# Multi-Dimensional Tolerance Analysis Basics

MEboost has tools that can perform multi-dimensional tolerance analysis.  This is the first in a series of articles on performing multi-dimensional tolerance analysis. This article will cover the basic theory behind tolerance analysis in MEboost.  In MEboost, multi-dimensional tolerance analysis is referred to as 1D/2D/3D.

2D worst case

2D Monte Carlo

3D worst case

3D Monte Carlo

## Use Cases

There are two use cases for the tolerance analysis tools:

Dimension Analysis Analyze the resultant dimension on a part or an assembly of parts. This is analogous to a 1D stack height.

Clearance Analysis The resultant dimension represents the clearance/interference between assembled parts.

## Multi-Dimensional Tolerance Analysis

Let's see what constitutes 1D/2D/3D tolerance analysis.

1D  All dimensions are parallel.

2D  All dimensions share the same plane, or are in parallel planes.

3D  Dimensions can be in any plane.

The tolerance analysis tools are capable of solving open loop problems where each input dimension is a vector.  The loop is "closed" by calculating the resultant dimension that starts at the beginning of the first input vector and ends at the end of the last input vector.  For 3D analysis, this concept is illustrated below.

The resultant dimension is determined by vector addition.

r = d1 + d2 + d3

Where:

r is the resultant dimension vector

d1 ... dn are the input dimension vectors

The resultant dimension vector begins at the start of d1 and ends at the end of dn.

The direction of the input dimension vectors are governed by two angles: alpha and beta. Alpha is the angle of the vector in the xy plane from the positive x-axis. Beta is the angle of the vector from the xy plane. In MEboost, alpha and beta are not required to be fixed and can vary.

The magnitude of the resultant dimension is given by:

Because of the sum of squares for each delta, the resultant dimension is always positive. For clearance analysis, we must use the deltas to determine the condition of clearance or interference.