This article will show a 3D Monte Carlo 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.

## 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 the Monte Carlo simulation, we will assume all dimensions are normally distributed with the following parameters.

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.

MEboost allows for two ways to model the dimensions.

**100% Inspection**We can use the tolerance limits to truncate the sampled dimensions so that dimensions only fall within tolerances. This mimics the case of 100% inspection and all dimensions are within tolerance.**Zero Inspection**Since we are using the normal distribution, there is no lower or upper limit on dimensions and some dimensions may be outside of their tolerance limits. This mimics the case of zero inspection.

We will run both scenarios to see the difference.

## Running a 3D Monte Carlo Tolerance Analysis

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

The tool form will appear. In the Select model dropdown box, select New model. Then enter a name for the model and click Save. A new worksheet will be created to save the model information and simulation data.

Now click on the Dimension Chain tab to enter information for each dimension. Dimension GT-1 information is already entered. For the first run, we are assuming 100% inspection and that all dimensions are within tolerance. Therefore, the LL (lower limit) and UL (upper limit) boxes have the tolerance limits specified. When this dimension is sampled, its values will be [-.003, .003]. Later when we assume zero inspection, these boxes are left blank.

Click the Add Dimension button to add the dimension to the chain.

The remaining dimensions have been added. You can click on a dimension to see its information and to edit the dimension. Click the Save button to save the dimension data to the model worksheet.

Click on the Set-up tab. For this simulation we will run 100,000 trials.

Since this is a clearance problem, we need to specify the direction of clearance for each delta. From the basics article, the resultant dimension is from the start of the first input dimension to the end of the last dimension. For this example, the resultant dimension starts at the corner of the channel and ends at the corner of the pocket. Based on the coordinate system we have chosen, clearance will occur when delta x and y are positive, and delta z is negative. We will check the appropriate buttons.

Click the Run Simulation button, to start the simulation. The results are shown below.

Because of the way the resultant dimension is calculated, it is always positive. This doesn't give us information as to whether the fit is clearance or interference. We can look at the deltas statistics on the deltas tab for more information, but this alone doesn't give us complete information. The interference statistic tells us the percentage of trials where at least one delta had interference. This is the most accurate measure since more than one delta may be in interference at the same time.

For 100% inspection where all dimensions are within tolerance, there was 0.016% interference and the assembly will fit together 99.984% of the time.

Now let's run the simulation by removing the lower and upper tolerance limits from each dimension and assuming zero inspection. We'll run it for 100,000 trials and the results are shown below.

For zero inspection, we have an interference fit 0.03% of the time. Since the part dimensions can be out of tolerance, it is to be expected that we will see more interference fits than the case of 100% inspection.