statistical analysis of product variability associated with continuous and cut sheet thermoforming...

Statistical Analysis of Product Variability Associated With Continuous and Cut Sheet Thermoforming

Operations

MICHAEL E. RYAN,* MARTIN J. STEPHENSON, and KEVIN GROSSER

Department of Chemical Engineering State University of New York at Bu-alo

Bu-alo, New York 14260

and

LARRY J. KARADIN

Firestone Synthetic Rubber & Latex Company Akron, Ohio 4431 9-0006

and

PAUL KAKNES

Comet Products, Znc. Chelmsford, Massachusetts 01 824

Extensive published data exist with regard to the variation of part weight and dimensions for products manufactured by injection molding and blow molding. Relatively little information is available with regard to thermoformed parts. Such data are of considerable practical and theoretical value in establishing realistic processing targets in commercial processing operations. Experimental data have been systematically collected over an extended time from three continuous roll-fed thermoforming processes, as well as a cut sheet forming process. Two of the continuous processes studied were high-volume production lines. One of the operations produced 16-ounce drinking cups from a blend of a styrene-butadiene block copolymer with polystyrene. The other commercial continuous process manufactured tubs from high-density polyethylene. The third process studied involved a pilot plant test former used to produce 10-ounce drinking cups from the styrene- butadiene /polystyrene blend material. All three continuous processes employ plug assist in conjunction with a multi-cavity mold. The measured parameters included the weight of individual parts, and the wall thickness measured at several different locations. The cut sheet forming process employed a plug assist with a single-cavity mold for the production of a scanner cover. The polymer used consisted of a blend of an acrylic and a poly(viny1 chloride) resin. The deformation and wall thickness of the scanner cover were measured at several different locations.

INTRODUCTION

he constant demand of delivering quality parts has T become stringent for both custom and captive plastics processors. Many companies have, or are currently seeking to, become certified under the IS0 9000 series quality standard established by the Interna- tional Organization for Standardization located in Ge-

To whom correspondence should be addressed

neva, Switzerland, to attest to their customers that their operations are in conformance with a high standard of quality control and assurance. In a recent survey (l), 83% of the managers of custom plastics processors indicated that they were either exploring or expecting to receive IS0 9000 certification. About 70% of these respondents were involved in injection molding. Currently, a relatively smaller proportion of thermoformers appear to be pursuing total quality man- agement along these lines. However, in 1993 two

2432 POLYMER ENGINEERING AND SCIENCE, MID-OCTOBER 1996, Vd. 36, No. 19

Statistical Analysis of Product Variability

10

11

12

l--- I

8 I s 9 / 6

Machine Direction

I

Machine Direction

(b)

Fig. I . Cavity locations for styrenic drinking cups: (a) 16-02 cups (commercial production); (b) 10-oz cups (test former).

Corner I

Bottom/Center Fig. 2 . Locations of crtp thickness measurements.

Machine Direction

major thermoformers re(-eived IS0 900 1 and IS0 9002 certification (2).

Apart from IS0 9000 certification, the use of statistical process control (SF‘C) and statistical quality control [SQC) have been widely embraced by the plastics industry. A knowledge of the expected variation of product dimensions and properties is important for the design, operation, and control of a processing operation. Several articles have addressed the use of SPC and SQC in relation to process and product variability in conjunction with the injection molding process (3-6). While many processes concentrate on pro- ducing products that will pass visual inspection, the inherent objective of any process is to produce parts consistently with identical weight, dimensions, and appearance (7). Statistical process control can be used to measure and reduce the variation of these critical

Fig. 3. Cavity locations for HDPE tubs.

parameters. In injection molding, part weight is be- lieved to be the single most important parameter in determining process consistency (8). Various process parameters, such as part dimensions and weight, are routinely monitored and control charts relating to the final target specifcations are frequently employed (4, 5). A “quality standard yardstick to assess the capa- bility of an injection molding machine has been pro- posed (9, 10). The quality classification was based on a survey of over 1800 injection molding machines operating over several million cycles. Relatively little information in this regard is available for thermoforming. Many thermoforming operations are gaining unprecedented levels of dimensional precision and re- peatability. Dimensional precision within 20.0762

POLYMER ENGINEERING AND SCIENCE, MID-OCTOBER l-, Vol. 36, No. 19 2433

Michael E . Ryan et al.

