A Knowledge-Navigation System for Dimensional Metrology

Geometric dimensioning and tolerancing (GD&T) is a method to specify the dimensions and form of a part so that it will meet its design intent. GD&T is difficult to master for two main reasons. First, it is based on complex 3D geometric entities and relationships. Second, the geometry is associated with a large, diverse knowledge base of dimensional metrology with many interconnections. This paper describes an approach to create a dimensional metrology knowledge base that is organized around a set of key concepts and to represent those concepts as virtual objects that can be navigated with interactive, computer visualization techniques to access the associated knowledge. The approach can enable several applications. First is the application to convey the definition and meaning of GD&T over a broad range of tolerance types. Second is the application to provide a visualization of dimensional metrology knowledge within a control hierarchy of the inspection process. Third is the application to show the coverage of interoperability standards to enable industry to make decisions on standards development and harmonization efforts. A prototype system has been implemented to demonstrate the principles involved in the approach.     

Tolerance specification and comparative analysis for computer-integrated dimensional inspection

Two important issues in the development of a computer-integrated dimensional inspection environment for manufactured parts are described, namely tolerance specification and comparative analysis. These two issues are related directly and therefore, should be addressed together. For supporting the computer-integrated dimensional inspection, a geometric dimensioning and tolerancing (GD&T) specification module and a comparative analysis module are developed and integrated with CATTA of the IBM CAD/CAM system. The proposed specification module supports ISO and ANSI geometric tolerances and allows multiple tolerance assignments on each single feature as well as on a group of same pattern features. Using this specification module, various tolerance information can be directly specified to the 3D CAD model of a part and can be used to support the subsequent planning and operation for manfacturing and inspection. The comparative analysis module is created to work with the GD&T module for constructing datum reference frames and comparing the actual measurement data with nominal design. After specifying all necessary tolerance information, using discrete measurement data from coordinate measuring machines (CMM), one can evaluate the dimensional quality of an actual feature through the comparative analysis module.     

Tolerance transfer in sheet metal forming

A literature review of sheet metal forming errors as well as geometrical dimensions and tolerances (GD&T) shows that the theoretical means for the allocation of process tolerances with respect to GD&T are insufficient. In order to judge the influence of geometrical process errors (e.g., angular errors of bends), two typical sheet metal designs with parallelism and a position tolerance are studied. These case studies comprise a detailed analysis of tolerance chains including angular errors of bends and their positions. The resulting errors are compared with those resulting from length dimensional process errors and conclusions are drawn.     

Graph-based set-up planning and tolerance decomposition for computer-aided fixture design

Set-up planning plays an important role in integrating design with process planning and fixture design. Its main task is to determine the number and sequence of set-ups, and select locating datum, machining features and operations in each setup. Computer-based set-up planning may be used to generate automatically a setup plan based on tolerance analysis for minimizing locating error, calculating machining error stack-up and improving CAD/CAPP/CAFD (Computer-aided Fixture Design) integration efficiency. Most of the current set-up planning systems were based on empirical methods (such as rule and knowledge base) and their applications background was plus/minus a dimensioning and tolerancing (GD&T) scheme. Today, more and more industries are using a true positioning Geometric Dimensioning and Tolerancing (GD&T) scheme in design and manufacturing. To support this requirement, this paper presents an analytical set-up planning approach with three techniques, (1) an extended graph to describe a Feature and Tolerance Relationship Graph (FTG) and a Datum and Machining Feature Relationship Graph (DMG), which could be transferred to an analytical computer model; (2) seven set-up planning principles to minimize machining error stack-up under a true positioning GD&T scheme; and (3) tolerance decomposition models to partition a tolerance into interoperable machining errors, which could be used for locating error analysis or for feedback to design stage for design improvement. These techniques are implemented in a computer system and it is integrated with a commercial CAD/CAM system to support an automobile manufacturing enterprise in fixture design and production planning.     

