Subtract the two and divide this answer by two to get the worst case tolerance: Example of worst case scenario in context to Figure 1:Īdd all of these together to the lower specification limit: Tighter tolerances intensify manufacturing costs due to the increased amount of scraping, production time for inspection, and cost of tooling used on these parts. Often this method requires tight tolerances because the total stack up at maximum conditions is the primary feature used in design. While these analyses can be expensive for manufacturing, it provides peace of mind to machinists by guaranteeing that all assemblies will function properly. It should be noted that the worst case scenario rarely ever occurs in actual production. Once this scenario is identified, the machinist or engineer can make the appropriate adjustments to keep the part within the dimensions specified on the print. Worst case analysis can also be used when choosing the appropriate cutting tool for your job, as the tool’s tolerance can be added to the parts tolerance for a worst case scenario. This is typically used for only 1 dimension (Only 1 plane, therefore no angles involved) and for assemblies with a small number of parts. This total tolerance can then be compared to the performance limits of the part to make sure the assembly is designed properly. When performing this type of analysis, each tolerance is set to its largest or smallest limit in its respective range. Worst case analysis is the practice of adding up all the tolerances of a part to find the total part tolerance. In this equation represents the standard deviation. 002”.įor this example, let’s find the standard deviation (σ) of each section using equation 1. 001” and for the middle flat region this would be. Since they are bilateral, the standard deviation from the mean would simply be whatever the + or – tolerance value is. In this example, we have 3 bilateral tolerances with their standard deviations already available. 003” tolerance, but there is no need for the radii (.125”) and the flat (.250”) to be exact as long as they fit within the slot. The statistical analysis method is used if there is a requirement that the slot must be. This is necessary because some tolerances may have different distribution factors based on the tightness of the tolerance range. In this case, the beans are the standard deviations, the grinder is the tolerance distribution factor, and the coffee filter is the root sum squared equation. In order to make a delicious cup of joe, you must first grind down all of the beans to the same size so they can be added to the coffee filter. Think of it like a cup of coffee being made with 3 different sized beans. Once this has been done, the root sum squared can be taken to find the standard deviation of the assembly. The standard deviations of all the tolerances must be divided by this tolerance distribution factor to normalize them from a distribution of 3 to a distribution of 1. This means that most of the data (or in this case tolerances) will be within 3 standard deviations of the mean. Further, placing a tolerance on this callout would cause it to be over dimensioned, and thus the reference dimension “REF” must be left to take the tolerance’s place.įigure 2: Tolerance Stacking: Normal distributionīefore starting a statistical tolerance analysis, you must calculate or choose a tolerance distribution factor. 004”, but is oftentimes miscalculated during part dimensioning. In this case, the tolerance window for the cutter diameter would be +/. For example, a corner radius end mill with a right and left corner radii might have a tolerance of +/. When an upper and lower tolerance is labeled on every feature of a part, over-dimensioning can become a problem. The cost of high quality tool holders and tooling with tighter tolerances can also be an added expense.Īdditionally, unnecessarily small tolerances will lead to longer manufacturing times, as more work goes in to ensure that the part meets strict criteria during machining, and after machining in the inspection process. This higher cost is often due to the increased amount of scrapped parts that can occur when dimensions are found to be out of tolerance. ![]() ![]() Tips for Successful Tolerance Stacking Avoid Using Tolerances That are Unnecessarily SmallĪs stated above, tighter tolerances lead to a higher manufacturing cost as the part is more difficult to make.
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