Left side V i W

Left Front Right Front Comer Comer , .

Bonom/ center 0 I I

( 0 \@) Left Rear Right Rear Comer Bonom View Comer

Left @ FrontLip

@ Front Wall Right :i wallo

Front View

Fig. 4 . Locations for thickness measurements of HDPE tubs.

mm (20.003 inch) for small parts to t0.127 mm (t0.005 inch) for large parts is presently attainable (1 1).

Statistical process control can be especially important in high-volume, continuous production thermoforming operations. A thermoforming process that is not monitored can easily lead to the generation of a large number of off-specification parts, which can result in considerable loss of productivity and profit. Cut sheet forming processes are commonly used to produce low volume, expensive parts. Thus, cut sheet forming operations are subject to loss of productivity and profit if not properly monitored. Although a considerable amount of information has been published in relation to the variability of part dimensions or part weight in conventional processing operations such as extrusion or injection molding, little information is available regarding the inherent variation of product dimensions or weight associated with thermoforming or vacuum forming operations. An understanding of the variability and sensitivity of the thermoforming process is helpful in developing appropriate mathe- matical models or computer simulations of the process, as well as for establishing appropriate production and process control strategies.

This paper provides results obtained from three continuous roll-fed thermoforming processes and a cut sheet forming process. Two of the continuous processes studied were commercial high production vol-

7

9

T 7 114"

1

Fig. 5 . Schematic diagram of scanner cover.

ume operations while the third continuous process was conducted on a pilot plant test former. The commercial processes are used in the manufacture of 16-oz styrenic drinking cups (15 cups/shot) and high- density polyethylene (HDPE) tubs ( 15 tubs/shot). The pilot plant test former was used to produce 10-02 styrenic drinking cups (9 cups/shot). A statistical analysis was conducted for each of these processes to explore the weight and dimensional variability of parts from each cavity in the mold and to compute control limits where feasible. The cut sheet former produced a scanner cover (1 part/shot). A statistical analysis was conducted for the cut sheet forming process to deter- mine the dimensional variability of the part.

PROCESS DESCRIPTION

Styrenk Drinking Cups

The commercial production process used to produce 16-02 drinking cups is a pressure forming process with plug assist located at Comet Products, Inc. The production mold used contains a family of 15 cavities. The pilot plant test former was located at Firestone Synthetic Rubber & Latex Company and was used to produce 10-oz drinking cups with a mold having a family of nine cavities. The numbering scheme for the cavity location in these two molds is shown in Ffg. 1 . The production mold consists of three rows of five cavities whereas the test mold consists of three rows of three cavities.

2434 POLYMER ENGINEERING AND SCIENCE, MID-OCTOBER 1996, Vol. 36, NO. 19


I I

The material used to produce the cups is a blend of a styrene-butadiene block coipolymer (Stereon 900, manufactured by Firestone Synthetic Rubber & Latex Com- pany) with polystyrene (MolWBASF 2524). The operating temperatures studied were in the range of 130 to 150°C (270 to 310°F). The commercial production process uses a roll-fed sheet having a thickness of 0.2 mm (80 mils), whereas the pilot i.est former employs a roll-fed sheet having a thickness of 0.1 mm (42 mils).

Five measurements weie made on individual cups produced in the commercial operation and six measurements were made on individual cups produced on the test former. These measurements were the weight of each individual cup, arid the wall thickness at the top, middle, and bottom of each cup as shown sche- matically in Fig. 2. An additional wall thickness mea- surement was made at the bottom/center for cups produced by the test former.

Approximately six months of production data were analyzed on the commerciial process. An experimental run was made on the test former over a period of six days and ten cups were collected from each cavity. The test former was operated for a period of 2 hrs prior to the collection of any samples.

