2010 IPP Sensor Thicknesses

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7/30/2019 2010 IPP Sensor Thicknesses http://slidepdf.com/reader/full/2010-ipp-sensor-thicknesses 1/45 1 Validation of in-mold shrinkage sensor for different cavity thicknesses ABSTRACT The injection molding process is one of the most popular polymer processing techniques due to its versatility and mass production capability with complex geometries having higher quality at economical part cost for a wide range of the polymeric materials where nominal wall thickness of a convention injection molded part is considered between 2 to 4 mm. During the past decade, there has been much work done worldwide on an adaption of convention molding processes to thin wall molding, resulting in the emerging technology and capability to produce the parts with wall thickness less than 1.5 mm from variety of polymeric materials. Dimensional consistency is a critical attribute for injection molded part quality yet highly dependent on the polymer morphology, the thermal expansion, and various processing parameters. With a view to measure in-mold shrinkage, a button cell type in-mold shrinkage sensor was developed, validated, and compared against the traditional shrinkage estimation methods for two different wall thicknesses using an amorphous polymer, HIPS. The amorphous polymers show relatively isotropic shrinkage behavior but the flow and shrinkage dynamics of the same material is different for different wall thicknesses. The shrinkage sensor consists of an elastic deflectable diaphragm instrumented with strain gages connected in a full bridge circuit. The sensor diaphragm is deflected due to the melt pressure into the mold cavity and is retracted back towards its original Rahul R. Panchal* Department of Plastics Engineering University of Massachusetts Lowell 1 University Avenue, Lowell, MA 01854  David O. Kazmer Department of Plastics Engineering University of Massachusetts Lowell 1 University Avenue, Lowell, MA 01854 *Corresponding author: [email protected]

Transcript of 2010 IPP Sensor Thicknesses

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Validation of in-mold shrinkage sensor for different cavity thicknesses

ABSTRACT

The injection molding process is one of the most popular polymer processing techniques due to

its versatility and mass production capability with complex geometries having higher quality at

economical part cost for a wide range of the polymeric materials where nominal wall thickness of 

a convention injection molded part is considered between 2 to 4 mm. During the past decade,

there has been much work done worldwide on an adaption of convention molding processes to

thin wall molding, resulting in the emerging technology and capability to produce the parts with

wall thickness less than 1.5 mm from variety of polymeric materials. Dimensional consistency is

a critical attribute for injection molded part quality yet highly dependent on the polymer 

morphology, the thermal expansion, and various processing parameters. With a view to measure

in-mold shrinkage, a button cell type in-mold shrinkage sensor was developed, validated, and

compared against the traditional shrinkage estimation methods for two different wall thicknesses

using an amorphous polymer, HIPS. The amorphous polymers show relatively isotropic

shrinkage behavior but the flow and shrinkage dynamics of the same material is different for 

different wall thicknesses. The shrinkage sensor consists of an elastic deflectable diaphragm

instrumented with strain gages connected in a full bridge circuit. The sensor diaphragm is

deflected due to the melt pressure into the mold cavity and is retracted back towards its original

Rahul R. Panchal*

Department of Plastics Engineering

University of Massachusetts Lowell1 University Avenue, Lowell, MA 01854 

David O. Kazmer 

Department of Plastics Engineering

University of Massachusetts Lowell1 University Avenue, Lowell, MA 01854 

*Corresponding author: [email protected]

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 position as the melt solidifies and shrinks away from the mold cavity wall. The sensor signals

acquired during each molding cycle are analyzed to validate the sensor performance in a design

of experiments as a function of packing pressure, packing time, melts temperature, cooling time

and coolant temperature. High impact polystyrene was selected material for the sensor validation.

For HIPS, the shrinkage sensor is able to measure the shrinkage with a mean absolute percentage

error of 0.6867 and 0.5688 for molded parts with a nominal thickness of 2.5 mm and 1.5 mm

respectively. With 2.5 mm cavity thickness, the coefficient of correlation,  R2, to the final part

thickness for HIPS was 0.939 and with 1.5 mm cavity thickness, the coefficient of correlation,

 R2, to the final part thickness for HIPS was 0.966 for the in-mold shrinkage sensor. Also, the

observed main effects for the in-mold shrinkage sensor validate common shrinkage guidelines.

INTRODUCTION

The dimensional and the aesthetic quality of the injection molded parts are directly influenced by

the tool design, the material characteristics, and process induced effects like ―shrinkage‖. The

shrinkage mainly depends on the polymer morphology, the thermal expansion, the cooling rate of 

the polymer melt to the solid state, especially for semi-crystalline materials, and the temperature

difference between the melt to the solid state temperature and other various process parameters

during the processing [1-11]. The shrinkage value for many plastics materials (in order of 0.6%)

are high relative to dimensional tolerances (in order of 0.2%) and the shrinkage is not always

isotropic in nature. Shrinkage varies with the part geometry and processing conditions but is

commonly assumed during part and mold design. As a result, errors in shrinkage can limit the

achievable part tolerances, require increased cycle time, and incur excessive rejection rates.