相关要求与边界设计

相关要求是一种边界控制的公差设计方法。用最大实体边界( MMB) 或最小实体边界( LMB) 及综合公差( T t ) , 来满足装配或强度要求, 并为制造提供更好的经济效益。此方法应该在公差设计中积极推广应用。     

Statistical tolerance synthesis using distribution function zones

Tolerance is one of the most important parameters in design and manufacturing. Tolerance synthesis has a significant impact on manufacturing cost and product quality. In the international standards community two approaches for statistical tolerancing of mechanical parts are being discussed: process capability indices and distribution function zone. The distribution function zone (DFZone) approach defines the acceptability of a population of parts by requiring that the distribution function of relevant values of the parts be bounded by a pair of specified distribution functions. In order to apply this approach to statistical tolerancing, one needs a method to decompose the assembly level tolerance specification to obtain tolerance parameters for each component in conjunction with a corresponding tolerance-cost model. This paper introduces an optimization-based statistical tolerance synthesis model based on the DFZone tolerance specifications. A new tolerance-cost model is proposed and the model is illustrated with an assembly example.     

设计与制造中的统计几何公差建模及应用

几何与尺寸公差(形位公差GD&T)广泛用于机械工程设计与制造中重要几何特征的偏差控制.相对较成熟和简单的尺度公差建模与分析,几何公差统计建模与分析更具挑战性,是当前CAD技术中尚未但亟待解决的课题之一.现提出采用统计几何模态模型(SMA)方法解决这一问题.SMA可识别刻划与解释测量数据中的几何特征信号模式及其变化,从而服务于制造中的(公差)质量检验、诊断及变化模式的统计建模.在设计中SMA可进行模态重组综合,从而再现或仿真几何特征偏差的随机变化进行统计几何公差分析.     

Evaluating Process Capability for Geometrically Toleranced Parts: A Practical Approach

The practice of geometric tolerancing has gained in industry popularity since the 1990s. This approach has advantages over conventional tolerancing in defining both geometry and associated tolerance and, thus, generating a more realistic “acceptable design space.” There have been a number of highly mathematical treatments of the subject over the years which have not found their way into popular usage. We look at a specific example of geometric tolerancing and derive a simple approach based on the geometry of the situation and standard C_p and C_pk calculations. The study describes an approach based on understanding the limiting conditions of acceptable operation. In the example of a pin and clearance hole, we derive the limiting condition as a zero radial gap for a hole and a perfectly centered pin at maximum metal condition. We then performed a standard C_pk calculation with the limiting condition acting as the effective tolerance limit. Because we are dealing with radial gaps, we have an effective one-sided tolerance with a minimum acceptable value of 0 for the radial gaps. We tested the approach using Normally distributed simulated data and found that it provides an accurate evaluation of process capability and projected scrap levels. With minor cautions, we conclude that this methodological approach could be extrapolated to other geometrically toleranced situations.     

Statistical Analysis of Geometrical Tolerances: A Case Study

Tolerancing is one of the most important but complex activities in design. Tolerance information takes place at every phase of design activity. It represents the fundamental link between the theoretical model of the mechanical product and the actual one. During the two previous decades, engineering projects and scientific researches demonstrated that ongoing miniaturization increased the influence of geometric tolerances. They also admit that mass production is mainly based on statistical techniques. On the other hand, the decomposition of the global tolerancing process into functional-level, assembly-level, part-level, and manufacturing-level, reduces dramatically the domain of the solution. In this paper, the global tolerancing process is described and a novel method for statistical analysis of geometrical tolerances is discussed. Then the statistical approach is introduced and its performance is evaluated on a best case study. The analysis of the technical drawing of a part is given in order to highlight the advantages of the statistical approach.     

Statistical Tolerancing for Combinations of Coaxial Features and Clearance Fits

A method for statistically tolerancing the eccentricity of a mechanical assembly consisting of coaxial components has been developed. The method provides for a linear combination of variances of coaxial features within components and clearance fits between components. The resulting predicted tolerance of assembly eccentricity includes variation introduced by the manufacturing processes and by the assembly processes. Various conditions and the associated assumptions for both coaxial features and clearance fits are provided. Some application details are discussed.     

