Stratégies de mise en oeuvre des polytopes en analyse de tolérance

In geometric tolerancing analysis area, a classical approach consists in handling polyhedrons coming from sets of linear constraints. The relative position between any two surfaces of a mechanism is determined by operations (Minkowski sum and intersection) on these polyhedrons. The polyhedrons are generally unbounded due to the inclusion of degrees of invariance for surfaces and degrees of freedom for joints defining theoretically unlimited displacements.In a first part are introduced the cap half-spaces to limit these displacements in order to transform the polyhedron into polytopes. This method requires controlling the influence of these additional half-spaces on the topology of calculated polytopes. This is necessary to ensure the traceability of these half-spaces through the tolerancing analysis process.A second part provides an inventory of the issues related to the numerical implementation of polytopes. One of them depends on the choice of a computation configuration (expression point and base, homogenization coefficients) to define a polytope. After proving that the modification of a computation configuration is an affine transformation, several simulation strategies are listed in order to understand the problems of numerical precision and computation time.En analyse de tolérances géométriques, une approche consiste à manipuler des polyèdres de R' issus d’ensembles de contraintes linéaires. La position relative entre deux surfaces quelconques d'un mécanisme est déterminée par des opérations (somme de Minkowski et intersection) sur ces polyèdres. Ces polyèdres ne sont pas bornés selon les déplacements illimités dus aux degrés d’invariance des surfaces et aux degrés de liberté des liaisons.Dans une première partie sont introduits des demi-espaces "bouchons" destinés à limiter ces déplacements afin de transformer les polyèdres en polytopes. Cette méthode implique de maîtriser l’influence des demi-espaces bouchons sur la topologie des polytopes résultants. Ceci est primordial pour garantir la traçabilité de ces demi-espaces dans le processus d’analyse de tolérances.Une seconde partie dresse un inventaire des problématiques de mise en oeuvre numérique des polytopes. L’une d’entre elles repose sur le choix d’une configuration de calcul (point et base d’expression, coefficients d’homogénéisation) pour définir un polytope. Après avoir montré que le changement de configuration de calcul est une transformation affine, plusieurs stratégies de simulations sont déclinées afin d’appréhender les problèmes de précision numérique et de temps de calculs

Tolerance Analysis by Polytopes

To determine the relative position of any two surfaces in a system, one approach is to useoperations (Minkowski sum and intersection) on sets of constraints. These constraints aremade compliant with half-spaces of R^n where each set of half-spaces defines an operandpolyhedron. These operands are generally unbounded due to the inclusion of degrees ofinvariance for surfaces and degrees of freedom for joints defining theoretically unlimiteddisplacements. To solve operations on operands, Minkowski sums in particular, "cap" halfspacesare added to each polyhedron to make it compliant with a polytope which is bydefinition a bounded polyhedron. The difficulty of this method lies in controlling the influenceof these additional half-spaces on the topology of polytopes calculated by sum or intersection.This is necessary to validate the geometric tolerances that ensure the compliance of amechanical system in terms of functional requirements

Review of data mining applications for quality assessment in manufacturing industry: Support Vector Machines

In many modern manufacturing industries, data that characterize the manufacturing process are electronically collected and stored in the databases. Due to advances in data collection systems and analysis tools, data mining (DM) has widely been applied for quality assessment (QA) in manufacturing industries. In DM, the choice of technique to use in analyzing a dataset and assessing the quality depend on the understanding of the analyst. On the other hand, with the advent of improved and efficient prediction techniques, there is a need for an analyst to know which tool performs best for a particular type of data set. Although a few review papers have recently been published to discuss DM applications in manufacturing for QA, this paper provides an extensive review to investigate the application of a special DM technique, namely support vector machine (SVM) to solve QA problems. The review provides a comprehensive analysis of the literature from various points of view as DM preliminaries, data preprocessing, DM applications for each quality task, SVM preliminaries, and application results. Summary tables and figures are also provided besides to the analyses. Finally, conclusions and future research directions are provided

Comparison of optimization techniques in a tolerance analysis approach considering form defects

In tolerancing analysis area, the most various existing approaches do not take form defects of parts into consideration. As high precisions assemblies cannot be analyzed with the assumption that form defects are negligible, the paper focuses in particular on the study of the form defects impacts on the assembly simulation and that by comparing two optimization algorithms (iHLRF and Quapro). The study is limited firstly to the cylinders. For the optimization, two main types of surfaces modelling are considered: difference surface-based method and real model. The compared models allow assessing the non-interferences between cylinders with form defects, potentially in contact. This is in the main issue to validate a tolerance analysis approach

Probabilistic-based approach using Kernel Density Estimation for gap modeling in a statistical tolerance analysis

