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Tolerance analysis is receiving renewed emphasis as industry recognizes that tolerance management is a key element in their programs for

  1. improving quality
  2. reducing overall costs
  3. retaining market share.

The quest for quality has focused attention on the effects of variation on manufactured products' cost and performance. Excess cost or poor performance will eventually result in a market share loss. Therefore, the specification of tolerance limits on each dimension and feature of engineering drawings is considered by many to be a vital design function. Tolerance requirements have a far-reaching influence that touches nearly every aspect of manufacturing as shown in Figure 1-1.

Figure 1-1. The Link between Engineering and Manufacturing.

Both engineering design and manufacturing personnel are concerned about the effects of tolerances. Engineers like tight tolerances to assure design fit and function. Manufacturers prefer loose tolerances which make parts easier and less expensive to produce. Therefore, tolerance specifications become a critical link between engineering and manufacturing, a common meeting ground where competing requirements may be resolved.


CATS is a family of Computer-Aided Tolerancing Software developed at Brigham Young University for assembly tolerance analysis and the production design of mechanical assemblies. With the CATS Analyzer, vector models of 2-D mechanical assemblies created by the CATS Modeler may be analyzed. The Analyzer interactively assists designers in the selection and allocation of component tolerances for these assemblies in order to assure manufacturability, least cost, and minimum rejection rates.

The analysis may use worst case or statistical methods to predict the magnitude of variations and probable rejects for critical clearance, position, and other assembly specifications. Three sources of variation may be accounted for:

  1. Dimensional variations ( lengths and angles )
  2. Form and feature variations ( flatness, roundness, angularity, etc. )
  3. Kinematic variations ( small adjustments between mating parts )

Analysis tools available in the CATS 2-D Analyzer include models for:

  1. 2-D Tolerance accumulation - worst case or statistical
  2. Accumulation of process mean shifts - both fixed bias or drifting means using the Motorola Six Sigma statistical model.
  3. Statistical prediction of the percent contribution of each variation source and the resulting percent rejects for an assembly in parts per million (ppm).

In turn, the Analyzer may be used to allocate or select tolerances for an assembly to meet these same critical assembly specifications. Several levels of tolerance selection aids are available (see Fig. 1-2):

  1. Tolerance Reference Handbook - an on-line set of charts and tables
  2. Geometric Tolerancing - ANSI Y14.5
  3. Tolerance Allocation - by proportional scaling
  4. Tolerance Allocation - by weight factors
  5. Tolerance Allocation - by least cost optimization


Figure 1-2. CATS Tolerance Selection Aids.


The CATS Modeler is an interactive graphical preprocessor for the CATS Analyzer. It provides a powerful environment in which a kinematic assembly model may be created and prepared for tolerance analysis. As illustrated in Figure 1-3, the CATS modeler is an AutoCADreg. extension which operates on an existing geometric model for a mechanical assembly. A menu-driven user-interface commands the modeler and appends the assembly tolerance model to the AutoCAD database just as AutoCAD itself accesses geometry from its database. The modeler passes information to the CATS Analyzer via a "neutral file" which contains the tolerance model.

Figure 1-3. CATS Modeling System for Tolerance Analysis.

Kinematic models define a set of relationships which describe how the parts in an assembly interact due to manufacturing variations. These relationships are generally in the form of chains or loops of parts joined by kinematic joints placed at the contact points between mating parts. CATS is used to obtain additional kinematic and geometric information, creating a graphic version of the kinematic model which is overlaid on the AutoCAD drawing. The kinematic model is used by the CATS Analyzer to generate the governing equations for an assembly and estimate the effects of process variations.

Form or geometric tolerances may also be applied to the model. Due to manufacturing variations, all part surfaces and features vary from their ideal geometry. Thus, the effects of form and feature variations must be correctly represented. Form or geometric tolerances allow the engineer to account for these surface variations by applying a tolerance zone to the part surface. Each tolerance is specified by an ANSI Y14.5 feature control symbol which is added to the model. The CATS Analyzer has the capability of inserting form variations into the kinematic model to see how they accumulate and propagate in an assembly.

Once the tolerance assembly model is complete, a neutral file is generated and is used by the CATS Analyzer for analysis. The CATS Analyzer analysis software determines variations in critical assembly variables--variations which will occur at assembly time.

 PRO-E 2 D
Title | Overview | Modeling | Commands
Title | Overview | Analysis | Allocation | Interface
Verification: Overview

 AutoCAD 2 D
Title | Overview | Modeling | Commands
Analyzer: Title | Overview | Analysis | Allocation | Interface
Verification: Title | Overview

 Catia 3 D
Title | Overview | Modeling | Commands | Building a Tolerance Model

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