James L. Throne Sherwood Technologies, Inc. Dunedin Florida 34698-3347

Frictional Coefficients Between Plug and

[Problems with Theories, Experiments in Plug Assist]

James L. ThroneSherwood Technologies, Inc.Dunedin Florida 34698-3347

Paper presented at

2004 Thermoforming Conference

Indianapolis IN

Objective

To better understand the problems with theories and experiments in plug assist thermoforming

TF Conference 2004 – Throne

Frictional Coefficients Between Plug and Sheet

Caveat

It is my intent to raise concerns about the ways in which we view the interaction between the plug and the sheet

Caveat

It is my intent to raise concerns about the ways in which we view the interaction between the plug and the sheet

It is NOT my intent to provide answers to the questions about the interfacial conditions between the plug and the sheet

Think about this Question!

In plug-assist thermoforming,In plug-assist thermoforming,what is sliding against what?what is sliding against what?

Outline

I. A discussion of the coefficient of friction issue

II. A sliding experimentIII. Some prototypical plug

experimentsIV. Conclusions

I. Some thoughts on the coefficient of friction

Coefficient of FrictionCoefficient of Friction• Frictional characteristics

considered part of tribology• Tribology is study of friction,

lubrication and wear• Traditional view is that all three are

extant in thermoforming

“The relation that the power required to move a body bears to the weight or pressure on the body is known as the coefficient of friction.”

W.M. Davis, Friction and Lubrication, A Handbook For Engineers, Mechanics, Superintendents and Managers, The Lubrication Publishing Co., Pittsburgh PA, 1903.

Historical views of coefficient of friction-I

“The coefficient of friction is the ratio between the resistance to motion and the perpendicular pressure.”

W.M. Davis, Friction and Lubrication, A Handbook For Engineers, Mechanics, Superintendents and Managers, The Lubrication Publishing Co., Pittsburgh PA, 1903.

Historical Views of coefficient of friction-II

“There is no other element in connection with… lubrication… that has received so much consideration as that of the coefficient of friction, and yet there is no other that is in so indeterminable a state…”

Mr. Hall, Car Lubrication, ca. 1900 - cited in W.M. Davis,Friction and Lubrication, A Handbook For Engineers, Mechanics, Superintendents and Managers, The Lubrication Publishing Co., Pittsburgh PA, 1903.

Historical Views of coefficient of friction-III

“While the coefficient of friction must always be taken into consideration when designing and constructing machinery, it is not always practicable to calculate it with any degree of accuracy, [and] in fact it can only be determined absolutely by experiment.”

W.M. Davis,Friction and Lubrication, A Handbook For Engineers, Mechanics, Superintendents and Managers, The Lubrication Publishing Co., Pittsburgh PA, 1903.

Historical views of coefficient of friction-IV

Coefficient of FrictionCoefficient of Friction

Following discussion assumes that frictional effects are extant in plug-assisted thermoforming

Blunt-nose plug moving into sheetContact may involve some sheet sliding

Frictional Conditions Between Plug* And Sheet

• Static CoF, no sliding (coefficient max)

• Sliding CoF, no static (coefficient zero)

• Some static, some sliding• Slip-stick behavior

*or mold wall

Frictional Conditions Between Plug* And Sheet

• Static CoF, no sliding (coefficient max)• Sliding CoF, no static (coefficient zero)• Some static, some sliding• Slip-stick behavior

*or mold wallWhich of these are relevant when plastic

stretches against plug surface?

Coefficient of FrictionCoefficient of Friction• Static CoF - Initiation of sliding

between plug (and mold wall) and sheet

• Sliding CoF- Continuation of sliding between plug (and mold wall) and sheet

• Sliding CoF - Continuation of sliding between plug (and mold wall) and sheet

• Static friction value usually 100s to 1000s greater than sliding friction value, but not always!

