Virtual Part Arrangement in Assemblies for Automatic Tolerance Chart Based Stackup Analysis

Manual construction of design tolerance charts is a popular technique for analyzing tolerance accumulation in parts and assemblies, even though it is limited to one-dimensional worst-case analysis. Since charting rules are GD&T (geometric dimensioning & tolerancing) specification dependent, and the user has to remember all the different rules to construct a valid tolerance chart, manual charting technique is time-consuming and error-prone. The computer can be used for automated tolerance charting, which can relieve the user from the tedious and error-prone procedure while obtain the valid results faster. The automation of tolerance charting, based on the ASU GD&T mathematical model, involves (1) automation of stackup loop detection, (2) formulation of the charting rules for different geometric tolerances and determination of the closed form function for statistical analysis, (3) automatic part arrangement for an assembly level chart analysis, (4) development of the algorithms for chart analysis and automatic application of the charting rules. Since the authors’ previous DETC/CIE’03 paper already discussed tasks 1~2 and part of task 4, this paper will focus upon task 3, i.e. virtual part arrangement in assemblies for tolerance charts, and update the analysis algorithm (related to task 4). These two papers together will provide a complete coverage of automated tolerance charting technique popularly used in industry. The implementation will be briefly discussed as well, and case studies will be provided to demonstrate the approach to virtual part arrangement.

A Comparative Study Of Tolerance Analysis Methods

This paper reviews four major methods for tolerance analysis and compares them. The methods discussed are: (1) one-dimensional tolerance charts; (2) parametric tolerance analysis, especially parametric analysis based on the Monte Carlo simulation; (3) vector loop (or kinematic) based tolerance analysis; and (4) ASU Tolerance-Map® (T-Map®) (Patent pending; nonprovisional patent application number: 09/507, 542 (2002)) based tolerance analysis. Tolerance charts deal with worst-case tolerance analysis in one direction at a time and ignore possible contributions from the other directions. Manual charting is tedious and error prone, hence, attempts have been made for automation. The parametric approach to tolerance analysis is based on parametric constraint solving; its inherent drawback is that the accuracy of the simulation results are dependent on the user-defined modeling scheme, and its inability to incorporate all Y14.5 rules. The vector loop method uses kinematic joints to model assembly constraints. It is also not fully consistent with Y14.5 standard. The ASU T-Map® based tolerance analysis method can model geometric tolerances and their interaction in truly three-dimensional context. It is completely consistent with Y14.5 standard but its use by designers may be quite challenging. The T-Map® based tolerance analysis method is still under development. Despite the shortcomings of each of these tolerance analysis methods, each may be used to provide reasonable results under certain circumstances. Through a comprehensive comparison of these methods, this paper will offer some recommendations for selecting the best method to use for a given tolerance accumulation problem.

A Comparative Study of Tolerance Analysis Methods

This paper reviews four major methods for tolerance analysis and compares them. The methods discussed are (1) 1D tolerance charts, (2) variational analysis based on Monte Carlo simulation, (3) vector loop (or kinematic) based analysis, and (4) ASU T-Maps© based tolerance analysis. Tolerance charts deal with tolerance analysis in one direction at a time and ignore possible contributions from the other directions. Manual charting is tedious and error-prone, hence attempts have been made for automation. Monte Carlo simulation based tolerance analysis is based on parametric solid modeling; its inherent drawback is that simulation results highly depend on the user-defined modeling scheme, and its inability to obey all Y14.5 rules. The vector loop method uses kinematic joints to model assembly constraints. It is also not fully consistent with Y14.5 standard. ASU T-Maps based tolerance analysis method can model geometric tolerances and their interaction in truly 3-dimensional context. It is completely consistent with Y14.5 standard but its use by designers may be quite challenging. T-Maps based tolerance analysis is still under development. Despite the shortcomings of each of these tolerance analysis methods, each may be used to provide reasonable results under certain circumstances. No guidelines exist for such a purpose. Through a comprehensive comparison of these methods, this paper will develop some guidelines for selecting the best method to use for a given tolerance accumulation problem.

A CAD/CAM Representation Model Applied to Tolerance Transfer Methods

This paper presents the adaptation of tolerance transfer techniques to a model called TTRS for Technologically and Topologically Related Surfaces. According to this model, any three-dimensional part can be represented as a succession of surface associations forming a tree. Additional tolerancing information can be associated to each surface association represented as a node on the tree. This information includes dimensional tolerances as well as tolerance chart values. Rules are then established to infer tolerance chains or stack up along with tolerance charts directly from the graph. This way it becomes possible to combine traditional one dimensional tolerance transfer techniques with a powerful three-dimensional representation model providing high technological contents.

Automation of Linear Tolerance Charts and Extension to Statistical Tolerance Analysis

Manual construction of tolerance charts is a popular technique for analyzing tolerance accumulation in parts and assemblies. But this technique has some limitations: (1) it only deals with the worst-case analysis, and not statistical analysis (2) it is time-consuming and errorprone (3) it considers variations in only one direction at a time, i.e. radial or linear. This paper proposes a method to automate 1-D tolerance charting, based on the ASU GD&T global model and to add statistical tolerance analysis functionality to the charting analysis. The automation of tolerance charting involves automation of stackup loop detection, automatic application of the rules for chart construction and determination of the closed form function for statistical analysis. The automated analysis considers both dimensional and geometric tolerances defined as per the ASME Y14.5 – 1994 standard at part and assembly level. The implementation of a prototype charting analysis system is described and two case studies are presented to demonstrate the approach.

Design the Angular Feature for Manufacturability With Tolerance Chart

Many products have angular features for certain special functions. Although the design engineers have considered the capability of manufacturing process when they design the parts of a product, some hidden problems about the manufacturability of the angular features are still difficult to be discovered by most of the design engineers. In this paper tolerance charts are used to design the angular features for manufacturability. Using the tolerance chart for a simple tapered part, the work dimensions and tolerances at each operation stage of manufacturing are obtained. A very tight tolerance on adjacent surfaces is created because of the tapered feature. This problem will not be discovered until the tolerance chart is employed to analyze the designed tolerances and the operation sequence. Therefore, either the design of the tolerance or the process plan of the workpiece should be modified in order to fabricate the part at a small cost of manufacturing.

A CAD/CAM Representation Model Applied to Tolerance Transfer Methods

This paper presents the adaptation of tolerance transfer techniques to a model called TTRS for Technologically and Topologically Related Surfaces. According to this model, any three-dimensional part can be represented as a succession of surface associations forming a tree. Additional tolerancing information can be associated to each TTRS represented as a node on the tree. This information includes dimensional tolerances as well as tolerance chart values. Rules are then established to simulate tolerance chains or stack up along with tolerance charts directly from the graph. This way it becomes possible to combine traditional one dimensional tolerance transfer techniques with a powerful three-dimensional representation model providing high technological contents.