-
or 65.5 Ib I ft3. The convection heat transfer coefficient to
forced air is hair =28.4 W/m2 0C or 5 Btu/ft2 h 0F. The air
temperature is 75F or 24C. The heattransfer coefficient to the
coolant is hcool = 284 W/m2 0C or 50 Btu/ft2 h 0F. Thecoolant
temperature is 75F or 24C.
All the values for Equation 5.41 are known except the
equilibrium moldtemperature, Tmold avg. The first term on the right
is:
N rcp tavg(Tx - Tf) = 90 65.5 0.45 ~ (375 - 175) = 2650 J ^
This is the heat that must be removed from the sheet. The second
term onthe right is the amount of heat convected from the sheet to
the air. Here0cool/0T = 0.5. The average sheet temperature is Tavg
= 375 175 = 275F.
ha i r(Tavg-Ta i r)-0.5 = 5 0 0 ^
The average heat loss from the uncovered mold is given as the
third part ofthe right side of Equation 5.41:
hair(Tmold,avg - Tair)(l - 0.5) = 5 0.5 (TmokUvg - 75)And the
average heat loss to the coolant is given as the term on the left
inEquation 5.41:
hcool ' ( l m o l d , a v g ^ cool) = ^ ' V ^ mold,avg ' ^ )
The mold temperature is then obtained from:
(50 + 2.5) (TmokUvg - 75) = 2650 - 500 = 2150 J ^OrTm o l d , a
v g=116For46.6C.
5.6 Transient Heat Transfer During Sheet Coolingon the Mold
SurfaceComputer Models
As shown in Fig. 5.1, the convective and conductive elements
discussed aboverepresent resistances to heat removal from the
sheet. Time-dependent sheet tempera-ture is determined by
simultaneously solving the transient heat conduction equationsfor
both the formed plastic sheet and the mold1:
(5.42)
(5.43)
1 The general transient one-dimensional heat conduction equation
was described in detail in
Chapter 3.
Previous Page
-
The first two equations represent convection conditions at the
free surface and themold/coolant interface, respectively. The third
set of three equations represents theheat conduction across the
interfacial air trapped between the plastic sheet and themold
surface. The last two equations represent the initial sheet and
mold tempera-tures, respectively. The solution to these equations
uses finite difference [14,15]. Theexplicit method uses a time step
defined as:
At = Fo Ax2/oc (5.49)where Fo is the Fourier number. For
mathematical stability, Fo
-
Figure 5.15 Schematic temperature profilesthrough coolant, mold
and polymer with increas-ing mold thermal conductivity [top] and
increas-ing coolant convection heat transfer [bottom]
cooling time is less important for prototype materials such as
plaster than forproduction materials such as aluminum. The effect
of mold thickness for productionmold materials such as aluminum is
essentially nil.
In all conduction heat transfer models, such as that used to
produce Fig. 5.12, theunaccomplished temperature change, Y, is
shown to be proportional to the Fouriernumber of the polymer, Fo =
oc9/L2, where a is the polymer thermal diffusivity, 6 istime and L
is the thickness of the polymer sheet. If the average sheet
temperature atremoval from the mold surface is fixed, the
unaccomplished temperature change, Y,is fixed and so is the Fourier
number. The time required to cool the sheet to thattemperature
should then be proportional to the square of the sheet
thickness:
ecooi = (Fofixed/a)-L2 (5.54)Doubling the sheet thickness should
increase the cooling time by a factor of four.This concept is
confounded in practice by the presence of the mold and the
attendanttransient heat conduction to the coolant. Figure 5.16
shows that the effective coolingtime of a polymeric sheet in
contact with a mold having finite thermal conductivityis not in
proportion to the square of the sheet thickness, but rather to a
powdersomewhat less than 21. The heat conduction square law,
Equation 5.54, is thereforeconservative.
1 For the example shown, 0 is proportional to L17.
Tem
pera
ture
Tem
pera
ture
Coolant
Increasing MoldThermal Conductivity
Mold
Plastic
MoldCoolant
PlasticIncreasing Convection
Heat Transfer
-
Table 5.6 Parametric Study of Cooling of Polystyrene Sheet to an
Average Temperature of 1500F Against a Mold of Various
Materials
Surfacetemperature*(0F)
171.1187.6182.3183.5182.2162.8146.9149.2149.3152.6192.4187.6171.178.5
171.1171.3170.9167.8180.7171.3156.1135.2
Interfacetemperature*(0F)
77.777.186.285.688.1
117.6149.5144.1144.4145.076.877.177.778.177.777.176.176.176.577.175.272.6
Timeto cool(S)
19.426.428.328.828.545.5
236.4116.9116.9200.029.726.419.47.4
19.419.219.119.55.7
19.261.1
190.5
Moldthickness(in)
0.5000.5000.5000.5000.5000.5000.5000.5000.5000.5000.5000.5000.5000.5000.5001.0002.0004.0001.0001.0001.0001.000
Plasticthickness(in)
0.1000.1000.1000.1000.1000.1000.1000.1000.1000.1000.1000.1000.1000.1000.1000.1000.1000.1000.0500.1000.2000.400
Surfacecooling
Forced airNatural airNatural airNatural airNatural airNatural
airNatural airNatural airNatural airNoneNoneNatural airForced
airWater spray
Forced airForced airForced airForced airForced airForced
airForced airForced air
Coolanttype
WaterWaterOilOilOilOilOilOilNoneNoneWaterWaterWaterWaterWaterWaterWaterWater
WaterWaterWaterWater
Moldmaterial
AluminumAluminumSteelCu/bronzeZn
alloyAl-epoxyMaplePlasterPlasterPlasterAluminumAluminumAluminumAluminumAluminumAluminumAluminumAluminumAluminumAluminumAluminumAluminum
* When average sheet temperature
-
Sheet Thickness, inFigure 5.16 Calculated sheet
thickness-dependent cooling time and free surface
temperaturepara-metric study
Interfacial Air
The actual thickness of the interstitial air layer between the
polymer sheet and themold is unknown. Arithmetically, Equation 5.44
is used with two interfacial temper-atures, T11 being the polymer
surface temperature at the polymer/air interface and T12being the
mold surface temperature at the air/mold interface. With some
manipula-tion, these interfacial temperatures are related to the
interior plastic and moldtemperatures, Tp and Tm, respectively.
(5.55)(5.56)(5.57)
(5.58)
(5.59)
Free
Su
rface
Te
mpe
ratur
e, 0 F
or
Ti
me,
s
Free Surface Temperature,F
Time, s
-
The numerical solution to the coupled transient heat transfer
equations proceeds asbefore, using standard finite difference
equations. Table 5.7 shows the results of oneparametric study. As
redone in Fig. 5.17 for this specific study, the overall cycle
time
Cooli
ng Tim
e, s
Air lnnerlayer Thickness, in
Figure 5.17 The effect of trapped air gap thickness on cooling
timeparametric study
Table 5.7 Parametric Study of Cooling of Polystyrene Sheet to
anAverage Temperature of 1500F Against an Aluminum Mold UsingForced
Air and Water as Coolants With an Air Interstitial Layer
(Plastic sheet thickness = 0.100 in)(Mold thickness = 1.00
in)
Interfacialair layerthickness(in)
00.00010.00100.00200.00300.00500.00800.0100
Surfacetemperature
(0F)171.2170.4165.8162.1158.8153.8149.4147.2
Plastic/airinterfacialtemperature(0F)
77.178.286.994.9
101.2110.7120.5124.9
Timeto cool
(S)
19.219.521.924.226.530.836.339.7
-
increases with interstitial layer thickness in a power-law
fashion. Example 5.12 showsanother way in which this arithmetic can
be used in thermoforming.
Example 5.12 Finding Air Bubbles
Can infrared scanning detect an air bubble in an opaque plastic
sheet while it is incontact with the mold surface?
Consider the database used in the parametric study of Table 5.7.
Assume thegap between the plastic and the mold in the air bubble is
0.005 in, Fig. 5.18.The bulk of the plastic, in intimate contact
with the mold surface, reaches anaverage sheet temperature of 1500F
in 19.2 s. At that time, the free sheetsurface temperature is
1710F. From the computer model at 19.2 s, theaverage temperature in
the plastic over the air bubble is 185F, the temper-ature of the
polymer/air bubble interface is 128F and the surface tempera-ture
of the plastic over the air bubble is 1910F. The 2O0F
temperaturedifference in plastic free surface temperature should be
easily detected witha standard infrared scanning device.
