Diagnosing and eliminating warpage.

In complex shapes, plastics tend to exhibit extremely complex patterns of warpage, which often make it very difficult to achieve specified dimensions. Using conventional technology, engineers can sometimes spend literally years of expensive trial and error in an effort to eliminate warpage. Often, improving one processing factor only makes the overall problem worse because another factor that had previously been offset becomes more prominent. The relatively recent development of computer-aided engineering software modules that model the molding and cooling process in order to predict the actual deformed shape of an injection molded part offers substantial benefits, but they leave one problem remaining.

This revolves around the fact that the causes of warpage are so numerous and complex that even being able to accurately predict the problem on a computer is often not sufficient to enable its solution. Recently, a new approach has been developed that not only predicts the amount of warpage and residual stress in a component, but also pinpoints which factors are causing the warpage and details the precise contribution of each factor to the overall warpage. These advanced diagnostic capabilities greatly simplify the process of controlling warpage and residual stress in an injection molded part. With this information at hand, the engineer can vary part and mold design and processing conditions in order to achieve true uniform global shrinkage, which will minimize both warpage and residual stress.

WHY WARPAGE?

Local shrinkage variations introduce a bending moment to the geometry and thus cause warpage -- or, if the part is constrained, introduce residual stresses that can substantially reduce component life, and whose structural effects are very difficult to predict using conventional analytical tools.

Let's look at the simple case of a flat molding with a temperature differential over its cross-section. The layer in contact with the hotter, upper side of the mold contracts more during the cooling cycle and thus causes warpage by setting up a bending moment. A similar effect can occur with thick and thin sections because the thick section will typically be hotter on demolding than the thin section, even if the mold temperature is consistent.

It may be useful to apply these ideas to a simple part such as a flat disk. Imagine that the shrinkage in the outer region is higher than the shrinkage in the center. The disk takes on a dome shape: the center may pop either up or down. On the other hand, if the shrinkage in the outer region is lower than the shrinkage in the center, the part will warp into the classic "dishpan" shape. Note that differential shrinkages may occur that are lower than the threshold value required to warp the part; in that case, a residual stress distribution will be set up within the part.

CLASSIFYING SHRINKAGE

In diagnosing and correcting warpage, it is necessary to distinguish the various factors that can cause differential shrinkage. The most useful method yet developed is to divide overall differential shrinkage of parts into three categories:

1) Area shrinkage, which is an average of the directional shrinkage values for a given area of the part;

2) Cross-sectional shrinkage, which varies across the thickness of the part and is caused by temperature variations in the mold;

3) Directional shrinkage, which is the difference between the shrinkage parallel and perpendicular to the melt-flow pat.

The reason for selecting these categories is that they can be accurately measured for a given polymer through physical testing. Also, each corresponds to one or two design or process parameters, which can be easily controlled during the molding operation.

Area shrinkage is a function of local variations in crystallization and packing pressure. Volumetric reduction normally takes place when a plastic material is cooled and forms a crystalline structure. (This is true, to a greater or lesser degree, even with what are known as "amorphous" polymers.) But when a molten plastic flowing through the mold contacts a relatively cold wall, it freezes instantly into a virtually amorphous or noncrystalline outer layer with almost no shrinkage occurring. The inner portion of the part cools more slowly and thus undergoes greater crystallization and greater shrinkage. In addition, the noncrystalline outer layer of the part can vary in size, depending on the temperature of the area of the mold that it contacts and the local thickness of the part.

Variations in packing pressure have an effect on area shrinkage that is quite similar to that caused by local crystallization variations. Packing pressure can be greatly reduced in certain areas that are constricted either by the geometry of the part or by freezing-off of an area between that section and the gate. Further variations in packing pressure are caused by the natural elasticity of polymers, which means that packing pressure is automatically reduced in proportion to distance from the gate. Since packing pressure and crystallization effects are very similar, and crystallization is extremely difficult to control, area shrinkages due to both effects are normally dealt with by packing-pressure adjustments.

Cross-sectional shrinkage is usually caused by less-than-optimal placement of, or inefficiencies in, cooling lines. As explained earlier, a difference in temperature between the top and bottom of the mold as the part is removed will introduce a bending moment in the part. In other cases, temperature differences can be generated without mold-temperature variations by differences in the thicknesses of adjoining areas of the part.

Directional shrinkage variations are almost completely caused by the difference in shrinkage parallel and perpendicular to the flow-path direction at the time of freeze-off. As the plastic is forced through the mold under pressure, molecules are stretched out in the direction of flow. As the part cools, molecules tend to return to their original state, which means that shrinkage is significantly greater in the direction of flow and smaller perpendicular to flow. If the material is filled with glass fibers, these too will undergo orientation, again affecting the degree of shrinkage that occurs. However, with fibers the general effect is to give less shrinkage parallel to flow than perpendicular to flow.

Thus, each of these three factors--area, cross-sectional, and directional shrinkage--acts to set up stresses that will either distort the part or reduce its life.

ATTACKING THE

PROBLEM

Here is one approach to computerized calculation of shrinkage, warpage, and stress that will allow an engineer to vary part design and processing conditions until uniform local shrinkage is achieved, thus eliminating warpage and residual stress. A series of software modules is used to analyze flow, cooling, shrinkage, warpage, and stress in an injection molded part, including the filling, holding, and cooling stages of the process, so that conditions within the mold are monitored until the part is actually ejected. An important requirement is the use of a common geometric database so that each module generates the necessary input data for the next module in the analysis sequence. This greatly reduces the time required to perform the analysis, as the time-consuming data-entry step is drastically shortened. Errors caused by inaccurate data entry are also minimized.

