Introduction

Tolerance Analysis is the only way to determine the allowable variation between the features of a part or between part sizes in an assembly and whether parts will satisfy their dimensional objectives. The analysis is iterative in nature and it could be done from the Top-Down (letting the assembly requirements determine the part tolerances) or the Bottom-Up (part tolerance determine assembly goal). The information gained leads to better understanding of the machine or device in consideration.

Stack-up Analysis & Reporting

In order to perform the stack-up analysis shown here all tolerance styles must be converted to equal-bilateral form. The figure below shows how this is done.

The Report & Sketch

The report can be formatted to return the worst-case or statistical tolerance variation. Worse-case determines the absolute maximum variation possible for a selected distance gap. Statistical determine the probable or likely maximum variation possible for a selected dimension. A simple rule of thump to determine which format to use is that as the number of tolerances in the stack increases, the benefits and validity of using a statistical analysis increases.

A sample of a Worse-case report and sketch is shown below. Note how assembly shift due to floating fastener variation is calculated (two entries) and the importance of how the dimension-chain direction affect the summation of the stack. Fixed fastener variation would only require one entry line in the spreadsheet.

A sample of a Statistical report and sketch is shown below. Note that the Root-sum-square (RSS) of the tolerance is used to determine the max. and min. size of the gap. The Worse-case calculation was also included as a way of comparison. As you can see, it shows a possible 3.7mm interference upon assembly.

It is important to note that these calculations apply only to parts and assemblies functioning at 25° C. Thermal expansion or shrinkage must be considered when the device is expected to endure extreme temperatures.

In Case One the perpendicularity tolerance applied to datum feature B allows portions of the Datum Feature to tilt and/or have form error relative to datum B, which is perfectly perpendicular to Datum A. Therefore the tolerance analyst may choose to include the perpendicularity tolerance in the tolerance stack-up. The Perpendicularity tolerance only allows the distance between datum feature B and the groove to decrease, so it must be accompanied by a negative zone shift. The perpendicularity tolerance is added as an equal-bilateral tolerance of ±0.25, with a Zone Shift of 0.25, which is half the perpendicularity tolerance value. The zone shift is indicated by placing the 0.25 value in the -Dir column on the same line as ±Tol. column. Case two is very self explanatory.

Form Tolerances in Tolerance Stackups

The location of features is typically the most important characteristic of features in linear tolerance stackups (TS), which is why position and profile tolerance are more commonly included in TS than form tolerances. This is because TS are done to find a minimum or maximum distance and in the majority of cases the form or shape of a feature has little to no effect on the distance being studied.