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This paper's goal is to give an overview to tolerance analysis. The cost and quality of a product can be significantly impacted by decisions about tolerating. Increased focus on tolerance design is required if high-precision assemblies are to be produced at cheaper costs. After a component's tolerance has been determined, tolerance analysis looks to propagate the manufacturing imprecisions (geometrical defects) and to validate the value of the functional requirements. The mathematical modelling is absolutely necessary for this validation. Models for tolerance analysis are discussed in a lot of literature. There are summaries of the current state of the art, the most recent advancements, and the upcoming trends in tolerancing research. From a mathematical perspective, this paper provides a taxonomy of mathematical concepts for tolerance analysis. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The need for highly reliable and precise products has forced industries to study potential uncertainties during designing needed parts. The reliability and acceptance of the product rely on several factors and tolerancing activity plays an important role to assure that the manufactured product meets the requirements. The importance of tolerancing activity can be noticed once designers prefer tight tolerances to ensure product performance and in contrast manufacturers want loose tolerances to reduce manufacturing and assembly complexity and then cost, to decrease the non-conformance rate. Therefore, tolerance allocation and inspection-planning design can be formalized as an optimization problem which the objective function represents the cost impacted by several aspects of the quality management: cost of failure, cost of the inspection. This paper details a modular cost model which includes four components: the manufacturing cost, the inspection cost, the scrap cost (internal failure), and the cost of external failure. Moreover, to improve the efficiency of the cost model, it integrates several factors such as frequencies of the monitoring and inspection activities, probability of conformed product, probability of non-detection of non-conformity, and probability of non-detection of confirmed. The applications of this model are illustrated and demonstrated through an industrial case study. [ABSTRACT FROM AUTHOR]

Designers consider multiple parameters to attain a suitable solution for the initial requirements during a production system design. The design approach determines the choice of parameters used during the design process, and it can significantly affect the final result. A poor choice of information or an oversight of a crucial element might produce unexpected results. The goal of the work presented in this article is to provide the appropriate models for each step of the design process structured as a method and considering technological and human factors. These tools use basic functions and the production system's internal energy flow to model its behavior and collect the pertinent information needed to develop the design problem's final solution. This proposed method integrates elements from different design approaches, considering cost, time, and performance, simplifying the incorporation of safety factors through energy functions and organizational rearrangements. This approach also proposes a multi-view analysis of the production system that englobes the project and the product points of view and the impact of the designer's activities to produce safe, reliable, and efficient production systems. [ABSTRACT FROM AUTHOR]

Designers consider multiple parameters to attain a suitable solution for the initial requirements during a production system design. The design approach determines the choice of parameters used during the design process, and it can significantly affect the final result. A poor choice of information or an oversight of a crucial element might produce unexpected results. The goal of the work presented in this article is to provide the appropriate models for each step of the design process structured as a method and considering technological and human factors. These tools use basic functions and the production system's internal energy flow to model its behavior and collect the pertinent information needed to develop the design problem's final solution. This proposed method integrates elements from different design approaches, considering cost, time, and performance, simplifying the incorporation of safety factors through energy functions and organizational rearrangements. This approach also proposes a multi-view analysis of the production system that englobes the project and the product points of view and the impact of the designer's activities to produce safe, reliable, and efficient production systems. [ABSTRACT FROM AUTHOR]

Traditionally, performance, time and cost have been the main guidelines for production systems design, but other aspect such as human factors and safety are starting to emerge and take a main role for designers. Considering these findings, we are developing a multi-criteria design framework based on a Behavior-Energy-Structure model (BES) that makes use of energy flow through components to characterize its behavior via Energetic Technical Functions and their structural properties. This approach eases the incorporation of human factors and safety through the design phases, allowing designers to create safe, reliable and efficient production systems. [ABSTRACT FROM AUTHOR]

Additive manufacturing (AM), and particularly metal laser powder bed fusion (L-PBF) processes are rapidly being industrialized. Still, the current L-PBF process lacks both process quality and reproducibility. For that reason, robust process monitoring needs to be developed to reduce the process variation and ensure quality. Accordingly, to deal with this issue, this work proposes a new approach to predict the quality of L-PBF products. The approach consists of selecting relevant statistical features from optical data and validating these features by assessing their ability to predict the different products' density classes. The approach was applied on cubical specimens produced with different process parameters. Support vector machines (SVMs) were used as classification tools, and the first results are promising with a prediction accuracy higher than 90%." [ABSTRACT FROM AUTHOR]

The tolerance analysis aims to check if the tolerances specified on mechanism components allow to respect the assembly and functional requirements. Several papers illustrate that the form defects have an impact on the mechanism behavior, but most tolerance analysis techniques neglected them. To perform the tolerance analysis, three issues must be addressed: the geometrical deviations modelling, the geometrical behavior modelling and the technique of tolerance analysis. Therefore, this paper presents one contribution for each issue to perform tolerance analysis of over-constrained mechanism with form defect: • Modal representation of the form defect • Behavior modelling technique of the contact with form defect • Tolerance analysis technique with the integration of the different contact types. [ABSTRACT FROM AUTHOR]

