PRO- E Analyzer


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1.0 Motivation

Increased international competition has made it clear that U.S. industry can no longer continue to produce products by 1950's and 60's manufacturing methods. It is not enough to excel in research and innovation of new products. Our products must be built to competitive quality standards at competitive costs.

In the past, the engineer's design goal was to produce a working prototype, usually without considering future steps such as manufacturing. But this is short-sighted, comparable to driving a car along a dark rural highway at night with the headlights on low beam. The problems ahead cannot be seen. Today's designers must be far-sighted, like driving with the high beams on. They must look ahead to the manufacturing and long term consequences of their design decisions.

Figure 1.1: Short- and far-sighted engineering.

Tolerance design is an engineering function with an immense influence on the final cost of a manufactured product. The seemingly trivial task of assigning tolerances to each component dimension of an engineering drawing is not just a make-work exercise. Excessively tight tolerances can require costly machines, tooling or secondary processes. Extensive inspection, gauging and statistical quality control procedures must then be set up to monitor production and assure that tolerance specifications are met.

Tolerance analysis is often detested by engineering designers. Sometimes it is avoided or procrastinated until no time is left to do an adequate job. Yet, tolerance analysis can do more to reduce manufacturing cost, improve quality and retain market share than almost any other design activity. Even modest efforts in this area can yield significant benefits for very little capital investment.

1.1 Sources of Variation

The three major sources of variation in mechanical assemblies are illustrated in Figure 1.2.

Figure 1.2: Sources of variation in mechanical assemblies.

Manufactured parts are seldom used in isolation. They are used in assemblies of parts. The dimensional variations which occur in an assembly accumulate statistically and propagate kinematically, causing the overall assembly dimensions to vary with each contributing source of variation. Critical clearances and fits which affect the assembly's performance are thus subject to variation.

TI/TOL 2D is an engineering tool which uses statistical methods to enable a designer to predict the effects of manufacturing variation on design performance and to improve this performance.

1.2 TI/TOL 2D Overview

TI/TOL 2D is a Pro/ENGINEER-based tolerancing software package for assembly tolerance analysis and the production design of mechanical assemblies. It was developed by Texas Instruments and Brigham Young University It provides a powerful CAE environment in which mathematical models of 2-D assemblies may be created and used for predicting the design consequences of manufacturing variations.

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

  1. 2-D Tolerance accumulation - worst case or statistical
  2. Propagation of variations by kinematic adjustments - both dimensional and form variations.
  3. Accumulation of process mean shifts using the Motorola Six Sigma statistical model.
  4. Statistical prediction of the percent contribution of each variation source and the resulting percent rejects for an assembly in parts per million (PPM) and defects per unit (DPU).

Several levels of tolerance selection aids are also available (see Fig. 1.3).

Figure 1.3: TI/TOL 2D Tolerance Selection Aids.

The TI/TOL 2D Analyzer user interface is well suited to design iteration. Tolerance and assembly data is stored by the modeler in the assembly file. The analyzer accesses this database and sets up the mathematical model of the assembly. Using the tool built into the Analyzer, the designer can then analyze the assembly using one or more of the analysis models.

1.3 Tolerance Analysis vs. Tolerance Allocation

Tolerance analysis and tolerance allocation differ in their inputs and outputs. In tolerance analysis, the component tolerances are all known and the resulting assembly limits are calculated directly using a worst case or statistical model of an assembly. In tolerance allocation, an assembly tolerance is specified by the design requirements and must be distributed among the component parts. How the tolerances are distributed depends on the allocation rule applied and whether a worst case or statistical assembly model is used. This contrast is shown in figure 1.4.

Figure 1.4: Tolerance Analysis vs. Tolerance Allocation.

In tolerance analysis, the calculated assembly limits are compared to the specified assembly limits and the yield or percent of acceptable assemblies is predicted. In tolerance allocation, however, the designer specifies the yield then determines a set of component tolerances which will assure that the specified yield will be met.

Direct tolerance analysis is principally intended for parts and assemblies that are currently in production. Tolerance allocation is the typical problem encountered in design, long before production has begun. It is a much more difficult problem because of the number of design variables to be determined and a lack of manufacturing data.

1.4 Tolerance Analysis Models

To obtain the resulting assembly tolerance, the component tolerances are summed by the Analyzer using one of the following three models:

1. Worst Case Analysis (WC) -- The specified component tolerances are summed arithmetically (Linear Sum) to determine the extreme cases of assembly dimensions. If these calculated extremes fall within specified assembly limits, 100% of the assemblies created from components with the specified tolerances can be expected to be within spec.

2. Root-Summed-Squares Analysis (RSS) -- Component tolerances are summed statistically by the root-summed-square method to determine the probable variation in critical assembly dimensions. If the +/-3[[sigma]] limits of the normal distribution for an assembly's critical dimension fall on the specified assembly limits, these component tolerances can be expected to produce 99.73% of assemblies within specification. An acceptance fraction greater or less than 99.73% may also be selected.

