# Shrinkage Measurement and Compensation Exercise for Injection

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```					Injection Molding of Polymers Lab and Mold Design Exercise
By Daniel Walczyk, 7/22/2010

This lab is broken up into two parts: Part 1 involves determining the shrinkage rate of different
polymers that are commonly injection molding into parts in the AML, and Part 2 involves
performing a paper design of an injection molding tool set and process. First, general
background information and manufacturing science dealing with the injection molding process
will be presented.

Injection Molding
Injection molding uses high pressure to deliver a metered amount of heated and
plasticized thermoplastic into a relatively cold mold, which solidifies the plastic material. The
process is shown schematically in Figure 1.

(a)

(b)
Figure 1 – (a) Cutaway view of an injection molding machine
[www.xcentricmold.com/images/injection-molding-machine.gif] and (b) details of the injection
molding cycle [www.milmour.com/milmour/injection_molding_images.asp].

Heat Required to Melt Plastic Pellets
The raw plastic, usually in pellet form, is heated by a rotating single-stage screw until
melted and then injected into the mold by axial movement of the screw. The heat required, Qmelt,
to melt plastic pellets of mass m from their starting temperature, Tp (may not be ambient), to the
melt temperature, Tm, can be estimated using
,
where: cp = specific heat capacity of the plastic. This relationship can be used to determine
whether or not the heater capacity of an injection molding machine is sufficient.
When a range of Tm values is given for a particular plastic, it is common to pick a melt
temperature in the middle of that range. For example, if the suggested range of temperatures
were 150-200°C, then Tm = 175°C would be a reasonable choice for the injection molding
machine.
Mold Clamping Force
As the mold is packed with molten plastic, the machine must provide sufficient clamping
force to prevent separation of the pressurized mold halves at the parting line, which if not
prevented, would result in excessive part flash. The minimum clamping force, Fclamping, can be
estimated by                                            ,
where: pi = maximum injection pressure and Ap = projected area of the molded part at the parting
line.
Plastic Shrinkage and Mold Expansion Compensation
In manufacturing processes, materials that undergo a phase change (i.e. from liquid to
solid) involve a decrease in specific volume and a resulting shrinkage. A certain amount of
shrinkage is inevitable in any process that involves cooling of plastic from elevated temperature
and this is certainly the case with injection molded polymers. The plastic packed into the mold
under high pressure shrinks from the time it solidifies at cooling to Tmelt (melting temperature of
the plastic) in the mold until reaching room temperature. The shrink rate, S, is used to scale
mold dimensions to compensate for shrinkage. Assuming perfectly isotropic shrinkage, the total
volumetric shrinkage rate of a material, Sv, is related to the linear shrinkage rate S by the
relationship
1
S = 1 − (1 − Sv ) 3
An often-used simplification of this relationship, based on neglecting higher order terms of the
Sv
binomial theorem expansion of (1 − S ) 3 , is    S≈
1
.
3
Hence, a material exhibiting 3% volumetric shrinkage should be undersize in all directions by
1.01% after cooling. Determining a single shrinkage compensation factor using either of the
preceding equations for S is suitable for most applications you will encounter in AML, although
this typically not needed because tables of S values are quite common.
Even though linear shrinkage rates are available for a wide range of plastics, the reported
values are usually given as a range. Shrinkage can vary based on material, processing, part
geometry, etc. Furthermore, shrinkage may vary in the direction of flow versus transverse
direction (anisotropic shrinkage). For example, Table 1 shows typical shrinkage rates for
different polymers. A common practice is to pick the S value in the middle of its reported range.