Polyethylene Tubs

The production of HDPE tubs was done using a pressure forming process with a plug assist. The mold used produced 15 tubs per shot consisting of five rows of three cavities. The numbering of the cavity locations in this mold is shown in Fig. 3. The operating temper- ature was -55°C (130'17) and the thickness of the roll-fed sheet was 67 mils. Sixteen measurements were taken on individual units (tub weight plus 15 wall thickness measureinents at various locations). The locations for the wall thickness measurements are shown schematicalty in Fig. 4. A lid is subse- quently welded on to the molded flange along the top edge of the tub. Hence, Lhe flange, hinge, and lip dimensions of the tubs are all critical to ensure that the welding of the lid can be done properly resulting in a snug fit over the tub. Experimental data were collected

I - - X = 13.7 I

2000 v1 a

; E 1000 i

0 5.5 9.5 '13.5 17.5 21.5 25.5

Thickness (mil)

Fig. 6. Histogram of top wall thickness.

k

b

2

: 0

c1

k ; b

2

D

!z

I " ' 1 - ' I ' ' ' " " " I [ p= 10.4 I I 2000

I I I I I I I

I I

I I

I i

6.25 10.25 14.25 18.25 22.25 Thickness (mil)

Fig. 7. Histogram of middle wall thickness.

2000

P

5 1000

V

b

2

ry

D

0

3.5 7.5 11.5 15.5 19.5 23.5 27.5 Thickness (mil)

Fig. 8. Histogram of bottom wall thickness.

I

I >CkX = 4.5 UCLx I= 32.4

I I I I I I I I I I I

5.5 13.5 21.5 29.5 37.5 Thickness (mil)

Fig. 9. Histogram of corner wall thickness.

for 25 parts per cavity over a five day period (5 parts cavitylday).

Scanner Cover

The production of the scanner cover employed a cut sheet forming process. The material used was a 250- mil-thick sheet of an acrylic /polyvinyl chloride alloy

POLYMER ENGINEERING AND SCIENCE, MID-OCTOBER 1996, VOl. 36, NO. 19 2435

Michael E. Ryan et al.

Table 1. Summary of Styrenic Drinking Cup Wall Thickness Parameters. (Commercial Production Process).

Location Average mm (in) u mm (in) Skewness Peakedness 0

TOP 0.373 (0.0147) 0.0587 (0.00231) 0.5245 1.4635 -0.00476 Middle 0.264 (0.0104) 0.0300 (0.001 18) 0.8995 5.0086 0.00152 Corner 0.348 (0.0137) 0.1 120 (0.00441) 0.7787 1.1 096 -0.00260 Bottom 0.300 (0.01 18) 0.0704 (0.00277) 0.921 4 1.5710 0.00197

Table 2. Cavity Parameters for Top Wall Thickness Measurements.

Table 3. Cavity Parameters for Middle Wall Thickness Measurements.

Yo > Yo c Yo > Yo c Cavity Average 0 UCL LCL UCL LCL Cavity Average 0 UCL LCL UCL LCL

1 0.01486 -0.02491 0.02249 0.00835 0.29 0.71 1 0.01044 0.00191 0.01546 0.00714 0.43 0.43 2 0.01481 -0.00190 0.02310 0.00906 0.43 0.28 2 0.01042 0.00403 0.01538 0.00749 0.43 0.14 3 0.01500 0.00044 0.02344 0.00944 0.43 0.00 3 0.01051 0.00250 0.01534 0.00736 0.28 0.43 4 0.01500 0.00112 0.02312 0.00966 0.43 0.28 4 0.01043 -0.01290 0.01371 0.00750 0.43 0.57

6 0.01415 -0.01131 0.02119 0.00850 0.28 0.14 6 0.01017 -0.00198 0.01350 0.00750 0.43 0.57

8 0.01479 0.00153 0.02295 0.00952 0.28 0.14 8 0.01034 0.00004 0.01386 0.00764 0.43 0.71

