By Tim Bogard
President
Sigmetrix
McKinney, Tex.

Edited by Paul Dvorak

Companies in nearly every industry save time and money when designers and manufacturers pin down product requirements and production capabilities early in development. Mechanical-tolerance specifications are a big issue in these early discussions. Determining optimal tolerances, especially for complex mechanisms, can make the difference between cost-effective, on-schedule products and those burdened by scrap, rework, and delay.

Traditional tolerance analysis often provides too little, too late. Designers might perform a 1D or 2D analysis for a few contact surfaces that appear critical, but they usually wait to do this until right before a release to manufacturing. Unless manufacturers understand design intent, changing tolerances during production can result in products that miss customer requirements and cost targets.

Current analysis software provides reliable information about tolerances early in design cycles even when little is known about the final geometry. The example of an engine valve train illustrates how using tolerance analysis software can lead to better products.

CRITICAL PERFORMANCE SPECS
The focus of tolerance analysis should be on the mechanism's critical dimensions and parameters. For internal combustion engines, important dimensions are the timing angle on the camshafts and the exhaust-valve seat clearance. The proper camshaft-timing angle maximizes engine power and efficiency, and the proper exhaust-valve seat clearance controls emissions. An automotive engine with optimized tolerances will have more horsepower, greater efficiency, and lower emissions than an engine with the same displacement that has not been optimized.

The goal of tolerance optimization is to balance assembly performance against manufacturing costs. Optimization software identifies dimensions that do not affect performance so their tolerances can be traded off to critical surfaces. In this way, tolerance optimization improves product quality without increasing costs. It also streamlines development cycles by requiring fewer physical prototypes.

Tolerance-optimization software has a role to play throughout every stage of design. In concept product modeling, it highlights variations in component interfaces that affect design feasibility. In functional assembly modeling, the technology tells engineers which variations in assembly constraints will affect performance in the "as-designed" model. During detailed part modeling, tolerance analysis labels changes in part dimensions that affect performance in the "asmanufactured" model. And in manufacturing process modeling, the software identifies manufacturing variations that affect part producibility.

CONCEPT PRODUCT MODELING
The goal in concept modeling is to understand basic requirements for the system under design and then determine the best approach. Using only skeleton geometry, tolerance-optimization software proves whether a design is feasible or not.

For the valve train, it's necessary to identify part surfaces most critical to maintaining two specs: the camshaft-timing angle and exhaust-valve seat clearance. Engine designs are more robust when variations can be controlled on the surfaces most sensitive to performance specs.

Assumptions made during concept modeling have repercussions throughout development. It is vital to be as precise as possible to avoid expensive errors. But a lot is not known. For example, what are the critical surfaces? What tolerances can machine tools hold? Are the ranges within the capability of current capital assets, or will manufacturing require new technology and tools?

FUNCTIONAL ASSEMBLY MODELING
This step determines the assembly constraints that meet performance requirements. Doing so requires modeling part interfaces that create the required joint behavior for the assembly.

Questions that need answers at this point include: Will parts be bolted together or pinned? Will parts be free to move with respect to each other and still stay in contact with a source load? And will there be a singlepoint contact or multiple surfaces simultaneously in contact? Each answer describes a dimension with tolerance. For example, bolted joints need clearance holes of a certain dimension. Tolerance-optimization software assesses how much that dimension will vary during production.

As physical geometry begins defining how parts go together, skeleton geometry is replaced with flanges, bolt-hole patterns, ball joints, bearing interfaces, and so on. At this point, it is important to pay attention to production planning and to combine manufacturing process information with modeling practices. There is often a disconnect between design and manufacturing during functional assembly modeling. Without analyzing sensitivities of new part interface surfaces with respect to material properties, one often wrongly assumes manufacturing can produce assemblies that meet performance objectives.

Many ECOs stem from mistaken assumptions about the capability of manufacturing processes to produce features that are critical to assembly performance. Prototyping is not a safeguard because it does not sample the population variability inherent in manufacturing processes.

Analysis at this point reveals which part interfaces are most sensitive and ensures that the design centers on critical dimensions before assigning tolerances. Adjusting a nominal dimension, instead of requiring tighter tolerances than manufacturing can deliver, solves problems before they occur.

For the valve train, a sensitivity plot shows several dimensions, such as the position of the center hole in the exhaust-valve guide, that contribute to the variability of the seat-clearance measurement. Even a slight adjustment to the nominal geometry
could bring the design to within acceptable limits.

DETAILED PART MODELING
Manufacturers usually plan their work so it uses the fewest set ups. Therefore, they may set up a part on a machine using datum references that differ from those in the design. Defective parts can be the unfortunate result. Product models that include dimension schemes to optimize manufacturing lessen the risk of defects.

Most companies would like to make manufacturing knowledge available to designers as well as make design intent available to manufacturers. Tolerance-optimization software provides the bridge in what's called an overlay mode. This mode offers engineers a manufacturing-process dimension scheme to analyze tolerances without changing geometry or drawings.

The overlay mode allows exploring alternative dimensions and quantitative discussion about changes to manufacturing processes or the design. The overlay mode also makes it easy to zero in on sources of variation that contribute the most to defects.

