# 2D Monte Carlo Tolerance Analysis

In this article, we will perform 2D Monte Carlo tolerance analysis on an assembly. 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

3D worst case

3D Monte Carlo

## Clearance Analysis Example

We will use the same assembly used in the 2D worst case analysis example.  A rectangular bar must fit inside an extrusion and we want to know the percentage of assemblies that will have an interference fit.

The drawing for the bar is shown below, and the tolerances for dimensions are ±.005.

The drawing for the extrusion is shown below, and the tolerances for dimensions are ±.005.

The assembly is shown below with all dimensions required for the tolerance model.

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

MEboost allows for two ways to model the dimensions.

1. 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.
2. 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 2D Monte Carlo Tolerance Analysis

To open the 1D/2D/3D Monte Carlo tool, click 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 A 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 [3.72, 3.73].  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 upper right corner of the bar and ends at the upper right inside corner of the extrusion.  Therefore, both a positive delta x and delta y will result in clearance (up and to the right).  We will check the appropriate buttons.  Note that delta z doesn't matter since this is a 2D problem, delta z will always be zero.

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 0.001% interference and the assembly will fit together 99.999% 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 1.122% 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.