About Tolerance Analysis

1D Tolerance Stackup Analysis

Inventor Tolerance Analysis is a 1-Dimensional tolerance analysis tool that reports the tolerance stackup of parts in a single linear direction such as X. The analysis lets you determine if the parts in an assembly meet mechanical fit and performance requirements based on the cumulative part tolerances.

Note: Inventor Tolerance Analysis is included in the Product Design and Manufacturing Collection.

A 1D analysis is typically captured in a spreadsheet, but the spreadsheet method is difficult to set up and maintain because it must:

Manage all product requirements simultaneously.
Use common dimensions and tolerances for each part involved in multiple stackups.
Accurately calculate the effects of geometric tolerances.
Automatically include the effects of the clearances around fasteners and pins which results in assembly shift and variation in locating one part relative to another.
Accurately calculate the statistical results.

Inventor Tolerance Analysis replaces the spreadsheet method by automating these and many other common tolerance stackup tasks.

Tolerance Stackup Analysis Fundamentals

The following information explains why tolerance analysis is important, the differences between 1D, 2D, and 3D analysis problems, and the different tolerance analysis types. If you are familiar with performing tolerance stackups, you can skip this section and go directly to Define and Edit Tolerance Stackups .

When you design a part in a CAD system it is a perfect representation of the part. In reality, when you manufacture a part there are slight differences in each part. The purpose of tolerance design is to consider the allowable variation in each part to determine if the engineering requirements are met when the parts are assembled.

To determine how much tolerance is permitted, you must consider the accumulation, or stackup, of variation in individual dimensions. Dimensional variation in the parts combines to produce variation in a critical distance, usually between two different parts in an assembly. For each critical distance, you must determine what constitutes an acceptable range of values within which the system still functions as desired.

Tolerance stackup analysis provides a way to understand the relationship between dimensional variation and functional requirements.

Inventor Tolerance Analysis can solve 1-dimensional (1D) stackup problems, but not 2D or 3D stackup problems. Often it can recognize 2D or 3D influences on the defined stackup and provides a warning to alert you. The following section defines the difference between 1D, 2D, and 3D stackups to help you understand why the message appears.

A 1D tolerance stackup means the distance being analyzed and all dimensions that contribute to the distance variation are acting in the same linear direction. Linear variation of the surfaces on either side of the stackup direction is considered; angular variation of the surfaces relative to each other is not. Sometimes the effects of angular variation are overlooked, and the analysis is considered to be 1D. However, when significant differences exist in the size of the surfaces included in the stackup, angular variation on smaller surfaces can have a greater effect on the edges of the larger surfaces. If larger surfaces follow the orientation of the smaller surfaces, they move back and forth in the direction of the analysis by more than the simple translation of the surfaces would permit. Tolerance Analysis warns you when this scenario, and others with similar effects, is detected.

In a 1D problem, the sensitivity of the overall stackup distance to each contributing dimension is usually 1.0 or -1.0 for standard dimensions. Sensitivities to size dimensions, for example, diameter or width, may be 0.5 or -0.5.

A 2D tolerance stackup is one in which the distance being analyzed and all dimensions that contribute to the variation of that distance can be represented in a single plane. A 3D tolerance stackup may have contributing dimensions in any direction. Both usually involve complex trigonometric calculations to determine the sensitivity of the measurement to each dimension in the assembly.

Tolerance Analysis Types

Inventor Tolerance Analysis supports Worst-case, general Statistical, and Root Sum of Squares (RSS) analysis methods. RSS is a special case of the Statistical analysis method and is described after the Statistical section.

Worst-case tolerance analysis is the traditional type of tolerance stackup calculation. The individual variables are all placed at either the maximum or minimum limits to make the stackup distance as large or as small as possible.

The Worst-case method does not consider the distribution of the individual variables. Instead it assumes that all parts have been produced at the extreme limit of acceptability when they are assembled. This method predicts the absolute upper and lower limits of the stackup distance that can be achieved.

Designing to Worst-case tolerance requirements means that all parts produced to, but not beyond, their extreme limits assemble and function properly. The major drawback with the Worst-case method is that it often requires tight individual component tolerances. Worst-case can result in expensive manufacturing and inspection processes and high scrap rates.

Assigning tolerance that meet Worst-case analysis methods is often used for critical mechanical interfaces and spare part replacement interfaces. When Worst-case tolerancing is not a contract requirement, properly applied statistical tolerancing can ensure acceptable assembly yields with increased component tolerances and lower fabrication costs.

The Statistical analysis method takes advantage of the principles of statistics to relax the component tolerances without sacrificing quality. Each contributing dimension is assumed to have a statistical distribution. These distributions are combined to predict the distribution of the assembly stackup distance. Statistical analysis predicts a distribution of the stackup distance instead of the extreme limits that the Worst-case method determines. Statistical analysis provides increased design flexibility to design to any quality level, not just 100 percent. Statistical analysis differs from the RSS method because it does not assume that the assembly quality level must be the same as the part quality level.

The standard deviation calculated for the normal distribution of each dimension is calculated from the following formula for Cp:

Solving for the standard deviation yields:

The most common assumption of Cp=1.0 stems from the assumption of a manufacturing process that places the defined tolerances at +/- 3 standard deviations from center of the tolerance zone, assumed to be the mean, so that the probability of a part complying to the required tolerances is 99.7%. For all statistical analyses, Tolerance Analysis assumes that manufacturing targets the midpoint of the tolerance range, therefore the mean is assumed to be the midpoint of the tolerance range.

Root Sum of Squares, or RSS, analysis leverages the principals of the general statistical analysis method described in the previous section but with some simplifying assumptions to enable calculations with tolerances instead of standard deviations. One of the primary assumptions is that the ratios of each of the tolerances to their associated standard deviations on the dimensions and the stackup result are the same. For an RSS analysis, Tolerance Analysis assumes a Cp of 1.0 for all dimensions and the resulting stackup limits.