5.7 Shrinkage
As with all materials, plastics increase in specific volume or
decrease in density withincreasing temperature1. The specific
volume of any polymer changes in slope withtemperature at the glass
transition temperature (Fig. 5.19). The specific volume of
acrystalline polymer shows a distinct discontinuity in slope during
melting. The
1 Volumetric change at thermodynamic equilibrium, Ve, the result
of increased molecular motion,
such as rotation and reptation, is related to the coefficient of
thermal expansion, COE, in thefollowing way. Volumetric change is a
function of temperature and pressure, according to:
(5.60)
(5.61)
(5.62)
where k is the volume expansivity or coefficient of thermal
expansion, k = COE, with units oftemperature"1, and P is the
isothermal or bulk compressibility, with units of pressure"1.
Thermalexpansion is usually restricted to dimensional changes of
the polymer over a temperature rangein which the polymer has no
thermodynamic transitions. Typical values for coefficients of
thermalexpansion of many polymers and some mold materials are given
in Table 5.8.
Rearranging:
-
Figure 5.18 Schematic of air bubble or lake in molded part
volumetric change in the polymer during cooling from the forming
temperature toroom temperature is called "shrinkage". All polymers
shrink when cooled, regardlessof the process. Shrinkage occurs in
thermoforming when the hot polymer sheet iscooled against a rigid
mold. There are two general types of shrinkage:
Unconstrained shrinkage, sometimes called isotropic shrinkage.
The formed partdecreases uniformly in dimension to the densities
shown in Fig. 5.19. The finalpart is said to be in thermodynamic
equilibrium.
Constrained shrinkage. The formed part is constrained from
shrinking in at leastone direction. The final part density may not
achieve the thermodynamicallyequilibrated value until some time
after the part has been removed from the moldand trimmed from its
web.
Unconstrained Shrinkage
Crystalline polymers heated above their melt temperatures
typically have greaterunconstrained shrinkage values than amorphous
polymer, as seen in Fig. 5.19 andTable 5.9 [16]. This figure shows
the difference in volumetric change between anamorphous and a
crystalline polypropylene. The volumetric change is convertedto
isotropic linear dimensional change as follows. Volumetric
shrinkage, Sv is definedas [17]:
(5.63)
Air Bubble or ,,Lake"
Sheet
Mold
Air Gap
-
Table 5.8 Coefficients of Thermal Expansion For Plastics[ASTM D
696]
Material
ABSABS/PVCABS/PC20% GR ABSPOM acetal copolymerCast PMMAExtruded
PMMAEthyl celluloseCellulose acetateCellulose butyrateCellulose
propionatePCTFEPVDFPTFEPolyamide 6 (PA 6)Polyamide 66 (PA
66)PolybutylenePolycarbonatePolybutylene terephthalatePolyethylene
terephthalatePETGPolyetherimideLDPEHDPEPolyimidePolymethyl
pentenemPPOPPSPP homopolymerPP copolymerPSunmodifiedFR
PSrubberizedSANSMAThermoplastic polyurethanePolysulfonePolyether
sulfoneThermoplastic elastomerPVC-rigidPVC-flexible
Thermal expansion (solid)
CF)"1
60-13050-90702060-8550-9050-90
100-20080-180
110-17080-12035-7070-14070-1208080
125-1507060-956550-7050-55
100-22060-11045-556540-7025-5080-10070-9550-804565-7080
100-200555585-1907070-250
(0C)-1
35-7030-50401035-4530-5030-9055-11045-10060-9545-6520-4040-8040-65454570-854035-553530-403055-12035-6025-303520-4015-3045-5540-5530-452535-404555-110303050-1054040-140
-
Temperature, 0C
Figure 5.19 Temperature-dependent specific volume of amorphous
and crystalline polypropylene,PP homopolymer [16]. Figure used with
permission of copyright owner
where Vm and Vf are the specific volumes of the polymer at room
temperature andthe forming temperature, respectively. Linear
shrinkage, S1, is given as:
(5.64)
When the cube root is expanded in series form, the linear
shrinkage is approximatedas:
S1 -^ + higher order terms (5.65)Shrinkage values are usually
given as ranges. The actual values depend on thetemperature
difference between forming temperature and room temperature. Table
5.9gives representative shrinkage ranges for thermoformed polymers.
The recommendedshrinkage values are used when actual experience
with shrinkage of a specific polymeris unknown. The following
processing aspects influence the extent of shrinkage [18]: Part
Design. Draft on both female and male surfaces influence the extent
of
constraint on the sheet as it cools. This is discussed below and
again in the
Spec
ific Vo
lume,
cm
3 /g
Amorphous PP
Crystalline PP
-
Table 5.9 Shrinkage Values for Thermoformable Polymers
Polymer Shrinkage range (%) Recommended shrinkage (%)
ABS-Medium impact 0.6-0.9 0.7ABS-Heat resistant 0.5-0.8
0.7ABS-Flame retarded 0.5-0.8 0.7Cellulose acetate 0.4-0.9
0.5Cellulose butyrate 0.3-0.9 0.4Cellulose propionate 0.3-0.9
0.5Ethylene vinyl acetate (20%) 0.3-0.8 0.6FEP fluoropolymer
1.5-4.5 3.0PTFE fluoropolymer 5.0-10.0 7.0Polycarbonate 0.5-0.7
0.6Polyetherimide 0.6-0.8 0.7PEEK 0.8-1.0 0.8Polyethersulfone
0.6-0.8 0.7LDPE 1.5-4.5 3.0HDPE 2.0-4.5 2.5PMMA 0.2-0.8 0.6mPPO
0.5-0.7 0.7PP 1.0-2.5 2.0HIPS 0.5-0.8 0.6PS 0.5-0.7 0.6Polysulfone
0.7-0.9 0.8Thermoplastic urethane 0.5-1.0 0.8Flexible PVC 10.0-15.0
12.0Flexible PVC (filled) 2.0-3.5 3.0Rigid PVC 0.1-0.5 0.3PVDC
0.5-2.5 1.5Rubberized styrene (Kraton) 0.1-0.5 0.3SMA 0.5-0.9
0.7SAN 0.3-0.5 0.5K-Resin 0.4-0.8 0.7PBT 0.2-0.4 0.4Amorphous PET
0.3-0.6 0.5Crystallized PET 10.0-18.0 12.0XT Polymer 0.4-0.8
0.7
chapter on mold design. Male elements such as posts, bosses,
partitions andgussets in female molds also influence shrinkage.
Part Wall Thickness Uniformity. Thin sections cool more rapidly
than heavysections and as a result differential shrinkage will
result when part wall thick-nesses are not very uniform.
Mold Temperature. A 100C or 18F difference in mold surface
temperature maychange shrinkage values by as much as 0.1%.
Depth of Draw. Deeply drawn parts are usually characterized by
nonuniform wallthickness, part regions that are formed at lower
temperatures than others, and
-
Temperature
Figure 5.20 The schematic effect of cooling rate on specific
volume of an amorphous polymer
regions that have contacted lower temperature plugs. All these
aspects influencelocal shrinkage.
Initial Sheet Forming Temperature. Lower forming temperatures
result in lowershrinkage.
Constrained Shrinkage
Applied stresses inhibit shrinkage. When the plastic sheet is
constrained against themold surface by part design, mold
temperature or applied force, complete isotropicshrinkage may be
inhibited. Even if mold design and processing conditions are
ideal,differential shrinkage may result due to differences in part
wall thickness. When thestresses holding the sheet against the mold
surface are removed, shrinkage continues.As noted, volumetric
change is temperature dependent. Rapid cooling of the plasticsheet
forces the polymer into a thermodynamically non-equilibrium state
since thereis insufficient time for molecular relaxation before the
molecular mobility is inhibited.Consider the temperature-dependent
volumetric change schematic of Fig. 5.20. Thespecific volume of the
polymer is written as:
(5.66)
Spec
ific Vo
lume
Rapid Cooling Rate
Slow Cooling Rate
Mobile State
Solid State
-
Time
Figure 5.21 Characteristic time-dependent change in specific
volume of an amorphous polymer to astep change in environmental
temperature [19]. Figure used with permission of copyright owner.