The first step in the process is a finite-element-based flow analysis in order to eliminate basic flow problems, such as poorly placed weld and meld lines. This type of analysis typically makes use of the simplifying assumption of a standard temperature profile, rather than attempting to depict actual temperature conditions. The accuracy of a finite-element analysis has been found to be excellent in the filling stage, but somewhat less in the packing and cooling stages. It can be accomplished in approximately one-tenth of the time required for a finite-element/finite-difference method of analysis that calculates the true temperature profile, thus it is ideally suited to this early phase of the analysis where basic flow problems are being eliminated by following an iterative approach.

Flow-analysis software graphically depicts the flow path from the gate to the last point to be filled. A three-dimensional view of the cavity clearly depicts weld lines, meld lines, overpack areas, etc. The program also determines mold temperature, melt temperature, first-stage injection time, injection pressure, cycle time, and clamp tonnage. Areas of overpack can be eliminated by local changes in wall thickness or gate location changes. Filling patterns and weld-line locations can be modified by altering the number and position of gates along with the feed system and part dimensions. Flow defects such as "race-tracking," gas traps, hesitation, and underflow can be detected and eliminated. Molecular orientation in the direction of flow provides extra strength in that direction. With flow analysis, the direction and level of orientation can be aligned with the principal stresses on the part.

The next step is a cooling analysis that calculates water flow and heat-transfer capability for each section of the cooling channel, temperature-distribution profiles at the metal-to-plastic interface, pressure drop in the cooling circuit, and coolant temperature rise. Thermally conductive inserts and external heat sources can be included in this analysis. The results of this cooling analysis are then fed into a finite-difference/finite-element flow analysis, which uses the finite-difference method to calculate temperature, rate of cooling, shear stress, and direction of flow for each cross-sectional layer in each segment or element of the flow model.

This approach divides each element of the part into a user-specified number of layers. As flow is laminar, this allows the capture of a representation of the formation of the plastic throughout the cross-section of each flow element. Direction of flow, shear stress, pressure, temperature profile across the thickness, and cooling rate are calculated and recorded at the time each layer freezes off. The sum effect of conditions in each layer is then calculated for each element, thereby determining an orientation vector. The analysis uses the calculated temperature profile, thus its accuracy extends into both the packing and cooling phases of the processing cycle. This allows the holding pressure and time for minimum shrinkage to be determined and the parameters controlling shrinkage to be monitored throughout.

The next step is to calculate elemental volumetric shrinkage by calculating density during filling and packing of every layer within each element. This is done using pressure-volume-temperature (pvT) characteristics of the material. But because those pvT data are determined under experimental conditions of very slow cooling to achieve maximum crystallinity, the calculated volumetric shrinkage must be mathematically corrected to account for the very different cooling rate and crystallinity actually experienced in the process. This involves splitting the entire cooling time into a number of equal temperature steps and calculating the cooling rate within each step in order to arrive at a cumulative calculation of crystallinity, and thus, of a realistic area shrinkage value for that elemental layer. Then the results of individual layer shrinkage calculations are combined to arrive at an overall area shrinkage calculation for that flow element.

The final step is to combine the local orthogonal shrinkage values generated in the shrinkage analysis with the mechanical constraints on the part, such as gates, to determine the net distorted shape. Processing-induced stress values for each section of the part are also generated. The end result is separate deformed representations of the part for each of the three differential-shrinkage categories, as well as a net deformed shape, which includes the effects of all three causes acting in unison. These graphic representations provide the information required to eliminate warpage on the computer without even producing a trial part, except as a final verification. Here's how this is accomplished.

USING THE RESULTS

The deformed representations for each cause of warpage help easily pinpoint the source of the warpage so that the user can determine which cause is dominant and make appropriate changes in the tool design or mold conditions. To be more specific, area-shrinkage variations can be resolved by adjusting packing pressure and, in extreme cases, by changing part thickness in local areas.

Cross-sectional shrinkage variations are attacked by altering the cooling system design. Finally, changing the gating location or, in extreme cases, altering part design to change the polymer orientation at freeze-off is the recommended cure for directional-shrinkage variations.

Cases in which two different effects cancel each other out are also easily spotted so that the user can address both causes simultaneously and thus avoid an unpleasant surprise later. Cures can be verified by viewing a new deformed representation for that cause after the change has been made.

Every analysis depends on having an accurate database of material properties, which, with new plastic grades being developed daily, takes a lot of effort to maintain. As an example, Moldflow performs over 40 different experiments on each material sample using a wide variety of molding parameters to completely determine its molding and shrinkage characteristics. These experiments use a specially developed measuring apparatus involving a high-resolution video camera mounted on a high-precision, fully instrumented x-y axis table. This apparatus is connected to dataloggers and results in a statistical multivariable regression analysis to determine how each master variable affects shrinkage parallel and perpendicular to flow.

Difficult warpage problems are virtually impossible to solve using conventional technology because of the complex way in which the various causes of the phenomenon interact. The new computerized approach to warpage eliminates these difficulties by accurately separating out the effects of each warpage cause, thus making it much easier than ever before for warpage problems to be addressed and eliminated. The ability to eliminate warpage at the source frequently makes it possible to eliminate the need for long cooling cycles or cooling fixtures, thus reducing machine time, labor, and tooling costs. Another benefit is elimination of residual stresses that can substantially reduce part life, and whose effects on structural properties are very difficult to predict using conventional analytical tools.