The statistical tolerance analysis has become a key element used in the design stage to reduce the manufacturing cost, the rejection rate and to have high quality products. One of the frequently used methods is the Monte Carlo simulation, employed to compute the non-conformity rate due to its efficiency in handling the tolerance analysis of over-constrained mechanical systems. However, this simulation technique requires excessive numerical efforts. The goal of this paper is to improve this method by proposing a probabilistic model of gaps in fixed and sliding contacts and involved in the tolerance analysis of an assembly. The probabilistic model is carried out on the clearance components of the sliding and fixed contacts for their assembly feasibility considering all the imperfections on the surfaces. The kernel density estimation method is used to deal with the probabilistic model. The proposed method is applied to an over-constrained mechanical system and compared to the classical method regarding their computation time

A Framework for Integration of Resource Allocation and Reworking Concept into Design Optimisation Problem

The life cycle of an assembled product faces various uncertainties considering the current state of the manufacturing line. Varied of activities are integrated with the manufacturing line including processing, inspection, reworking, assembly, etc. Therefore, any decision taken concerning each activity, will affect the end-product of the manufacturing line. In an early stage, designers define tolerances on parts to ensure the functionality of the end-product. In this regard, this paper integrates resource allocation (as a decision to assign practical resources to parts) and reworking decision (as a decision to improve parts conformity rate) into the tolerance allocation problem. A modular-based cost modelling approach is proposed objecting to minimisation of manufacturing cost concerning resource allocation and reworking decisions. Eventually, a genetic algorithm and Monte-Carlo simulation are adapted to analyse the applicability of the model

Key Characteristics identification by global sensitivity analysis

During the design stage of product manufacturing, the designers try to specify only the necessary critical dimensions or what is called “Key Characteristics”. Knowing that dealing with Key Characteristics is time consuming and costly, it is preferable to reduce their number and exclude the non-contributing parameters. Different strategies that are based on qualitative or quantitative approaches for the identification of these dimensions are followed by the companies. The common way is to define the critical functional requirements which are expressed in terms of dimensions. When the functional requirements are set as critical, all the involved dimensions are labelled as Key Characteristics. However they do not have the same importance and need to be classified between contributing and non-contributing parameters. There is not a quantitative method that serves for the identification of Key Characteristics in the critical functional requirements. This paper suggests a numerical methodology which can be a step forward to a better ranking of the Key Characteristics. It is based on the global sensitivity analysis and more precisely on Sobol’ approach. The sensitivity of the Non Conformity Rate corresponding to the production of the product is measured with respect to the variable parameters characterizing the dimensions. The method is applied, first on a simple two-part example, then on a system having a linearised functional requirement and finally on a system with two non-linear functional requirements. The results show the main effects of the dimensions in addition to their interactions. Consequently it is possible to prioritize some and neglect the effect of the others and classify them respectively as Key Characteristics or not

A Framework for Integration of Resource Allocation and Reworking Concept into Design Optimisation Problem

The life cycle of an assembled product faces various uncertainties considering the current state of the manufacturing line. Varied of activities are integrated with the manufacturing line including processing, inspection, reworking, assembly, etc. Therefore, any decision taken concerning each activity, will affect the end-product of the manufacturing line. In an early stage, designers define tolerances on parts to ensure the functionality of the end-product. In this regard, this paper integrates resource allocation (as a decision to assign practical resources to parts) and reworking decision (as a decision to improve parts conformity rate) into the tolerance allocation problem. A modular-based cost modelling approach is proposed objecting to minimisation of manufacturing cost concerning resource allocation and reworking decisions. Eventually, a genetic algorithm and Monte-Carlo simulation are adapted to analyse the applicability of the model

An integrated resource allocation and tolerance allocation optimization: A statistical-based dimensional tolerancing

Today’s industrial world is facing rising demand for highly reliable and safe products. Complex industries, such as automobiles, medical, and aircraft, require a well-designed engineering plan which has a comprehensive understanding of the various certainties and uncertainties that occur in reality. Consequently, the need for reliable and precise parts has impacted the tolerancing activity. Key functions of complex products can often be realized by high precision part use. Thus, producers are confronted with high-quality requirements, cost pressure, and a rising number of demands. The introduction of new technologies and the need to meet the requirements have broadened the scope of tolerancing. In this paper, a statistical tolerance allocation model is developed to study the economic impact of allocated tolerances on an assembled product. The problem is aimed at optimizing the allocated tolerances to each part of the product while minimizing manufacturing costs. A modular cost model is proposed to determine the manufacturing costs related to each activity and part. The manufacturing costs include processing cost, inspection cost, scrap cost, assembly cost, and warranty cost. Furthermore, a genetic algorithm is adapted to study the applicability of the model developed on an exemplary assembled product