V1is the initial volume. Ve is the final volume of the polymer
where T is temperature and 9 is time. The differential form for
the volume is:
(5.67)
(5.68)where r = dT/d6, the rate of cooling. Consider a
time-dependent change in specificvolume in response to a step
change in environmental temperature for an amorphouspolymer such as
polystyrene (Fig. 5.21) [19]. The initial change in specific volume
isgiven as V1 and the time-dependent change is:
(5.69)where Ve is the equilibrium value of the specific volume
and x is the isothermal rateconstant. If the constant pressure
temperature-dependent equilibrium volume iswritten as:
Ve = aT + b (5.70)the rate of change of actual volume with
temperature is given as:
(5.71)Equation 5.71 shows that the maximum amount of shrinkage
owing to a step changein sheet temperature for an amorphous polymer
is a function of the isothermal rateconstant, x, and the degree of
quench, r. The isothermal rate constant, x, is relatedto material
relaxation once applied stresses are removed. Stress relaxation
time, X9
Spec
ific Vo
lume,
cm
3 /gv-ve
Ve
V1
The temperature-dependent volumetric change is given as:
-
at the glass transition temperature, Tg, for most polymers is
about 1000 s [20]. Thestress relaxation time, X, usually increases
exponentially with increasing temperature:
X = A exp(AE/RT) (5.72)where A is a pre-exponential constant and
AE is the energy of activation. Values forAE are predicted for
amorphous and some crystalline polymers for temperaturesabove Tg
[21]. Extrapolation to most crystalline polymers and to
temperatures belowTg is unwarranted. The isothermal rate constant,
T, mirrors the stress relaxation timeconstant, X:
T = K e-c/T (5.73)where K has the units of time"1 and C has the
units of temperature. The solution toEquation 5.71 with Equation
5.73 substituted for x is not available in closed form.For intense
quenching, r-> oo. Thus:
g - > x (5.74)That is, the final specific volume change
simply equals the initial instantaneousvolume change. When r->0,
V = Ve. Figure 5.22 shows the effect of quenching onthe final
specific volume of polystyrene. Example 5.13 illustrates the
time-dependencyof specific volume as determined through stress
relaxation. As a practical example,the effect of mold temperature
on HDPE shrinkage is seen in Table 5.10 [22].
Example 5.13 Temperature-Dependent Stress RelaxationConsider a
polymer with AE 40 kcal/g mol K. Its glass transition
temperatureTg= WO0C= 2100F. Determine the stress relaxation time at
T= 800C= 176Frelative to that at the glass transition
temperature.
Taking the logarithm of Equation 5.72 yields:AF
In(X) = InA + -
For the two temperatures:
in (X100) - in (X80) ~ ( ^3 " 3^3) ~ (2-681 - 2.833) = -3.058X80
= 21.3 times that of X100
As noted for most polymers, XT 1000 s. As a result, the
approximaterelaxation time for PS at 800C is5.9 h.
About 70% to 80% of the dimensional change due to shrinkage
occurs as thesheet cools from the forming temperature to the set
temperature or the heatdistortion temperature at 455 kPa or 66
lbf/in2 [23]. Stabilization to final dimensionmay take several
hours, however. Strain recovery is one of the major causes of
the
-
Temperature, 0KFigure 5.22 Temperature-dependent specific volume
of amorphous polystyrene, PS. r is the rate ofquenching. Figure
used with permission of copyright owner
Table 5.10 Effect of Mold Tempera-ture on HDPE Shrinkage
Drawninto a H:D = 1 Symmetric Mold [22]
Mold temperature Shrinkage(0C) (%)40 1.865 1.975 1.990 2.4
long times needed to achieve stable part dimensions. Uneven
strain recovery causedby nonuniform orientation in the trim area,
as an example, is the major cause oflong-term part distortion and
warping [18]. In difficult cases, 24 h annealing attemperatures
approaching mold temperature or maximum part use temperature
priorto trimming can reduce warping.
Spec
ific Vo
lume,
cm
3 /g
-
Shrinkage can cause serious part removal problems when forming
onto malemolds. Draft angles are estimated from:
0draft = tan"1 (2 x shrinkage fraction) (5.75)Example 5.14 shows
the difference in recommended draft angles for amorphous
andcrystalline polymers [24]. For amorphous plastics, draft angles
can be as small as \degree to 1 degree. For crystalline polymers,
it should be greater than 2 degree to 3degrees. Female portions of
molds require no draft if smooth and \ degree iftextured. Draft
angles are also discussed in Chapter 6 on mold design.
Example 5.14 Draft Angles for Amorphous and Crystalline
PolymersA mold designed for PS has recently been used to run PC.
Are the draft anglescorrect? Can this mold be used to run POM,
acetal? POM has a recommended
- shrinkage value of 3.0%.
From Table 5.9, the recommended shrinkage values for both PS and
PC are0.6%. Therefore if the draft angles for PS were initially
correct, they arecorrect for PC.
To estimate draft angles for POM, consider Equation 5.75:9draft
= tan"1 (2 x shrinkage fraction)
For PS and PC, the recommended draft angle is:0draft = tan-1 (2
x 0.006) = 0.7 degrees
For POM:6draft = tan-1 (2 x 0.03) = 3.4 degrees
The original draft angles are too small for POM.
5.8 Trimming
There are many acceptable ways of efficiently separating formed
parts from thesurrounding plastic. Thin-gage parts are usually
trimmed automatically. Very heavy-gage parts are trimmed manually.
Medium-gage and heavy-gage parts are usuallyfixtured and trimmed
manually or with computer-aided robots. Routers, water-jetsand
lasers are used for automatic trimming. As discussed below, the
cutting surfacemust be fed at a fixed rate in a plane -
perpendicular to the cutting direction.Prototype parts are usually
trimmed manually with routers and bandsaws. Very thinparts can be
trimmed with a paper cutter or hand scissors.
Typical trimming devices are shown in schematic in Fig. 5.23.
The trimmingdevices include: Manual knives, including
Bread knives for low-density foams,
-
Linoleum knives or knives with recurving blades,Knives with
replaceable blades,
Routers, such asHand-held, high-speed routers at 20,000 RPM with
carbide router tips,Table-mounted fixed-position routers,Multi-axis
routers,
Band saws, Circular saws, including
Stationary saws,Hand-held, small diameter saws,Saws with
toothless blades for foams,
Abrasive wheels,
Toothed Saw or Router
Bandsaw
Hot Wire
Die Cut, Prototype
Nibble Cut
Shear Cut
Hot Gas Jet
Water Jet
Laser
Abrasive Wheel
In-MoId Die Cut
Figure 5.23 Schematic examples of various trimming methods
-
Sharp-edged compression blades, includingSteel-rule dies,Ground
forged dies,Machined dies,
Guillotines, includingOne-sided linear shear,Two-sided linear
shear,
Flames, Lasers, Water jets, and So on.
Trimming Heavy-Gage Parts
Heavy-gage parts are usually removed from the molds with the web
attached, thenplaced on trimming fixtures and trimmed with manual
or computer-aided trimmingdevices. For prototype parts and a few
hundred parts, hand operated routers, sawsand bandsaws are commonly
used. For parts having a planar trim path, simplecompression or
dinking presses are used (Fig. 5.24). The press consists of a steel
ruledie mounted in a wooden frame and mounted to the movable top
platen and aductile cutting surface mounted to the stationary
bottom platen. The part and webis registered against stops on the
bottom platen cutting surface and the press is closedpneumatically,
mechanically or hydromechanically.
For production runs, steel rule dies are mounted in rigid steel
or aluminumframes (Fig. 5.25). The trim is removed by compression.
Specifications for the steelrule die are given below. For very
heavy-gage plastic where the trim surface is
Figure 5.24 Schematic of steel rule die prototype trim or dink
station
Upper Platen
Hold-Down ScrewShim
Steel Rule DieFormed Part
UHMWPE Pad
Lower Platen
-
Figure 5.25 Characteristic steel rule die mounting assembly
piecewise linear, a standard sheet guillotine is used. Forged
and machined dies arealso growing in popularity. For longer
production runs, computer-driven multi-axisrouters and saws are
used. Figure 5.26 shows a typical five-axis table used to drivea
multiple router head. When using a multi-axis trimmer, the part to
be trimmed isfastened tightly against a fixture using clips or
vacuum. The cut is initially pro-grammed by leading the router head
manually around the fixture. The computer
Figure 5.26 Multiple-axis computer-driven router trimmer. Figure
used with permission of Therm-wood Corporation
Trim Die Platen
Bracket
Adjusting Screw
Steel Rule Die
-
learns the correct path in this manner. Minor changes in the
cutting path are usuallyincorporated in this first-pass program in
order to fine tune the trim path.
For heavy-gage parts, trimming can also involve other
post-molding operationssuch as:
Drilling, Slotting, Grooving, Ultrasonic welding, Solvent
welding or other forms of gluing, Ultrasonic insertion of
fasteners, Grinding or milling local wall thickness to tolerance,
and So on.