Sliding Coefficient of FrictionSliding Coefficient of Friction• Contact area increases with increasing

Plastic sheet

Sliding Coefficient of FrictionSliding Coefficient of Friction• Contact area increases with increasing load• Ergo, coefficient independent of load

Plastic sheet

• Are there other factors influencing the interaction between the plug and the sheet?

• Wear

Sliding Coefficient of FrictionSliding Coefficient of FrictionWear v. sliding friction

Friction maximum in polymer transition region

Wear minimum in polymer transition region

Sliding Coefficient of FrictionSliding Coefficient of Friction

Friction maximum, wear minimum in polymer transition region

Glass Transition Region

• Wear• Dry v. wet sliding

Dry v. “wet” slidingDry v. “wet” sliding• Dry sliding assumes no lube between

surfaces

surfaces• Plastics exude small molecules (low MW

polymers, additives, processing aids)

polymers, additives, processing aids)• Small molecules reside between plug and

sheet• Small molecules transfer from sheet to

sheet• Small molecules transfer from sheet to plug• Interface may go from dry to wet (or wet to

dry!) as plug advances into sheet

• Wear• Dry v. wet sliding

– More than one type of wet sliding

Two types of wet sliding• Boundary lubrication – low sliding

velocity, low interfacial viscosity, high loading

• Hydraulic or hydrodynamic lubrication – high sliding velocity, high viscosity, low loading

• Boundary lubrication occurs during start/top activities [as might be the case with plugs in contact with sheet]

Two types of wet sliding• Boundary lubrication – low sliding velocity,

low interfacial viscosity, high loading• Hydraulic or hydrodynamic lubrication –

high sliding velocity, high viscosity, low loading

• Boundary lubrication occurs during start/top activities [as might be the case with plugs in contact with sheet]

• Boundary lube friction 100s greater than hydraulic lube friction

Two types of wet slidingSheet does not move far under plug

Measuring Frictional Coefficients

Traditional methods ofmeasuring coefficient of friction

• Weight sliding on inclined surface

Traditional methods ofmeasuring coefficient of friction

• Tabor “Abrasor” – stylus rubbing on rotating disk

Traditional…• Other

methods• No methods

entirely applicable to measuring plug-sheet friction…

Observations• Frictional resistance is a complex

issue:o Static v. slidingo Dry v. weto The extent of slidingo Boundary v. hydrodynamic effects

Observations• Frictional resistance is a complex

issue:o Static v. slidingo Dry v. weto The extent of slidingo Boundary v. hydrodynamic effects

• Standard frictional devices may not give reliable results

Are We Answering the Question?

In plug-assist thermoforming,In plug-assist thermoforming,

what is sliding against what?what is sliding against what?

II. A sliding experiment

Traditional…• Other methods• No methods

entirely applicable to measuring plug-sheet friction (except g but modified)

Plug-sheet friction – experiment• Consider figure below…

– A is plug material, B is plastic sheet, p is applied load

– Plug material moved against sheet…

– First, plug, sheet surfaces examined optically (100X or SEM)

– Plug mounted in fixture, load similar to applied plug force applied…

– Sheet placed on hot plate, heated to forming temperature

– Plug heated to 20C of the sheet temperature…

– Plug pressed against sheet– Moved at slow rate (~ 1 mm/sec, say)

against sheet, then stopped…

– Plug then lifted and indexed to new place on sheet

– Plug held away from sheet for period of time (10 sec, say)…

– Plug then placed against sheet and moved other direction at (~ 1 mm/sec, say)

– After 10 (say) to-and-fro motions, plug removed from fixture and examined…

– Plug surface examined optically (100X or SEM)

– Scrapings from plug surface chemically analyzed (FTIR) to determine mat’l transfer…

– New plug examined, then heated and brought in contact with fresh sheet surface

– Plug moved to-and-fro 100 times, then examined optically and chemically…

– Only after material transfer level reaches constant value…

– is resistance to sliding measured, using strain gauge or load cell…

Experiment #1• E&C Syntactic Foam, sanded w/180 grit,

blown with oil-free air• Normal stress= 3 lb/in2

• Hot plate temp setting = 162+/-2oF• 0.120 inch black GP-PS sheet• Block held on sheet 10 s, moved 10 cm in

