You can accurately predict warpage.

Computer simulation of injection molded part warpage comes pretty close to the real world. In this study, actual part dimensions closely matched the computer's predictions.

As a relative newcomer to the growing field of computer-aided molding analysis, warpage-simulation software does not yet enjoy the level of confidence inspired by mold-filling and cooling analysis programs. That lack of confidence could change with the publication of more "benchmarking" studies comparing the computer's predictions to real-world results.

One such study was conducted by graduate student Scott Post, Associate Professor Kosuke Ishii, and myself at the Engineering Research Center (ERC) for Net Shape Manufacturing at Ohio State University in Columbus. The results indicate that warpage simulation can indeed be a useful tool for optimizing part, mold, and process design. With a few exceptions, OSU's computer predictions - made with Moldflow software from Moldflow Inc., Shelton, Conn. - compared favorably with warpage measured on experimental parts. In fact, the majority of simulations in this study yielded warpage predictions within 0.020 in. of the experimental parts.

Unlike most previous studies, which focused upon the software's qualitative advantages as an aid to designers and manufacturers, this research took a quantitative approach. All the results come from a statistically designed set of experiments (DOE) that compared simulation results to actual parts produced by a well-instrumented and well-controlled injection molding machine.

Perhaps of more use to engineers than the accurate prediction of warpage is the ability to discover methods of reducing warpage through changes in processing conditions and part design. To that end, the study also investigated the effects of part geometry upon warpage. In addition, the individual effects of five processing conditions were isolated for two of the part geometries.

REPRESENTATIVE SHAPES

One basic requirement of the research was to mold parts that would easily show warpage while remaining representative of commercial applications. A long, thin polypropylene specimen achieved both goals: The shape produces highly directional shrinkage which in turn produces warpage. Since plates and channels form a basis for many common injection molded parts, we produced a succession of four parts based on those shapes. An 8-n.-long, 1-in.-wide flat plate was run first to get a baseline measurement of warpage using an uncomplicated geometry. The second geometry was an i-in.-long, 1-in.-wide high-channel section, which commonly occurs in molded parts.

The third geometry, a channel with a rib on the back edge, and the fourth, a channel with a third wall, both show the effects of structural support on warpage and illustrate the trade-off between stiffness and shrinkage. For example, the third wall support adds stiffness to the part, but the way in which the wall shrinks affects the magnitude of warpage.

The experimental parts were molded on a 75-metric-ton injection machine and tooling with interchangeable cavity inserts to control the part geometry. The mold also employed a hot sprue bushing, a modified trapezoidal runner system, and an edge gate.

All parts were measured on a Sheffield coordinate-measuring machine (CMM) fitted with a noncontacting laser probe to monitor any deflection. During warpage measurement, the parts rested upon three pins. With four locating posts in the measurement jig [ILLUSTRATION FOR FIGURE 1 OMITTED] defining the x and y axes, a plane was defined by measuring the z-coordinate of the tips of the three pins. The plane was then shifted in the z direction to account for the part thickness. Eight-eight points were measured in a 4 x 22 grid across the part surface. The deviation from the plane described by the pins was recorded for each point.

STATISTICAL DESIGN

We used the Taguchi method in designing the experiments and the simulations, employing three levels for each processing variable as follows:

* The levels of mold and melt temperature spanned the range of common conditions for PP.

* The cooling time varied from the minimum necessary to solidify the part to roughly twice that value.

* The packing pressure began at a level well below the maximum pressure experienced during filling, while the upper level was the maximum value before parts began to stick in the mold.

* The range of injection time was chosen using 2-D flow analysis. The lower value was based on the lowest allowable end-of-fill temperature, just above the no-flow temperature. The upper level was based on the maximum allowable shear rate.

Plots of "factor effects" - or the effects of changing values of each variable - isolated the contribution to warpage of the individual processing conditions [ILLUSTRATION FOR FIGURE 2 OMITTED]. These effects were calculated by averaging all warpages across each factor level.

WHICH VARIABLES DOMINATE?

Experimental results indicate that warpage is minimized in the first two geometries by processing at the largest values of mold and melt temperature, injection time, and cooling time. For the first geometry, warpage is minimized at the middle level of packing pressure, while the high level produces least warpage in the second geometry. For both geometries, injection time contributes the most to warpage, while packing pressure comes in a distant second.