Trimming Thin-Gage Parts
Typically, many parts are simultaneously formed on roll-fed
presses. Thin-gage,roll-fed parts are typically trimmed either:
After forming but while the sheet and web are still on the mold,
usually referred
to as "trim in place", or After the sheet and web are stripped
from the mold, in a separate in-line
mechanical or hydromechanical press.These trimming systems are
quite different and represent a major early decision whenchoosing a
thermoforming line. Trim-in-place punch-and-die systems are
usuallyconsidered as part of the mold design (Fig. 5.27). If the
parts are completely punchedfrom the web, methods must be used to
remove the parts from the mold region asquickly and thoroughly as
possible. Common methods are vacuum suction, mechan-ical part
removal and mold rotation [25]. For vacuum suction, a vacuum tube
is usedfor each cavity. The parts adhering to the tubes are
shuttled from the press to a dropbox. The drop box feeds an
orienting and stacking device. In mold rotation, themold containing
the parts drops free of the web plane, then rotates to dump the
partsinto the drop box (Fig. 5.28). Frequently, air assist blows
the parts free of the cavity.Frequently, the trim die is tabbed so
that a small portion of the part remainsattached to the web. As a
result, the parts are not quite separated from the web inthe mold.
However, once the tabbed part-web structure is free of the mold,
air ormechanical assists punch the parts from the web. The primary
concerns withon-mold trimming are:
Incomplete separation of all parts from the web. The parts that
are still attachedto the web as it exits the mold area may foul
downstream machinery or webwind-up equipment. In addition, these
good parts are not saleable,
Parts that remain in some mold cavities after the removal
process, due toundercuts, poor mechanical or vacuum picking, or
static charge between the partand the mold cavity,
-
Figure 5.27 Trim-in-place or in-situ trim die. As shown,
trimming is by compression
Parts that accidentally drop back into the cavity plane after
picking, and Dust and microflbers that remain on the mold surface.
This detritus is usually
transferred to as-molded parts.Punch-and-die design and tabbing
are discussed in detail below.
In most thin-gage forming operations, the web and formed part
sheet isremoved from the mold to an in-line trimming press. Usually
the sheet is held ina vertical plane while being trimmed. As a
result, the sheet is brought fromthe horizontal position to the
vertical position by means of a hump-back orcamel-back arch (Fig.
5.29). The hump-back trimming press allows the punchedout parts to
be collected on horizontal tables, thus simplifying the counting
andbagging process. The die used in in-line trimming can be steel
rule die, but isusually machined or forged. Again, punch and die
design is discussed in detailbelow. Technically, punch and die
trimming uses the shear mechanism of cutting, asdescribed
below.
5.9 Mechanics of Cutting
There are five general mechanisms of cutting (Fig. 5.30) [26].
They are: In-plane uniaxial compression or die-cutting, Mode III
antiplane pure shear or nibbling and shear cutting,
Sheet
Sheet
Die As Isolator
Die As Trim
Steel Rule DiePlug
Mold
Steel Rule DiePlug
Mold
-
Figure 5.29 Camel-back or hump-back in-line roll-fed former
trimming press with cam-operatedpunch-and-die trimmer. Figure
redrawn from [27]
Abrasion or abrasive cutting, grinding, riling, buffing and
water jet cutting, Brittle tensile fracture or routering, drilling
and sawing, and Thermal or hot knife, hot wire and laser
cutting.
A: Forming Step B: Trimming Step
Hot SheetTrim Die
Mold
Web
Formed Parts
Rotating Mold
Collection Bin
D: Part RemovalC: Mold and Web Separation
Figure 5.28 In-mold trimming with part removal by mold
rotation
Formed Parts
Web
Registry CamFormed Parts
Trim DieCam
TrimPunch
-
Figure 5.30 Five characteristic cutting mechanisms. Figure
redrawn from [26]
Mechanical compression and shear cutting dominate the trimming
industry. Thecharacteristics of some of these mechanisms are
detailed below.
The Trim Region
Typically, the trim region is relatively well-defined as the
linear edge where the partends. In certain cases, the region is
demarked in the forming process as a trimchannel (Fig. 5.31). The
accuracy of trimming to tolerance depends on severalelements: Local
polymer shrinkage at the trim line, Whether the polymer is
crystalline or amorphous, Whether the polymer continues to shrink
for some time after forming but before
trimming, Whether the polymer is tough or brittle at the trim
temperature, The tightness of the fixture to the formed part, The
allowable variation in part temperature at the trim station, The
presence of registry or locating cones, The trim die temperature
and its variation with time, The thickness and thickness variation
of the part at the trim line, The allowable variation in local part
wall thickness,
Compression
Abrasion
Shear Thermal
Chip or Fracture Cutting
-
Figure 5.31 Compression (left) and shear or pinch trimming
(right) configurations
The increase in trim die temperature from the temperature at
which the die gapswere set,
The strength of the die clamping frames, and The amount of
flexure in the die during cutting.
Registering the Trim Site
Trim registers or locators are usually designed into the mold.
These are cones ortruncated pyramidal structures, as shown in
schematic in Fig. 5.32. For heavy-gagesheet, risers or indentations
are used by the operator to positively position the sheetagainst
the trim fixture prior to trimming. For thin-gage sheet, the
locators catchindexing lugs ahead of the in-line trim die. For
thin-gage sheet, peripheral locatorsare located on the four corners
of the multicavity mold and interstitial locators are
Trim Die Trim Die
0.003 to 0.005 in
Trim Channel
Figure 5.32 Various shapes for sheet registry on punch
station
Pyramidal Conical Cubical
3 to 10 Times Local Sheet Thickness
-
located on at least a few of the web regions between cavities.
The indexing lugs onthe trim press are usually adjusted to ensure
full engagement of all locators on thesheet surface prior to
start-up and then once or twice a shift as the various elementsof
the forming and trimming presses warm to equilibrium. During long
productionruns, periodic examination of locators after contact with
trimming lugs may indicateif long-term forming problems are
developing.
The actual number of trim locators is not as important as the
shape. Typically,the locator riser should have substantial draft of
at least 15 degrees. Truncated conesare frequently used. Truncated
boxes, wedges and pyramids are used, albeit with verygenerous
vertical side radii, where trimming tolerance is critical and where
thepolymer may move locally between the forming and trimming
stations.
The Nature of the Cut
The toughness of the polymer at the time of trimming dictates
the nature of thefracture, as discussed below. The polymer
toughness is best demonstrated by thepolymer resistance to applied
compression stress, as delivered by a toothless trim die(Fig.
5.33). As seen, for tough, ductile or hot polymers such as HDPE, PC
andFPVC, the cutting blade forces the polymer to essentially flow
away from the bladetip. The tip of the cut is therefore just ahead
of the blade tip. For brittle polymerssuch as PS, APET and PMMA,
the crack propagates very quickly from the initialpoint of blade
tip insertion. For rubber-modified polymers such as HIPS and
ABS,the crack propagation is arrested by the rubber particles.
Microscopic examination of
Figure 5.33 Characteristic polymer response to trim die
penetration
Soft, Hot Polymer
Hard, Cold, Brittle Polymer
Hard, Cold, Tough Polymer
Distance
PlasticForce
Distance
ForceTrim Die
Trim Die
Plastic
PlasticForce
Trim Die
Distance
-
Figure 5.34 Characteristic problems in trimming of brittle
polymers
the trim surface of rubber-modified polymers shows fragments of
rubber and holeswhere the rubber particles have been torn from the
crack surface. Since the crackpropagates very rapidly during
compression cutting of brittle polymers, the crack pathcan meander
(Fig. 5.34). Multiple cracks can occur as the cutting blade passes
throughthe cutting zone. These cracks generate discrete particles,
which are typically calledtrim dust. Microscopic examination of
these particles reveals chunky, sharp-edgedparticles of 1 to 50 (xm
in dimension. The high surface area of these high-surface
energyparticles implies high static attraction to surrounding
ungrounded surfaces, such asthe plastic parts and web structure.
Although PS has the most tenacious trim dust,adhering trim dust is
a problem with PMMA, APET, CPET, PC and other brittle
andtough-brittle polymers. In addition to the production of
micron-sized particles, edgemicrocracks are also formed
perpendicular to the cutting plane during trimming ofbrittle
plastics. These microcracks produce near-serrated edges under
30-power optical
Figure 5.35 Optical microphotograph of compression cut of
polystyrene, PS
Meandering Crack Multiple Cracks
-
micrography (Fig. 5.35). In addition to yielding an undesirable
rough lip, thesemicrocracks are sources for crack propagation or
splitting into the part.