Representation of geometric variations using matrix transforms for statistical tolerance analysis in assemblies

The goal of this article is to develop a tolerance representation for assemblies compatible with tolerance analysis based on a closed-form algorithm used in robotic applications. A methodology is described that represents standard Y14.5M-1982 tolerances using homogeneous 4×4 matrix transforms. Transforms represent both the nominal relations between parts and the variations caused by geometric deviations allowed by the tolerances. The analysis calculates a statistical estimate of the location of theNth part in an assembly starting from the first part or a fixture. Except forform tolerances, most types of tolerance specifications are compatible with the proposed representation. This approach is well suited to integration with CAD systems and feature-based design. Since assembly apparatus errors can be calculated using the same methodology, one can predict the relative position and angle errors between two parts about to be mated. This permits useful evaluation of assembly equipment errors, comparison of different product tolerance assignments, and calculations of assembly process capability.     

Manufacturing signature and operating conditions in a variational model for tolerance analysis of rigid assemblies

The need of a univocal language for geometrical product specification considering all steps of the product life cycle such as design, manufacturing, and inspection is inevitable. Most models for Computer-Aided Tolerancing proposed by researchers and used in industry do not fully conform with standards. Moreover, most of them make severe assumptions on observable geometric deviations and can therefore hardly handle all kinds of 3D tolerances. These lacks inspired the idea and the development of a discrete geometry framework that is capable of considering geometric deviations of different stages of the product life cycle and is versatile regarding current and future tolerancing standards. This work uses a point cloud-based geometry representation scheme to implement the pattern left on the surfaces by a manufacturing process; then, this scheme has been inserted in a variational approach for tolerance analysis. Moreover, gravity and friction among the parts to assemble have been simulated too. In this way, a new Computer Aided Tolerancing (CAT) simulation tool has been developed; it approaches reality more than existing software packages do. To verify the effectiveness of the new CAT simulation tool, it has been applied to two case studies. The obtained results have been compared with those due to a geometrical model that has been developed by simulating what happens among the parts in the actual assembly. The obtained results show how the new CAT simulation tool gives results nearer to reality than literature models do.     

Generalization and evaluation of vectorial tolerances

In recent years, vectorial tolerancing has emerged as a new alternative for representing workpiece tolerances. In contrast to conventional geometric tolerances which originated from hard gauging practices, vectorial tolerancing follows the working principle of coordinate measuring machines and CAD/ CAM systems. Moreover it provides feedback from measurement directly to manufacturing process control. Many believe it is a better tolerancing method to tie design, manufacuturing, and measurement together. However, the current proposal of vectorial tolerancing has some limitations. First, the currently adopted orientation vector is not sufficient for representing true 3D orientations. As a result, the orientation of a free form surface cannot be properly established. Second, there is lacking a unified and consistent method for the evaluation of vectorial tolerances. This paper proposes a new orientation vector which provides a more general mathematical basis for representing vectorial tolerances. It enables true 3D orientation representation and relates tolerances to the functional requirement. With the improved mathematical definition, a systematic tolerance evaluation approach becomes possible for both analytical geometric elements and free-form surfaces. Computer simulations and real-world applications are studied to validate this new approach.     

Tolerancing algebra: A building block for handling tolerance interactions in design and manufacturing Part 1: Concept and representation

As a fundamental building block for 3D tolerance transfer analysis, tolerancing algebra on a deviation space has been proposed and elaborated. Based on the investigation of the spatial characteristic and the propagation mechanism of geometric tolerances and manufacturing process dispersions, a set of primitives and operations has been defined, which forms the algebraic structure of tolerancing algebra. Some important algebraic properties have been derived that will be extensively used to establish a tolerance transfer technique for process planning. Companion papers present the idea of tolerancing algebra in two parts. Part 1 presents some important concepts and their representations. Part 2 endeavours to show the interactions between product tolerances and process dispersions by way of the basic algebraic operations on deviation volumes.     

