Tolerance Stack-Up Analysis

What is Tolerance Stack-Up Analysis?

Tolerance stack-up analysis is a fundamental process in mechanical design used to study the accumulation of variation in an assembly. Each component of a product has dimensional tolerances (a permitted variation in its size). This analysis calculates the combined effect of these tolerances to predict the final dimensional variation of the assembly, ensuring that parts fit together correctly and the product functions as intended.

Brief History

The concept of interchangeable parts dates back to the Industrial Revolution, but the systematic analysis of their accumulation gained momentum in the 20th century, especially with the rise of mass production. The need to predict and control variation became critical. Walter A. Shewhart's work in the 1920s on Statistical Process Control (SPC) laid the groundwork for probabilistic methods. Later, the development and standardization of Geometric Dimensioning and Tolerancing (GD&T) provided a precise language for defining tolerances, making analyses more robust and reliable.

How This Tool Works (Methods)

This tool implements three of the most common methods for performing tolerance stack-up analysis:

1. Arithmetic Method (Worst-Case)

This is the simplest and most conservative method. It assumes that all component tolerances are in their most unfavorable condition at the same time. All tolerances are linearly summed to find the maximum and minimum possible range of the assembly.

• Advantage: Guarantees that 100% of assemblies will meet specifications.
• Disadvantage: Often leads to excessively tight and expensive component tolerances, as the "worst-case" scenario is statistically very unlikely.

2. Probabilistic Method (RSS - Root Sum Square)

This statistical method, also known as Root Sum of Squares (RSS), assumes that component variations follow a normal distribution and that it is highly unlikely that all deviations will occur in the same direction simultaneously. The total tolerance is calculated as the square root of the sum of the squares of the individual tolerances.

• Advantage: Allows for wider, more economical component tolerances, reflecting a more realistic production scenario.
• Disadvantage: There is a small statistical probability that an assembly will fall outside the calculated limits. This tool assumes that the input tolerances represent a range of ±3 standard deviations (±3σ).

3. Monte Carlo Simulation

This is the most powerful and flexible method. It uses computational power to simulate the assembly thousands of times. In each "simulation," a random value is assigned to each dimension within its specified tolerance range. The result is a complete statistical distribution of the possible assembly outcomes.

• Advantage: Provides the most accurate view of actual variation, allowing for the analysis of non-normal distributions and the calculation of failure probability (scrap rate) with high reliability.
• Disadvantage: Requires more computational power, which this online tool handles for you.