For certain ductile polymers such as PP, HDPE and CPET under
certain cuttingconditions, microfibers are formed. These
microfibers are usually called angel hair orfuzz, are typically 50
to 150 um in cross-sectional dimension and can be 50 mm
long.Although there is no consensus as to the primary cause of
microfibers [27,28], theyusually occur when trimming fiber-forming
or crystalline polymers. Some of theconditions that are thought to
minimize microfibers include:
Reducing the polymer temperature prior to trimming, Resharpening
the cutting blade, Using a single-sided honed blade with a hardened
tip, Increasing the rate of travel of the blade into the sheet,
Ensuring that the cutter blade fully contacts the cutting anvil for
steel rule dies, Ensuring that the steel rule die does not move out
of plane during its travel
through the sheet, Reducing the gap between the punch and die
for in-line trimming, Ensuring that the blade engages the sheet at
all places on the trim line simulta-
neously, and Ensuring that the only mode of cutting is
compression cutting.The dulled cutting tip is probably the most
common cause of microfiber generation.Like cutter dust, microfibers
are tenacious, particularly on PP and CPET. Since foodcontainers
are the primary products of these polymers, microfibers are
unacceptableboth from an appearance viewpoint, as they resemble
human hair, and a healthviewpoint, since these polymers are not
approved as "food additives" [29].
Fracture Mechanics
Trimming is semi-controlled fracture mechanics. The purpose of
the trimmingprocess is to separate one piece of plastic into at
least two pieces. Mechanicalchipping such as drilling, abrasive
sanding, multi-tooth cutting and routering, resultsin many granular
pieces of plastic, in addition to the desired part and the
web.Ideally, compression and shear cutting with toothless blades
should result only in thedesired part and the web. Unfortunately,
such is not the case. The toughness of thepolymer at the time of
trimming dictates the nature of the fracture, as discussedabove.
The mechanics of multi-tooth and toothless cutting are relatively
well known.Kobayashi [30] considers all mechanical cutting as
controlled tensile fracture of theplastic. This section develops
the mechanics of fracture as it pertains to trimming.
Mechanical Chipping
As a first step to understanding trimming parameters, examine
the interaction of asingle cutting-edge tool with the polymer (Fig.
5.36). A single cutting-edge tool is
-
Figure 5.36 Orthogonal single-edge cutting geometry [30]. Figure
used with permission of copyrightowner
used in machining, turning and shaping but not in trimming of
thermoformed parts.But the cutting actions of tools having multiple
edges, such as saws, drills, routersand mills represent the sum of
cutting actions of many single-edged tools. Thephysical factors
affecting cutting actions on plastics are summarized in Table
5.11.Tool geometry factors are more complex for multiple-edged
tools. The nature of the
Table 5.11 Factors Affecting Cutting Characteristics of
Plastics1
X = Major effectx = Minor effect
Cutting Tool
Polymer
Factor
Tool design:Tool geometry*:Rake angleRelief anglePoint
radius
Tool materialMachining conditions:Depth of cut**Cutting
speedFeeding speedAmbient work
Temperature:Cooling system
Effect
Chipformation
X
XXXX
Cut surfaceroughness
X
X
Toolwear
X
XXX
Heatgenerated
x
X
X
X
X
Gumming,burning
X
X
X
X1 Adapted from [26], with permission of the author
* For single-edged cutting tools. Tool geometry effects are more
complicated for multiple-edgedcutting tools
** Tooth depth of cut
-
chip formed in cutting is used as a guide cutting tool
selection, and as an indicationof how cutting is proceeding (Table
5.12). For example, PS chips in multiple-edgesaw cutting should be
discrete and separate easily, with no evidence of
softening,gumming, or threadlines.
Multiple-Edged Tool or Toothed Saw Performance
Kobayashi [26] presents extensive experimental results for
plastics performance whencut with single-edge tools. A cutting
force balance is shown in Fig. 5.36. When theperpendicular
cutting-force component F t is zero, the cutting tool obtains
themaximum cut surface accuracy. The cutting tool rake angle at
this condition isknown as the critical rake angle. All tools should
have cutting angles equal to orgreater than this value. The optimum
cutting conditions for nearly all polymersshould produce continuous
chips of uniform thickness. If the cutting depth or toothdepth is
too large, discontinuous chips are produced and the cutting surface
hasmany microcracks. If the cutting depth is too small, the plastic
will heat from frictionand may burn or gum the cutting tool.
Multiple-edged tool performance is determined by comparing the
tooth depth ofcut and the cutting speeds with single-edged tool
performance. For a circular saw(Fig. 5.37), the tooth depth of cut,
g, is:
g = V - ^ (5.76)
where U is the peripheral speed of the blade [m/min], U = TTDN,
D is its outsidediameter [m], D = 2R, N is the blade speed [RPM], v
is the cut-off speed or the workfeed rate [m/min], and p is the
tooth spacing [mm]. The angle is given as:
= co,-'^> (5.77)
where h is the cut-off height or the distance between the saw
centerline and thebottom of the plastic sheet [m], and b is the
sheet thickness [m]. Example 5.15illustrates these
relationships.
Figure 5.37 Toothed saw trimming geometry [30]. Figureused with
permission of copyright owner
-
Table 5.12 Classification of Plastic Machining Chips1
Commentson cause
High elasticdeformation
Slippage con-tinuously byshear stress
Plastic fractureby simple shearshear
Plastic fractureby shear withcompressive and/ortensile
stress
Elastic fracture,brittle fracture
Plastic fractureby shear withcompressive and/ortensile
stress
Typicalplastics
PE, PTFE,FEP, PP
PS, ABS
PMMA
PMMA, PS
PMMA, PS
High modulus,Low-elongation
Cuttingspeed
Slow
Medium-high
Medium
High,
sticky
High
High
Materialtype
High elongation,rubber-like
Brittle
Brittle
Brittle
Brittle
Brittle
Nature ofdeformation
Elastic
Plastic
Plastic
Elastic
Brittle,elasticfracture
Brittlefracture
Surfaceroughness
Small
Irregular,shear marks
Irregular
Very irreg-ular, wavy
Hacklemarks
Gouges
Cuttingforcefluctuation
Small
Small
Moderate
Large
Verylarge
Verylarge
Thickness-to-cut depth
> 1
>1
Irregular
Irregular
>1
IrregularChips
Nature ofchip
Continuous
Continuous
Discontinuous
Discontinuous
Discontinuous
Discontinuous
Classification
Continuous-flow
Continuous-shear
Discontinuoussimple shear
Discontinuous-complex
Discontinuous-crack
Discontinuous-complex
(shear withcracks)1 Adapted from [26], with permission of
author
-
Example 5.15 Cutting with a SawConsider a D = 15.2 cm or 6 in
diameter saw having four teeth per in. The bladerevolves at 1000
RPM. The sheet is 0.100 in or 0.254 cm thick. The cut-off heightis
2 in or 5.1 cm. A minimum tooth depth, g, is selected to be 0.004
in or 0.1 mmto minimize gumming or burning. Determine the maximum
feed rate.
From Equation 5.76:v _ u - g
p sin (j)p is the tooth spacing or 1/4 (teeth/in) = 0.25 in or
0.637 cm. The peripheralspeed of the blade, U = TCDN. For this
example:
U = Ti 15.2 cm = 47,750 cm/minmm
The angle is given from Equation 5.77 as:. l (h-b/2) 1
(5.1-0.254/2)
* = C0S
- D / ^ = C0S 15.2/2(j) = 49 degrees
Therefore:47,750 0.01 cm2/min , .
v = = 990 cm/mm =16.5 cm/s = 6.5 m/s0.637 cm 0.756This is the
maximum feed rate of this stock into the saw.
Note that the feed rate is proportional to blade speed and
diameter and inverselyproportional to tooth spacing. Thermal damage
to the plastic is minimized by: Wide tooth spacing, Coarse toothed
blades, Small blades, Low speed blades, and High feed rates.However
wide tooth spacing causes relatively rough cut edges with many
brittlepolymers such as PS, ABS, SAN, PMMA, and RPVC. Hollow-ground
blades withno tooth set and wide-kerf carbide blades yield smooth
cut edges. Spring-set andswag-set teeth also produce quality cut
edges (Fig. 5.38).
Abrasive Cut-Off Wheel
Abrasive wheels with 30- to 200-grit surfaces produce relatively
smooth cut surfacesat high cut-off rates with about one-half to
one-third the heat generated by toothed
-
Feed Rate, v, mm/min
Figure 5.39 Comparison of abrasive disk and toothed saw trimming
forces as function of polymerfeed rate [30]. Figure used with
permission of copyright owner
saws [26]. Typical abrasives include aluminum oxide or alumina,
silicon carbide,tungsten carbide and diamond. Diamond abrasive
wheels are the most expensive butlast longest. Abrasives are held
together with thermosetting binders such as pheno-lics, ureas and
epoxies. Cutting forces are usually higher for abrasive wheels than
fortoothed wheels at the same feed rate (Fig. 5.39). Abrasive wheel
cut surfaceroughness is usually smaller (Table 5.13). Finer grit
wheels produce smoothersurfaces but at reduced cut-off rates (Table
5.14).
