A mechanism for validating dimensioning and tolerancing schemes in CAD systems
Introduction
The shapes of real parts depend on many geometric parameters that cannot be produced exactly under normal production conditions. Tolerances signify the acceptable range of deviation of these parameters from the nominal size and shape. The representation of allowed variations of part shapes is traditionally based on standards for dimensioning and tolerancing [1], [6], which have emerged from engineering practice and experience. The representation of the nominal shape of mechanical parts with computers is successfully performed with solid models, but more needs to be done for the adequate representation of dimensions and tolerances. The lack of a computational model prevents the full integration of solid models, geometric parameters, features, and dimensioning and tolerancing.
Computer-based tolerance representation in commercial systems is application oriented and in some aspects different from ISO/ANSI/ASME standards for dimensioning and tolerancing. Most common are variational geometry constraint-based systems in which tolerances are specified on sketches. Tolerances are specified as the variation of dimension constraints (for example, distance between two points) and geometric constraints (for example, parallel lines). Tolerances are represented as the variation of the position of control points (at an intersection of lines, center of a circle). To model a dimension tolerance between parallel lines, two contributors are considered separately: variation of distance between lines, and variation of parallelism (angle) between lines. Dimension and geometric tolerances are hard to distinguish. Datum reference frames (DRFs) and position tolerances cannot be represented, although this information can be defined and displayed as a standard like tolerance frames. These systems find their application in sensitivity analysis and worst-case and statistical tolerance analysis. Non-linear two dimensional assembly analysis can also be performed with these systems.
Tolerance representation models proposed in the literature can be classified into documentation oriented, analysis oriented, production oriented and control oriented. The first attempts to include dimensioning and tolerancing information in CAD systems were documentation oriented, i.e. simply recording tolerance information as attributes of geometric entities. Frames and objects were used to better structure these attribute types. Shah and Miller [16] represented all standard tolerance classes using the object-oriented approach and created validity checks for tolerance specification. The validation of tolerance specification was limited, because inappropriate DRFs and conflicting tolerance specs could not be checked. Guilford and Turner [4] also used the object-oriented approach to represent different classes of tolerances but only the syntax of tolerance representation was considered.
Analysis oriented tolerance representation models are mostly based on variational geometry. In the context of variational geometry, tolerances are represented as the variation of the position of control points in space, which influences equations of geometric entities. Turner [20] proposed the modeling of tolerances applying variations to the coefficients of the surface equations of each face. Using this system, tolerance synthesis and analysis can be performed using linear programming, Monte Carlo and least square methods.
Systems oriented towards tolerance control focus on determining the boundaries of the tolerance zone and conformance to tolerance. In the early work of Requicha [9], tolerance zones are represented as offsets of the faces in a solid model. This representation is incomplete with respect to the standards, because different types of geometric tolerances cannot be distinguished. Roy and Liu [12] use face adjacency graphs to represent tolerance information as offsets of part faces in BRep models and as variation of parameters in CSG models of the part. In his more recent work, Roy [13] gives a theoretically complete representation of the boundary of form tolerance zone with variation of the surface coefficients and algebraic constraints.
In systems designed for assembly analysis [2], [10], tolerances are interpreted as the deviation of position and orientation of the coordinate system of each part involved in a dimension chain. Chase [2] has developed a variational approach to tolerance analysis for assemblies, based on direct linearization.
Production oriented schemes use graph-based tolerance representation for manufacturing, setup and fixture planning [5], [11], [17], [18], [19]. Graph representation of dimensioning and tolerancing enables control of tolerance specification compatible with the standards. Many graph-based tolerance representation schemes consider only orthogonal directions and lack a general validation check of all tolerances and dimension constraints in arbitrary directions.
In order to perform a validation of tolerance specifications, one must have a semantic model of geometric variations. This quest has led to the degree of freedom (DOF) approach [1], [3], [4], [10], [14], [21], [22]. Most well-known of these approaches is that of Clément [3] who introduced the concept of technologically and topologically related surfaces (TTRS). The tolerance specification is controlled according to the type of association between faces, similar to the dimensioning and tolerancing standards. Zhang and co-workers [19], [22] proposed a similar approach that uses a DOF analysis for checks of completeness and validity.
