**Richard M. Rots Account Manager**

**Dimensional Control**

**Systems Inc.**

Troy, Mich.

Troy, Mich.

Typical design practices and CAD software consider an assembly only from a nominalbuild perspective. Collision detection in most CAD programs can spot interference in a mechanism, but the feature is limited in that it ignores variations in part dimensions and the assembly process. What's more, when manufacturers focus only on parts and ignore the assembly as a whole, they almost certainly run into a situation in which a set of components that meets detail quality specs builds a faulty assembly. Quality components do not guarantee a quality assembly.

A solution to the dilemma applies variation analysis to an assembly. For example, the 3DCS software developed by **Dimensional Control Systems **creates a virtual digital prototype of an assembly and predicts its variation using a Monte Carlo random-number generator to assign a value for each tolerance during simulated builds. The software provides a summary of the overall assemblybuild variations and an outline of contributors to the variation for each measurement, such as a given part tolerance or an inherent design issue.

Inherent design issues are important because they can lead to a sensitive design that will haunt a team throughout the production life cycle. For example, geometry effects of a given part feature can cause an overall variation many times larger then the tolerance. To understand this concept, picture a seesaw with the pivot point on center. Push down one end 3 ft, and the other end moves up 3 ft. But shift the pivot point to one side and pushing one end down 3 ft might make the other end move up 6 ft. With the pivot point off center, this condition is inherent in the design. No matter how much you change the tolerance (the amount of allowable movement of the seesaw), there will always be an amplification factor (variation).

Inputs needed to run a variation analysis include:

**Part geometry**, or the CAD data, provides a visual representation of parts and the math data as a baseline for the analysis. The software lets users animate assemblies to ensure they will go together as planned. Features vary based on their GD&T callouts and parts move in their assemblies.

**Order of assembly, part-topart interrelationships, and locating fixtures **define the assembly process. The software provides a set of "Move" routines to mimic any assembly process. Features in the software let users accurately replicate the real-world assembly environment.

**Tolerances **are applied to detail parts. Tolerances define an allowable amount of variation for a given part feature. The software simulates any tolerance specification. Users select from a list of distributions including Normal, Uniform, Weibull, Min-Max, and User-Defined. The software allows a user to replace predictive tolerances with real part-inspection data to replicate manufacturing as closely as possible.

**Measurements **define where the variation of an assembly is analyzed such as fit-finish or functional. Fit-finish requirements are customer driven based on appearance. An example is how well a vehicle's hood and fenders match up. Functional requirements relate to how well an assembly works. An aircraft door, for example, must close, seal, and latch for safety reasons. Other functional objectives can include flow rates, pressures, and gasketseal gaps. Users can identify any number or combination of measurements within the variation model.

The software provides several outputs. For example:

A **Monte Carlo simulation **results window displays a report in the form of a histogram. The software generates a statistical report for each measurement in the model. For example, a histogram might show statistical data for a top-gap measurement — the variation between a point at the top of a headlamp and a point at the top of a turn lamp. Typical information provided includes the Mean, Nominal, Percentage Out, and Min and Max deviations.

A **Sensitivity analysis**, also referred to as High-Low-Mean analysis, determines which tolerances within the assembly contribute most to variation for a particular measurement. The analysis works by varying an individual tolerance to a High, Low, and Median value, while holding the rest of the tolerances at their nominal values. This process is repeated for all toleranced features. The software ranks contributors from highest to lowest for each measurement.

**Geofactor analysis**examines the geometric effect of each tolerance on a given measurement and calculates a coefficient of influence, which the software calls the G-Factor. (Geofactor analysis differs from Sensitivity analysis in that Geofactor examines the contribution to variance resulting from the part geometry, tolerance distribution) and the part's tolerance range. A tolerance with a G-Factor of <1 doesn't contribute much to the variance of a measurement. But one with a value >1 noticeably affects the variance. The G-Factor number is the amplification of each tolerance in the model, such as in the seesaw example.

## A brief introduction to statistical terms

Here's a brief list of terms and abbreviations frequently encountered in statistical readings.

**LSL and USL **— Lower Specification Limit and Upper Specification Limit (the tolerance range).

**L-Out% **— The percentage of measurement values falling below the LSL.

**H-Out% **— The percentage of measurement values falling above the USL.

**STD **— "Standard deviation," which is a statistical measure of variation and a measure of the spread of data in relation to the mean. STD is the most common measure of the variability of a data set.

**6STD **— Standard Deviation value multiplied by 6. It represents the width of the normal curve.

**Pp **— Pp is a Process Performance index which measures the performance of the process. The index compares the variation of the process to the allowable variation set for the specification limits (USL and LSL)

**Ppk **— The Ppk indicator is a Process Performance index which tells how well the process is centered, or how distant the mean of the process is compared to its specification limit.

**MAKE CONTACT Dimensional Control Systems Inc., 580 Kirts Blvd, Suite 309, Troy, MI 48084, (248) 269-9777, **3dcs.com