A new approach to tolerance analysis

Journal ArticleTolerance analysis is seen as part of a more general problem, namely handling data with uncertainty. Uncertain geometric data arises when interpreting measured data, but also in solid modeling where floating point approximations are common, when representing design tolerances, or when dealing with limited manufacturing precision. The common question is whether parts with uncertain shape fulfill certain functional specification. The question is expressed as geometrical relationship between toleranced objects. Unfortunately, tolerance based relations are often inconsistent, unlike relations between exactly represented objects. In this paper we survey current tolerance representation and analysis methods. We then derive our method of intuitionistic tolerance handling from a method developed for robust solid modeling. A new representational framework is proposed, which serves as the basis for robust geometric modeling and tolerance analysis. We illustrate the framework with examples of assembly design

Explicitly representing the semantics of composite positional tolerance for patterns of holes

Representing the semantics of the interaction of two or more tolerances (i.e. composite tolerance) explicitly to make them computer-understandable is currently a challenging task in computer-aided tolerancing (CAT). We have proposed a description logic (DL) ontology based approach to complete this task recently. In this paper, the representation of the semantics of the composite positional tolerance (CPT) for patterns of holes (POHs) is used as an example to illustrate the proposed approach. This representation mainly includes: representing the structure knowledge of the CPT for POHs in DL terminological axioms; expressing the constraint knowledge with Horn rules; and describing the individual knowledge using DL assertional axioms. By implementing the representation with the web ontology language (OWL) and the semantic web rule language (SWRL), a CPT ontology is developed. This ontology has explicitly computer-understandable semantics due to the logic-based semantics of OWL and SWRL. As is illustrated by an engineering example, such semantics makes it possible to automatically check the consistency, reason out the new knowledge, and implement the semantic interoperability of CPT information. Benefiting from this, the ontology provides a semantic enrichment model for the CPT information extracted from CAD/CAM systems

Application of New Generation Geometrical Product Specifications—Position Tolerancing

The geometrical product specifications (GPSs) from new generation are composed of several standards issued by the ISO/TC 213. They are related to the way of denoting the requirements in the design engineering drawings, such as drawing indication, definition of tolerance and values of specifications, characteristic, parameters and definitions of actual features. They also include requirements relating to compare verification, measure instrument and calibrate size, distance, radius, angle, form and position of geometrical features, roughness profile, waviness profile, primary profile, surface imperfection and edges. A lot of new and mathematical terms, the size system, indications of dimensions other than linear sizes by using geometrical tolerances, uncertainty series, etc. are introduced in this chapter. The aim of this chapter is to explain the new requirements of new generation standards for geometrical product specifications related to positional deviation. The advantages and disadvantages of the possibility to indicate the accurate requirements for location of surfaces and axes are discussed

The measurand in ISO GPS verification

A clear definition of the measurand is an essential precondition for measuring. When verifying conformity to ISO GPS tolerances (verification), the measurand is often unclear, particularly for geometrical tolerances. The tolerance zone is a portion of space whereas the measurand is a scalar quantity, and many such quantities may be derived from the same portion of space. We propose a unified derivation of the measurand in ISO GPS verification matching the designer’s intent. Different types of tolerances are considered, from the easiest to the least obvious as to the derivation of the measurand

A graph-based method and a software tool for interactive tolerance specification

Abstract The paper deals with the problem of tolerance specification and, in particular, proposes a graph-based method and a preliminary software tool: (i) to accomplish the tolerance specification for a mechanical assembly; (ii) to verify the consistency of the specification and, (iii) to allow the tracing of relationships among parts and features of the assembly. The method adopts Minimum Reference Geometric Elements (MRGE), directed graphs (di-graphs) and a set of dedicated algorithms to tackle the problems of consistency that occur during an interactive tolerance specification activity. Finally, an application illustrates the proposed method and its actual implementation

