A Survey of Mathematical Methods for the Construction of Geometric Tolerance Zones

2003 ◽  
Vol 3 (1) ◽  
pp. 64-75 ◽  
Author(s):  
T. M. Kethara Pasupathy ◽  
Edward P. Morse ◽  
Robert G. Wilhelm
Keyword(s):  
Functional Requirements ◽  
Mathematical Methods ◽  
Geometric Tolerance ◽  
Manufacturing Enterprises ◽  
Computing Machinery ◽  
Geometric Tolerances ◽  
Tolerance Specification ◽  
Computer Based ◽  
Tolerance Zones ◽  
Application Specific

The physical realization of any part always yields imperfect forms with respect to the ideal geometry specified in the engineering design. To describe and preserve functional requirements of design, the allowable variation is specified using modern geometric tolerances via tolerance zones. Specification using geometric tolerances is intended for unambiguous communication. Mathematically unambiguous specification is required for the application of computing machinery across manufacturing enterprises to lower costs and improve efficiency. Several computer-based tools have been developed to aid in tolerance specification and also in subsequent processing, or applications that utilize tolerance specification information, such as analysis, synthesis, manufacture and measurement. In order to execute these activities, the tolerance zones have to be unambiguously captured by computer programs. The geometric tolerance specification is complex and not completely free of ambiguities. These difficulties pose as challenges in realizing the tolerance zones and limit the applicability of any particular method developed so far. This paper presents a survey of the current computer based methods available to capture tolerance zones of parts. The limitations of the methods are analyzed based on the following criteria: the range of applicability, compatibility with standards, ease in realization and the effects of singularities in shapes that are application specific. Various assembly analysis techniques that utilize the tolerance zone construction and other recent approaches for tolerance design are also reported.

Formation of Geometric Tolerance Zones for Polyhedral Objects

1997 ◽  
Author(s):  
Utpal Roy ◽  
Bing Li
Keyword(s):  
Variational Model ◽  
Tolerance Zone ◽  
Geometric Tolerance ◽  
Geometric Tolerances ◽  
Polyhedral Objects ◽  
Different Types ◽  
Tolerance Zones ◽  
Algebraic Constraints ◽  
Size Tolerance ◽  
Part Model

Abstract This paper presents a scheme for establishing geometric tolerance zones for polyhedral objects in solid modelers. The proposed scheme is based on a surface-based variational model. Variations are applied to a part model by varying each surface’s model variables. Those model variables are constrained by some algebraic relations derived from the specified geometric tolerances. For size tolerance, two types of tolerance zones are considered in order to reflect two different types of size tolerances. For any other geometric tolerance (form, orientation or positional), the resultant tolerance zone is defined by the combination of size tolerance and that particular geometric tolerance specifications. Appropriate algebraic constraints (on the model variables) are finally used to establish the tolerance zone boundaries in the surface-based variational model.

Representation and reasoning of geometric tolerances in design

1997 ◽  
Vol 11 (4) ◽  
pp. 325-341 ◽  
Author(s):  
Jhy-Cherng Tsai ◽  
Mark R. Cutkosky
Keyword(s):  
Quality Control ◽  
Recent Work ◽  
Functional Requirements ◽  
Geometric Tolerance ◽  
Geometric Dimensioning And Tolerancing ◽  
Design Specifications ◽  
Geometric Tolerances ◽  
Dimensioning And Tolerancing ◽  
Different Types ◽  
Representation Scheme

AbstractThe geometric dimensioning and tolerancing (GD&T) specifications of a design are directly associated with its performance and functional requirements. They also govern the manufacturing and quality control processes needed to achieve those requirements. This paper reviews recent work in geometric tolerance representation and reasoning and presents a generic and uniform graph-based representation scheme, called the Tolerance Network, to represent GD&T specifications across a part or assembly. The network can accommodate GD&T specifications related to the function, behavior, manufacturing, and inspection requirements embedded in design specifications and supports the use of different types of tolerances. The network also accommodates common design practices such as the specification of overconstrained features and parts. The necessary properties of such a network are discussed that allow under- and overconstrained design specifications to be detected and analyzed.