10 0.01523 0.00168 0.02393 0.00970 0.57 0.28 10 0.01068 0.00148 0.01430 0.00801 0.71 0.28 11 0.01490 -0.00457 0.02277 0.00911 0.71 0.57 11 0.01064 0.00242 0.01417 0.00808 0.43 0.28 12 0.01463 -0.00143 0.02323 0.00880 0.57 0.28 12 0.01059 0.00387 0.01425 0.00812 0.43 0.28 13 0.01413 4.00908 0.02183 0,00819 0.28 0.28 13 0.01043 0.00394 0.01560 0.00741 0.14 0.28 14 0.01418 0.02219 0.02219 0.00778 0.57 0.43 14 0.01051 0.00348 0.01610 0.00723 0.28 0.43 15 0.01392 0.02214 0.02214 0.00779 0.57 0.28 15 0.01029 0.00211 0.01497 0.00719 0.28 0.43

5 0.01466 0.00092 0.02198 0.00969 0.43 0.43 5 0.01026 -0.04029 0.01318 0.00748 0.43 0.43

7 0.01506 0.00236 0.02321 0.00988 0.00 0.00 7 0.01050 -0.00241 0.01421 0.00754 0.57 0.28

9 0.01475 0.00099 0.02367 0.00910 0.71 0.14 9 0.01030 -0.00299 0.01404 0.00732 0.57 0.43

(Kydex 100). This material has a glass transition tem- perature of 82°C (180°F). The sheet is heated to -245°C (475"F), inflated, and then subjected to an applied vacuum with the aid of a mechanical plug assist. Pressurized air is applied through the plug to ensure that the sheet is deformed into the corners of the mold. The locations for the 14 wall thickness measurements are shown in Fig. 5. Data were collected on a total of 126 parts formed over a nine day period.

Three measurements were taken on the right-hand side of the part depicted in FLg. 5 (Locations 1, 2. and 14). An additional component is attached to the formed part at this position in a secondary assembly operation. The thick sheet exhibits difficulty in being deformed into the sharp corners of the mold (Loca- tions 6 through 9). A urethane adhesive is used to fill the corners as part of the secondary operations.

STATISTICAL CONSIDERATIONS

Characterization of a sampled population generally entails calculation of an average (XI, unbiased standard deviation (a), skewness, kurtosis, and peakedness. These last three statistical parameters are defined as follows ( 1 2):

Peakedness = Kurtosis - 3.0 (3)

Table 4. Cavity Parameters for Bottom Wall Thickness Measurements.

Yo > Yo < Cavity Average 0 UCL LCL UCL LCL

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0.01 163 0.01 194 0.01 185 0.01214 0.01 209 0.01231 0.01 123 0.01 148 0.01 153 0.01 130 0.01 137 0.01 140 0.01 182 0.01215 0.01204

0.00301 0.00275 0.001 91 0.00280 0.00003 0.00213 0.00323 0.00185 0.00215 0.00273 0.001 07 0.00045 0.00127 0.00099 0.00123

0.02422 0.02491 0.0241 6 0.02474 0.02250 0.02501 0.02320 0.02222 0.02412 0.02218 0.021 92 0.02142 0.02325 0.02399 0.02429

0.0061 8 0.00622 0.00602 0.00644 0.00621 0.00631 0.0061 2 0.00610 0.00581 0.00621 0.00586 0.00588 0.00601 0.00607 0.00596

0.14 0.28 0.00 0.00 0.28 0.14 0.00 0.00 0.14 0.28 0.28 0.28 0.14 0.28 0.28 0.28 0.43 0.14 0.00 0.14 0.00 0.14 0.14 0.28 0.43 0.00 0.28 0.14 0.14 0.00

Table 5. Cavity Parameters for Corner Wall Thickness Measurements.

