Tolerance Stack Up Calculator | Worst Case and RSS

Tolerance stack up are the process of determining how the individual tolerance of each part that goes into an assembly will contribute to the total measurement error of that assembly. When a person assembles a number of different parts, each part may have a small error in it’s measurement. These errors in each of the individual parts will contributes to the total error that is present within the assembled portion of the project.

Tolerance stack up allow a person to determine if the assembled portion will fit into the designated portion of the project. Furthermore, if a person does not calculate the tolerance stack up, the assembled portion may have gap that are either too small or too large to allow the project to function as intended. There are a variety of ways to calculate the tolerance stack up for a given project.

How to Calculate Tolerance Stack-Up

Two of the most common methods, however, is the linear method and the root sum square method. The linear method is a conservative method of calculating the tolerance stack up of a project; all of the individual tolerances of the parts of the project are simply added together. The linear method assume that each of the parts will have errors in the same direction at the same time, which is unlikely when building a project in a workshop.

Thus, the linear method will result in a total tolerance that is much larger then the actual tolerance that are needed for the project. The root sum square method of calculating the tolerance stack up of a project is another common method. The root sum square method is more accurately than the linear method when applied to the random assemblies that are present within a workshop.

To determine the root sum square method for a project, the individual tolerance of each part of the project is squared. Each of those squared tolerances are summed together, and the square root of that sum is taken. This method is more accurate because it account for the possibility that errors of the parts will not occur in the same direction.

For instance, if each of six parts has a tolerance of.1 inches, the linear method will calculate the total tolerance as.6 inches. In contrast, the root sum square method will calculate the total tolerance to be approximately.25 inch. Another way of managing the tolerance stack up for a project is to introduce the concept of a safety band.

A safety band is an amount of clearance that is added to the project. A safety band is introduced into the calculations for a variety of factor that are introduced during the building of a project, such as for the movement of the wood due to humidity, or for the presence of small burr that are introduced to the edges of the parts being assembled. The person should subtract the safety band from the target gap that is to be created by the assembled portion of the project prior to calculating the tolerance stack up.

By including the safety band in the calculations, allowance is made for these variable that could introduce errors into the assembled portion. Furthermore, not all type of fits require the same tolerance bands for the assembled portion. For instance, the tolerance bands for clearances are much wider than tolerances for locating fits.

Locating fits are create to allow for a portion of the project to have a specific location relative to another portion of that project. Slips, on the other hand, require sufficient play to allow for the portions to be assembled, but not so much play as to allow those portions to become too loose within the project. In performing a tolerance stack up analysis of a project, it is helpful to utilize the actual measurement of the parts of the project, as measured with calipers.

Tolerance calculations with the nominal sizes of the parts is likely to result in inaccuracies, as the nominal sizes are provided with the part catalogs. Instead, it is more accurately to use the actual measurements of the parts of the project. Other factor in the workshop also impact the dimension of the project.

For instance, changes in humidity impact the shrinkage of wood, and the wear of tools impacts the precision of the fixtures that are utilized within the workshop. Finally, the use of presets for task like drawer slides or router jigs can make tolerance calculations easier. In determining whether or not the tolerance calculations for a project are acceptable, the remaining margin can be evaluated.

If the remaining margin is wide and positive, then the project will fit as intended. If the remaining margin is small (less than 20% of the target gap), then the safety band can be trimmed. If the remaining margin is negative, the project will not fit as intended, and the assembly must be shortened.

Finally, if the percentage of the utilization of the remaining margin is over 80%, the tolerance of the project is too high. Common mistake include the use of the linear method for every calculation. Instead, the root sum square method is often a better approach.

Other common mistake include the forgetting of the safety band. This creates no margin for error. Furthermore, care must be taken to ensure that all dimension are in the same units; inches should be converted to millimeter.

Finally, a more advanced and efficient approach is to utilize the linear method for critical portions of the project, while utilizing the root sum method for the remainder of the project.