A Mathematical Model for Geometric Tolerances

1993 ◽  
Vol 115 (1) ◽  
pp. 81-86 ◽  
Author(s):  
F. Etesami
Keyword(s):  
Mathematical Model ◽  
Specification Language ◽  
Theoretic Approach ◽  
One Dimensional ◽  
Dimensional Tolerance ◽  
Geometric Tolerancing ◽  
Geometric Tolerances ◽  
Tolerance Specification ◽  
Tolerance Zones

This paper presents a mathematical model for specifying geometric tolerances. This model along with a syntax of tolerance specification will be referred to as the Tolerance Specification Language (TSL). TSL can be used to interpret ANSI Y14.5 geometric tolerancing specifications. The formalization of TSL is based on a set theoretic approach, especially on the concept of offset solids. In this model there is no classification of tolerance types, and there are no restrictions on the use of feature types. Instead, TSL allows the designer to control a feature from expanding, shrinking, or deforming beyond a specified tolerance value. All the tolerancing assertions in TSL apply to surface features and generate uniform tolerance zones. Using two and one dimensional tolerance specification facilities, TSL can approximate ANSI statements that apply to derived features, or generate non-uniform tolerance zones. The appendix of this paper discusses many examples from ANSI and their equivalent TSL form.

Synthesis of Geometric Tolerances of a Gearbox Using a Deviation-Based Tolerance Synthesis Scheme

2003 ◽  
Author(s):  
N. Pramanik ◽  
U. Roy ◽  
R. Sudarsan ◽  
R. D. Sriram ◽  
K. W. Lyons
Keyword(s):  
Cost Functions ◽  
Functional Requirements ◽  
Total Cost ◽  
Tolerance Synthesis ◽  
Planetary Gearbox ◽  
Geometric Tolerances ◽  
Step Procedure ◽  
Non Linear ◽  
Tolerance Zones

In this paper a step-by-step procedure for carrying out synthesis of geometric tolerances of a planetary gearbox using a deviation-based tolerance synthesis (TS) scheme has been presented. The TS scheme uses an optimization for minimizing total cost of manufacturing, subject to constraints for assemblability of parts and constraints for functional requirements. The TS work is carried out in several stages. First the gearbox with its nominal dimensions is converted into a model that could serve as input to the synthesis module. Cost functions and constraints equations are then generated using deviation parameters of features. The optimization is carried out using these equations in standard non-linear minimization tools (Matlab) and the optimal deviation parameters are subsequently mapped into suitable tolerance specifications or tolerance zones as per ANSI Y14.5 tolerancing standards.

scholarly journals The Influence of Automated Machining Strategy on Geometric Deviations of Machined Surfaces

2021 ◽  
Vol 11 (5) ◽  
pp. 2353
Author(s):  
Ján Varga ◽  
Teodor Tóth ◽  
Peter Frankovský ◽  
Ľudmila Dulebová ◽  
Emil Spišák ◽  
...  
Keyword(s):  
Control System ◽  
Surface Quality ◽  
Coordinate Measuring Machine ◽  
Geometric Tolerance ◽  
Geometric Tolerances ◽  
Significant Difference ◽  
Geometric Deviations ◽  
Measuring Machine ◽  
Overlap Parameter ◽  
Total Average

This paper deals with various automated milling strategies and their influence on the accuracy of produced parts. Among the most important factors for surface quality is the automated milling strategy. Milling strategies were generated from two different programs, CAM system SolidCAM, with the help of workshop programming in the control system Heidenhain TNC 426. In the first step, simulations of different toolpaths were conducted. Using geometric tolerance is becoming increasingly important in robotized production, but its proper application requires a deeper understanding. This article presents the measurement of selected planes of robotized production to evaluate their flatness, parallelism and perpendicularity deviations after milling on the coordinate measuring machine Carl Zeiss Contura G2. Total average deviations, including all geometric tolerances, were 0.020 mm for SolidCAM and 0.016 mm for Heidenhain TNC 426. The result is significantly affected by the flatness of measured planes, where the overlap parameter of the tools has a significant impact on the flatness of the surface. With interchangeable cutter plate tools, it is better to use higher overlap to achieve better flatness. There is a significant difference in production time, with SolidCAM 25 min and 30 s, and Heidenhain 48 min and 19 s. In accordance with these findings, the SolidCAM system is more suitable for production.