Table 1 – Common Linear Shrinkage Values (S) For Various Thermoplastics (from
www.gepolymerland.com/research/tech/tip97dec.html)
Material                Shrinkage (S) in inches/inch (per
ASTM D955)
ABS- High Impact                              .005 - .007
ABS- Medium Impact                         .005 - .008
ABS-High Heat                              .004 - .006
ACETAL                                     .020 - .035
ACRYLIC- General Purpose                   .002 - .009
ACRYLIC- High Flow                         .002 - .007
ACRYLIC- High Heat                         .003 - .010
ACRYLIC- Impact                            .004 - .008
NYLON- 6,6                                 .010 - .025
NYLON- 6                                   .007 - .015
NYLON- Glass Reinforced                    .005 - .010
POLYCARBONATE                              .005 - .007
POLYESTER .025 - .050 thick               .006 - .0012
POLYESTER .050 - .100 thick                .012 - .017
POLYESTER .100 - .180 thick                .016 - .022
POLYETHERIMIDE                             .005 - .007
POLYETHYLENE- LDPE                         .015 - .035
POLYETHYLENE- HDPE                         .015 - .030
POLYPROPYLENE                              .010 - .030
PPO®/HIPS (NORYL®)                         .005 - .007
POLYSTYRENE- Crystal                       .002 - .008
POLYSTYRENE- Impact                        .003 - .006
POLYURETHANE                               .010 - .020
PVC-RIGID                                  .002 - .004
PVC-FLEXIBLE                               .015 - .030
SAN                                        .002 - .006

To compensate for shrinkage, the cavity dimensions of an injection mold must be made
larger than the specified part dimension. The dimension of the cavity is then

where: Dc = dimension of cavity and Dp = molded part dimension. For example, if the length of
an injection molded polypropylene part is 5.0 inches, the corresponding cavity dimension using
the preceding equation and assuming a linear shrinkage value of 1.0% is 5.05 inches.
Since the mold is almost always heated, it experiences an expansion from room
temperature. Hence, the room temperature dimensions (Dca) of the mold must also compensate
for this expansion (i.e. be slightly undersized) using

where: α = coefficient of thermal expansion of tool material, Tmold = mold temperature, and
Tambient = ambient temperature.
It is clear that a mold shape must be designed for each combination of polymer to be injected and
the mold material. However, the mold dimensions calculated using S values from Table 1 and
the Dc and Dca equations above represent a gross simplification of the part shrinkage issue.
There are number of process factors that affect shrinkage, any of which change the amount of
contraction experienced by a particular polymer. The most important factors and affect they
have on part shrinkage are given below.
• Injection pressure – higher pressure forces more material into the mold cavity and
shrinkage is reduced.
•   Compaction time – assuming polymer in the gate does not freeze, more compaction time
allows more material to be forced into the mold cavity while shrinkage is taking place,
thereby reducing shrinkage.

•   Melt temperature – higher melt temperatures actually reduce shrinkage, since polymer melt
viscosity is lowered allowing more material to be packed into the mold.

•   Part thickness – Thicker parts shrink more, since there is more molten plastic to contract
inside the surface skin formed with thicker sections.
Mold Cycle Time
Mold cycle time can be estimated by considering the various actions that occur during
injection molding, as shown in Figure 1(b), using
,
where: topen/close = time required to open or close the molds before and after part ejection,
respectively; tf = mold fill time including pack and hold; tc = part cooling time after filling mold
with plastic; and te = part ejection time. Both topen/close and te are set at the injection molding
machine based on experience. However, minimum values for tf and tc can be estimated.
For a given flow rate (if not limited by the fluid dynamics of mold filling), the mold fill
time is

where: Vt = total fill volume of the part and runner system and Qt = total volumetric flow rate
from the injection molding machine (not to be confused with Q used for heat required).
Estimating the actual mold fill time, especially for a complicated part shape, will require
sophisticated simulation software such as Moldflow or SimTech, because of the complicated
physics involved (see Figure 2 for behavior of the melt front, for example) and uncertainty about
how long the mold must be packed at high pressure.
Cooling Lines

Melt Front

Velocity      Thickness
Frozen Layers          Profile

Fountain Flow

Figure 2 – Development of a solidified layer during injection mold filling

Cooling time depends on the maximum wall thickness in the injection molded part. An
estimate of the cooling time require for a part wall of thickness h is given by

where: αd = thermal diffusivity of the melt, Tm = melt temperature (temperature of the molten
plastic during injection) as before, Tmold = mold wall temperature (temperature that mold is
maintained at), and Te = desired ejection temperature of the part. The cooling load, Qcool, for a
heater/chiller unit to maintain the mold at a specific temperature, Tmold, can be estimated using
.
All variables in this equation have been previously defined.
Part Ejection Force
Ejection pins force the part out of the mold after the part has cooled and solidified
enough. As an injection molded part shrinks, it can literally form an interference fit around mold
cores, especially if the part draft angle is not sufficient. The ejection force, Fe, can be estimated
using                                               ,
where: µ = frictional coefficient, p = pressure and A = area at the interference interface.

