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Tolerance analysis of mechanical assemblies is an integral part of the overall design process. The appropriate selection of tolerances can yield significant results in terms of fewer rejects, less cost due to re-work of out-of-spec assemblies, reduced production cost, and a higher quality end product. It is a link between the design and manufacturing phases of product development, since tolerances affect the performance of the design as well as its manufacturability and cost. The scope of tolerance specification and control is broad. It affects nearly every aspect of the manufacturing enterprise, as shown in Fig. 1-1.

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

However, tolerance analysis by hand can involve tedious and error-prone calculations, and can be rather complicated for some assemblies. Few engineers even know how to correctly perform a tolerance analysis. In view of this, a 3D tolerance analysis system called CATS has been developed at the Brigham Young University. CATS stands for Computer-Aided Tolerance Specification. CATS 3D is a program for assembly tolerance analysis for the production design of mechanical assemblies. It includes an assembly modeler and a tolerance analysis package. The tolerance modeler is linked to a CAD system to extract information directly from the CAD geometry of the assembly. The tolerance analysis package uses the information generated by the modeler to create an engineering model of the assembly. The engineering model is then used to predict the design consequences of manufacturing variations.

This user guide explains how to use the CATS tolerance modeler to build a 3D tolerance model from within the CATIA CAD/CAM system. It first explains, in general, how to prepare a tolerance model for analysis. Next, it explains the features included in this version of the tolerance modeler and how to use the interface. Finally, it presents a step-by-step tutorial for creating a 3D tolerance model.

A diagram of the CATS system components is shown in Fig. 1-2.

Figure 1- 2. The CATS system for computer-aided tolerance analysis integrated with a CAD system.


There are three main sources of variation in mechanical assemblies:

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

Dimensional and form variations are the result of variations in the manufacturing processes or raw materials used in production. Kinematic variations occur at assembly time, whenever small adjustments between mating parts are required to accommodate dimensional or form variations. Other variations occur due to thermal expansion or deflection of components, but these are not random variables. They may be included separtately.

Manufactured parts are seldom used as single parts. They are used in assemblies of parts. The dimensional variations which occur in an assembly accumulate statistically and propagate kinematically, causing the overall dimensions to vary according to the number of contributing sources of variation. Critical clearances and fits which affect performance are thus subject to variation.

Analysis tools available in CATS include mathematical and statistical models for:

  1. Tolerance accumulation - worst case or statistical
  2. Propagation of variations by kinematic adjustments - both dimensional and form variations.
  3. Accounting for process mean shifts - both fixed bias or drifting means using the Motorola Six-Sigma statistical model.
  4. Predicting the percent rejects in parts per million (ppm).

Several tolerance selection aids are also available to assist designers as shown in Figure 1-3:


Figure 1-3. CATS tolerance selection aids.


A 3-D tolerance model can be created by CATIA/CATS using familiar engineering elements such as parts, datums, vectors, kinematic joints, and form tolerances. The 3-D tolerance model is constructed on a previously prepared CATIA assembly model. First, each part is given a Datum Reference Frame (DRF). The DRF is a local coordinate system from which all features on that part will be referenced. Contact joints between parts are then identified by type and located with respect to the DRF for both mating parts. Next, vector loops are created which relate the component dimensions to the assembly dimensions. ANSI Y14.5 feature controls, or tolerances accounting for surface variations, can be added to the model. Finally, a file is created which contains all the essential information for tolerance analysis by the CATS 3D analyzer (see Figure 1-4).

Figure 1-4. 3D tolerance modeling procedure.

 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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