The machinability of a plastic, r\, is written as [26]:
^V^s{ (5-78)where V1n is the volume of polymer cut per unit time
[mm3/min], Vw is the amountof tool wear per unit time [mm3/min], HP
is power consumption [kg m/min], and Sfis the cut surface roughness
[urn]. For properly selected cutting wheels, the amountof tool wear
is essentially negligible, and machinability is redefined as:
Tang
entia
l Cut
ting
Forc
e, F t
, kg
f
Figure 5.38 Typical saw tooth designs
CarbideTip
HollowGround Spring-Set Swaged
36 Grit SiliconCarbide Abrasive
Hollow-GroundTooth Saw, No Set
36 Grit AluminumOxide Abrasive
Hollow-GroundTooth Saw, Spring-Set
-
1 After [26], with permission of author
Key:A: 36 Grit silicon carbide, resinoidmedium gradeB: 36 Grit
aluminum oxide, resinoidmedium gradeC: Saw, hollow-ground, zero-set
teeth, 300 mm, diameter, 2 mm
thick, 2.3 teeth/cm or 5.8 teeth/in, 0 rake-angle, 60 relief
angleD: Saw same as C except 0.2 mm set to teeth
Table 5.14 Finishing Operations Sanding Belt Surface
Roughness1
Silicon carbride sanding belt2000 m/min, 0.5 kg/cm2 applied
force, 20 min
1 Adapted from [26], with permission of author
For cutting wheels:
where b is the sheet thickness, B is the wheel thickness and Ft
is the tangentialcomponent of the cutting force. The ratio of
efficiencies of abrasive and toothedwheels operating at the same
feed rates and peripheral speeds is written as:
(5.81)
(5.79)
(5.80)
Polymer
PMMARPVCPC
Surface roughness (um)60 Grit
363941
240 Grit
222
Amount removed (g)60 Grit
295360235
240 Grit
2889
Removal rate (mg/s)60 Grit
246300196
240 Grit
23.36.77.5
Table 5.13 Cutting-Off Operation1
Peripheral speed 2500 m/min
Polymer
SANABSPA-610 (a nylon)PC
Surface roughess (urn)
Abrasive wheel
A
3228348
B
2316166
Circular saw
C
81065
D
2002003625
-
Abrasive wheels are typically 2 to 5 times thicker than toothed
wheels. Both produceabout the same surface roughness on the cut
edge at the same cut-off speeds (Table5.13). The cut-off forces for
abrasive wheels are about 2 to 5 times those for toothedwheels.
Therefore:
Although the cut-off efficiencies of abrasive and toothed wheels
are about the same,the cost of operating abrasive wheels is about 5
to 10% that of toothed wheels. Whenloaded, abrasive wheels are
redressed with a gum block or a wire brush. Toothedwheels require
resharpening and tooth resetting.
Toothless or Shear and Compression Cutting
Saw cutting depends on brittle tensile fracture of the plastic
under the force of thetooth. In solids, Young's modulus, E, is the
proportionality between pure elastictensile stress and strain:
G = E - e (5.83)When a solid is sheared, the proportionality
between pure shear stress and strain isthe modulus of rigidity or
shear modulus, G:
O5 = G es (5.84)The bulk modulus, B, is the ratio of hydrostatic
pressure to solid volume change perunit volume. Solid
compressibility is the reciprocal of the bulk modulus. Thesemoduli
are related through Poisson's ratio, v, the ratio of unit width
change to unitlength change [31]:
E = 2G (1 + v) = 3B (1 - 2 v) (5.85)Poisson's ratio, v = 0.5 for
a material with constant volume under stress. For mostplastics,
0.3
-
Table 5.15 Poisson's Ratio forSeveral Thermoformable Poly-mers
[50]
Polymer Poisson's ratio
LDPE 0.49HDPE 0.47PP 0.43PIB 0.47PS 0.38Rigid PVC 0.42PCTFE
0.44PTFE 0.46PMMA 0.40mPPO 0.41PPS 0.42PET 0.43PBT 0.44PA 66 0.46PA
6 0.44PC 0.42Polysulfone 0.42Polyimide 0.42
by the stress in the direction parallel to the crack [32]. Shear
cutting is considered asMode III, antiplane shear. This fracture
mode is also found in torsion of notchedrods. Mode I fracture,
cleavage or tensile-opening, dominates classical fractureanalysis
since it is the most common form of material failure and since it
is theeasiest to study in the laboratory.
If the plastic is not held tightly, Mode III crack propagation
control is difficult tomaintain. The advancing crack tends to
meander uncontrollably, and secondly,tangent cracks can form. The
amount of force required to propagate a crack in anymode and the
rate at which a stable crack is propagated can only be estimated
fromthe extensive studies of Mode I failures. The amount of energy
needed to initiate acrack in any polymer is substantially less than
its theoretical cohesive strength.Cracks begin at flaws or defects
in the polymer. They propagate when the decreasein elastic strain
energy equals or exceeds the energy needed to create a new
cracksurface. When a tensile specimen with a small horizontal
crack, a in length, isstressed, it is in plane stress. The stress
needed to propagate that crack is:
(5.86)
(5.87)where E is Young's modulus and G* is the fracture
energy:
-
Figure 5.40 Characteristic fracture modes [32]. Redrawn Figure
used with permission of Prentice-Hall Publications, Inc.
where P is the plastic work done during yielding and y is the
surface energy of thepolymer. In Equation 5.86, Kc is the fracture
toughness. The stress needed to initiatea crack is frequently far
greater than that needed to sustain crack propagation [33].For PMMA
for example, the ratio of stress levels is about 1000. For
vulcanizednatural rubber, it is about 325. The plastic deformation
stretching energy is usuallymuch greater than the surface energy.
For ductile plastics such as PTFE, PP, PETand TPO, P y. Even for
very brittle plastics such as PS and PMMA, P > 2 y.Example 5.16
illustrates these relative values. One measure of the fracture
toughnessof a polymer is the area under its tensile stress-strain
curve. If the area is large, thepolymer is tough. Polymers that
show great plastic flow after yielding, such asHDPE, PP and PET,
have high fracture toughness. If the area under the
tensilestress-strain curve is small, as with PS and PMMA, the
polymer is brittle. The stresslevel that produces fracture is
analogous to the crack tip stress intensity level thatproduces
sustained fracture. As noted in the second part of Equation 5.86,
fracturetoughness or stress intensity factor, Kc is written as:
(5.88)
(5.89)Characteristically, the stress intensity factor is written
as:
Mode III, Anti-Plane Shearor Tearing Fracture
Mode II, In-Plane Shear orSliding Fracture
Mode I, Tensile Fracture
-
Example 5.16 Fracture Energies for Ductile and Brittle
PolymersConsider vulcanized rubber and PMMA as typical of ductile
and brittle polymers,respectively. Determine the relative ratio of
yielding work to surface energy of eachof these polymers.
The plastic work during yielding of PMMA is P = 0.185 ft-lbf/in2
= 0.211kJ/m2. The surface energy for PMMA is about y = 0.039 kJ/m2
= 0.0342ft-lbf/in2. The fracture energy is given as:
G* = 2(P + Y) = 2(0.211 + 0.039) = 0.5 kJ/m2 = 0.44
ft-lbf/in2
The ratio of plastic work to surface energy, P/y = 0.211/0.039 =
5.4. This isa strong indication of a very brittle polymer.
The plastic work for vulcanized rubber, P, is unknown. However,
thefracture energy, G* = 13 kJ/m2= 11.4 ft-lbf/in2 and the surface
energy forvulcanized rubber is about y = 0.012 kJ/m2 = 0.010
ft-lbf/in2. The calculatedvalue of plastic work is:
P = ^ - - Y = y - 0.012 = 6.49 kJ/m2 = 5.67 ft-lbf/in2
Thus the ratio of plastic work to surface energy, P/y 6.49/0.012
= 567.This is a strong indication of a very ductile polymer.
The coefficient C depends on the geometry of the crack and the
surface beingfractured. One example of C is given in Fig. 5.41
[32], for an edge crack of length ain a sheet of width W under
uniaxial tension. For unreinforced polymers, values forKc range
from about 0.5 to 10. Typical values for Kc for a few polymers are
givenin Table 5.16. The fracture stress given in Equation 5.88 is
written symbolically as:
Material Parameter ^_a = : (5.90)Geometric Parameter
Stre
ss In
tens
ity Fa
ctor
Reduced Crack Width, a/W
Figure 5.41 Geometric parameters for stress concen-tration
factor for mode I, tensile fracture [32]. Re-drawn Figure used with
permission of Prentice-HallPublications, Inc.