Automatic evaluation of form errors in high-density acquired surfaces

In this paper the authors present an original methodology aiming at the automation of the geometric inspection, starting from a high-density acquired surface. The concept of intrinsic nominal reference is herein introduced in order to evaluate geometric errors. Starting from these concepts, a new specification language, which is based on recognisable geometric entities, is defined. This work also proposes some surface differential properties, such as the intrinsic nominal references, from which new categories of form errors can be introduced. Well-defined rules are then necessary for the unambiguous identification of these intrinsic nominal references. These rules are an integral part of the tolerance specification. This new approach requires that a recognition process be performed on the acquired model so as to automatically identify the already-mentioned intrinsic nominal references. The assessable errors refer to recognisable geometric entities and their evaluation leaves the nominal reference specification aside since they can be intrinsically associated with a recognised geometric shape. Tolerance specification is defined based on the error categories which can be automatically evaluated and which are an integral part of the specification language.     

Functional tolerancing: A design for manufacturing methodology

The problem addressed in this paper is the development of a physico-mathematical basis for mechanical tolerances. The lack of such a basis has fostered a decoupling of design (function) and manufacturing. The groundwork for a tolerancing methodology is laid by a model of profile errors, whose components are justified by physical reasoning and estimated using mathematical tools. The methodology is then presented as an evolutionary procedure that harnesses the various tools, as required, toanalyze profiles in terms of a minimum set of profile parameters and tore-generate them from the parameters. This equips the designer with a rational means for estimating performance prior to manufacturing, hence integrating design and manufacturing. The utility of thefunctional tolerancing methodology is demonstrated with performance simulations of a lathe-head-stock design, focusing on gear transmission with synthesized errors.     

A freeform surface manufacturing approach by integration of inspection and tool path generation

Freeform surfaces have been widely used in various engineering applications. Increasing requirements for the accuracy of freeform surfaces have led to significant challenges for the manufacturing of these surfaces. A method for manufacturing of freeform surfaces is introduced in this paper by integrating inspection and tool path generation to improve manufacturing quality while reducing manufacturing efforts. Inspection is conducted by comparing the digitised manufactured surface with the design surface to identify the error regions. In this new inspection technique, the areas on the manufactured surface that are beyond the design tolerance boundaries are used as the objective function during the localisation process, in order to minimise post-inspection machining efforts. The tool path generation methods are then selected based on the geometric characteristics of the identified error regions, for creating tool paths to remove the errors. Computational efficiency, machining efficiency, and quality are considered in this integrated method.     

Integrating GD&T into dimensional variation models for multistage machining processes

Recently, the modelling of variation propagation in multistage machining processes has drawn significant attention. In most of the recently developed variation propagation models, the dimensional variation is determined through kinematic analysis of the relationships among error sources and dimensional quality of the product, represented by homogeneous transformations of the actual location of a product's features from their nominal locations. In design and manufacturing, however, the dimensional quality is often evaluated using Geometric Dimensioning and Tolerancing (GD&T) standards. The method developed in this paper translates the GD&T characteristic of the features into a homogeneous transformation representation that can be integrated in existing variation propagation models for machining processes. A mathematical representation using homogeneous transformation matrices is developed for position, orientation and form characteristics as defined in ANSI Y14.5; further, a numerical case study is conducted to validate the developed methods.     

虚拟产品开发中的并行公差设计

并行公差设计能够有效解决VPD中的公差控制与公差分配问题，有利于VPD的全面集成以及面向加工和面向装配的实现。本文介绍了并行公差设计的内涵和特点，并提出了并行公差设计的系统结构。在此基础上开发的基于PDM的并行公差设计系统是虚拟开发平台的一个重要组成部分，已经通过863CIMS主题专家组的验收。     

Automated manufacturability assessment of rotational parts by grinding

Automated manufacturability assessment of a given design is a key requirement in realizing complete integration of design (CAD) and manufacturing (CAM). The paper deals with a system developed for automated manufacturability assessment by machining processes. The purpose of this system is to assist designers in their effort to come up with manufacturable parts economising in terms of cost and time. Unlike most of the work done in the past, which concentrates on assessment by primary machining processes such as turning and milling, the present work deals with grinding operation. The present system uses geometric reasoning to extract manufacturing specific information from a part model. It uses a knowledge base consisting of grinding process knowledge and control rules, which are activated by the designer. It also has a provision to account for company-specific manufacturing resources to come up with meaningful assessment for part manufacturability. The use of the proposed system is demonstrated for the assessment of axisymmetric parts to be manufactured by cylindrical and internal grinding processes.