The third and fourth geometries exhibit different behavior. Although mold temperature, melt temperature, and cooling time exhibit trends similar to those of the first two geometries, injection time and packing pressure do not. Packing pressure plays a larger role in driving warpage in these geometries, while the importance of injection time is reduced. Also, injection rate reverses its trend, so that a lower injection time decreases warpage.

THE COMPUTER'S PREDICTIONS

In the simulation phase of the study, Moldflow's MF/Flow software first ran though a 3-D flow analysis at a specified mold temperature. MF/Flow was also used for a packing-phase simulation. Predicted filling patterns for each geometry correlated well with short shots of the experimental mold.

We then ran a Moldflow cooling analysis (MF/Cool) using the flow-analysis results as input. Other inputs to MF/Cool included the packing time, cooling time, cooling-water inlet temperature, and cooling-water flow rate. Results from the cooling simulations agreed with the temperature given by thermocouples in the test mold.

Finally, Moldflow's MF/Warp was used to compute the part shrinkage and warpage. The inputs to this calculation were the meshed model from the MF/Flow analysis, Young's modulus parallel and perpendicular to flow, and Poisson's ratio. MF/Warp offers three warpage analyses: small displacement, large displacement, and linear buckling. A linear buckling analysis was run for each experiment and indicated that buckling was [TABULAR DATA FOR TABLE 1 OMITTED] not a concern with these parts. Several test runs using large-displacement analyses showed that nodal deflection occurred in a linear manner over the load steps. This finding indicated that the linear assumption of the small-displacement analysis was sufficient. Small-displacement analysis was therefore used in each case to reduce computing time.

Both the first and second geometries warped toward the cavity side of the tooling. Meanwhile, mold thermocouple traces and simulation results showed that the cavity side was about one degree warmer than the core side.

The warpage-direction trend reversed for the third and fourth geometries: Although the cavity side was again hotter, these parts warped toward the core side. Evidently, the small temperature difference did not have a major effect on warpage direction.

SIMULATION VS. REALITY

In the experimental phase, the measured absolute values of 88 points on each part were averaged to define warpage. This definition was applied to simulation results of the first two geometries in order to compare factor effects [ILLUSTRATION FOR FIGURE 2 OMITTED]. Except for melt temperature, the trends were similar. The effect of injection time, however, was not as pronounced for the simulations. Also, the cooling time showed no distinct trend.

We wrote a computer program to extract the nodal coordinates from the Moldflow node file. Next, the program read the nodal deflections from the warpage output file. The deflections were added to the original nodal locations to produce the deflected coordinates of each node. These coordinates were then translated in the x and y directions such that the same origin was used by both the CMM and the nodal coordinates. The program then extracted the coordinates of the three points corresponding to the pins on the experimental jig. These points defined a base plane from which deviations were measured.

To study the accuracy of simulation results, warpage was defined as the maximum deviation minus the minimum deviation. The simulation predictions for the first two geometries usually were within 0.02 in. of experimental results, Several predictions fell within 0.01 in. of experimental measurements (see table). One exception is that large differences occurred for experiments that used the shortest injection time (0.5 sec). Mold-flow personnel suggests that this lack of correlation most likely springs from shrinkages occurring outside the range of available resin characterization data.

A FEW PROBLEMS

The third and fourth geometries proved tougher to model than the first two. The simulations were unable to replicate the large warpage that was actually observed in the gate area of geometries three and four. According to Moldflow representatives, this problem most likely can be attributed to the extreme conditions of pressure, temperature, shear rate, and shrinkage occurring near the gate. Another source of error in simulating the gate area may rest on a compromise in the modeling approach: The beam-element method that best models heat transfer in the gate area does not yield the most accurate representation of the gate area's actual geometry.

To get around these problems, we looked instead at 22 points from the back rib of the parts. This view of the part yielded a more favorable comparison between simulated and actual results. The simulations predicted the warpage along the back wall of Part 3 to within 0.010 in. for four of the experiments. The predictions were not as accurate for the fourth geometry, but were still within 0.015 in. in most cases.