-
1 Adapted from [33], with permission of copyright holder
* J-Contour Integral. See [33: p. 82]
In the tensile Mode I, an infinite stress is needed to initiate
a crack of zero length.Once the crack is propagating, the stress
diminishes rapidly.
The rate of crack propagation is also important. For fatigue
failure where theload is applied in cyclic fashion, the following
relationship is used:
^ = Af-AK (5.91)
where N is the number of cycles, AK is the stress intensity
factor range, AK =Kmax Kmm, and m and Af are polymer material
properties [33]. Some values for Afand m are given in Table 5.17.
AK is proportional to Kc, the fracture toughness. Formany polymers
[33,34], 0.5 < [AK/KJ < 0.67. Cyclic crack propagation rate
is usedonly as a guide to determine crack speed in Mode I tensile
fracture. Cyclic fatigue crackgrowth occurs at substantially lower
stress levels than those needed to sustain crackgrowth in
continuous loading. In turn, this guideline can be used only as an
estimateof the shear stress needed to control crack propagation in
Mode III antiplane shearfracture. As noted, Mode III fracture is
the apparent mode occurring during shearcutting of plastics such as
guillotining, diagonal brake cutting, nibbling and papercutting. An
appropriate relationship for the rate of crack propagation, a =
da/d9 is:
daa = = P am ocm/2 (5.92)d(3
where a is the shear stress and (3 includes geometric factors
and material constants.If the crack length ahead of the shear is to
remain stable, or a is to be constant, the
Materials
Vulcanizedrubber
PolyethylenePSHIPSPMMAEpoxyRubber-mod-ified epoxy
FRPGlassWoodAluminum
Young's modulus, E
(GPa)
0.001
0.153.02.12.52.82.4
7702.1
69
(1000 lbf/in2)
0.145
21.8435305363406348
1,01510,150
30510,000
Fracture energy, G*
(kJ/m2)
13
20*0.4
15.8*0.50.12
70.0070.12
20
(ft-lb/in2)
11.4
17.50.35
13.80.480.0871.75
6.120.00610.105
17.5
Stress intensity factor, K
(MN/m3/2)
( 0.114)
( 1.73)1.1)
( 5.76)1.10.52.2
70.70.5
37
(1000 lb/in3/2)
( 2.05)
( 31.2)19.8
(104)19.89.0
39.8
12612.69.0
666
Table 5.16 Stress Intensity Factors for Some Plastics and Other
Materials1
Values in parentheses obtained from Kc ^JE G*
-
Table 5.17 Crack Propagation Parametersda/dN = Af AKm
da/dN units are mm/cycleAK units are MN/m3/2
Af units are [MN/m1 / 2]-m
Note: For crystalline polymers, the general relationship
is:da/dN = A* (AK/E)7 where 0.5 < A* < 3
(AK/E) units are m1/2
Polymer Af x 1000 m Range of AK
PS 2.65 3.73 0.5 to 1.2PMMA 99 10.0 0.4 to 1.0PES 1.5 9.5 0.6 to
1.2HDPE 0.35 5.22 1.0 to 2.5PC 0.118 4.81 1.0 to 3.0mPPO 0.0365 6.2
1.0 to 3.0RPVC 0.164 2.2 0.5 to 1.0PA 66 0.00728 3.63 1.5 to 8.0PVF
0.0087 3.2 1.5 to 8.0
rate of shear is approximately proportional to the applied force
to the mth power. ForRPVC in Table 5.17, m = 2.2 and the shear rate
should increase about four timeswhen the applied load is doubled.
On the other hand, for PMMA, m = 10 and theshear rate should
increase about four times with only a 15% increase in applied
load.
Compression cutting occurs when the steel rule die is pressed
perpendicularly intoplastic sheet that is resting on an unyielding
surface. Load compression follows thetrue material stress-strain
curve. A modification of compression molding that em-ploys uniaxial
plane-strain compression is used to determine stress-strain curves
forpolymers that neck or fracture easily [35]. Compression cutting
is particularly usefulwhen the polymer yields in compression but
fractures brittlely in tension or shear.RPVC, PC and PMMA are
typical polymers that lend themselves well to compres-sion cutting.
Compression yield stresses are usually higher than tensile or shear
yieldstresses (Table 5.18). Thus more force per unit cutting area
is required to die cut aplastic than to shear cut it. Comparison of
typical stress-deformation curves, Fig.5.42 [35], shows that the
area under the compression curve continues to increase
withincreasing strain. As a result, crack propagation in
compression is more stable forpolymers that are brittle or neck
badly. Compression cutting is the preferred methodfor cutting LDPE
and should be considered for trimming PET, PA or nylon, POMor
acetal, low-density foams and thin-gage OPS and PMMA.
For a very brittle polymer being trimmed with a very sharp, wide
die, aperpendicular crack is created ahead of the blade. The crack
can propagate as aMode I fracture, as shown in schematic in Fig.
5.43. The crack can be uncontrollablewith an irregular reverse side
cut surface, microcracking and crazing. The stressrequired to cut
through the material is given in terms of the stress intensity
factor,
-
Table 5.18 Yield Stresses and Cutting Shear Stresses
Sharp knife cutting stressFlexure stress (yield)Compressive
stress (yield)Tensile yield stress
(10001bf/in2)
13-1815.8
8.66.4-7.1
(MPa)
91-126110
6045-50
(10001bf/in2)
6.51413.5111155
1217654
1314
(MPa)
4598947777353584
1194235289198
(10001bf/in2)
3
61212.51012
61115
12
16
(MPa)
20
4183866983
4176
103
2183
110
(10001bf/in2)
41.55
96
357
8
10
(MPa)
281034
6241
213448
55
69
Polymer
HDPELDPEPPPETPCRPVCPSHIPSABSmPPOPA 66*CACABCAPPMMA
POM**
* Dry nylon** Polyoxymethylene, acetal homopolymer
-
Figure 5.43 Characteristic mode I fracture with wedge effect of
trim die into brittle polymer sheet
Equation 5.89, and is frequently much less than the compression
yield strength. Oneway of partially controlling crack propagation
in very brittle polymers such as PSand PMMA is to place a very
slightly resilient mat between the plastic sheet and thetable. Very
hard rubber or heavy-gage UHMWPE works well. If the plastic
orrubber is too soft, the plastic may bind the cutting blade and
chipping, splitting anduncontrolled fracture may be aggravated.
Typically the force required to cut through a polymer sheet is
proportional to thecut length and the sheet thickness to some power
a,
Force a (cut length) x (sheet thickness)a (5.93)Since the crack
proceeds the cutting blade tip, the force required to cut through
abrittle polymer may be only weakly dependent on sheet
thickness.
For a ductile polymer and a blunt die, the deformation stress is
obtained directlyfrom the stress-strain curve. Since most polymers
strain harden to some extent in
Stre
ss
Deformation
Figure 5.42 Stress-strain curves for various typesof fracture in
a notch-sensitive ductile polymer[35]. Figure used with permission
of John Wiley &Sons, Inc.
Uniaxial Compression
Uniaxial Tension
Tension on a Notched Specimen
Trim Die
Polymer
-
Figure 5.44 Characteristic combined shear and compression punch-
and die-cutting of tough orductile polymer
compression, the force required to cut through a tough polymer
increases with thedepth of cut [36] and a 1:
Force oc (cut length) x (sheet thickness)1 (5.94)For ductile
polymers, a combination shear and compression die cut is used
(Fig.5.44). With this type of cut, the lower force of a shear cut
is combined with the stablecrack propagation at increasing
stress-strain of a compression cut. Heavy-gageplasticized PVC or
FPVC, HDPE and PP are cut in this way. Combination shearcutting
forces for several cutter blade designs are shown in Figs. 5.45 and
5.46 [37]for RPVC and PS, respectively. It is apparent that cutter
force is proportional tosheet thickness, or a = 1 in Equation 5.93.
Cutting forces for dull knives at 200C or680F are measurably higher
for polymers that yield, such as PVC, as seen in Table5.19. These
values compare well with blanking force guidelines for thin-gage
sheet(Table 5.20) [38]. Values for effective shear stress or
cutting force per unit thicknessand cutter length are about the
same as compressive yield stress values in Table 5.18.Cutting
forces at 600C or 1400F are about 10% lower than those at 200C or
68F.
Nibbling
Nibbling is a cyclic trimming process. An estimate of nibbling
force is made fromMode I tensile fracture crack propagation.
