#96 – TOLERANCE ANALYSIS – FRED SCHENKELBERG

ABC FredIf you are reviewing a drawing or set of specifications and all the tolerances are set at a blanket value, this should raise your suspicions, for it implies that every tolerance has the same importance as all others. This may be true, yet it is often not possible nor necessary for the design and resulting system to function correctly.

We know that there are many sources of variability when components or parts are created. That is the purpose of tolerances: in part, to acknowledge the amount of variation that will be present and limit the variability such that the system still functions.

In the design process, setting tolerances balances the act of creating a robust and reliable product that performs even with a random set of actual sizes and values of the assembled components. Thus a crucial step in the design process is to understand the variability of the components, parts, and assembly processes. In many cases, we have the expected variability and in some we have to collect measurements and estimate the range of variability that will occur. In any case, to properly set the tolerances we need to do a tolerance analysis.

Why Do Tolerance Analysis?

The short answer is that everything varies. The longer answer involves the agreement between what is possible and what is desired. If we could design a product and it could be replicated exactly, including every element of the product, we would not need tolerances. Any part would work with any assembly. We would simply specify the dimensions required. Instead, variation happens.

Width, length, weight, roughness, hardness, and any measure you deem worth specifying will vary from one part to the next. Manufacturing processes impart some amount of variation among each item produced. In many cases the variation is acceptable for the intended function. In some cases the variation is unacceptably large and leads to failures. When the design does not account for the variation, holes will not align, components will not fit, or performance will be poor.

When the designer understands the manufacturing process and naturally occurring variation, the design tolerances balance what is possible with what is necessary.

Functionality

The final product performance relies on each component functioning as expected. Gears mesh and wheels turn. The inputs to the system provide the desired output. Doors close securely, being neither too tight nor too loose. Tolerances provide the range of values for each element of the design that enables the desired results to occur with each product produced. Instead of making the parts exactly to the drawing dimensions, the manufacturer creates the item such that it is within the tolerances, so that the assembly will perform as the designer intended.

The customer’s perception of quality relies on the components fitting and working well together. Alignment, fit, and finish have to be just right, and not noticeably off. If the tolerances are off, the customer will notice and perceive this as a lack of quality.

Manufacturability

Tolerances stack up to the extent that, if they are carelessly considered, parts will not fit at all or fit poorly, leading to failures and scrap. When parts do not fit, holes do not align, or connectors do not mate, the product is, at a minimum, not assembled correctly, requiring repairs, or is simply scrapped. In either case, the unnecessary costs mount.

The creation of individual parts, plus the variation of assembly processes, leads to the need for generous tolerances. Yet the design may require tight tolerances for the product to function as intended. The key lies in finding the balance between performance and the ability to assemble the system. This is an economic balance. It may cost more to maintain very tight tolerances. The cost of advanced manufacturing processes or the cost of inspection and scrap has to be balanced by the economic benefit of the customer-perceived quality and willingness to purchase the product.

Appropriateness of Costs

There are many ways to form parts: from casting to stamping and from die cutting to hand cutting. Each process has inherent variability. When the process is stable and the equipment well maintained, the parts will reflect the inherent variability of the manufacturing process. Each type of manufacturing process has limits on precision and, generally, the more precise methods are more expensive.

Using only very tight tolerances may require using expensive manufacturing processes for the parts. If not all part precision contributes to final performance then some if not most of the part tolerances may be less stringent. This may allow less expensive part manufacturing methods and still create a product with the desired performance.

Tolerance and Reliability

Ideally, every part has exactly the same dimensions and each product created fits together exactly the same, thus performing exactly the same (and as expected.) Unfortunately, in practice this does not occur and everything varies. Products fail due to variation that leads to excessive wear of parts that are too large or due to electronics running hotter than expected or connectors fitting too loosely, for example. There are many sources for the variation and, if the design accommodates the expected range of variation, the product will not suffer adverse effects of the variation that occurs.

One of the issues that reliability engineers should consider has to do with parts that are difficult to manufacture within the specified tolerances. If it is more likely that some parts are at or beyond their tolerances, this can lead to premature failure, if not poor product performance. By identifying the parts with tight tolerances or low process capability we can work with the design team or supplier to improve the ability of the parts to meet the needs of the design. As a minimum, we can take steps to monitor and control the process to create parts that are within tolerance specifications.

Regardless of the situation, to gain an understanding of the effects of tolerance on reliability requires performing a tolerance analysis. The three principal methods of tolerance analysis are

1. the worst-case method,

2. the root sum squared method, and

3. the Monte Carlo method.

Many design teams use either worst-case analysis for setting tolerances or root-sum-squared analysis to set tolerances if they are not using a default setting. Worst-case analysis is conservative: It estimates the ability of the design to function even if the collection of parts are at their extreme values. Will the circuit still work if the resister is at its maximum value and the capacitor is on the low end of its range of values? The same issue applies to mechanical systems.

Although worst-case analysis is conservative and fairly easy to implement, given the technology and assembly processes, it is still possible that the design will not function or that the product cannot be assembled under worst-case situations. Instead, we count on the very rare probability of every part in a system being at worst-case values. This is not likely to occur, so using a root-sum-squared analysis approach provides a way to combine the standard deviations of the part variations. Although this latter approach will yield values that are not as conservative as the absolute worst case values, it will minimize failures to only a small fraction of the total systems created. Basically, it implies that most parts will be near their nominal or target value and few will exist near the extremes.

Monte Carlo analysis is more accurate but requires more information. It enables us to simulate, for example, a hole alignment by using the distributions of the part variation. Indeed, this requires knowledge of the part variation distribution, not just the mean and standard deviation values, yet it allows the distributions to accurately reflect the spread of values and precludes us from having to assume a normal distribution.

Whichever method is used, it is important to understand its realm of validity and its limitations. Making a reliable product depends on doing a proper tolerance analysis. One size does not fit all.

Bio:

Fred Schenkelberg is an experienced reliability engineering and management consultant with his firm FMS Reliability. His passion is working with teams to create cost-effective reliability programs that solve problems, create durable and reliable products, increase customer satisfaction, and reduce warranty costs. If you enjoyed this articles consider subscribing to the ongoing series Musings on Reliability and Maintenance Topics.

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