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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.


Figure 1-1. The link between engineering and manufacturing.

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 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.

Both engineering design and manufacturing personnel are concerned about the effects of tolerances. Engineers prefer tight tolerances to assure design fit and function. Manufacturing 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.


The TI/TOL 2D Modeler is an interactive graphical preprocessor for the TI/TOL 2D Analyzer. It provides a powerful environment in which a kinematic assembly model may be created and prepared for tolerance analysis. As illustrated in Figure 1-2, the TI/TOL 2D modeler is a Pro/ENGINEERreg. extension which operates on an existing geometric model of a mechanical assembly. The menu-driven modeler accesses assembly information from and appends the tolerance model to the Pro/E database, just as Pro/E itself accesses geometry from its database. The Modeler and Analyzer pass information back and forth through the assembly file.


Figure 1-2. TI/TOL 2D 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. TI/TOL 2D is used to obtain additional kinematic and geometric information, creating a graphical version of the kinematic model which is overlaid on the Pro/E drawing. The kinematic model is used by the TI/TOL 2D 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 TI/TOL 2D Analyzer has the capability of inserting form variations into the kinematic model to see how they accumulate and propagate in an assembly.

The Modeler provides engineers with methods of specifying how much variation in specific assembly variables is acceptable. Assmbly variables include angles and lengths formed by mating parts (kinematic variables), gaps between two surfaces, orientation of one surface relative to another, and position of a feature on one part relative to a feature on another part. TI/TOL 2D estimates the magnitude of the assembly variations. The results can then be used to modify component tolerances.


The TI/TOL 2D Analyzer uses the vector models of mechanical assemblies created by the TI/TOL 2D Modeler. The Analyzer interactively assists designers in the selection and allocation of component tolerances for these assemblies in order to assure manufacturability and minimum rejection rates. The user may choose 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)
  2. Form and feature variations (flatness, roundness, angularity, etc.)
  3. Kinematic variations (small adjustments between mating parts)

Analysis tools available in the TI/TOL 2D Analyzer include:

  1. 2-D Tolerance accumulation - worst case or statistical
  2. Accumulation of process mean shifts--drifting component or assembly means using the Motorola Six Sigma statistical model.
  3. Prediction of the percent contribution of each variation source and the resulting percent rejects for an assembly in parts per million (ppm).
  4. Allocation of tolerances for an assembly to meet the critical assembly specifications.


The TI/TOL 2D menus are accessed through the TOLERANCE function under the Pro/E INFO menu. The TI/TOL 2D menus parallel the Pro/E menu structure both in form and function as shown in Figure 1-3.

Figure 1-3. TI/TOL 2D main menu.

While TI/TOL 2D is running, the only available Pro/E functions are the view manipulation and environment controls. For this reason, all planes and points that will be used as reference points in the tolerance application need to be created before entering TI/TOL 2D.


A TI/TOL 2D model is created using familiar engineering elements, such as parts, part datums, kinematic joints and form tolerances. The TI/TOL 2D model is constructed as an overlay on a previously prepared Pro/E assembly drawing. Before beginning the TI/TOL 2D application, all assembly datum planes and assembly datum points that will be needed must be created in the assembly drawing. When beginning the application, an assembly plane oriented to pass through all important parts of the assembly must be defined as a reference plane. Second, each part in the assembly is given a Datum Reference Frame (DRF) with the help of TI/TOL 2D prompts. The DRF is a local coordinate system from which all dimensions on that part will be referenced. Contact joints between parts are then identified by type and located with respect to each part's DRF using TI/TOL 2D menus. Next, vector loops are created, either by the user or by the TI/TOL 2D Autoloop function. ANSI Y14.5 geometric tolerances can also be associated with the kinematic joints to account for surface variations. Design specifications may be incorporated into the model as well. The essential information for tolerance analysis is stored in the assembly database for access by the Analyzer (See Figure 1-2).

 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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