and Heats.

Temperature Heat of Combustion

Fuel °F °C Btu/ft3 MJ/m3

Acetylene (C2H2) 5589 3087 1470 54.8

MAPP1 (C3H4) 5301 2927 5460 91.7

Hydrogen (H2) 4820 2660 325 12.1

Propylene (C3H6) 5250 2900 2400 89.4

Propane (C3H8) 4579 2526 2498 93.1

Natural Gas 4600 2538 1000 37.3

1) Methylacetylene propadiene

Just know that there are different fuels and obtainable temperatures.


review

Arc Welding


review

Arc Welding A fusion process wherein the coalescence of the metals is

achieved from the heat of an electric arc formed between an electrode and the work.

An electric arc is a discharge of electric current across a gap I a circuit.It is sustained by the presence of a thermally ionized column of gas (called a plasma).

Temperatures up to 30,000°C (54,000°F) a generated


review

Shielded Metal Arc Welding


review

Gas Metal Arc Welding


review

Gas Metal Arc Welding Originally called “MIG” welding (for metal inert gas) Used widely in factory fabrication

Better metal usage (no stubs)– Sticks or filler

High deposition ratesNo slag


review

Non-consumable Electrodes Gas Tungsten Arc Welding Known as “TIG” (tungsten inert gas) welding The electrode is W (tungsten)

Tm = 6170°F (3410°C)

Actually it is slowly consumed Shielding gases include Ar, He or a mixture


review

Gas Tungsten Arc Welding (TIG)


Resistance weldingResistance welding


review

Resistance Welding In order to obtain a strong bond

in the weld nugget pressure is applied until the current is turned off.

Strength depends on the initial surface condition

SmoothnessCleanlinessPresence of uniform thin oxides is not critical


review

Resistance Welding The reason that the current is

so high is because the R is usually so low ~~ 0.0001 ohm

2Q I Rt

Where: I = current (amperes) R = resistance (ohms) T = time of current

(seconds) Q = heat in Joules


review

Resistance weldingResistance welding

Pay attention to the energy problemHow much heat is used and how much is dissipated.

Understand the current – pressure cycle


review

Brazing and Soldering


review

Brazing A process which a filler metal is placed at or between the

faying surfaces, the temperature is raised high enough to melt the filler metal but not the base metal.

The molten metal fills the spaces by capillary attraction. Two types

Ordinary brazing (above)Braze welding (similar to oxy-welding)

Faying surfaces = the surfaces to be joined.


review

Brazing Capabilities Typical joints

Dissimilar metals can be assembled with good joint strength.Shear strength can reach 120 ksi (800 MPa) using alloys containing silver.

ConcernsClearance too small, metal will not penetrateClearance to big, insufficient capillary attraction.


review

Soldering


review

Soldering Used extensively in the electronics industry Soldering temperatures are low Not used in load bearing members Butt joints rarely made If strength is needed, the joint may be mechanically

interlocked


review

Solder joints Typical joints Note that the starred

examples are mechanically joined first.

Copper and silver are easy

Fe, Al hard to solder because of their tough oxide films.


review

Adhesive Joints


review

Adhesive Bonding Joining process whereby a filler material is used to hold

two closely spaced parts together by surface attachment Filler material (adhesive)

Usually non-metalUsually a polymer

CuringProcess (usually chemical) whereby the adhesive physical properties are changed from a liquid to a solid.


review

General Properties of some adhesives Acrylic

Thermoplastic, quick setting, tough bond at r.t.Tennis racquets, metal parts

EpoxyThermoset, strongest engineering adhesiveMetal, ceramic, rigid plastic parts

CyanoacrylateThermoplastic, touch“Crazy Glue”

Hot MeltThermoplastic, quick setting, easy to applyBonds most anything –Packaging, book binding, metal can joints


review

General Properties of some adhesives Phenolic

Thermoset, strong, brittleBrake lining, clutch pads, honeycomb structures

SiliconeThermoset, slow curing, flexible, rubber likeGaskets sealants

Water base AnimalVegetableRubbers

Inexpensive, non-toxicWood, paper, fabricLeather, dry seal envelopes


review

Joint Design Usually not as strong as welding or brazing joints Design principles

Maximize joint contact areaJoints are strongest in shear and or tension so joints should be designed to accommodate thisJoints are weakest in cleavage or peel. Avoid these stresses


review

Adhesive bonding Disadvantages Joints are not as strong Adhesive must be compatible with materials being joined Service temperatures are limited Cleanliness and surface preparation prior to adhesive

application are important Curing times can impose a limit on production rates Inspection of the bonded joint is limited.

spring 2001isat 430 dr. ken lewis1 things to know review isat 430

Documents

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review spring

insulating slide

laminar flow slide

ken lewis1 things

assembly line slide

individual piece slide

newtons law of viscosity