Animated visualization of the maximum material requirement

The usage of animation technique applied as a powerful tool to explain the complex concept of the maximum material requirement (MMR) is shown. The concepts of datum system and the maximum material virtual condition envelope, that is located by theoretically exact dimensions are highlighted. The maximum material virtual condition state, that limits the collective effect of the feature maximum material size and the maximum acceptable geometrical deviation for that size is examined. The tolerances of perpendicularity and position with the maximum material modifiers applied in the tolerance frames for the toleranced features or respectively for the datum features are explored. The simplicity of the verification of the conformance with the specification employing the MMR by the gauge that represents the matting counter part is emphasized.     

Modelling of tolerances and manufacturing dimensions

To obtain imposed dimensional and geometrical specifications for any mechanical piece, production tolerances must be calculated. So a simulation of workpiece behavior when it is machined, has permitted calculations of deviations on machined surfaces.The method of deviation calculation is based on a comparison between imposed functional tolerance and the tolerance calculated in relation to deviations on two machined surfaces or between a machined surface and the operational datum.The one direction modelling of deviations inquires practical inputs such as the planning process, the operational datum, the deviations on rough surfaces, and deviations on surface datum for any stage of machining. The developed method allows determining the deviations on machined surfaces. Then, tolerances on production dimensions were calculated in three directions. These results have permitted to define average production dimensions, which may be used for NC machine programming and to prepare an optimal rough piece configuration.The developed method has been applied for the machining of a fixing screw.     

A hybrid method of artificial neural networks and simulated annealing in monitoring auto-correlated multi-attribute processes

In mechanical assemblies, individual components are placed together to deliver a certain function. The performance, quality, and cost of the mechanical assembly are significantly affected by its tolerances. Toleranced dimensions inherently generate an uncertain environment in a mechanical assembly. This paper presents a proper method for tolerance analysis of mechanical assemblies with asymmetric tolerances based on an uncertainty model. This mathematical approach is based on fuzzy logic and tolerance accumulation models such as worst-case and root-sum-square methods. A fuzzy-based tolerance representation is developed to model uncertainty of tolerance components in the mechanical assemblies. According to this scheme, toleranced components are described as fuzzy numbers with their membership functions constructed using the statistical distributions of manufactured variables. In this way, the uncertainty of assembly requirements and accumulation of tolerances are represented in the form of fuzzy number. In this paper, a new factor, the fuzzy factor, is introduced that helps converting the membership functions into fuzzy intervals that can be used for modal interval analysis. Equations for estimation of percent contributions of individual tolerances are introduced in terms of uncertainty parameter. These equations yield percent contributions of upper and lower bounds of independent variables (manufactured dimensions) on the upper and lower bounds of dependent variables (assembly dimensions). The proposed method is applied to an example, and its results are discussed.     

Compliant assembly tolerance analysis: guidelines to formalize the resistance spot welding plasticity effects

The variational analysis of compliant assemblies is mainly based on linear elastic models. Some guidelines have been defined to integrate material plasticity into a tolerance analysis model in order to improve its results when considering the resistance spot welding (RSW) process. A finite element model that simulates the body-in-white and RSW processes has been applied to butt and slip joints, with parts subjected to dimensional and geometrical tolerances that cause gap mismatching condition and loading interference on fixtures. The dimensional quality of assemblies is affected by plasticization near the welding spot, at the base of welded flanges and near the locators. The springback evidenced relative rotation of parts.     

Fuzzy-small degrees of freedom representation of linear and angular variations in mechanical assemblies for tolerance analysis and allocation

Tolerances naturally generate an uncertain environment for design and manufacturing. In this paper, a novel fuzzy based tolerance representation approach for modeling the variations of geometric features due to dimensional tolerances is presented. The two concepts of fuzzy theory and small degrees of freedom are combined to introduce the fuzzy-small degrees of freedom model (F-SDOF). This model is suitable for tolerance analysis of mechanical assemblies with linear and angular tolerances. Based on the fuzzy concept, a new index (called the assemblability index) is introduced which signifies the fitting quality of parts in the assembly. Graphical and numerical representations of tolerance allocation by this method are presented. The goal of tolerance allocation is to adjust the tolerances assigned at the design stage so as to meet a functional requirement at the assembly stage. The presented method is compatible with the current dimensioning and tolerancing standards. The application of the proposed methodology is illustrated through presenting an example problem.     

Extraction/conversion of geometric dimensions and tolerances for machining features

It is important for a feature-based system to preserve feature integrity during feature operation, especially when feature interaction occurs. The paper presents a feature conversion approach to convert design features used in a design model into machining features for the downstream applications. This process includes both form features (geometric information) and non-geometric features conversion. Most researchers have concentrated on geometric information extraction and conversion without tackling the important problem of non-geometric feature information. This paper focuses on the extraction and conversion of feature geometric dimensions and tolerances (GD&T) for downstream machining application.The main barrier to the integration of a feature-based CAD/CAPP/CAM system – feature interaction – is discussed in this paper, which alters design features in their geometries and non-geometric information. How to identify and validate these feature dimensions and tolerances is one of the key issues in feature interaction conversion. The development of robust methodologies for preserving feature integrity for use in process planning application is the main thrust of the work reported in this paper.     