Yo > Yo c Cavity Average 0 UCL LCL UCL LCL

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0.01 436 0.01385 0.01 228 0.01292 0.01302 0.01335 0.01298 0.01369 0.01309 0.01409 0.01409 0.01 374 0.01449 0.01 470 0.01462

-0.00756 -0.00075 0.00143 0.00019

-0.00372 -0.00253 4.001 10 -0.00440 -0.00628 -0.01 898 -0.00574 0.001 04

-0.00519 -0.00323 -0.0021 0

0.031 32 0.00433 0.03338 0.00497 0.0321 5 0.00477 0.03137 0.00490 0.02739 0.00489 0.03000 0.00475 0.031 91 0.00440 0.03207 0.00406 0.03058 0.00341 0.02912 0.00339 0.031 60 0.00430 0.0351 1 0.00524 0.03316 0.00439 0.03657 0.00425 0.03397 0.0051 2

0.00 0.00 0.28 0.00 0.00 0.28 0.14 0.00 0.43 0.00 0.14 0.28 0.00 0.00 0.00 0.00 0.14 0.14 0.28 0.00 0.14 0.00 0.28 0.14 0.14 0.00 0.14 0.28 0.14 0.00

2436 POLYMER ENGINEERING AND SCIENCE, MID-OCTOBER 1996, Vol. 36, NO. 19


Table 6. Summary of Wall Thickness Parameters for Test Former.

Location Average mm (in) u mm (in) Skewness Peakedness

TOP 0.500 (0.0197) 0.1 290 (0.00508) 0.129 Middle 0.279 (0.01 10) 0.0269 (0.001 06) 0.044 Bottom 0.224 (0.0088) 0.041 1 (0.00162) 0.426 Corner 0.208 (0.0082) 0.0338 (0.00133) 0.239 Bottom/Center 0.544 (0.0214) 0.0584 (0.0023) 0.360

-0.376 -0.126 0.319 0.140 -0.486

The skewness is a measure of the deviation of the distribution from symmetry. A normal distribution has a skewness of zero. The deviations in the longer tail are large and raised to the third power; consequently they are more heavily weighted. The kurtosis and peakedness refer to the shape of the distribution. A normal distribution has a kurtosis of 3.0 and consequently a peakedness of zero. A distribution with a kurtosis greater than 3.0 is more peaked or concen- trated about the average and must therefore have longer tails in the distribution to compensate for the greater concentration about the mean. Since the deviations in Eq 2 are raised to the fourth power, the large deviations assume greater importance. Conse- quently, the more peaked curve will have a higher fourth moment about the mean as compared to a less peaked or flatter distribution (12).

Commonly encountered variables associated with various industrial proce.sses (such as the final wall thickness for thin parts) are typically non-normal. In order to construct contr’ol limits for use in SPC, the distribution is transformed to a normal distribution (13). The use of a logarithmic transformation can be used to transform a non-normal distribution to a normal distribution. This logarithmic transformation is defined as follows

y, = ln(x, - e ) e < x m m (4)

where the value of 0 is chosen so that the skewness of the transformed distribution is equal to zero. The up-

per and lower control limits can be determined ac- cording to the following expressions:

xucL = 0 + exp(5 + 36,) (54

xLcL = e + exp@ - 36,) (5b)

PRODUCTION DATA FOR STYRENIC CUPS

The number of cups measured from each cavity location was -700. All of the cavities yielded positive skewness values for the wall thickness measurements. These data indicated that the population distribution of the thickness data was not normal as a result of a tailing of the data from the origin “to the right.” Histograms of the wall thickness measurements taken from all 15 cavities are shown in Figs. 6 through 9 along with their respective control limits. Table I summarizes the wall thickness data over all cavities and Tables 2 through 5 show the wall thickness variability and control limits for cups produced from each individual cavity within the mold.

The values given in Tables 2 and 3 indicate that less than 1% of the cups produced were outside of the control limits for the top and middle wall thickness measurements, respectively. However, the bottom and corner thickness measurements (Tables 4 and 5) indicate that less than 0.4% of the cups produced were outside of the control limits. A process within t3awill produce less than 0.27% of the parts outside of this range. Additional discussion of these results has been given elsewhere (14).

Fig. tion.

