Tolerance formation is an important aspect of the manufacturing industry. It is a central feature of the Geometric Dimensioning and Tolerancing (GD&T) system that designers use to communicate key part characteristics and tolerances associated with production.
Tolerance stacking is an important technique in tolerance calculation applied to “stacked” geometric features. It helps ensure production processes are accurate, convenient and cost-effective.
This article discusses tolerance stacking in detail. It explains what it is, what types there are and what best practices are recommended by experts.
What is tolerance stacking?
The tolerance stack is the cumulative state of the geometric tolerances of connected features. Essentially, this can be understood simply as the individual tolerances of a part's features are added together and their cumulative effect occurs on the part's overall tolerance.
Tolerance stacking is a useful analysis that ensures the part and its components can be manufactured. Helps avoid situations where part features are within tolerance, but the part as a whole is out of tolerance and is discarded.
Tolerance Stacking Example
Let's look at the example of a plate with several holes next to each other. Holes and their positions on the plate are critical tolerance features. There is a possibility that all holes are within tolerance, but within maximum limits.
This can cause all the holes to become oversized by chance, leaving not enough material between them to support the board. This results in the part failing quality testing even though key features are within tolerance.
This highlights the practical need for using tolerance stacking analysis. Furthermore, it helps reduce wastage of time and money and reduces material waste.
Tolerance Stack Analysis Methods
Engineers use two main methods to stack tolerances. The main function is the same for both, but there are some important differences that make them suitable for certain situations.
Worst case tolerance analysis
The worst-case tolerance stack analysis is the simpler of the two. This assumes that all resources reach their maximum drift levels, which is the worst-case scenario for a manufacturer.
Although this is unlikely in a real production environment, the worst-case technique is used when risks are high. This is particularly true for high-precision parts in industries such as aviation and medicine.
For a part with n features and two-sided tolerances, the formula to find the total variation is:
The worst-case method ensures that all parts are within tolerances and achieve the desired technical fit. However, this security comes at the cost of stricter tolerances. For this reason, this method is best suited for low-volume production because the probability of producing parts within tolerances decreases as the number of parts increases.
Worst-Case Tolerance Analysis Example
Tolerance stacking can be complicated and difficult to understand. Therefore, we present a simple example of tolerance stacking to illustrate this point. The following figure shows a tolerance stack with multiple features, each with its own dimension and tolerance. The objective is to calculate X, the global assembly tolerance, based on the worst-case principle.
In the worst case of tolerance stacking, the nominal dimension and tolerance are the sum of the feature dimensions. Therefore, X is calculated as follows:
| element | Nominal | tolerance |
| A | 8th | ±4 |
| B | 5 | ±2 |
| W | 5 | ±2 |
| D | 5 | ±2 |
| Assembly (X) | 23 | ±10 |
Therefore, X = 23 ± 10
Statistical Analysis of Tolerance / RSS – Root Sum-Squared
The tolerance stacking statistical analysis method takes a slightly more realistic and methodical approach to tolerance stacking. Statistical analysis is used to estimate the probability distribution of deviations in each tolerance dimension.
The basic hypothesis for this is that each dimension is different. Some will deviate less, others more, just like in a real factory. Therefore, it is widely applicable in mass production environments where a small number of defects are acceptable.
After these individual probability distributions are calculated, they are summed to determine the probability of the part's overall tolerance. This provides a reasonable estimate of how many parts are unlikely to pass quality testing.
Various statistical techniques are used, but by far the most common method is the Root Sum Squared (RSS) method, which assumes a normal distribution of dimensional deviations.
The formula for calculating Tasm mounting tolerance is:
RSS Tolerance Analysis Example
To understand statistical tolerance stacking, let's use the same example. The nominal dimension X remains unchanged at 23. The tolerance is calculated using the RSS formula.
Therefore, using RSS, X is 23 ± 5.29.
Best Practices for Tolerance Stacking
Tolerance stacking is half science, half art. It requires technical skill to select the most appropriate dimension chain when performing stackup analysis. In the following sections, we summarize expert tips and tricks to help you optimize your tolerance stack analysis.
Keep your drawings clean
Technical drawings are the standard method of communicating design intent to production engineers. A common mistake made by inexperienced engineers is to add tolerances to each sub-feature, which is usually not necessary. Setting tolerances for only critical features is usually sufficient and automatically controls the dimensions of auxiliary features.
Therefore, it is recommended not to oversize your piece. This complicates the manufacturing process and overloads the technical drawing, causing confusion.
Understand manufacturing challenges
It's easy to get carried away and set tighter tolerances than necessary on some features. Designers must remember that although their production departments may produce high-quality parts, tolerances are determined by the functionality of the part.
Therefore, both designers and manufacturers need to evaluate their tolerances from a practical perspective and avoid an overly strict approach.
Consider the quality of parts after manufacturing
This is general advice, not something specific to tolerance stacking. When creating their designs and tolerances, engineers must consider the changes their parts will undergo during service. There is general wear and tear and maintenance that affects tolerances over time.
Therefore, it makes sense to take this into consideration and set appropriate tolerances to maximize service life.
Tolerance Stacking Tools
Tolerance stacking, like any other production schedule, has changed significantly in recent years. Modern CAD/CAE software has tools like a tolerance stack calculator. Designers can choose from a variety of tolerance stacking methods, identify all possible tolerance chains in the part, and easily incorporate changes into technical drawings.
Tools like this boost the manufacturing industry and help engineers implement precision manufacturing methods like 6-Sigma.
Concluding
Tolerance stacking is one of the most useful tools in production. Ensure parts fit together well and take ease of manufacturing into consideration. For engineers involved in product design and GD&T, this is an essential skill.
Common questions
Why is tolerance stacking important?
Tolerance stacking ensures that parts are manufactured within the tolerance limits defined for each geometric feature. This method preserves functionality while maximizing manufacturing convenience.
What is 1st and 2nd order tolerance stacking?
1st and 2nd order tolerance stacking are the terms used for worst case tolerance stacking and statistical tolerance stacking respectively.
What are the general challenges associated with tolerance stacking?
There are several challenges in tolerance stacking, such as: B. selecting the best variant of tolerance chains, considering manufacturing options, and finding the right balance between part tolerances and cost efficiency.