Dimensional and geometric tolerance design based on constraints

The paper presents a computer-aided approach of dimensional and geometric tolerance design. The method allows a designer to specify synthetically dimensional and geometric tolerances, including tolerance types and values. Firstly, tolerances are classified as self- and cross-referenced tolerances, and the rules for tolerance types design are presented. Secondly, the stack-up of 3D feature variation is formulated as a set of stack-up constraints (equation constraints), and the variation specified by tolerance forms tolerance constraints (inequality constraints). Tolerance value design is represented as the combinatorial optimization problem. The application of the variation and tolerance constraints to specify tolerance values is studied. Finally, a tolerance design example is used to illustrate the method.     

Conformance and nonconformance in segmentation-free X-ray computed tomography geometric inspection

Additive Manufacturing (AM) is changing the manufacturing paradigm as it makes it possible to generate complex geometries that are impossible using conventional technologies. However, conventional GPS/GD&T practices are inadequate both at specifying and verifying geometric tolerances. In both cases, they lack the required flexibility. Applying volumetric instead of surface representations helps to solve the problem of specifying tolerances and coheres with topological optimization. The verification paradigm must be modified, too, as AM allows an increase in part complexity without a corresponding increase of cost. Among measurement techniques, only X-ray computed tomography (XCT), which is volumetric, is capable of easily measure complex parts. Leaving the discussion of volumetric tolerance specifications to the future, the aim of this work is exploring a part geometric accuracy verification by direct comparison between its nominal geometry and geometric tolerance volumetric representation, and an XCT volumetric image of it. Unlike the conventional use of XCT for geometric verification, this is a segmentation-free verification. The method is based on the “mutual information” of the two, i.e. information shared by the measured and nominal representations. The output is a conformance statement that does rely on a measurement but nor on a specific measured value not rely on a measurement result. This makes defining a decision rule considering consumer's and producer's risks difficult: uncertainty does not exist in this case. Statistic and simulation techniques make it possible to estimate these risks, defining a numerical model of the distribution of the gray values in a specific portion of the XCT image. Finally, an additive manufacturing case study validates the methodology.     

Composite Planar Tolerance Allocation with Dimensional and Geometric Specifications

A new optimal approach for planar tolerance allocation is proposed in which dimensional and orientation geometric specifications are included. To deal with the increased complexity of planar tolerance analysis, a special relevance graph (SRG) is used to represent the relationships between manufactured elements and their size and tolerance information. In addition, the SRG is also applied for the geometric dimensions and tolerances. Using a suitable algorithm, planar tolerance chains that include geometric specifications can be generated automatically during process planning. Through a graph based analysis, stacks of tolerance zones are obtained. The resultant tolerance zone contains all of the composite links of the tolerance zones. The links are assigned according to the process capacities, which can be considered as constraints. A linear optimal model is established to solve the tolerance allocation problem. A practical example is used to demonstrate the feasibility and effectiveness of the proposed method.     

A dimensioning and tolerancing methodology for concurrent engineering applications II: comprehensive solution strategy

Dimensioning and tolerancing (D&T) is a multidisciplinary problem which requires the fulfillment of a large number of dimensional requirements. However, almost all of the currently available D&T tools are only intended for use by the designer. In addition, they typically provide solutions for the requirements one at time. This paper presents a methodology for determining the dimensional specifications of the component parts and sub-assemblies of a product by satisfying all of its requirements. The comprehensive solution strategy presented here includes: a strategy for separating D&T problems into groups, the determination of an optimum solution order for coupled functional equations, a generic tolerance allocation strategy, and strategies for solving different types of D&T problems. A number of commonly used cost minimization strategies, such as the use of standard parts, preferred sizes, preferred fits, and preferred tolerances, have also been incorporated into the proposed methodology. The methodology is interactive and intended for use in a concurrent engineering environment by members of a product development team.     

ISO manufacturing tolerancing: three-dimensional transfer with analysis line method

Functional tolerancing described in definition drawing of mechanical parts constitutes a contract to be respected by manufacturers. Process engineers have to choose process plans able to manufacture part respecting functional requirements and have to determine manufacturing specifications for each phase. Tolerance zone transfer method offers a three-dimensional algorithm of manufacturing specifications generation with International Organization for Standardization (ISO) standards. Analysis line method, developed in this article, establishes the calculus relation of the results of the tolerance chains according to the tolerances of manufacturing specifications to allow the tolerance synthesis. In this paper, the analysis line method is presented using an example. The aim is to show the hypotheses made during transfers in the context of ISO standards of tolerancing and to define accurately the datum reference frames used and deviations between these frames at particular points named analysis points.     