10. HDPE tub weight P $

6-10

11-15

CAVITY NUMBERS

ROW 5

POLYMER ENGINEERING AND SCIENCE, MID-OCTOBER 1- Vol. 3s, NO. 19 2437


50

40

v)

3 I- m

& 30

Fig. 11. Histogram of HDPE tub z weight data. 2 20

K Y m

10

0 57.6 58.4 59.2 60 60.8 61.6 62.4 63.2 64 64.8 65.6 66.4

WEIGHT (9)

The histogram of the middle wall thickness measurements (Fig. 7) exhibited a sharp peak near the mean accompanied by a small standard deviation. Only a relatively small number of measurements caused the long tailing to the right of the distribution. This suggests that the consistency of the wall thickness of the cups at this middle location was well con- trolled. In contrast, the histogram of the corner thickness measurements shown in Fig. 9 exhibits wide variability. This is due to the extreme thinness of the cups at the corner location. The thickness in the corner will be sensitive to small perturbations in the forming conditions. In addition, experimental thickness measurements at this location are subject to considerable experimental scatter since the thickness changes rapidly with position in this region. This rapid variation is due to the combination of the large deformation or stretching of the material into the corner

12. .tion

Front wall thickness dis- of HDPE tubs.

and the solidification of adjacent sections of the sheet from contact with the plug.

TEST FORMER RESULTS

The statistical parameters associated with the wall thickness measurements for the cups produced by the test former indicated a distribution that was close to normal as can be seen in Table 6. The overall weight results are 6.736 t 0.101 g, skewness = 0.0165, and peakedness = -0.0570.

In particular, the middle wall thickness data had a relatively small standard deviation. This result is similar to the middle wall thickness results obtained for the 16-ounce drinking cups discussed previously. The normal distribution of the wall thickness data was somewhat unexpected. These small standard deviations suggest that the test former operation did not

11

6-10 0 11-15

-1 5

CAVITY NUMBERS

2438

ROW

POLYMER ENGINEERING AND SCIENCE, MID-OCTOBER 1996, Yo/. 36, NO. 79


Fig. 13. Front tip thickness a bution of HDPE tubs.

I istri-

c C

cn UJ w z Y

- Y

0 E

ROW 5

11.

I

6-10 0 11-15

.15

CAVITY NUMBERS

radically change from day to day and was able to produce a very consistent product. The overall standard deviations were typically 10 to 15% of the mean, whereas the standard deviations observed for the cups produced in the commercial process were - 10 to 30% of the mean value.

survey (15) of injection molders indicated that im- provement of lot-to-lot consistency would be highly desirable. Most molders and resin suppliers have taken significant steps to ensure material feedstock consistency in conjunction with extrusion, injection molding, blow molding, and thermoforming operations (16).

The middle wall thickness histogram associated with the commercial production process (Fig. 7) indicated that most of the results follow a normal distribution. The long tail extending beyond the upper control limit is most likely the result of an out-of-specification lot of material resulting in the middle thickness dislribution to be non-normal.

COMMERCIAL C0NT:INUOUS PRODUCTION PROCESS AND C0NTI"uOUS TEST FORMER

COHP4WSONS

As discussed previously, the commercial production data were collected over a four-month interval using different lots of ma.terial. In contrast, the test former was run over a few days using a single lot of material. Therefore, the lot-to-lot material variation is likely to be the major factor in accounting for the lower HOPE TUB PRODUCTION RESULTS

variation observed with the test former as compared to the commercial production operation. In connection with this observation, it is noteworthy that a recent

The HDPE tubs yielded differences in part weight from cavity to cavity. The cups produced from cavities in the outer rows (cavities 1, 6, 11 and 5, 10, 15) were

Fig. 14. Rear wall thickness bution of HDPE tubs.

Yistri-

11-

6-10

15

CAVITY NUMBERS

5 ROW

POLYMER ENGINEERING AND SCIENCE, MID-OCTOBER 199s, YO/. 36, NO. 19 2439

Michael E . Ryan et al.