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Anisotropic shrinkage behavior can also lead to a degree of warpage (out-of-plane distortion) or 

internal stresses [1-3, 12-17].

Due to continuing demand for higher quality requirements with fewer rejections and

faster process cycle time, the plastics industry has observed continual innovations in the injection

molding technology [18-22]. One of the recent trends is on-line process monitoring to achieve

more robust process control. But still there is no technology or research available to directly

monitor the shrinkage on-line during the production in order to improve, optimize, and control

the part dimensions. This article describes the design and implementation of a button-cell type

sensor which can be placed underneath the ejector pin within the ejector assembly in order to

monitor and predict the in-mold shrinkage during the injection molding cycle.

PREVIOUS RESEARCH

There has been increasing recognition that the measurement and control of the polymer state

within the mold cavity is vital to product quality. Accordingly, there has been a proliferation of 

cavity pressure sensors based on load cells, strain gages, and piezoelectric materials [23,24].

Concurrently, other methods have been developed for measuring melt temperature in the mold

including infrared sensors [25,26] and thermocouples [26-28]; ultrasonic methods have also been

developed to detect the presence and solidification of the melt in the mold cavity [29-31].

Sensor fusion approaches have incorporated multiple sensor streams with on-line and/or 

 post-molding analyses to predict the part dimensions. The approaches are most often either 

mechanistic or statistical. Mechanistic approaches vary in complexity from relatively simple

analysis of pressure-volume-temperature relations [32-35] to complex thermo viscoelastic

modeling of residual stress relaxation [36-40]. Statistical models frequently rely on regression

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[41-43], neural networks [44-46], or other methods [47-49]. While these models are helpful

initially to assist process set-up, they are not sufficiently accurate for real time process assistance

or quality monitoring and control. Accordingly, there is currently no reliable method to detect and

compensate any sudden variations in the process parameters during the processing.

The closest known work to this research is that of Anthony Bur of NIST and Charles

Thomas of the University of Utah [50-52], who developed and patented an optical fiber sensor 

inserted into the ejector pin channel of a mold using an ejector pin sleeve with a sapphire

window at its end. The sapphire window was positioned flush with the wall of the mold; the fiber 

optic cable consisted of a bundle of nineteen 100 m diameter fibers, seven of which carried light

from a helium-neon laser and twelve of which transmitted reflected light back to a silicon

 photodiode. In operation, incident light was transmitted through the resin and then reflected back 

to the detector from every boundary at which there was a discontinuity in the index of refraction.

During the molding cycle, the detected light was analyzed to: 1) detect the arrival of the polymer 

melt, 2) detect separation of the resin from the mold wall upon shrinkage, and 3) monitor the

molded part shrinkage. While this research effort is to be commended, the size, cost, and

maintenance issues associated with the implemented designs prevent widespread adoption for in-

mold shrinkage measurement.

SHRINKAGE INSTRUMENTATION

The implemented sensor design for measuring in-mold shrinkage and cavity pressure is shown in

Figure 1. In this application, the implemented sensor is placed beneath a movable pin, and causes

the movable pin to protrude slightly when the mold is opened. After the mold is closed, the melt

 pressure exerted on the top surface of the movable pin causes the sensor to be fully actuated and

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impose strain on the diaphragm. As the melt in the cavity cools and shrinks, the melt pressure

will decay and the molded part will draw away from the cavity walls. The reaction force provided

 by the sensor diaphragm will cause the ejector pin to maintain contact with the face of the

molded part and provide a measurable relaxation of the imposed strain in the diaphragm.

The structural design of the sensor is initially guided by plate bending theory [53] which

states that the maximum stress,  , and deflection,  , of the diaphragm are:

where  P melt  is the melt pressure,   pin is the ejector pin diameter,  diaphragm is the diaphragm

diameter, hdiaphragm is the diaphragm thickness,  E  is the elastic modulus, and the coefficients k 1 

and k 2 are related to the aspect ratio and constraints of the diaphragm. Similar analyses apply for 

different sensor geometries as well as non-round ejectors, such as ejector blades etc. The voltage

output, V  , from a Wheatstone bridge of four strain gages is a function of the ejector pin

deflection:

3 g eV k S V      

Equation 3

where S  g  is the gage factor, V e is the excitation voltage, and k 3 is a coefficient relating the

diaphragm deflection to the imposed strain in the strain gages.