Compatibility of tolerancing

Tolerances are assigned to a mechanical engineering design either on the basis of functional and/or manufacturing requirements (toleranced dimensions, geometrical tolerances) or on the basis of the general categories—fine, medium, coarse—of the international standards or the designer's knowledge and experience (untoleranced dimensions). Conventional dimensions of the currently applicable dimensioning rules and implicit dimensions, including those attributed to geometrical tolerances, thus create four groups of tolerances which may or may not be compatible. In addition, any tolerance compromise, however tedious and difficult, not achieved systematically may well lead to accuracies which cannot be produced by the available machine tools. In the paper, a systematic approach to the above problems is presented. A methodology is demonstrated for the verification of the tolerance compatibility and for the assignment of compatible, producible and cost optimum tolerances.     

Part optimization and tolerances synthesis

A tolerance synthesis provides the distribution of tolerances on the functional specifications of parts for a mechanism, with the objective of satisfying a set of functional requirements. This approach involves adjusting the nominal dimensions of parts. The present article offers a six-step solution within an Excel solver environment. The designer is able to control the optimization process using a dashboard. The initial steps detect conflicting requirements and suggest compromises, while the subsequent steps optimize the nominal part dimensions in order to maximize mechanism quality with minimum tolerance. The final steps then seek to maximize tolerances with the aim of minimizing costs. The proposed method can also manage specifications with both maximum and minimum material requirements.     

Effect of uncertainties on substructure coupling: Modelling and reduction strategies

Different strategies for modelling and reducing the effect of uncertainties on the dynamic behaviour of coupled structures are discussed in this paper. In assembled structures, each component satisfies specifications about material properties and dimensional tolerances. Variability of design specifications within the tolerance field may affect the dynamic behaviour of the assembled structure more than that of any individual component substructure. Among modelling strategies, non-predictive techniques such as post-processing of data from a set of randomly assembled structures and analysis of sensitivities to uncertain variables are considered. However, emphasis is placed on a less trivial yet simple strategy such as the use of design of experiments to fit a regression model. Different reduction strategies are considered according to whether small design changes (even revised tolerance allocation) are still possible or not. In the latter case, selective assembly is extended to problems where the performance requirement is not the clearance between two parts, but a prescribed dynamic behaviour.     

采用SolidWorks的印刷机咬纸机构装配误差分析

研究采用SolidWorks软件辅助进行零件公差设计和改进的方法。首先,建立装配体模型,根据零/部件的装配约束关系、装配特征和装配信息,自动生成包含尺寸公差和形位公差的装配尺寸链并解算;然后根据计算结果对零件公差进行改进。通过分析国产某印刷机咬纸机构的装配误差这一实例,改进了咬纸机构零件的公差,最终解决了咬纸过程中咬纸面之间的点接触和线接触,以及咬纸力不够咬不住纸的情况。     

3D manufacturing tolerancing with probing of a local work coordinate system

The safety and performance requirements for mechanisms are such that the necessary accuracy of part geometry is difficult to reach using classical manufacturing processes. This paper proposes a manufacturing tolerance stack-up method based on the analysis line method. This technique enables both the analysis and the synthesis of ISO manufacturing specifications through a new approach which relies on production specifications, adjustment specifications, and their analysis to stack up the 3D resultant. The originality of the method resides in the 3D calculation for location requirements, which takes into account angular effects and probing operations on numerical-control machine-tools in order to define a local work coordinate system (WCS). For achieving tolerance analysis, deviations are modeled using small-displacement torsor. This tolerance analysis method enables one to determine explicit three-dimensional linear relations between manufacturing tolerances and functional requirements. These relations can be used as constraints for tolerance optimization.     

尺寸公差与形位公差混合优化分配

为解决尺寸公差与形位公差混合优化分配问题,提出了一种公差优化分配方法.根据成本-公差函数和尺寸公差与形位公差的关系,建立了以最小制造总成本为目标的非线性公差混合优化分配模型.该模型的约束包括装配尺寸链的功能要求和加工能力.求解该模型能同时得到优化的尺寸公差和形位公差.最后,分别用公差混合优化分配法和传统方法对一个实例进行公差分配,结果表明所提方法比传统方法更优越.     

A review of two models for tolerance analysis of an assembly: vector loop and matrix

Mechanical products are usually made by assembling many parts. The dimensional and geometrical variations of each part have to be limited by tolerances able to ensure both a standardized production and a certain level of quality, which is defined by satisfying functional requirements. The appropriate allocation of tolerances among the different parts of an assembly is the fundamental tool to ensure assemblies that work rightly at lower costs. Therefore, there is a strong need to develop a tolerance analysis to satisfy the requirements of the assembly by the tolerances imposed on the single parts. This tool has to be based on a mathematical model able to evaluate the cumulative effect of the single tolerances. Actually, there are some different models used or proposed by the literature to make the tolerance analysis of an assembly, but none of them is completely and univocally accepted. Some authors focus their attention on the solution of single problems found in these models or in their practical application in computer-aided tolerancing systems. But none of them has done an objective and complete comparison among them, analyzing the advantages and the weakness and furnishing a criterion for their choice and application. This paper briefly introduces two of the main models for tolerance analysis, the vector loop and the matrix. In this paper, these models are briefly described and then compared showing their analogies and differences.