Fig. butic

15. Rear lip thfckness In of HDPE tubs.

dfstrf-

h z Y

cn cn W z Y : c

ROW 5

1 11-15

CAVITY NUMBERS

typically heavier than those produced from the inner rows (cavities 2-4, 7-9, 12-14) as can be seen in Ffgs. 10 and 1 1 . The histogram of the weight data from all of the cavities (Fig. 1 1 ) exhibits a markedly non-normal distribution. A majority of the lighter weight tubs produced by the middle nine cavities comprised a single major peak centered at 59.2 g to the left of the histogram. Cavities from the outer rows produced smaller peaks in the distribution as indicated in the diagram.

The thickness distribution by cavity is shown for the front and rear walls and lips in Figs. 12 through 15. The wall thickness distributions exhibit qualitatively similar characteristics to the weight distribution shown in Figs. 10 and 1 1 . However, the lip thickness exhibits exactly

The variation of wall thickness with cavity location in the mold can be primarily attributed to sagging. High-density polyethylene is a semicrystalline polymer that exhibits pronounced sagging when heated ( 17). In many commercial operations sag rollers are used to support the sheet and prevent excessive drooping. Sagging results in the material at the ex- tremities being typically thicker than the material in the middle of the sheet. Consequently, less material is available in this central region and parts produced from the middle cavities will be lighter in weight and possess thinner walls. However, each cavity yielded wall thickness measurements that were close to a normal distribution.

CUT SHEET FORMER PRODUCTION PROCESS DATA

the opposite trend. The middle cavities yielded thicker lips than cavities in the outer rows (cavities 1 ,6 , 11 and cavities 5, 10, 15). The bottom/center wall thickness, hinge thickness, flange thickness, and flange width results are shown in Figs. 16 through 19.

The experimental results from the cut sheet former are summarized in Table 7. The location numbers in

i I I 1

FLg. nes

16. Bottomlcenter wall thick- :s distribution of HDPE tubs.

1

6-10

11-15

CAVITY

1

NUMBE !RS

2440

5 ROW

POLYMER ENGINEERING AND SCIENCE, MID-OCTOBER 1996, Vol. 36, NO. 19


Fig. tfon

17. Hinge thic of HDPE tubs.

: k n e s s dls tribu- rn rn W z Y 0 E

ROW 5

11. .15

CAVITY NUMBERS

Table 7 correspond to Fig. 5. The statistical parameters determined from the wall thickness measurements indicate that the distributions of the experimental data are close to normal at each location. The only exceptions occur at one of the corners (Location 7) and two positions corresponding to the bottom/ center and bottom/slant sections of the part (Loca- tions 10 and l l , respectively). It is interesting to note that this corner position (Location 7) had the lowest average value but had a large positive skewness. This seems to indicate that th.e thickness values for this particular corner approach zero as a natural limit yielding a distribution having a long tail to the right away from the origin.

The bottom/center and bottom/ slant locations had markedly negative skewness values. At these locations the moving plug contacts the sheet, which results in solidification. The average thickness at these locations was 5.080 mm (200 mils) and 5.182 mm

Fig. tfon

18. Flange th ickness distrfbu- of HDPE tubs.

rn rn w Z Y 0 E

(204 mils), respectively. Thus, the thickness at these locations is likely to be close to the thickness of the inflated sheet prior to contact with the moving plug. Since this thickness is an upper natural limit, the thickness distribution at these two locations would be expected to produce a skewed distribution with a long tail to the left away from the mean value.

The four corner locations had the largest standard deviations (> 10% of the mean).

CONCLUSIONS

The commercial production process for the 16-oz styrenic drinking cups was very stable. No signiflcant trend from cavity to cavity in the mold was detected. The wall thickness distributions were non-normal yielding a long tail to the right of the mean away from the origin. The overall process showed excellent control with -99% of the cups produced being within the established control limits.