2

1 2

melt pin

diaphragm

 P k 

h

    

Equation 12 2

2 3

melt pin diaphragm

diaphragm

 P k 

 Eh

    

Equation 2

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SHRINKAGE PREDICTION METHODS

The in-mold shrinkage can be predicted and estimated from traditional analysis. The simplest

model considers the shrinkage, s, as [3]:

 final eject  T T  s    

Equation 4

where    is the polymeric material’s coefficient of thermal expansion, T eject  is the ejection

temperature of the molded part upon ejection from the mold, and T  final  is the end use temperature

of the molding.

This model will typically over predict the shrinkage since it does not consider the

compressive stresses that develop during the filling and packing stages of the molding process. In

 particular, this model does not consider the expansive state of the melt caused by the melt

 pressure, which will tend to prevent the polymer from exhibiting any shrinkage until this pressure

is relieved.

Several researchers [8-14] have described a slightly more complex model based on

 pressure-volume-temperature ( P-v-T ) data of characterized materials. Plastics materials have

 positive coefficients of thermal expansion, and are highly compressible in the molten state. As a

result, the volume of a given mass of plastic material changes with both pressure and

temperature. The Spencer and Gilmore equation of state describes the expansion and contraction

of amorphous polystyrene [1-6]:

 M  RT bva P  ))((  

Equation 5

where P is the hydrostatic pressure, v is the specific volume, R is the universal gas constant, M is

molecular weight, T is the absolute temperature, a and b are material constants.

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From Equation 5, it can be observed that pressure, specific volume, temperature are

dependent to each other and the specific volume can be determined at any pressure and

temperature conditions. From the  P-v-T behavior it can be observed that increasing temperature

at constant pressure increases the specific volume due to positive thermal expansion and in the

same way increasing pressure at constant temperature decreases the specific volume due to

relatively higher compressibility.

The  P-v-T  behavior of the polymer melt can be modeled by the double domain Tait

equation, which specifies the specific volume, v (T, P), as a function of the melt’s pressure and

temperature (refer  Equation 7Error! Reference source not found.  & Equation 8Error!

Reference source not found.) [2-3]. The transition temperature, T t between solid and melt states

is a function of pressure,

 P bb P T t  65)(  

Equation 6

if  T < T t 

Specific Volume, )( 5,2,1 bT bbv  s so

 

Compressibility, ))(exp()( 5,4,3 bT bbT  B  s s  

if  T > T t 

Specific Volume, )( 5,2,1 bT bbv mmo  

Compressibility, ))(exp()( 5,4,3 bT bbT  B mm  

),()(

1ln0894.01)(),( P T vT  B

 P T v P T v T o

 

  

  

  

   

Equation 7

)))((exp(),( 987 P b P T T bb P T v t T   

Equation 8

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where b5 is the transition temperature at zero pressure, b6  is the rate of change of the transition

temperature with respect to pressure, b1…4,s and b1…4,m are material coefficients related to the

material properties in the solid and melt state respectively. The term vT  represents the additional

specific volume associated with the transition of semi-crystalline polymers from their closely

 packed semi-crystalline state to more loosely packed amorphous state.

The volumetric shrinkage of the molded part can be predicted by imposing the known

 processing conditions over the  P-v-T  behavior of the plastics. During plastication, the melt’s

specific volume increases due to the thermal expansion with temperature rise. Generally, the

cavity fills at a high flow rate hence the melt temperature remains almost constant during the

filling stage but the increasing injection pressure causes a reduction in the specific volume of the

melt flowing into the cavity. Then, the specific volume of the plastic melt continues to decrease

as the hot melt begins to cool down when it enters and flows in the relatively cool mold. This

reduction in the specific volume is generally compensated by packing additional material into the

cavity until the gate is completely frozen off at lower pressure and temperature than the filling

stage which in turn further reduces in the specific volume of the melt. Once the gate is frozen off,

additional melt cannot be pushed through the gate into the cavity and as the melt pressure decays

the melt continues to cool down to the ejection temperature. Accordingly the specific volume of 

the melt continues to decrease while the melt enters into a solid state where the plastic becomes

sufficiently rigid to sustain the ejection forces. At the time of ejection, the part volume is usually

less than the mold cavity and the part will continue to shrink until the part temperature reaches

ambient conditions. The isotropic linear shrinkage can be predicted and controlled by using

Equation 9 if the melt’s pressure, temperature, and specific volume history during a molding

cycle are known [3].

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3

 _  _ 

 _ 

),(

),(1

useend  flowend 

 pack  flowno

 P T v

 P T v s  

Equation 9 

where, s is the molded shrinkage, v(T no_flow , P  pack  ) is the specific volume of the plastic at the end

of the packing stage, v(T end_flow , P end_use ) is the specific volume of the plastic during end use of 

the molded part.

EXPERIMENTAL WORK

Experimentation with the shrinkage sensor was performed to understand and validate the sensor 

 behavior during the injection molding cycle. Statistical analysis of the resulting shrinkage

 behavior is compared with cavity pressure data.

