Tolerance Stackup - VTAstrobotics/Documentation GitHub Wiki

Tolerance Stackup

Contents

Prerequisites

To understand the content on this page, you should know how to

  • Taken Engineering Statistics

What is Tolerance Stack Up

Tolerance stack up is the process of adding individual tolerances of components to understand their cumulative effect on the final assembly. This analysis is crucial to ensure that all parts fit together properly and function as intended.

Example

In this example, each component's tolerance is considered to ensure the final assembly meets the required specifications.

Methods for Analysis

Statistical Tolerance Analysis

The statistical tolerance stack analysis method takes a slightly more realistic and methodical approach to tolerance stacking. It uses statistical analysis to estimate the probability distribution of deviations in each tolerance dimension.

For this, the basic hypothesis is that each dimension will be different. Some will be less off, some more, exactly like it is in a real factory. Consequently, it is widely applicable in mass production environments where a small number of errors are acceptable.

After calculating these individual probability distributions, it adds them up to compute the probability of the overall part tolerance, which gives a reasonable estimate of how many parts are expected to fail the quality tests.

It utilizes various statistical techniques, but the Root Sum Squared (RSS) method is by far the most popular, which assumes a normal distribution for the dimensional deviations.

The formula to calculate the assembly tolerance, Tasm, is:

Example

  1. To understand statistical tolerance stacking, let us use the same example. The nominal X dimension will remain the same at 23. The tolerance is calculated using the RSS formula.
  1. Therefore, using RSS, X is 23 ± 5.29.

Worst Case Tolerance Analysis

The worst case tolerance stack analysis is the simpler of the two. It assumes that all features are at their maximum deviation levels, which is the ‘worst-case scenario’ for a manufacturer.

While this is an unlikely event in a real production environment, the worse case technique is adopted when the stakes are high. Especially for high-accuracy parts in industries like aviation and medicine.

For a part with n features and bilateral tolerances, the formula to find the total variation is:

The worse case method guarantees that all parts will be within tolerance and achieve the desired engineering fit. However, this confidence comes at the cost of tighter tolerances. Due to this, it is more suitable for low-volume production as the likelihood of manufacturing parts within tolerance gets lower as the number of parts grows.

Example

  1. Tolerance stacking can be involved and difficult to comprehend. Thus, we present a simple tolerance stack up example to drive the point home. The figure below shows a tolerance stack with multiple features, each having its dimension and tolerance. The goal is to calculate X, the total assembly tolerance based on the worse case principle.

  1. In the worse case tolerance stacking, the nominal dimension and tolerance are the sum of feature dimensions. Hence, X is calculated as:

  2. Therefore, X = 23 ± 10

Tolerance Stacking Best Practices

Drawings

  • Ensure clear and detailed drawings with all necessary dimensions and tolerances.
  • Use Geometric Dimensioning and Tolerancing (GD&T) to communicate design intent effectively.

Understanding Machining Challenges

  • Be aware of the limitations and capabilities of manufacturing processes.
  • Consider the impact of machining variations on the final assembly.

Tools for Tolerance Stacking

  • Use software tools like CETOL 6 Sigma, VSA (Variation Simulation Analysis), and GEGCalculators for accurate tolerance stack up analysis.
  • Leverage statistical methods and simulations to predict and control variations.

References