11

ROW 5

-15

CAVITY NI JMBE IRS

POLYMER ENGINEERING AND SCIENCE, MID-OCTOBER 1996, Vol. 3s, No. 19 2441


W 6-10 0 11-15 1

. 19. Flange YDPE tubs.

width distrlbution

11 -1 5

CAVITY NUMBERS

ROW 5

Table 7. Summary of Cut Sheet Former Scanner Cover Production Data.

at the various locations on the scanner cover were normally distributed. The principal exceptions were at two locations at the bottom of the part where the data

Location Samples (mm) (mm) Skewness Peakedness indicated that an upper limit was encountered. After Thickness u

the sheet is inflated, the moving plug contacts the 1 126 2.185 0.156 0.428 -0.133 2 126 2.376 0.175 0.154 0.355 sheet. The two bottom locations exhibiting non-nor- 3 126 2.587 0.201 0.133 0.208 mal distributions correspond to these contact points. 4 126 1.967 0.176 -0.065 -0.523 5 126 2.093 0.119 -0.361 0.387 6 89 0.183 0.069 -0.170 -1.160 7 89 0.160 0.087 1.218 0.553 8 89 0.240 0.040 0.474 0.221 9 113 0.372 0.065 0.043 -0.486 10 110 5.080 0.268 -1.006 1.563 11 110 5.182 0.215 -1.597 4.314 12 110 4.013 0.229 -0.358 0.229 13 110 3.240 0.269 -0.355 0.067 14 110 2.161 0.130 0.323 -0.249

ACKNOWLEDGMENTS The authors would also like to express their appre-

ciation to John Manos and William P. Haessly of East- man Kodak Company for their invaluable contribu- tions and assistance with this project.

REFERENCES

The test former used to produce 10-oz styrenic drinking cups had standard deviations of -% to 1/z of the commercial production process. This may be due to the larger variation of the lot-to-lot consistency of the material being used in the commercial process. Statistical analysis of the wall thickness measurements indicated that the data were normally distributed.

The production of HDPE tubs showed a definite variation from cavity to cavity. The two outer rows of tubs were heavier and had thicker walls compared to the tubs produced from the three inner rows. How- ever, the lip thickness measurements showed the opposite variation from cavity to cavity. This is likely due to the effect of sagging in the heating chamber.

The scanner cover production process data indicated that most of the thickness measurements made

1. Plastics World, 61. 7, 16 (1993). 2. J. H. Schut, Plastics World, 62, 7, 28 (1994). 3. R. E. Burns, Plastics Technology, 36, 1, 74 (1989). 4. D. B. Hunkar, Plastics Technology, 36. 4 , 115 (1990). 5. T. E. Umscheid, Qudf ty Progress, 24, 12, 58 (1991). 6. D. B. Hunkar, SPE ANTEC Tech. Papers, 38, 2186

7. S. Wittlerr, Injection Molding, 2, 6, 42 (1994). 8. W. J. Tobin, Injection Molding, 2, 10, 56 (1994). 9. D. B. Hunkar, “An Engineering Approach to Process De-

velopment and the Determination of Process Compati- bility,” Document No. 228, Hunkar Laboratories, Inc.. Cincinnati (1991).

(1992).

10. M. H. Naitove. Plastics Technology, 39, 4, 15 (1993). 11. J . H. Schut. Plastics Technology, 38. 13, 44 (1992). 12. S. B. Richmond, Statistical Analysis, Second Ed., Ronald

13. D. C. Jacobs, Chem. Eng. Progr., 86, 1, 19 (1990). 14. M. J. Stephenson, M. E. Ryan, L. Karadin, and P.

Kaknes, SPE ANTEC Tech. Papers, 41, 822 (1995). 15. D. Smock, Plastics World, 62. 2, 22 (1994). 16. D. Smock, Plastics World, 62. 2, 18 (1994). 17. J. L. Throne, Thermoforrnlng, Hanser, New York (1987).

Press, New York (1964).

2442 POLYMER ENGINEERING AND SCIENCE, MID-OCTOBER 19S6, Vol. 36, NO. 19

statistical analysis of product variability associated with continuous and cut sheet thermoforming...

Documents