 Methodology

A four cavity plaque mold and 100 ton toggle type hydraulic injection molding machine

were used to validate the shrinkage sensor (refer  Table 1). All the mold cavities have different

wall thicknesses, 228.25 mm length and 38.1 mm width (refer Figure 2). For these experiments,

the cavity with 1.5 mm and 2.5 mm thicknesses were used where the shrinkage sensor and the

cavity pressure sensor were placed at the middle of the cavity length as shown in Figure 3. High

impact polystyrene was selected for the trials as detailed in Table 2. 

Four 350 ohm transducer class strain gages (SGT-1/350/TY11, Omega Engineering Inc.)

were wired as a full Wheatstone bridge to measure the strain on the shrinkage sensor as

configured according to Figure 1. The signals from the injection molding machine, the shrinkage

sensor, and the cavity pressure sensor were acquired using an RJG eDart system with a sampling

time of 5 milliseconds.

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 Data Collection

For real time data acquisition during the molding cycle, the machine signals for the screw

 position, ram velocity, mold open and close, machine hydraulic pressure were connected to an

RJG eDart system. Also, the shrinkage sensor and the cavity pressure sensor were connected to the

eDart system using RJG strain gage sensor adapters. RJG eDart system converted all the analog

signals into digital form generated from all the connected sensors with a graphical user interface

(refer  Figure 4). This process data was stored in the computer for further post processing

 purposes.

 Experimental Approach

A sixteen run design of experiments (DOE) as shown in the Table 4 was implemented

with a semi-automatic cycle using HIPS for 1.5 mm and 2.5 mm cavity thickness. The DOEs are

half-fractional designs with five processing factors. The shot size was set using the short-shot

method for each material to just fill the mold cavity prior to switching to the packing stage.

For each DOE run, five cycles of data and samples were collected after the process had

stabilized. The screw position, screw velocity, hydraulic pressure and mold open-close signals

from the molding machine as well the shrinkage and the cavity pressure sensors data were

obtained from the RJG eDart system to the computer for each cycle. The molded parts’ thickness

was measured at the gate, the shrinkage sensor, the cavity pressure sensor and at the end of flow.

The machine and sensors voltage signals were calibrated before starting the experimentation and

converted into actual values by eDart system in a tabular form.

MATLAB routines were developed to:

 –   Synchronize RJG data sets according to injected volume and start of injection signals,

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 –   Apply light filtering to strain gage data to remove signal noise,

 –   Detect the arrival of the polymer melt at sensors in the cavity,

 –   Identify the maximum shrinkage sensor position,

 –   Identify the shrinkage sensor position just prior to mold opening

 –   Check and eliminate outliers

 –   Perform regression of key process and quality relations. Regression results were applied

to compare the predictive capability of the developed sensor against conventional cavity

 pressure transducer and to compare the shrinkage sensor performance for both selected

materials.

RESULTS

Figure 5 and Figure 6 show the in-mold shrinkage and cavity pressure profiles respectively

during the injection molding cycle for run 1 of the DOE for both the thicknesses. It can be seen

from the Figure 5 and Figure 6 that the melt entered into the cavity and reached the shrinkage

sensor and the cavity pressure sensor location at point where the shrinkage sensor diaphragm

was still unstrained. As soon as the pressurized melt contacted the shrinkage sensor pin, the

sensor diaphragm experienced deflection in the backward direction under the force acting on the

sensor pin due to the melt pressure up to point which represents the maximum strained

 position of the sensor diaphragm due to the peak melt pressure within the cavity. The sensor 

diaphragm remained at the same position for a period of time during the packing and holding

 phase as the pressurized skin of the molded part prevents the extension of the sensor pin towards

the mold cavity.

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The melt cools down during the packing phase up to the end of cooling phase of the

molding cycle. As the melt cools, the plastic melt starts to shrink. Due to the shrinkage, the

 polymer melt starts to separate away from the mold cavity wall, which in turn results in the cavity

 pressure decay and the cavity pressure gradually reaches to point from point . After the

molded part gradually retracts from the mold wall, and the sensor diaphragm extends the sensor 

 pin up to point . During the entire molding cycle the plastic remains in contact with the sensor 

 pin, retracting and extending with the arrival of the melt and subsequent shrinkage under the melt

 pressure. Hence, the difference between points to represents the total in-mold shrinkage the

 plastic experienced during the molding cycle. But as soon as the polymer melt solidifies and

separates totally away from the mold cavity wall at the end of cooling stage the cavity pressure

reaches atmospheric pressure which can be seen from point and point . During the mold

opening, there was no force acting on the sensor pin and the sensor diaphragm extends to its

original position at point . After the mold opening, the part was ejected from the mold at point

. The shrinkage sensor behaved in a similar manner for different processing parameters with

respect to set DOE.