Automating GD&T Schema for Mechanical Assemblies

abstract: Parts are always manufactured with deviations from their nominal geometry due to many reasons such as inherent inaccuracies in the machine tools and environmental conditions. It is a designer job to devise a proper tolerance scheme to allow reasonable freedom to a manufacturer for imperfections without compromising performance. It takes years of experience and strong practical knowledge of the device function, manufacturing process and GD&T standards for a designer to create a good tolerance scheme. There is almost no theoretical resource to help designers in GD&T synthesis. As a result, designers often create inconsistent and incomplete tolerance schemes that lead to high assembly scrap rates. Auto-Tolerancing project was started in the Design Automation Lab (DAL) to investigate the degree to which tolerance synthesis can be automated. Tolerance synthesis includes tolerance schema generation (sans tolerance values) and tolerance value allocation. This thesis aims to address the tolerance schema generation. To develop an automated tolerance schema synthesis toolset, to-be-toleranced features need to be identified, required tolerance types should be determined, a scheme for computer representation of the GD&T information need to be developed, sequence of control should be identified, and a procedure for creating datum reference frames (DRFs) should be developed. The first three steps define the architecture of the tolerance schema generation module while the last two steps setup a base to create a proper tolerance scheme with the help of GD&T good practice rules obtained from experts. The GD&T scheme recommended by this module is used by the tolerance value allocation/analysis module to complete the process of automated tolerance synthesis. Various test cases are studied to verify the suitability of this module. The results show that software-generated schemas are proper enough to address the assemblability issues (first order tolerancing). Since this novel technology is at its initial stage of development, performing further researches and case studies will definitely help to improve the software for making more comprehensive tolerance schemas that cover design intent (second order tolerancing) and cost optimization (third order tolerancing).Dissertation/ThesisMasters Thesis Mechanical Engineering 201

An Example of Teaching Geometric Dimensioning and Tolerancing (GD&T) Concepts using 3D Printed Parts

Geometric Dimensioning and Tolerancing (GD&T) is an important tool for engineers to efficiently communicate design intent and requirements. GD&T has several advantages but can be difficult for students to learn due to the inherent 3D nature of the geometric tolerance zones. This paper describes an example of how 3D CAD models and 3D printed parts were used to illustrate several GD&T concepts including position tolerance zones, bonus tolerances, and designing functional gages for part inspection. The example described in this paper was implemented in a sophomore-level CAD course. The example was successfully delivered to a class of 45 students during the Fall 2017 semester. A description of the example is presented and, administering the example, requires simple 3D CAD modeling software and a 3D printer which are common in most engineering schools. Continuous improvements to the example are made based on faculty observations and assessments, as well as an end-of-semester survey administered to the students.Cockrell School of Engineerin

Geometric elements for tolerance definition in feature-based product models

Product modelling is an essential part of all computerised design and manufacturing activities. A precise mathematical model of the geometry of products is important, but must be supplemented with technological information such as the material, mechanical properties, functional specifications and tolerances. Modern CAD systems can model and manipulate components with complex geometry. However, technological information is represented as text symbols on the computer screen or drawing, and subsequent application programs are frequently unable to use this information effectively. This paper discusses this problem, and establishes the geometric elements required for the representation or dimensions and tolerances in a feature-based product modelling environment

Analysis of uncertainties and geometric tolerances in assemblies of parts

Computer models of the geometry of the real world have a tendency to assume that the shapes and positions of objects can be described exactly. However, real surfaces are subject to irregularities such as bumps and undulations and so do not have perfect, mathematically definable forms. Engineers recognise this fact and so assign tolerance specifications to their designs. This thesis develops a representation of geometric tolerance and uncertainty in assemblies of rigid parts. Geometric tolerances are defined by tolerance zones which are regions in which the real surface must lie. Parts in an assembly can slop about and so their positions are uncertain. Toleranced parts and assemblies of toleranced parts are represented by networks of tolerance zones and datums. Each arc in the network represents a relationship implied by the tolerance specification or by a contact between the parts. It is shown how all geometric constraints can be converted to an algebraic form. Useful results can be obtained from the network of tolerance zones and datums. For example it is possible to determine whether the parts of an assembly can be guaranteed to fit together. It is also possible to determine the maximum slop that could occur in the assembly assuming that the parts satisfy the tolerance specification. Two applications of this work are (1) tolerance checking during design and (2) analysis of uncertainty build-up in a robot assembly plan. I n the former, a designer could check a proposed tolerance specification to make sure that certain design requirements are satisfied. In the latter, knowledge of manufacturing tolerances of parts being manipulated can be used to determine the constraints on the positions of the parts when they are in contact with other parts