This paper focuses on the validation aspects of dimensions and tolerances. The validation mechanism is based on DOF models, such as the ones mentioned above. In our first attempts at implementing this model, it was possible to represent all tolerance classes, but the representation of dimensions and tolerance specification was limited to three orthogonal directions. This paper describes a generalization of that scheme. However, the main focus of this paper is on algorithms for validating dimensions and tolerances specified by a user in a CAD system. A DRF class with a control frame is used to represent and validate the mutual constraining of all combinations of datum features. With this representation scheme, constrained DOFs of the tolerance zone are determined progressively as the datum and target entities are paired in datum–target clusters.
Section snippets
Requirements
Two types of tolerancing principles are used in industry and supported by the standards: conventional tolerancing and geometric tolerancing. The former represents the traditional practice of using plus–minus tolerances that apply in the direction of the dimensions of the part. Geometric tolerancing provides a comprehensive set of controls for each specific characteristic of the geometry (form, orientation, location, etc.) to the degree required for satisfying the function or interchangeability
Graph structure
Graph-based structures are popular for solid modeling and constraint solving. Use of graph structures to represent dimensioning and tolerancing information also, facilitates integration of the latter with parametric CAD systems. The dimension and tolerance (D&T) graph used in our approach is a mixed graph, G(N,A,g,d,t). The nodes N represent geometric entities and their attributes; the arcs A represent geometric relations in terms of arc attributes of one or more of the following types:
Dimensioning scheme
The dimension graph is a subset of the D&T graph; it contains only the nominal dimensions between entities but has no information about tolerances. This graph is needed to create the basic structure for the D&T graph and is used in validating the dimensioning scheme. It is complete if all DOFs of all nodes are constrained by dimensions. The completeness needs to be checked after each change of the dimensioning scheme. Entities that are fully constrained with respect to each other are organized
Implementation
The representation of the dimension and tolerance graph is partially implemented as a module of the ASU features testbed modeler [15]. Development of this module started with the work of Zhang [22] and enhancements were done by Yan [21]. The implementation is based on C++ and ACIS and covers the representation of all types of tolerance classes, checks on over- and under-dimensioning, support for re-dimensioning, tolerance chain generation, and mapping of dimensioning and tolerancing from design
Discussion
Any model for the representation of dimensions and tolerances must be based on industry standards and has to ensure validity of the dimensioning and tolerancing scheme after design changes. The dimension and tolerance graph presented here satisfies both the computational requirements for CAD and the conformance requirements for engineering practice. The dimension and tolerance graph is implemented in a parametric modeling environment, but it can be applied to non-parametric types of
Acknowledgements
This work was performed at Arizona State while Dr Kandikjan was a Fulbright Scholar at the Design Automation Lab during 1997 and 1998. An earlier version of the paper was presented at the ASME Design Conference in 1998. Further work on tolerance modeling is being supported by NSF grant DMI-9821008.
Tatjana Kandikjan is an associate professor in engineering design at the University “St. Cyril and Methodius”, Skopje, Macedonia. She obtained her MS in mechanical engineering from the University of Ljubljana, Slovenia in 1986 and PhD in mechanical engineering from the University “St. Cyril and Methodius” in 1994. In 1997 she was a Fulbright scholar at Arizona State University. Her research interests are in CAD, mechanical assembly sequence planning, disassembly for recycling and representation
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2018, Knowledge-Based SystemsCitation Excerpt :Some step in the approach needs a great deal of know-how to complete human-computer interaction. Representative examples for this category are technologically and topologically related surface (TTRS) approach [15–18], degree of freedom (DOF) approach [19–21], and requirement decomposition approach [22–24]. The TTRS approach, which was presented by Clement et al. [15], implemented by Salomons et al. [16], and extended by Toulorge et al. [17] and Zhang et al. [18], is the first and most cited approach for computer-aided tolerance specification.
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Tatjana Kandikjan is an associate professor in engineering design at the University “St. Cyril and Methodius”, Skopje, Macedonia. She obtained her MS in mechanical engineering from the University of Ljubljana, Slovenia in 1986 and PhD in mechanical engineering from the University “St. Cyril and Methodius” in 1994. In 1997 she was a Fulbright scholar at Arizona State University. Her research interests are in CAD, mechanical assembly sequence planning, disassembly for recycling and representation of engineering tolerances.
Jami J. Shah is Professor of Mechanical and Aerospace Engineering at Arizona State University in Tempe, Arizona. He is the Director of the Design Automation Lab, which is known for research related to geometric and feature-based modeling, tolerance analysis, process planning, and engineering information systems. He is the founding Technical Editor of the new ASME Transactions, Journal of Computing and Information Science in Engineering (JCISE).