ANALYSIS

As mentioned in the previous section, the in-mold and post-mold shrinkages for each cycle were

calculated from the cavity pressure data for each molding cycle using the P-v-T model data of the

 particular polymeric material. The Ballman-Shusman equation [1-3, 14, 54] for plates was used to

estimate the average temperature of the polymer at the centerline within the cavity during the

molding cycle (refer Equation 10 & Equation 11). Equation 10 estimates the time required to cool

down the polymer melt at particular temperature with respect to the selected processing melt

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temperature, T m and mold coolant temperature, T w. The same equation can be used to calculate the

cooling time or cycle time for the injection molding cycle with respect to the desired ejection

temperature. It can be seen that the time required to cool down the same polymer melt at any

 particular temperature will be less in case of the molded part having thinner wall thickness

compared to thicker wall thickness. Equation 11 is derived from Equation 10 to estimate the melt

temperature within the cavity at any time instance. The double domain Tait equation was used to

calculate the specific volume of the polymer with respect to the cavity pressure and estimated melt

temperature during the cycle. Figure 7 and Figure 8 Error! Reference source not found.show the

typical temperature profile and P-v-T curve of the polymer during the molding cycle.

wt 

wm

T T 

T T ht 

    

4ln

2

2

 

Equation 10

w

wm

t T 

h

T T T 

 

  

 

2

2..exp

4

     

 

Equation 11

where t is the real time during the molding, h is the cavity thickness, α is thermal diffusitivity of 

the polymer which are 0.0816 mm2/sec for selected grades of HIPS, T m  is the processing melt

temperature of the polymer, T w  is the mold coolant temperature, T t   is the average melt

temperature of the polymer within the cavity at particular time instance during the molding cycle.

As shown in Figure 5 and Figure 6, the filling, the maximum cavity pressure, end of 

cooling, and the mold open stages were identified from the shrinkage sensor data and the cavity

 pressure data. Figure 7 and Figure 8Error! Reference source not found.  show the estimated

temperature and specific volume for the same cycle plotted in Figure 5 and Figure 6. From Figure

7 and Figure 8, it can be seen that during the filling stage the melt entered into the cavity at point

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and reached to point with small change in a melt temperature. Because of the higher melt

 pressure, the specific volume of the melt reduces significantly due to compressibility as modeled

 by Equation 7. The polymer melt experiences higher temperature drop and the compressibility

within the thin cavity (1.5 mm) compared to the thick cavity (2.5 mm) because of the smaller 

cross section area of the cavity for the thin cavity thickness. During filling stage, as the hot melt

comes in contact with the cooled mold wall thickness the frozen layer thickness grows faster for 

the thin cavity compared to the thick cavity due to faster heat transfer rate (refer  Equation 11 &

Figure 7) which further reduces the available cross sectional area to flow the polymer melt

following within the cavity. Hence, the parts with thinner wall thicknesses require to be filled

with faster injection velocity and higher injection pressure so they can be filled before the cavity

freezes off. From Figure 8, it can be seen that during the filling stage the thick cavity shows

lower change in the specific volume compared to the thin cavity due to faster melt temperature

decay and higher filling pressure within the thin cavity. At point , the machine switched over 

to the packing stage and continued to the cooling stage where point represents the end of 

cooling stage. During the packing stage the melt pressure was lower than the peak pressure which

in turn lowered the compressibility of the melt. The pressure still continued to decay until it

reached to the atmospheric pressure as the melt pulled away from the cavity wall upon the melt

solidification but at the same time the melt temperature started to decay due to the cooling effect

where the temperature decay mainly depends on the thermal properties of the polymer further 

reduces the specific volume of the melt. From Figure 8, it can be seen that during the packing

stage both the cavities show similar change in the specific volume with respect to the change in

 pressure and temperature also the polymer melt shows the similar  P-v-T behavior for both the

cavity thicknesses with the same polymer. But, overall change in the specific volume is lower in

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case of the thin cavity compared to the thick cavity which indicates comparatively lower 

shrinkage with the thin cavity. The difference between the specific volumes at point and

 point represents the in-mold volumetric shrinkage that the plastics experienced during the

injection molding cycle, though the shrinkage sensor cannot monitor the shrinkage after point.

The mold started opening at point and the part was ejected at point out of the mold during

this the part still continued to cool down to the temperature above the room temperature. But in

case of the thin cavity the part temperature at ejection is lower than the thick cavity because

higher heat transfers. After ejection, the part still continues to cool down until it reaches to the

room temperature and reduces the specific volume of the plastics. This volumetric change

represents the post mold shrinkage.