MANUFACTURING PROCESS MODELING
Once datum references and production tooling are set, it's necessary to determine whether the available processes can hold the planned dimensions. Tolerance-optimization software assists by statistically analyzing a dimension scheme in terms of the population of behaviors the scheme generates for production conditions. Population of behaviors is a statistical term describing a range of possible variations. For instance, a joint made with a square pin pressed into a round hole could be off center several ways. The collection of all the possible ways in which the pin could be off-center defines the population of behaviors.

The software can handle data such as the statistical capability of machining and molding operations. For example, it considers how well tools hold a work piece in place, how correctly robots position welds, how consistently technicians tighten bolts, and so on. Manufacturing engineers usually have records of this information.

Even at late design stages, the software lets users balance cost and quality. It can answer questions such as: Will a particular manufacturing process hold the required tolerance? How much variability can be allowed in a process before it affects the design? Will different processes with the same cost impair the design, and is it worth making the change? Changing tolerances on selected dimensions and rerunning the analysis shows which adjustments can be made to reduce the defect rate or maintain critical dimensions.

Cost savings often come at this stage. Manufacturing might find it less expensive to produce a particular part's surface on its highest quality machining center rather than setting it up again on another machine, for example. Learning this as early as possible makes it easier to reduce costs by adjusting tolerances on other parts.

A solid model of the engine valve-train assembly shows dual-overhead camshafts. A cross section of the cylinder head reveals intake and exhaust-valve assemblies. The two critical design specifications under analysis using CE/TOL 6 are the timing angle on the camshaft and the exhaust valve-to-seat clearance.	CE/TOL 6 software offers an easy-to-use interface with Pro/Engineer that simplifies tolerance analysis. A solid model of the valve train is shown at left. A CE/TOL assembly network diagram appears at the upper right, with a statistical analysis below. The software provides statistical tolerance analysis through each stage of product development, from concept sketch to final manufacturing.
Camshaft gears shows the critical timing angle. If this angle varies too much, it may produce inconsistent drive characteristics, loss of horsepower, and too much engine noise and vibration.	A model of the lower portion of the exhaust-valve assembly shows the critical seat-clearance measurement. If the valve does not close tightly against the seat, unburned fuel escapes into the exhaust and violates emission-control requirements.
Tolerance analysis can begin even with only skeleton geometry of the valve train. CE/TOL 6 software uses datum curves and surfaces to identify part interfaces that are sensitive to critical specifications and to check design feasibility. Yellow joint icons appear at these interfaces.	During functional-assembly modeling, geometric relationships between critical assembly components are more fully developed. From solid geometry, CE/TOL completes a statistical model that defines all possible sources of assembly variation affecting the critical design specifications.
The Assembly Network Diagram represents the assembly variation model. It contains each assembly constraint and defines the proper assembly sequence. Green squares indicate critical specs, blue polygons indicate parts, and different yellow icons show constraints. Statistical analysis of the assembly variation model gives the quality level for the critical spec under examination. In this case, it's the Exhaust Valve-to-Seat Clearance.	Results of a preliminary statistical analysis show (blue highlighted bar) a quality level of 1.9 sigma for the critical Exhaust Valve-to-Seat Clearance spec. This would result in about 61,400 defects per million assemblies. To improve quality, users might adjust tolerances or nominal dimensions on sensitive part surfaces.
The chart shows the impact of each variation source on the two critical specs. It shows that the two most sensitive dimensions for the Exhaust Valve-to-Seat Clearance spec are the valve-guide-hole position and the valve-guide position in the cylinder head. Red bars indicate a sensitivity level when closing the gap, and the blue bar shows sensitivity when opening it, thus making 3D analysis more meaningful.	The chart shows the percent contribution of each variable to the two critical specs. Changing tolerances on the larger contributors has the most influence on quality.
CE/TOL software includes an overlay mode which allows exploring alternative dimensioning schemes without changing part geometry.	The Part Network Diagram represents the overlay dimension scheme. After making process assignments to part dimensions that contribute most to the critical spec variation, CE/TOL performs another statistical analysis to generate a revised sigma rating. Each symbol represents a surface identified by the GD&T scheme and assigned by the engineer. The diagram shows manufacturers how the design engineer dimensioned parts and what he or she considers important.
After making process assignments, the final statistical analysis shows a revised quality level of 6.0 sigma for the Exhaust Valve-toSeat Clearance spec. The engineer can now be sure the assembly will meet or exceed goals for performance without incurring unexpected costs in fabrication.	In the final refinement of the assembly-variation model, process definitions and producibility requirements are set for every part in the assembly.
Users assign manufacturing process definitions from the CE/TOL process library. An updated library accurately describes process-variation data for each manufacturing process. The skewed distribution for a particular machine tool indicates that statistically more parts will be manufactured in the lower end of the tolerance specification, which is acceptable for quality goals. ">
Users assign manufacturing process definitions from the CE/TOL process library. An updated library accurately describes process-variation data for each manufacturing process. The skewed distribution for a particular machine tool indicates that statistically more parts will be manufactured in the lower end of the tolerance specification, which is acceptable for quality goals.