Example 5.17 illustrates this. As notedearlier, the force required
to initiate a crack is as much as 1000 times greater thanthat
needed to sustain it. Nibbling is a process requiring crack
initiation at eachstroke. Further additional force is required to
overcome friction between the nibbler
Trim Die
Polymer
Shear AnvilPinch Gap
-
Forc
e, 10
0 kg
f
Dulled Cutter
CutterDesign 4CutterDesign 3
SandwichCutter
RPVC
Thickness, mm
Figure 5.45 Experimental sheet thickness-dependent shearcutting
force for rigid polyvinyl chloride, RPVC, for severaltrim dies
[37]
Table 5.19 Shear Cutting Forces Data from Figs. 5.45 and 5.46
[37]Blade length = 10 in or 250 mm
Sheet thickness = 0.039 in or 1 mm
Polymer
PVC
PS
Bladedesign
# 3#4SandwichDull*#3#4SandwichDull**
Total force
(kgf)26002710310039002680268026802900
(Ib)
57205960682085805900590059006380
Cutting stress
(MPa)
104108124156107107107116
(10001bf/in2)
15.115.818.022.615.515.515.516.8
* Exhibits a "zero thickness" resistance of 1360 kgf or 2990
lbf, or an equivalent shear stressof 54 MPa or 7900 lbf/in2
** Exhibits a "zero thickness" resistance of 460 kgf or 1000
lbf, or an equivalent shear stressof 18 MPa or 2700 lbf/in2. In
addition, the force-thickness curve is nonlinear
-
blade and the plastic and to push the cut-off plastic piece from
the kerf. As withcompression cutters, a good first approximation of
the value of the cutting-off shearstress is the yield strength
value of the plastic (Table 5.18).
Example 5.17 Nibbling Force for PMMA
Thin-gage PMMA sheet, 0.025 in or 0.1 cm thick, is to be cut in
one cycle.Determine the force needed to sustain a crack. For PMMA,
Af= 0.1 (MN/m1/2)~mand m = 10.
Forc
e, 10
0 kg
f
Thickness, mmFigure 5.46 Experimental sheet thickness-dependent
shear cut-ting force for polystyrene, PS, for several trim dies
[37]
Table 5.20 Blanking Force Guidelines for 0.25 mm or 0.010 in
Sheet [38]
Nature ofpolymer
Soft
MediumHard,Tough
Type ofpolymer
Polyolefins,cellulosicsFlexible PVCOPS, PET, PSPMMA, RPVC
Force
(kgf/cm)
27
4691
(lbf/in)
150
250500
Total forcein 10 in or 25 cm
(kgf)680
11402280
(lbf)
1500
25005000
PS
Dulled Cutter
Sandwich CutterCutter Design 4
Cutter Design 3
-
From Equation 5.91, the stress intensity factor range is
obtained:AK = (da/dN)1/m-Af-1/m
Now da/dN>0.1 cm. Assume da/dN=l. Then AK =1.26 MN/m1/2. IfAK
= 0.5 Kc, the critical stress intensity factor for crack
propagation andC = 2, the tensile stress needed to sustain the
crack is given as:
a = ^ V ^ = 1-26 V*-0.001 = Q m M N / m 2 = 1Q 3 ^ 2
This is the tensile stress needed to propagate the crack. The
tensile yieldstress of PMMA is about 45 MN/m2 or 8500 lbf/in2.
Since nibble-cuttingshould require about the same expenditure of
force as compression-shearcutting, the apparent force needed to
sustain a crack in PMMA is onlyabout 0.1% of the total force needed
to cut the plastic.
Brittleness, Orientation and Trimming Temperature
Many brittle plastics exhibit uncontrolled fracture, secondary
crack propagation,reverse-side chipping, crazing and splitting when
compression or shear cut. Brittlefracture occurs when the brittle
strength of the polymer is less than its yield strength.The brittle
strength of a polymer below its glass transition temperature, Tg,
is weaklydependent on temperature over a wide range of temperature,
1000C or more. On theother hand, polymer yield stress is
essentially a linearly decreasing function oftemperature (Table
5.21) [35]. As the polymer temperature increases, the probabilityof
fracture at stresses below the yield stress decreases. The problems
associated withbrittle fracture trimming diminish as well. At
elevated temperatures approaching Tg,the polymer is ductile and
high-speed cutting-ofT techniques that depend on brittlefracture
crack propagation such as routering and sawing, become
inefficient.
Table 5.21 Temperature Effect on Yield Stress For Various
Polymers1
Polymer
PMMAPTFEPE*RPVCPP
PA 66APETPC
Linear region
(0C)50 to 100
-250 to -140- 6 0 to 20- 8 0 to 60- 4 0 to 20
-100 to 60- 2 0 to 60- 4 0 to 120
(0F)
122 to 212-420 to -220- 7 6 to 68
-112 to 140- 4 0 to 68
-150 to 140- 4 to 140
- 4 0 to 250
Temperature coefficientof yield stress
(MPa/C)
0.970.850.820.800.740.740.490.32
(lbf/in2 - 0F)
78.268.566.164.559.659.639.525.8
3 Adapted from [35], with permission of copyright owner
* Chlorinated polyethylene
-
Thermoformed shapes frequently have high degrees of orientation
in the trimareas. Part shape can enhance nonuniform orientation.
Cutting relieves local stresses.Although this aids crack
propagation to some degree, particularly in shear cutting, itcan
also cause: Nonuniform part dimensions, Binding of the cutting
tools, Part warping, and Part distortion.Secondary fracture effects
such as crazing can result. Uncontrolled crack propagationcan
proceed in the orientation direction rather than in the desired cut
path, or thecrack can meander. This results in splitting and
splintering, dust and angel hair.Highly nonuniformly oriented parts
of brittle polymers are frequently formed on hotmolds and then the
parts with the trim attached are partially annealed prior
totrimming. The trim is then cut away while the parts are still
warm. Heavy-gageamorphous polymers such as RPVC and ABS and easily
oriented crystalline polymerssuch as PA 66 and PP benefit by this
trimming approach.
As a general rule for all polymers, dust and angel hair problems
and part warpageand distortion may be minimized by increasing the
part temperature at the time oftrimming. Increasing trim die
temperature is usually ineffective. Part of the difficultyin
trimming with hot dies is in conduction heat transfer from the
heating source tothe cutting tip. The die is envisioned as a metal
fin. The effectiveness of conductionheat transfer to fins decreases
rapidly with the length-to-thickness ratio of the fin [39].This is
due primarily to convection heat transfer to the cool ambient
air:
where mL is given as:
mL = / ^ L (5.96)where h is the convection heat transfer
coefficient between the heated trim die and theambient air (Table
5.4), k is the thermal conductivity of the trim die steel, L is
thedistance between the heater and the cutting tip and t is the
thickness of the trim die.As is apparent in Fig. 5.47 [40], the
energy efficiency of heated dies decreases rapidlywith L/t ratio,
for both rectangular and tapered dies. In words, since heated dies
arevery inefficient heat transfer devices, it is usually difficult
to maintain cutting tips atthe proper temperature.
5.10 Steel Rule Die
As noted, the steel rule die is the most common method of
cutting prototype sheethaving thickness less than about 0.100 in or
2.5 mm. Steel rule dies are most effective
Next Page
Front MatterTable of Contents5. Cooling and Trimming the Part5.1
Introduction5.2 Overall Cooling Heat Balance5.3 Cooling the Formed
Shape5.4 Steady State Heat BalanceInterfacial ResistanceShape
FactorConvection Heat Transfer Coefficient
5.5 Cyclic Heat BalanceCooling the Free Surface of the
SheetCooling Thin Sheet in Ambient AirTransient Heat Removal from
the SheetQuiescent Ambient AirMoving Ambient AirCooling on
Nonmetallic Molds
5.6 Transient Heat Transfer during Sheet Cooling on the Mold
Surface - Computer ModelsInterfacial Air
5.7 ShrinkageUnconstrained ShrinkageConstrained Shrinkage
5.8 TrimmingTrimming Heavy-Gage PartsTrimming Thin-Gage
Parts
5.9 Mechanics of CuttingThe Trim RegionRegistering the Trim
SiteThe Nature of the CutFracture MechanicsMechanical
ChippingMultiple-Edged Tool or Toothed Saw PerformanceAbrasive
Cut-Off WheelToothless or Shear and Compression CuttingFracture
Mechanics in TrimmingNibblingBrittleness, Orientation and Trim
Temperature
5.10 Steel Rule DieResharpeningTabbing and Notching
5.11 Punch and Die TrimmingForged and Machined Dies
5.12 Drilling5.13 Other Cutting TechniquesThermal CuttingWater
Jet Cutting
5.14 Trimming - a Summary5.15 References
Index