Tolerance analysis is a well-accepted key element in industry for ensuring product quality as well as for reducing manufacturing costs. At the same time, and particularly in light of the recent advances in simulation technology, tolerancing decisions are also becoming increasingly important during earlier stages of design. One critical task hereby is the simulation of the "real-world" behavior of the product with minimum uncertainty, i.e. the calculation how geometrical deviations impact the mechanical behavior and/or multiple simultaneous physical phenomena in a multiphysical system. Given the short iterations in design, this usually represents a compromise between two contradictory requirements: an acceptable computation time and the accuracy of the results. The presented paper addresses this challenge by presenting a framework to assess the impact of model parameter uncertainty of the multiphysical system behavior on the accuracy of the results. The framework integrates evidence and probability theories to propagate geometrical variability and model imprecision for tolerance analysis. The information regarding geometrical variability is modelled using probability distributions; and the information regarding the model imprecision is more faithfully modelled using families of probability distributions encoded by probability-boxes (upper & lower cumulative distribution functions). Monte Carlo simulation is used for probabilistic analysis while nonlinear optimization is used for interval analysis. [ABSTRACT FROM AUTHOR]

This paper deals with production variabilities and their formalization: Geometrical variability that affects the product quality and Time variability that affects the productivity. Due to the manufacturing imperfections, the manufacturing system faults, the human factors,... it is not possible to attain the theoretical dimensions and the theoretical time in a repetitive manner. This causes degradations of the product & production system performances. In order to ensure the desired behavior and the performance of the engineering system in spite of uncertainty, the system features are assigned a permissible tolerance or a margin. Time margin allocation consists in establishing a certain level of work flexibility, which gives the operator the possibility to develop different ways of working to meet production targets, without having adverse effects on his or her health. The concepts of geometric tolerance and time margin are very similar; they directly have an impact on the Overall Equipment Effectiveness (OEE): An OEE of 100% means that only good parts are produced (100% quality), at the maximum speed (100% performance), and without interruption (100% availability). The human or manufacturing system fatigue and reliability affect directly the respect of the time margin and indirectly the product conformance. There exists a strong link between tolerance and time margin. [ABSTRACT FROM AUTHOR]

The tolerance analysis aims to check if the tolerances specified on mechanism components allow to respect the assembly and functional requirements. Several papers illustrate that the form defects have an impact on the mechanism behavior, but most tolerance analysis techniques neglected them. To perform the tolerance analysis, three issues must be addressed: the geometrical deviations modelling, the geometrical behavior modelling and the technique of tolerance analysis. Therefore, this paper presents one contribution for each issue to perform tolerance analysis of over-constrained mechanism with form defect: • Modal representation of the form defect • Behavior modelling technique of the contact with form defect • Tolerance analysis technique with the integration of the different contact types. [ABSTRACT FROM AUTHOR]

Tolerance analysis is a well-accepted key element in industry for ensuring product quality as well as for reducing manufacturing costs. At the same time, and particularly in light of the recent advances in simulation technology, tolerancing decisions are also becoming increasingly important during earlier stages of design. One critical task hereby is the simulation of the "real-world" behavior of the product with minimum uncertainty, i.e. the calculation how geometrical deviations impact the mechanical behavior and/or multiple simultaneous physical phenomena in a multiphysical system. Given the short iterations in design, this usually represents a compromise between two contradictory requirements: an acceptable computation time and the accuracy of the results. The presented paper addresses this challenge by presenting a framework to assess the impact of model parameter uncertainty of the multiphysical system behavior on the accuracy of the results. The framework integrates evidence and probability theories to propagate geometrical variability and model imprecision for tolerance analysis. The information regarding geometrical variability is modelled using probability distributions; and the information regarding the model imprecision is more faithfully modelled using families of probability distributions encoded by probability-boxes (upper & lower cumulative distribution functions). Monte Carlo simulation is used for probabilistic analysis while nonlinear optimization is used for interval analysis. [ABSTRACT FROM AUTHOR]

This paper deals with production variabilities and their formalization: Geometrical variability that affects the product quality and Time variability that affects the productivity. Due to the manufacturing imperfections, the manufacturing system faults, the human factors,... it is not possible to attain the theoretical dimensions and the theoretical time in a repetitive manner. This causes degradations of the product & production system performances. In order to ensure the desired behavior and the performance of the engineering system in spite of uncertainty, the system features are assigned a permissible tolerance or a margin. Time margin allocation consists in establishing a certain level of work flexibility, which gives the operator the possibility to develop different ways of working to meet production targets, without having adverse effects on his or her health. The concepts of geometric tolerance and time margin are very similar; they directly have an impact on the Overall Equipment Effectiveness (OEE): An OEE of 100% means that only good parts are produced (100% quality), at the maximum speed (100% performance), and without interruption (100% availability). The human or manufacturing system fatigue and reliability affect directly the respect of the time margin and indirectly the product conformance. There exists a strong link between tolerance and time margin. [ABSTRACT FROM AUTHOR]

