# 3D Worst Case Tolerance Analysis

This article will show a 3D worst case tolerance analysis of a clearance problem. This is part of a series of articles on multi-dimensional tolerance analysis, and it's highly recommended to read the Multi-Dimensional Tolerance Analysis Basics article first to get background information on how MEboost performs the analysis.

Multi-dimensional tolerance analysis basics

2D worst case

2D Monte Carlo

3D Monte Carlo

## Clearance Analysis Example

A channel is placed in a pocket and a cover is mounted over the pocket to completely encase the channel. The blue lines represent the inside envelope of the pocket. The gaps between the channel and inside of the pocket are greatly exaggerated. The red line in each view is the resultant dimension.

All letter dimensions (A through F) have a tolerance of ±.005.

The channel also has geometric tolerances and a drawing of it is shown below.

For modeling purposes, the geometric tolerances have a nominal dimension of 0, a minimum of -.003, and a maximum of .003.  They are summarized in the table below.

This is a 3D situation since width, height, and length all can result in an interference fit. Selection of the dimension chain requires that we capture all dimensions that contribute to the variation of fit.

It’s important to understand and apply the coordinate system to correctly interpret the results. In this example, to achieve a clearance fit delta x and delta y must be positive. Delta z must be negative.

The dimension chain is ordered A-B-C-D-E-F. The resultant dimension starts at the corner
of the channel and ends at the corner of the pocket.

## Running a 3D Worst Case Tolerance Analysis

To run a 3D worst case tolerance analysis, open the 1D/2D/3D worst case tool by clicking the following button on the MEboost ribbon.

The tool form will appear.  Click the "Dimension Chain" tab to enter the input dimensions in the chain.  Dimension GT-1 information is shown.

Now click the Results tab.  We can save the model for use later by selecting "New Model", entering a name, and clicking the Save button.  Note that you need to also save the workbook to make the changes permanent.

For 2D and 3D, the extreme resultant values may occur with input dimensions at intermediate values.  The problem is we don't necessarily know what intermediate values result in extreme values of the resultant.

To estimate the resultant extreme values, input dimensions are sampled as uniformly distributed random variables and the resultant dimension is calculated.  This process is repeated for the number of iterations specified.  The greater the iterations, the better chance of finding a close approximation of the resultant extremes.

To determine if enough iterations are used, start with a nominal value such as 50,000.  Then increase iterations and see if the results are changing by an unacceptable amount.  If there is little change after increasing iterations, the true extremes have been estimated.

For this example, we'll use 250,000 iterations by entering this number in the iterations box.  This is a clearance problem and since the resultant magnitude is always positive, it does not tell us if there is clearance or interference.  Therefore, select the Find deltas button to determine the min/max value of each delta.

Click the Calculate button to start the calculation process.

Recall from earlier that for clearance, delta x and y must be positive and delta z must be negative.  This is because of the coordinate system that was chosen.  From the results, minimum delta x and delta y are negative and this indicates an interference fit is possible.

If an interference fit is to be avoided, some combination of tolerances and nominal dimensions must be adjusted and the analysis rerun to verify the results.

We can also see that the results are more sensitive to the letter dimensions (A through F) than the geometric dimensions since each letter dimension has a maximum absolute sensitivity of .0033.