3. Six Sigma Analysis -- During any production process, the mean of the process may not be centered between the assembly tolerance limits. Tool wear, setup error, fixture bias, etc. can cause the mean to drift or shift off center. Mean shifts of the several components in an assembly can accumulate similar to the way tolerances accumulate, resulting in significant increases in the number of rejects. The Six Sigma model is a mathematical model for tolerance accumulation which accounts for both mean shifts and statistical tolerance stackups. This model was developed by the Motorola Corporation as part of their award-winning Six Sigma program for quality assurance. It allows more realistic estimates of the effects of process variations, but it requires better information about each process. Both Six Sigma Assembly Drift Factors and Six Sigma Component Drift Factors are available as part of the Six Sigma Analysis in TI/TOL 2D.

Two forms of the Six Sigma model are included in the TI/TOL 2D Analyzer.

a) Six Sigma Assembly Drift Factor (SSA) -- This version of the Six Sigma model performs analysis using the RSS method. After the number of assembly variable standard deviations inside the specification limits is calculated based on that model, the assembly mean shift is estimated by subtracting 1.5 from that number of standard deviations. This has the effect of increasing the reject fraction. It is a model that estimates the influence of mean shifts on the assembly level.

b) Six Sigma Component Drift Factor (SSC) -- This version allows the user to estimate the effects of shifting component means on the assembly. The user applies a mean shift factor to each component. These component mean shifts propagate through the analysis, increasing the variation calculated for the assembly variable(s). It estimates the effect of mean shifts on the component level.

1.5 Tolerance Allocation Options

When an assembly tolerance is specified by the designer, the sum of the component tolerances is compared to the specified assembly tolerance. If they do not agree, a set of "Allocated Tolerances" can be computed by the Analyzer's built-in allocation rule to assure that both assembly tolerance and yield specifications are met.

TI/TOL 2D tolerance allocation is based on the use of weight factors. This is an allocation method in which the designer assigns weight factors to individual component tolerances. If the component tolerances sum to less than the assembly tolerance, then the component tolerances are increased until the sum is equal to the assembly limit. The weight factors determine which tolerances should be increased and in what proportion. A large weight factor (relative to the other weight factors) means the designer wants that component tolerance to be as large as possible. If the assembly variation is smaller than the specified design limits, that component will receive a larger portion of the excess variation. If the assembly variation is greater than the specified design limits, that component tolerance will be reduced less than tolerances with smaller weight factors.

Selected tolerances may be designated as "fixed" by setting a flag in the edit screen. This allows the designer to hold individual component tolerances from being modified by the built-in allocation option. Such action may be necessary for:

  1. Vendor-supplied components
  2. Critical component tolerances
  3. Interdependent assemblies, where the same component appears in more than one assembly and may have previously been optimized or re-scaled.

1.6 Additional Software Features

Several convenient design tools are included in this version of the TI/TOL 2D Analyzer:

1. Report Generator -- Analysis output is displayed to the user through a text window. The designer has the option of saving the contents of the text window to a text file. All analysis results performed prior to that point are saved to the file. Any further analysis results are not included in the file. If the user wants to save the new results, they can do so by choosing the save option again. All results currently stored in the text window will be saved to the out file.

2. Sensitivity and Contribution Graphs -- TI/TOL 2D provides the user with a graphical representation of the sensitivities of each component dimension to a design variable. It does the same for the actual contribution of each component dimension to the assembly variation. These graphs can be saved to a PostScript file for printing.

3. Component Tolerances -- The tolerances applied to the component dimensions inside the modeler can be altered manually inside the Analyzer. This allows the designer to perform "what it" studies without ever needing to leave the Analyzer.

4. Acceptance Fraction -- The option to change the desired acceptance fraction is also available. This also makes it convenient to perform "what if" studies when the designer is interested in what level of process capability is required for a specific quality level.

5. Degrees of Freedom -- Kinematic degrees of freedom are central to the TI/TOL 2D analysis method. Occasionally, when setting up a model in the Modeler, an incorrect combination of degrees of freedom are left active. These modeling issues can often be corrected directly inside the Analyzer through the Degree of Freedom window.

1.7 Reference Handbook

An on-line Tolerance Reference Handbook has been initiated in this first version of TI/TOL. It contains tables to help the designer select reasonable tolerances for components. It may be accessed from the "help" menu option of the main menu. Useful options include:

1. Typical Machine Tolerances. A bar chart and table showing the range of tolerances typically produced by common manual machining operations. The tolerances are dependent upon the basic dimension of the part being machined. The range for different size parts is reflected in the table.

2. Drilled Hole Tolerances. A table which gives curves for the average, maximum, and minimum tolerance as a function of the drill diameter. Currently, this option gives tolerances for drill diameters from 0 to 1 inch.

1.9 Process Database

TI/TOL includes a database of standard deviations for common machining processes. There are six sections in the database:

Each section can hold up to 30 different process standard deviations. The entire database can contain a total of 180 process standard deviations. The database can be edited by the user to match the process descriptions and standard deviations used in their own company.

1.10 TI/TOL 2D Modeler

The TI/TOL 2D Modeler is an application program that runs inside the Pro/ENGINEER environment. The TI/TOL 2D Analyzer exist as a separate, X-Window based module inside of the modeler. The program architecture is illustrated in figure 1.5. This integrated structure puts all the tools to perform tolerance analysis an allocation conveniently at the designers' finger-tips. A geometric model of an assembly can be created, a tolerance model built on top of it, and the assembly tolerances analyzed and adjusted without ever leaving Pro/ENGINEER.

Figure 1.5: Integrated TI/TOL 2D modeling system.

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