Isotropic linear in-mold shrinkage was calculated using Equation 9 from the  P-v-T curve

of the molding cycle where the no-flow temperature for the selected grade of HIPS is 95°C. Table

5 and Table 6 show the average, µ, and standard deviation, σ  , of the shrinkage values predicted

from the cavity pressure data and temperature estimate as well as the measured shrinkage from the

shrinkage sensor. As mentioned earlier, five replicates were performed at each run condition to

collect the experimental data.

DISCUSSION

The shrinkage sensor position was calculated from the sensor output signals for each molding

cycle. Figure 5 shows the typical sensor pin displacement with respect to the sensor diaphragm

deflection for a run of the DOE. This calculation is based on the maximum allowable shrinkage

sensor diaphragm deflection (0.52 mm) and the actual sensor diaphragm deflection during each

stage of the molding cycle. The actual sensor position with respect to the time indicates the real

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time change in the volume of the plastic cooling from the melt state to the solid state as well

from amorphous melt phase to the semi-crystalline solid phase upon. By comparison, the cavity

 pressure transducer data (refer Figure 6) provides information about the melt pressure within the

cavity only until the plastic pulls away from the mold wall. The cavity pressure data can be used

to predict the volumetric shrinkage using P-v-T behavior as mentioned earlier. But the shrinkage

 prediction using cavity pressure data is not very accurate and only gives indirect estimation of the

shrinkage.

Regression analyses were carried out for the shrinkage sensor with respect to the part

thickness measured at four different locations as shown in Figure 3 for both cavity thicknesses.

Figure 9 shows the regression results for the part thickness at the sensor location versus the

measured in-mold shrinkage from the shrinkage sensor for the thin cavity (1.5mm). The sensor 

 positions were calculated from the sensor travel during the molding cycle and the actual pin

indentation within the cavity. The sensor final position was the pin indentation/protrusion at the

end of the cooling stage of the molding cycle. The horizontal and vertical error bars indicate the

standard deviation of the observed in-mold shrinkage and measured part thickness respectively.

The R 2

value of the regression analysis is 0.966 which indicates very good correlation and ability

of the shrinkage sensor to measure the part thickness and final in-mold shrinkage. As discussed

earlier, being an amorphous material, HIPS shows relatively higher isotropic shrinkage and lower 

change even for the smaller cavity thickness, which allows the shrinkage sensor to measure the

final in-mold shrinkage at higher accuracy that can be estimated from cavity pressure data [55]. 

Figure 10 shows the main effects from regression analysis with respect to the performed

DOE for the thin cavity. The main effect regression analysis was carried out for the actual

shrinkage and measured shrinkage from the shrinkage sensor, and the using  P-v-T  relationship.

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The actual shrinkage is calculated taking the difference between the actual cavity thickness of 1.5

mm to the part thickness at the cavity pressure sensor. From the figure it can be seen that the

shrinkage sensor showed very similar shrinkage behavior as the theoretical processing guidelines

[1-6] compared to the shrinkage calculated using  P-v-T  relationship. According to standard

 processing guidelines, shrinkage increases with melt temperature, coolant temperature and cooling

time whereas the shrinkage decreases with increasing hold pressure, and time. The same behavior 

was observed for the measured shrinkage from the shrinkage sensor data which can also be

verified from the actual shrinkage behavior with respect the process conditions.

Figure 11 shows the regression results for the part thickness at the sensor location versus

the sensor final position for the thick cavity (2.5 mm). The sensor positions were calculated from

the sensor travel during the molding cycle and the actual pin indentation within the cavity. The

sensor final position was the pin indentation/protrusion at the end of the cooling stage of the

molding cycle. The horizontal and vertical error bars indicate the standard deviation of the

observed in-mold shrinkage and measured part thickness respectively. The R 2

value of the

regression analysis is 0.939 which indicates very good correlation and ability of the shrinkage

sensor to measure the part thickness/ final in-mold shrinkage at higher accuracy.

Figure 12 shows the main effect regression analysis with respect to the performed DOE for 

the thick cavity. The main effect regression analysis was carried out for the actual shrinkage and

measured shrinkage from the shrinkage sensor, and the using  P-v-T  relationship. The actual

shrinkage is calculated taking the difference between the actual cavity thickness of 2.5 mm to the

 part thickness at the cavity pressure sensor. From the figure it can be seen that the shrinkage

sensor showed the very similar shrinkage behavior as the theoretical processing guidelines [1-6]

compare to the shrinkage calculated using  P-v-T  relationship. According to standard processing

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guideline, shrinkage increases with melt temperature, coolant temperature and cooling time

whereas the shrinkage decreases with increasing hold pressure, and time. The same behavior was

observed for the measured shrinkage from the shrinkage sensor data which can also be verified

from the actual shrinkage behavior with respect the process conditions.

From, the error bars in Figure 9 and Figure 11 can be seen that the shrinkage sensor 

 performed very consistently and accurately having smaller deviation for both the materials. The

larger error bars for the thickness values might only be due to human error or the molded parts

might have reached to the ambient conditions at different rate and showed deviation in the part

thickness for different cycle of each run.