10 sec, then removed and cooled 15 s• Force measured once block moved• Concluded after 10 contacts

Experiment #2• E&C Syntactic Foam, sanded w/180 grit,

blown with oil-free air• Normal stress= 3 lb/in2

• Hot plate temp setting = 162+/-2oF• 0.120 inch black GP-PS sheet• Block immediately moved 10 cm in 10 s,

then removed and cooled 15 s• Force measured once block moved• Concluded after 40 contacts

ParametersFixed

Sheet, heater temperatureSliding length, times

MeasuredForceBlock surface temperature

Visual Observations• After 10 contacts in Expt #1, plug

surface is smoother and grayer

Visual Observations• After 10 contacts in Expt #1, plug

surface is smoother and grayer• After 40 contacts in Expt #2, plug

surface is gray, with small <1 micron specks in surface

Mea Culpa• Syntactic foam blocks were sent to

local university for FTIR reflectance and ESCA measurements in August 2001

• Blocks mysteriously disappeared (!)• Retesting to obtain new samples

has not yet begun

Observations• Hot plate experiments yield time-

dependent force

Observations• Hot plate experiments yield time-

dependent force• Force is dependent on plug surface

temperature

III. Some prototypical plug experiments

[Focus on ball or spherical plugs]

Plug design characteristics - Plug types

Tapered, bullet- or bull-nosed

Plug design characteristics - Plug typesTapered, bullet- or bull-nosed

ApplicationsVery deep drawsWhere thinning of sidewall is

criticalWhere wall thickness is criticalWhere polymer chills rapidly

Blunt-nose plug moving into sheetContact may involve some sheet sliding

Load Creep• Rough acrylic

under load – increasing time or increasing temperature

under load• Red – low temp

under load• Red – low temp• Yellow – medium

temp• Blue – high temp

temp• Blue – high temp• Note increasing

contact area with increasing temperature

Sheet stretching characteristics• Sheet stretched in uniaxial, biaxial,

equibiaxial and plane strain modes• Mathematical models include

Ogden doubly-infinite power-law Mooney form of Rivlin strain energy

function Plane strain linear law K-BKZ viscoelastic model

Sheet stretching characteristics• Sheet stretched in uniaxial, biaxial,

equibiaxial and plane strain modes• Mathematical models include

Ogden doubly-infinite power-law Mooney form of Rivlin strain energy

function Plane strain linear law K-BKZ viscoelastic model

• Plugs stretch sheet in plane strain

Plane strain stretching, cont.

Top and side view of plug-assisted stretching

[Circles appear as circles from top…]

Plane strain stretching, cont.

Top and side view of plug-assisted stretching

[Circles appear as circles from top, are actually distorted]

Plane strain stretching, cont.Mooney-Rivlin equation: = (2-1/)(2C1+2C2/)

For plane strain:(l

2-1)1/2(1-1/l2)=(F/2r)(2C1-2C2)/to

Where 1/l= h = t/to

Plane strain stretchingForce F required to stretch sheet to a

depth with a flat plug:

F = 2E(T)to/ln (a/b)

Where E(T) is temperature-dependent modulus, to is initial sheet thickness, a is plug diameter, b is sheet diameter

Plane strain stretching,

cont.Comparison of

theories and flat plug

experimental data –

JLT, 1986

2004 Experiments on Spherical PlugsInto Circular Sheets

• 0.015-inch natural rubber sheet, 6.75-inch diameter

• Two wooden sphere diametersSmall ball diameter = 0.75 inchLarge ball diameter = 3 inch

