High resin costs and requirements that medical parts comply with Six Sigma standards demand the use of statistics to help control the extruding of thermoplastics, whether film, pipe, coating, or profiles. Of all these methods, profile extrusion is the most difficult because it requires holding many dimensions to satisfy shape requirements. The focus here is on how statistics help pinpoint ways to troubleshoot errors in profile extrusion.

Let's start by examining a basic profile-extrusion line. It includes an extruder, die, sizing mechanism or calibrators, haul-off (puller or conveyor belt for part removal), and ancillary equipment. When profile dimensions vary too much, it is necessary to find out which component has the highest probability of being the problem's root cause. This means tracking process and part deviations.

First, as a quick refresher, processing conditions of most fluids, are related by:

P = VRQ

where P = pressure, V = fluid viscosity, R = die resistance, and Q = material output. Empirical studies show a direct correlation between the standard deviation of the pressure and the standard deviation of the part dimensions. In fact, the two are proportional. In profile extrusion, the two major problems are size variance (in statistics, this is also called the mean-square deviation) and flow shifts of the extrudate, the material that comes out of the extruder.

Another important statistic — the numerical mean of pressure, useful in determining what is called flow balance. When the profile die is balanced for velocity at a given output, the result is a viscosity with a mean of pressure (expected value). Should the screw speed or melt temperature change, the viscosity, and therefore the mean of pressure, also change. In other words, a changing mean of pressure shows that the flow is not constant.

Viscosity change in a thermoplastic is most dramatic in what is called viscous heat generation. Here, a faster screw speed increases frictional heat so much that the resulting decrease in fluid velocity makes for an unacceptable pressure drop. On high-viscosity resins such as RPVC, typical pressures run from 210 to 350 bar. This application is considered stable when the standard deviation is about 2.41 bar.

Experimenting with Six Sigma

A recent Six Sigma experiment involving three separate studies illustrates the use of statistics in a profile extrusion. Study One of the experiment provided the baseline for the other two. Equipment consisted of a 2½ in. extruder with a Barrier Maddock RPVC screw. Material was a standard RPVC formula interior grade. A pressure transducer mounted to the barrel of the extruder metered the extrudate. The transducer signal led into conditioners and ultimately to a PC that performed statistical calculations.

The die, a 0.059-in.-thick tool with a calibration mechanism for sizing, has a 4.100-in. profile. The tool had been producing acceptable parts for three years. Study One ran under normal operating conditions at typical barrel and die temperatures. Here, the mean of pressure was 209.4 bar and its standard deviation was 2.4 bar. (It is important to note that a typical extrusion machine exhibits relatively higher and lower pressure readings, depending on which edge of the screw is passing by the transducer port.)

Study Two dropped the temperature on two of the barrel zones. Here, statistical data showed a pressure mean of 221.4 bar, and a standard deviation of 7.6 bar. Study Three raised temperatures on two of the barrel zones. In this case, data had a mean of 205.5 bar and a statistical variance of 2.52 bar.

Technicians took samples of extruded profiles in consecutive order and measured the profile width (perpendicular to the extrusion direction). In study One, the dimension had a mean of 4.079 in. and a standard deviation of 0.003 in. Study Two showed a mean of 4.089 and a standard deviation of 0.013 in. Study Three also exhibited a mean of 4.089, but showed a standard deviation of 0.004 in.

The difference between the mean of pressure in study One and Two was 12 bar. This was expected for RPVC, given the reduction in barrel temperature. More significantly, the standard deviation of the pressure between studies One and Two increased by a factor of three. And the standard deviation of the profile width increased by a factor of four. This bears out the observation that the standard deviations of the pressure and the part dimensions are proportional.

Also noted, wall thicknesses in study One were within ±0.001 in. In study Two, the thickness was the same as in study One, except for the middle of the part where it was 0.019-in. thinner at the center of the profile. Increased barrel flows (study Three) thickened the wall at the center by 0.002 in. over nominal.

Sources of size variance

The standard deviation of the pressure can help determine if part-size variance comes from the extruder or the puller. When automated data-acquisition equipment is not handy, take pressure samples every thirty seconds for 18 minutes for a total of 36 discrete data points.

If the standard deviation of the pressure is less than 2.5 bar (part sizes here range ± 0.060 in.), look at the haul-off and the extruder first. To check the haul-off, solid-mount a digital tachometer against a puller driveshaft and measure its rpm. A standard deviation of less than 0.01% of rpm is considered normal.

Useful information also comes from a digital encoder on the part profile or puller belt. Make sure there is no belt slippage for an accurate reading. The encoder reading indicates line speed in in./min. Puller and extruder drives come in a wide range of speed tolerances. Precise systems are within 0.01% of the speed resolution. A typical variance on a 1,750-rpm motor at 1% is 17.5 rpm. In contrast, on a precise system, it would amount to 1.75 rpm, or only one tenth of an extrude screw revolution. An acceptable standard deviation is less than 0.01% of the line speed. Should the haul-off show an acceptable reading, check the extruder driveshaft in a similar fashion.

A standard deviation of the pressure greater than 2.5 bar indicates a condition called surging. It comes from abnormal pressure and is seen with the naked eye as the extrudate enters the vacuum calibration table. Pressures surge when the:

• Extrudate is misaligned.

• Extruder screw is poorly matched to a material.

• Extruder or puller is improperly geared so speeds cannot be regulated.

• Regrind particle size is inconsistent, so pellet size varies too much. This makes for an erratic feed.

• Water jacket around the feed throat overheats, causing the material to stick. When the water is too cold, moisture collects in the feed throat and contaminates the extrudate.

A normal bell curve

A normal bell curve illustrates a few statistical terms. The curve is centered on the mean or average value being checked for a particular extrudate population. Here, plus and minus three sigma accounts for 99.73% of the population (sigma is the Greek letter used to indicate the standard deviation of a distribution, a measure of the spread of its values), which means that only three in a thousand fall outside these limits. A normal distribution fits 68% of the population within plus or minus one standard deviation of the average. Standard deviation is defined as the square root of the variance. The variance of a probability distribution is one measure of the spread of values, averaging the squared distance of possible values from the expected value (mean).