CONCLUSIONS

The developed shrinkage sensor was successfully validated for different cavity thicknesses. For 

 both the cavity thicknesses, the shrinkage sensor showed very good results and capability to

monitor and measure the real time in-mold shrinkage. The shrinkage sensor outperformed the

cavity pressure correlation at all the thickness measurements. The monitored shrinkage values

can be used to predict the post-molding shrinkage knowing the ejection temperature and material

thermal expansion co-efficient. This could also be used to optimize the part annealing conditions

or processing conditions with respect to end use conditions of the molded part which can be very

useful in injection molding to achieve higher dimensional precision and accuracy. Future research

will characterize a variety of polymeric materials especially different amorphous and semi-

crystalline polymers as well polymer based compounds, blends and alloys especially the

materials for which no  P-v-T  behavior or theoretical shrinkage range is fully established.

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However, the sensor strains were very low and no evidence of the wear or the plastic deformation

of the diaphragm was observed from the sensor traces.

ACKNOWLEDGMENTS

Portions of this work were funded by the National Science Foundation Division of Design,

Manufacturing, and Industrial Innovation, Grant No. 02-045309. The contents of this paper do not

represent the opinions of the National Science Foundation or the United States Government. The

authors are highly thankful to RJG Inc. for providing eDart system, strain gage sensor adapters

and necessary accessories. The authors also thank Dr. Stephen Johnston for his assistance with the

RJG eDart system. The authors are highly thankful to “Tripathy Memorial Summer Graduate

 Fellowship” for selecting Mr. Rahul R. Panchal as an outstanding research fellowship recipient

for 2008.

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List of Tables

Table 1: Specification of Injection Machine ................................................................................. 28 Table 2: Specification of Material ................................................................................................. 29 Table 3: Specification of Cavity Pressure Transducer .................................................................. 30 Table 4: Design of Experiments for HIPS..................................................................................... 31 Table 5: Predicted, Monitored and Observed Shrinkage Values for Thin Cavity (1.5mm) .......... 32 Table 6: Predicted, Measured and Observed Shrinkage Values for Thick Cavity (2.5 mm) ......... 33 

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List of Figures

Figure 1: Implemented sensor design ........................................................................................... 34 Figure 2: Four cavity plaque mold ................................................................................................ 35 Figure 3: Thickness measurement location on plaque .................................................................. 36 Figure 4: Setup for real time data acquisition ............................................................................... 37 Figure 5: Typical shrinkage sensor data profile ............................................................................ 38 Figure 6: Cavity pressure transducer data profile ......................................................................... 39 Figure 7: Melt temperature profile for a molding cycle ................................................................ 40 Figure 8: P-v-T data curves of the polymers for the molding cycle .............................................. 41 Figure 9: Shrinkage correlation for thin cavity ............................................................................. 42 Figure 10: Effect of process parameters on the shrinkage of thin cavity ...................................... 43 Figure 11: Shrinkage correlation for thick cavity ......................................................................... 44 Figure 12: Effect of process parameters on the shrinkage for thick cavity ................................... 45 

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Tables

Table 1: Specification of Injection Machine

Equipment Type Injection Molding

Manufacturer Cincinnati Milacron

Machine Code T100

Serial Number 4061A21/84-26

Clamp Type Toggle/ Hydraulic

Clamp Force 100 Ton

Screw Diameter 41.275 mm

Intensification Ratio 10 : 1

Barrel Capacity 352g (GPPS)

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Table 2: Specification of Material

Resin High Impact Polystyrene (HIPS)

Grade 550-11

Supplier American Polymers

Type Amorphous

Density 1.04 g/cc (ASTM D792)

Melt Flow 12.0 g/10 min (ASTM D1238)

Shrinkage 0.005-0.0065 (mm/mm)

Thermal Diffusitivity 0.081665 mm2/sec

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Table 3: Specification of Cavity Pressure Transducer

Equipment Type Cavity Pressure Sensor 

Manufacturer DYNISCO

Product Code PT449

Type Wheatstone bridge strain gage

Pressure Range 0 - 138 MPa

Socket Type 6 pin

Pin Diameter 6 mm

Input 0-10 volts

Output 1.5-1.6 mV/V

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Table 4: Design of Experiments for HIPS

DOE

RUN

Melt

Temp, °C

Coolant

Temp, °C

Cooling

Time, sec

Hold

Pressure, %

Hold Time,

sec

1 240 40 10 20 15

2 240 40 10 40 103 240 40 20 20 10

4 240 40 20 40 15

5 240 60 10 20 10

6 240 60 10 40 15

7 240 60 20 20 15

8 240 60 20 40 10

9 255 40 10 20 10

10 255 40 10 40 15

11 255 40 20 20 15

12 255 40 20 40 10

13 255 60 10 20 15

14 255 60 10 40 10

15 255 60 20 20 10

16 255 60 20 40 15

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Table 5: Predicted, Monitored and Observed Shrinkage Values for Thin Cavity (1.5mm)