• Force and penetration measured with scales

Schematic of Plug Experiment

Left Half-Initial Plug Position

Schematic of Plug Experiment

Right Half-Plug Position During Sheet Stretching

Large Sphere Surface Treatment1. As-is [rough-grained exterior pine]2. Sanded w/200 grit paper3. Wood-putty-filled, sanded w/320 grit

paper4. Filled, sanded, and polished5. Filled, sanded, polished and talc-

coated6. Filled, sanded, polished and coated

with lube

Measurements• Height of plug into sheet• Force• Diameter of spherical cap

Calculations• Area of spherical cap• Area of truncated cone• Thickness of sheet

Thickness of free portion of membrane

Two extremes shown in next figure

Two extremes shown in next figure• If sheet slides on surface (friction

coeff=0), thickness is uniform everywhere

Two extremes shown in next figure• If sheet slides on surface (friction

coeff=0), thickness is uniform everywhere

• If sheet sticks to surface (friction coeff=1), sheet on cap is original thickness

ExperimentDraw a circle on the free portion of the

sheet…

sheet…Press the plug into the sheet to a given

depth…

depth…Measure the major and minor axes of

the ellipse (a and b)…

depth…Measure the major and minor axes of the

ellipse (a and b)…Use the relative areal draw ratio equation

Rarel = r2/ab

to calculate reduced thickness, 1/ Rarel

Comparison of Theory and ExperimentPenetration No Frict Max Frict

Exptl*2.0 in 0.832 0.813 0.8052.4 in 0.778 0.738 0.744

* Average of 9-10 experiments

Solid Circles – Measured Red Tk

Sheet ThicknessWhat about the relationship between

stretching force and sheet thickness?

Sheet ThicknessWhat about the relationship between

stretching force and sheet thickness?

According to plane strain theory, the force increases in proportion to the thickness.

Does this hold true for this experiment?

ObservationsThe nature of the dry plug surface

does not substantially affect the amount of force needed to stretch the membrane

ObservationsThe nature of the dry plug surface

does not substantially affect the amount of force needed to stretch the membrane

It appears that from simple measurements, the sheet adheres to rather than slides on the dry plug

Lubed InterfaceSo far, all experiments have been

with a presumed dry interface…

Remember the discussion on wet v. dry sliding?

Remember the discussion on wet v. dry sliding? What happens if the interface is lubricated?

Lubed Interface

Large plug coated with…• Heavy grease [oil-based]• Glycerin [water-based]

ObservationsSo, what happened when the

interface is lubricated?

interface is lubricated?If it’s oil-lubed, essentially nothing..

interface is lubricated?If it’s oil-lubed, essentially nothing..But if it’s water-lubed, stretching

force is reduced…

interface is lubricated?If it’s oil-lubed, essentially nothing..But if it’s water-lubed, stretching

force is reduced…[This obviously needs more study!]

IV. Conclusions

ConclusionsFrom simple plug experiments, it is

apparent (at least to me) that the interaction between the plug and the sheet is not clearly defined

ConclusionsFrom simple plug experiments, it is

apparent (at least to me) that the interaction between the plug and the sheet is not clearly defined

It is not apparent (again, at least to me) that coefficient of friction is an appropriate measure of this interaction

ConclusionsSimple measurements show applied

force increases with increasing sheet thickness

ConclusionsSimple measurements show applied

force increases with increasing sheet thickness

Something is going on when the interface is lubricated. But why is the force reduced only when the lube is water-based?

ConclusionsFurthermore, one might anticipate

that with thick-gauge sheet, compression and shear might also be important - in addition to (or instead of) sliding.

ConclusionsFurthermore, one might anticipate

that with thick-gauge sheet, compression and shear might also be important - in addition to (or instead of) sliding.

But the question remains…

In plug-assist In plug-assist thermoforming,thermoforming,

what is sliding against what?what is sliding against what?

Questions?

THANK YOU THANK YOU FOR YOUR FOR YOUR ATTENTIONATTENTION!!

James L. Throne Sherwood Technologies, Inc. Dunedin Florida 34698-3347

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