Study on Geometric Tolerances Information in Integrated Manufacturing Processes

2010 ◽  
Vol 37-38 ◽  
pp. 1292-1295
Author(s):  
Yan Chao ◽  
Hai Feng Zhang ◽  
Li Qun Wu
Keyword(s):  
Life Cycle ◽  
Data Model ◽  
Manufacturing Process ◽  
Product Life Cycle ◽  
Critical Role ◽  
Manufacturing Processes ◽  
Product Life ◽  
Internet Technologies ◽  
Geometric Tolerance ◽  
Geometric Tolerances

Tolerance information plays a critical role in many steps of the product life cycle. It is especially important due to the advances in Internet technologies and increasing integration requirements from industry. In this paper, geometric tolerances information in manufacturing process (IMP) is studied, and the layered conformance level of geometric tolerances is established according to ASME Y14.5-1994, STEP and DMIS. An EXPRESS-G data model of geometric tolerance information in IMP is established. The XML language is used to represent and program the geometric tolerances information in IMP.

Description logic-based automatic generation of geometric tolerance zones

2015 ◽  
Vol 79 (5-8) ◽  
pp. 1221-1237 ◽  
Author(s):  
Yuchu Qin ◽  
Wenlong Lu ◽  
Xiaojun Liu ◽  
Meifa Huang ◽  
Liping Zhou ◽  
...  
Keyword(s):  
Description Logic ◽  
Automatic Generation ◽  
Geometric Tolerance ◽  
Tolerance Zones

Architectures of Concurrent Engineering System for Composites

1996 ◽  
Author(s):  
Jian Zhang ◽  
H. Thomas Hahn
Keyword(s):  
Concurrent Engineering ◽  
Life Cycle Cost ◽  
Engineering System ◽  
Functional Requirements ◽  
System Architectures ◽  
Composite Manufacturing ◽  
Manufacturing Enterprises ◽  
System Requirements ◽  
Points Of View ◽  
Process Productivity

Abstract The demand for the better quality products with shorter lead-time and lower life-cycle cost forces the manufacturing enterprises all around the world to optimize their production strategies from both enterprise engineering and enterprise operation respectively. This paper addresses the architectural issue of applying the Concurrent Engineering (CE) approach in the composite manufacturing area. It first discussed briefly the characteristics of composite manufacturing process to examine the feasibility and possibility of applying the CE approach to improve its process productivity and product quality. Then the functional requirements for a concurrent engineering system for composites (CESC) were defined from both operational and architectural points of view. Finally, the integrated infrastructure based system architectures for the CESC were presented in accordance with the physical system requirements, and so were the associated and currently conducted R&D focuses for the system.

scholarly journals Implementation of Parameterized Work Piece Deviations and Measurement Uncertainties into Performant Meta-models for an Improved Tolerance Specification

2019 ◽  
Vol 1 (1) ◽  
pp. 3501-3510
Author(s):  
Andreas Michael Müller ◽  
Thomas Oberleiter ◽  
Kai Willner ◽  
Tino Hausotte
Keyword(s):  
Production Costs ◽  
Work Piece ◽  
Geometric Tolerances ◽  
Tolerance Specification ◽  
Close Cooperation ◽  
And Function ◽  
Product Description ◽  
Tolerance Management ◽  
Technological Products

AbstractGeometrical work piece deviations are unavoidable and directly affect the function and quality of technological products. Tolerance management is regarded as a crucial subtask of the development of technological products, because it ensures the function as well as a sufficient product quality while maintaining reasonable production costs. That means, that geometric tolerances as an essential part of the product description greatly affect the functional capability, manufacturability, mountability, verifiability and the costs of the final product. The research group FOR 2271 was founded to enable the computer-aided specification of tolerances, which meet the requirements of production, assembly, verification and function by close cooperation between the departments responsible for product design, assembly and metrology. The aim of this contribution is to determine the manufacturing process scatter as well as the measurement uncertainty and establish ways and means to include that information into efficient meta-models, ultimately enabling improved and accurate tolerance analyses.

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