The choice of an adapted production system is essential in today's volatile market environment. For this choice the identification of common and distinct assemblies in between the product variants is of high importance. This paper presents four new similarity indices which are aggregated to categorize products. The categorization will support the choice of an assembly system type (dedicated, reconfigurable or hybrid) for a selection of product subassemblies when designing a new production facility. On this way, operational areas for a reconfigurable system can be defined. The novel approach is applied to an industrial case study in automotive industry. [ABSTRACT FROM AUTHOR]

Abstract The aim of this paper is to provide an overview of a developed statistical tolerance analysis technique for over-constrained mechanism. Statistical tolerance analysis is a more practical and economical way of looking at tolerances and works on setting the tolerances so as to assure a desired functionality; however, most of statistical tolerance analysis techniques are dedicated to isoconstrained mechanisms and simple over-constrained mechanisms, they need an explicit assembly response function. The developed technique is based on: –the formalization of the geometrical behavior of the mechanism by an implicit assembly response function, –the formalization of the tolerancing requirement by the quantifier notion, –the coupling of some optimization techniques and reliability techniques. [ABSTRACT FROM AUTHOR]

In today’s business environment, the trend towards more product variety and customization is unbroken. Due to this development, the need of agile and reconfigurable production systems emerged to cope with various products and product families. To design and optimize production systems as well as to choose the optimal product matches, product analysis methods are needed. Indeed, most of the known methods aim to analyze a product or one product family on the physical level. Different product families, however, may differ largely in terms of the number and nature of components. This fact impedes an efficient comparison and choice of appropriate product family combinations for the production system. A new methodology is proposed to analyze existing products in view of their functional and physical architecture. The aim is to cluster these products in new assembly oriented product families for the optimization of existing assembly lines and the creation of future reconfigurable assembly systems. Based on Datum Flow Chain, the physical structure of the products is analyzed. Functional subassemblies are identified, and a functional analysis is performed. Moreover, a hybrid functional and physical architecture graph (HyFPAG) is the output which depicts the similarity between product families by providing design support to both, production system planners and product designers. An illustrative example of a nail-clipper is used to explain the proposed methodology. An industrial case study on two product families of steering columns of thyssenkrupp Presta France is then carried out to give a first industrial evaluation of the proposed approach. [ABSTRACT FROM AUTHOR]

In the product design process, the designer needs to figure out how to integrate tolerancing process to ensure the transition from function to tolerances. Our proposition is to use energy flow modeling in Characteristics-Properties Modeling (CPM). CPM creates a framework containing function and structure of the product. Energy flow creates the link between function and structure in CPM using energy-based behavior modeling. Considering both qualitative and quantitative aspects, the result is an approach to create a quantitative function-behavior- structure relationship to ensure the transition from function to geometrical specifications. This systematic approach can be used to evaluate the tolerance impact on system's function. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract: Cost engineering key objectives is to ensure cost estimates’ accuracy and to avoid cost overruns. In such a global context, this paper focuses on the manner through which the uncertainties as well as variations, impact the cost dimensions during different phases of product lifecycle: Tolerance allocation, Process Planning, Inspection Planning. What is investigated is the adaptability of a modified Activity-Based Costing model in evaluation of cost regarding the activities in different stages of the product's life cycle. This effective model encloses the cost estimation of tolerancing, process and inspection planning, via the impact of variations and uncertainties (i.e. inspection risk). The aim is to take into account not only the cost but also the quality (quality-driven activity-based costing) of product. [Copyright &y& Elsevier]

Abstract: Uncertainty is ubiquitous in tolerance analysis problem. This paper deals with tolerance analysis formulation, more particularly, with the uncertainty which is necessary to take into account into the foundation of this formulation. It presents: [•] a brief view of the uncertainty classification: Aleatory uncertainty comes from the inherent uncertain nature and phenomena and epistemic uncertainty comes from the lack of knowledge [•] a formulation of the tolerance analysis problem based on this classification [•] its development: Aleatory uncertainty is modeled by probability distributions while epistemic uncertainty is modeled by intervals; Monte Carlo simulation is employed for probabilistic analysis while nonlinear optimization is used for interval analysis. [Copyright &y& Elsevier]

Abstract: One of the aim of statistical tolerance analysis is to evaluate a predicted quality level in the design stage. A method consists in computing the defect probability P expressed in parts per million (ppm). It represents the probability that a functional requirement D will not be satisfied in mass production. This paper focuses on the statistical tolerance analysis of over-constrained mechanism with gaps. In this case, the values of the functional characteristics depend on the gap situations, and are not explicitly formulated as a function of part deviations. To compute P, two different methodologies will be presented and confronted. The first one is based on D an optimization algorithm and Monte Carlo simulations. The second methodology uses system reliability methods. The whole approach is illustrated on a basic academic problem inspired by industrial interests. [Copyright &y& Elsevier]