PART 1 – Plastic Injection Mold Design and Analysis
Design the tooling and injection molding process to make two identical ABS parts (one shown
below in Figure 4 with all dimensions in centimeters) using a two-cavity mold. The mold will be
machined out of aluminum (α = 23×10-6/°C).. Relevant properties for high impact ABS include:
Injection molding temperature range = 180-260°C
Melting temperature = 105°C
S from Table 1
Recommended molding pressure pi = 100 MPa
αd = thermal diffusivity = 9×10-8 m2/sec
cp = 1470 J/(kgºC)
(a) What’s a reasonable injection molding temperature to use?
(b) Calculate and show the mold cavity dimensions (one cavity only at room temperature if
the temperature that mold walls are maintained at during production is Tmold = 60°C.
(c) Design a suitable mold set with two mold cavities including parting line, sprue, runner
system, gates, vent holes and ejector pin details. Hand-draw your final design
(dimensions not needed).
(d) What is the minimum clamping force required for the injection molding machine?
(e) Estimate how long (tc) it will take the part to cool down to an ejection temperature of
80°C.
(f) Estimate the heat required to melt the enough plastic for the two plastic parts (neglect
runner system for now) in the injection molding screw, and to cool the parts after
injection molding to their ejection temperature.
(g) Where do you expect the part to bind within the mold during ejection?
(h) What major part defect do you anticipate with this part? If the part didn’t have to be
solid, how could you minimize the defect?
Write a memo responding to each design question above (a-h) including all assumptions and
calculations.
Figure 4 – Dimensions (in centimeters) for injection molded ABS part.

PART 2 – Experimentally Determining Shrinkage Rate of Plastics
Part 1 of your Injection Molding of Polymers lab involves determining the shrinkage rate
of different polymers that are commonly injection molded into parts in the AML. To accurately
predict shrinkage in injection molded parts, accurate shrinkage rates for the plastic your AML
team will be using is required. This lab exercise allows you to experimentally determine
shrinkage rates for five common polymers using a statistically significant number of test
samples. Specifically, the length of injection molded tensile test specimens (ASTM D638), as
shown in Figure 3, will be measured. The five polymers and the order in which they will be
tested are listed in Table 2.

Specimen Length
Figure 3 – ASTM D638 tensile test specimen being used to measure polymer shrinkage values.

Table 2 – Polymers available in AML to be tested.
Polymer              Relative Melting
Temperature
Polypropylene                  Low
Polyethylene                  Low
ABS                     Medium
Acrylic                Medium-High
Polycarbonate                  High

Specific tasks for this lab exercise are as follows:

1. Measure the length dimension L in the AML tensile test specimen injection mold. Note
that this dimension will change as the mold is heated up due to the circulating water.
Based on the previous equation, the actual mold cavity length Lc during injection molding
will be                       Lc = L ⎡1 + α (Tmold − Tambient ) ⎤
⎣                          ⎦
where: α = coefficient of thermal expansion for aluminum mold = 12.8×10-6 1/ºF
Tmold = mold temperature in ºF (probably the heating water temperature)
Tambient = ambient temperature of the AML in ºF.

2. For a particular polymer, injection mold 30 standard tensile test specimens using the
AML mold. Measure the lengths of all 30 specimens after they cool to room temperature
using a Vernier Caliper, and calculate the average length Lave and standard deviation σL.

3. Calculate the shrinkage rate for the polymer S using the following equation:
L − Lave
S= c
Lc

4. Repeat Steps 1-3 for each polymer.

5. As a group, submit a 2-3 page memo that describes the results of the shrinkage rate
measurements, discusses the variability in the data as measured in Step 2, and includes all
of the raw measurement data.

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