Run

HIPS

In-Mold from PVT In-Mold from Sensor Observed

µ σ µ σ µ σ 

1 0.0076 0.0000 0.1129 0.0497 0.1030 0.0000

2 0.0076 0.0000 0.0556 0.0180 0.0940 0.0053

3 0.0076 0.0000 0.2253 0.0234 0.1290 0.0062

4 0.0076 0.0000 0.0761 0.0048 0.1038 0.0013

5 0.0048 0.0000 0.0799 0.0252 0.1030 0.0014

6 0.0048 0.0000 0.0348 0.0079 0.0895 0.0017

7 0.0048 0.0000 0.0513 0.0181 0.0977 0.0025

8 0.0048 0.0000 0.0578 0.0253 0.0980 0.0000

9 0.0076 0.0000 0.3857 0.0183 0.1955 0.0019

10 0.0076 0.0000 0.2611 0.0160 0.1600 0.0030

11 0.0076 0.0000 0.4063 0.0103 0.1990 0.002912 0.0076 0.0000 0.2216 0.0453 0.1690 0.0008

13 0.0048 0.0000 0.3296 0.0314 0.1795 0.0007

14 0.0048 0.0000 0.0778 0.0375 0.1030 0.0012

15 0.0048 0.0000 0.3895 0.0245 0.1883 0.0022

16 0.0048 0.0000 0.2514 0.0332 0.1608 0.0010

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Table 6: Predicted, Measured and Observed Shrinkage Values for Thick Cavity (2.5 mm)

Run

PP

In-Mold from PVT In-Mold from Sensor Observed

µ σ µ σ µ σ 

1 0.0115 9.70E-06 0.4925 0.0001 0.3190 0.0079

2 0.0089 2.59E-05 0.0683 0.0052 0.2398 0.0059

3 0.0124 2.73E-05 0.5002 0.0150 0.2993 0.0090

4 0.0118 1.82E-05 0.0654 0.0041 0.2520 0.0014

5 0.0051 8.06E-06 0.5030 0.0070 0.3193 0.0080

6 0.0064 8.72E-05 0.1029 0.0060 0.2557 0.0047

7 0.0081 2.00E-05 0.5559 0.0059 0.3058 0.0028

8 0.0074 1.06E-04 0.1569 0.0152 0.2563 0.0028

9 0.0093 7.49E-06 0.5484 0.0041 0.3267 0.0015

10 0.0102 2.04E-05 0.0481 0.0141 0.2562 0.0054

11 0.0129 1.08E-05 0.5460 0.0008 0.3258 0.006312 0.0111 3.65E-05 0.0249 0.0050 0.2463 0.0019

13 0.0071 6.65E-04 0.5806 0.0038 0.3343 0.0025

14 0.0042 3.78E-05 0.0609 0.0126 0.2457 0.0040

15 0.0075 8.27E-06 0.5798 0.0149 0.3343 0.0055

16 0.0072 7.15E-06 0.0403 0.0027 0.2600 0.0034

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Figures

Figure 1: Implemented sensor design

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Figure 2: Four cavity plaque mold

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ShrinkageSensor 

 Figure 3: Thickness measurement location on plaque

38.1

T

228.25

T for thick cavity = 2.5 mmT for thin cavity = 1.5 mm

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RJG eDART system

RJG Sensor Adaptors

   F  r  o  m    M

  o   l   d   –

   S   h  r   i  n   k  a  g  e  a  n   d   C  a  v   i   t  y   P  r  e  s  s  u  r  e   S

  e  n  s  o  r  s

F r  om M

 a c h i  n

 e–

H y  d r  a

 ul  i   c P r  e

 s  s  ur 

 e ,I  n j   e c  t  i   on

V  el   o

 c i   t   y 

 , C l   am

 pi  n

 g Uni   t   ,

 O t  h  er T r i   g

 g er  s  e t   c .

 Figure 4: Setup for real time data acquisition

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Figure 5: Typical shrinkage sensor data profile

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 Figure 6: Cavity pressure transducer data profile 

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Room Temperature

 Figure 7: Melt temperature profile for a molding cycle

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20

Post MoldShrinkage

 Figure 8: P-v-T data curves of the polymers for the molding cycle  

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Figure 9: Shrinkage correlation for thin cavity

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Figure 10: Effect of process parameters on the shrinkage of thin cavity

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Figure 11: Shrinkage correlation for thick cavity

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Figure 12: Effect of process parameters on the shrinkage for thick cavity