New relational algorithm takes the guesswork out of critical dimension control (Web-exclusive expanded content)New relational algorithm takes the guesswork out of critical dimension control (Web-exclusive expanded content)

Editor’s note: A free one-year license is being offered for Correlation Master during the introductory pricing period with purchase of a one-year software maintenance contract.

Author Steve Tuszynski, principal of Algoryx Inc., has developed a relational algorithm that identifies and uses the interrelationships among molded part characteristics to help molders, toolmakers, designers, and their customers achieve Six Sigma goals by reducing costs, improving part quality, and speeding time to market.

Injection molders and their customers are leaving money and quality on the table. Redundant measurement, statistical process control (SPC) analyses, and process capability (Cpk and Ppk) analyses waste time and money during both production and development. Trial-and-error, iteration, and guesswork can result in multiple mold changes, multiple design tolerance relaxations, difficulty in establishing press settings, increased costs and risk, and delays during development. New technologies are available that provide solutions to these problems.

Difficult Problems Span the Entire Molding Process

Our customers often have difficulty deciding which dimensions should be measured and analyzed using SPC and Cpk analyses. The default but costly answer has been to measure and analyze all critical dimensions. This ignores the interrelatedness between dimensions and wastes time and money. Design tolerances can be specified with little or no regard for process capability. Material selection and replacement of obsolete material can be problematic.

The manufacturability window may be small or nonexistent—meaning it may be difficult or impossible to produce good (conforming) parts using the initial design tolerances and the preproduction mold. Operators and process engineers can waste significant time learning this through repeated trial-and-error attempts.

Preproduction molds can be modified numerous times before the part is qualified. This is costly, causes schedule delays, and can be risky. There can be repeated trips back to the design engineer asking for design tolerance relaxation. The requested mold modifications and design tolerance relaxations are a function of the press settings used by the process engineer or operator. Any change to those settings can invalidate previous mold and design changes.

Design of Experiments (DOE) is useful when one dimension needs to be optimized and there are few complexities such as nonlinearities, reversals, different dimensional responses, and simple and complex interactions. When more than one dimension needs to be optimized, as is usually the case, DOE can give conflicting results. When complexities do exist, it can be difficult or too costly to model the molding process with DOE.

Finite-element analysis (FEA) programs sometimes work for a limited category of designs, but they do not eliminate redundant measurement and analysis or identify required tolerance relaxations to increase the producibility window.

Finger-pointing resulting from the inability to produce good parts can create conflict and adversarial relationships within the project team between design engineers (tolerances are too tight), tooling engineers (created a bad mold), and process engineers (can’t find the correct process settings).

Principles Underlying TRA

Tuszynski’s Relational Algorithm (TRA), available through a software program called Correlation Master, is based on the fact that although the relationships between causes (press settings) and effects (dimensions) may be difficult or impossible to determine, the relationships between effects are consistent and predictable for molded parts.

Figure 1 illustrates how a correlation chart is generated. In this example, a design has two critical dimensions. Five sample parts are made, each under a different combination of press settings. The two dimensions on each part are measured and plotted as a point on the chart. One dimension is identified by the software as the predictor dimension (P), which is the statistically best predictor of all other dimensions. A linear regression line is fitted through the five points. (We have not encountered nonlinear dimensional relationships, although they can easily be modeled.)

Figure 2 illustrates a part with four interrelated dimensions—A, B, C, and P—and shows the entire universe of possible relationships between the four dimensions. Further, the system of relationships in Figure 2 has a single degree of freedom. When the value of the predictor dimension (P) is known, the value for all predicted dimensions (A, B, C) can be determined.

The operating point is defined as a point on any of the regression lines. The operating point is adjusted by changing one or more press settings. This is analogous to sliding a bead along a wire.

Figure 3 (p. 65) adds structure to Figure 1 by adding the upper (USL) and lower specification limits (LSL) for the critical and predictor dimensions. The blue area within the four specification limits is defined as the region of conformance and is the area in which good parts are produced. The intersection of the target values for the two dimensions is defined as the target intersection. It is not possible to produce a part with both dimensions at their target values unless the regression line passes through the target intersection.

Four Possible Relationship Conditions

There are four possible relationship conditions. The first condition is defined as “robust” (Figure 4). The critical dimension will always be within its specification limits, irrespective of the value of the predictor dimension. The robust critical dimension never needs to be measured.

The second condition is defined as “unconstrained” (Figure 3). When the predictor dimension is within its specification limits, then the critical dimension will be within its specification limits and never needs to be measured.

The third condition is defined as “constrained” (Figure 5). When the predictor dimension is between P-min and P-max, then the part will be a good part and the constraining critical dimension never needs to be measured.

The fourth condition is defined as “defects” (Figure 6). When the regression line lies outside the region of conformance, only defective parts will be produced and neither dimension needs to be measured. Instead, the mold must be modified and/or the design must be changed.

Operating Range and Operating Target

Figure 7 is a one-dimensional representation of a part that has three dimensions—two critical dimensions (C1, C2) and the predictor dimension (P). The top arrow represents the range of P for which C1 will be in specification. The middle arrow represents the range of P for which C2 will be in specification. The operating range is the range of P over which all three dimensions are within specification. The software extends this logic to any number of dimensions.

For symmetrical process output, the operating target is located at the center of the operating range. For nonsymmetrical process output, the operating target is best selected as the point at which there is equal area in each of the tails of the process distribution outside the operating range.

Reducing Measurement and Analysis Costs

TRA capitalizes on the interrelatedness of part dimensions to achieve reductions in measurement and analysis costs. Assuming that any defect conditions have been fixed (as discussed below), the part is guaranteed to be a good part when the predictor dimension is within the operating range. The predictor dimension is the only dimension we need to measure and is the only dimension for which we need to do SPC and process capability analysis. Analysis and measurement costs can be drastically reduced.

One-step Tooling Modification

Figure 8 shows one technique to fix a defect condition like the one shown in Figure 6. In this example, the regression line is shifted (down) out of the bad part (nonconforming) region into the good part region. This is done by changing the internal mold size for the critical dimension. The software computes the direction and magnitude of the mold change necessary to pass the regression line through the target intersection. By doing this, mold changes are optimized in a single step and are independent of operator press settings.

One-step Tolerance Relaxation

Figure 9 shows a second technique to fix a defect condition. In this example, the upper specification limit is increased until the region of conformance contains the regression line. The software prioritizes and computes the tolerance relaxations needed to achieve any specified increase in the size of the operating range.

Material Selection

Different materials produce different-sized operating ranges for the same design. The software identifies the most producible material as that with the largest operating range.