Statistical tolerance analysis of over-constrained mechanisms with gaps using system reliability methods

One of the aims of statistical tolerance analysis is to evaluate a predicted quality level at the design stage. One method consists of computing the defect probability PD expressed in parts per million (ppm). It represents the probability that a functional requirement will not be satisfied in mass production. This paper focuses on the statistical tolerance analysis of over-constrained mechanisms containing gaps. In this case, the values of the functional characteristics depend on the gap situations and are not explicitly formulated with respect to part deviations. To compute PD, an innovative methodology using system reliability methods is presented. This new approach is compared with an existing one based on an optimization algorithm and Monte Carlo simulations. The whole approach is illustrated using two industrial mechanisms: one inspired by a producer of coaxial connectors and one prismatic pair. Its major advantage is to considerably reduce computation time

Statistical tolerance analysis of a hyperstatic mechanism, using system reliability methods

The quality level of a mechanism can be evaluated a posteriori after several months by following the number of warranty returns. However, it is more interesting to evaluate a predicted quality level in the design stage: this is one of the aims of statistical tolerance analysis. A possible method consists of computing the defect probability (PD) expressed in ppm. It represents the probability that a functional requirement will not be satisfied in mass production. For assembly reasons, many hyperstatic mechanisms require gaps, which their functional requirements depend on. The defect probability assessment of such mechanisms is not straightforward, and requires advanced numerical methods. This problem particularly interests the VALEO W.S. company, which experiences problems with an assembly containing gaps. This paper proposes an innovative methodology to formulate and compute the defect probability of hyperstatic mechanisms with gaps in two steps. First, a complex feasibility problem is converted into a simpler problem. Then the defect probability is efficiently computed thanks to system reliability methods and the m-dimensional multivariate normal distribution Um. Finally, a sensitivity analysis is provided to improve the original design. The whole approach is illustrated with an industrial case study, but can be adapted to other similar problems

A statistical tolerance analysis approach for over-constrained mechanism based on optimization and Monte Carlo simulation

Tolerancing decisions can profoundly impact the quality and cost of the mechanism. To evaluate the impact of tolerance on mechanism quality, designers need to simulate the influences of tolerances with respect to the functional requirements. This paper proposes a mathematical formulation of tolerance analysis which integrates the notion of quantifier: ‘‘For all acceptable deviations (deviations which are inside tolerances), there exists a gap configuration such as the assembly requirements and the behavior constraints are verified’’ & ‘‘For all acceptable deviations (deviations which are inside tolerances), and for all admissible gap configurations, the assembly and functional requirements and the behavior constraints are verified’’. The quantifiers provide a univocal expression of the condition corresponding to a geometrical product requirement. This opens a wide area for research in tolerance analysis. To solve the mechanical problem, an approach based on optimization is proposed. Monte Carlo simulation is implemented for the statistical analysis. The proposed approach is tested on an over-constrained mechanism

Statistical tolerance analysis of over-constrained mechanisms with gaps using system reliability methods

One of the aims of statistical tolerance analysis is to evaluate a predicted quality level at the design stage. One method consists of computing the defect probability PD expressed in parts per million (ppm). It represents the probability that a functional requirement will not be satisfied in mass production. This paper focuses on the statistical tolerance analysis of over-constrained mechanisms containing gaps. In this case, the values of the functional characteristics depend on the gap situations and are not explicitly formulated with respect to part deviations. To compute PD, an innovative methodology using system reliability methods is presented. This new approach is compared with an existing one based on an optimization algorithm and Monte Carlo simulations. The whole approach is illustrated using two industrial mechanisms: one inspired by a producer of coaxial connectors and one prismatic pair. Its major advantage is to considerably reduce computation time

Statistical tolerance analysis of a mechanism with gaps based on system reliability methods

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 D P expressed in parts per million (ppm). It represents the probability that a functional requirement 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 D P , two different methodologies will be presented and confronted. The first one is based on 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

Statistical tolerance analysis of a hyperstatic mechanism, using system reliability methods

The quality level of a mechanism can be evaluated a posteriori after several months by following the number of warranty returns. However, it is more interesting to evaluate a predicted quality level in the design stage: this is one of the aims of statistical tolerance analysis. A possible method consists of computing the defect probability (PD) expressed in ppm. It represents the probability that a functional requirement will not be satisfied in mass production. For assembly reasons, many hyperstatic mechanisms require gaps, which their functional requirements depend on. The defect probability assessment of such mechanisms is not straightforward, and requires advanced numerical methods. This problem particularly interests the VALEO W.S. company, which experiences problems with an assembly containing gaps. This paper proposes an innovative methodology to formulate and compute the defect probability of hyperstatic mechanisms with gaps in two steps. First, a complex feasibility problem is converted into a simpler problem. Then the defect probability is efficiently computed thanks to system reliability methods and the m-dimensional multivariate normal distribution Um. Finally, a sensitivity analysis is provided to improve the original design. The whole approach is illustrated with an industrial case study, but can be adapted to other similar problems

A statistical tolerance analysis approach for over-constrained mechanism based on optimization and Monte Carlo simulation

Tolerancing decisions can profoundly impact the quality and cost of the mechanism. To evaluate the impact of tolerance on mechanism quality, designers need to simulate the influences of tolerances with respect to the functional requirements. This paper proposes a mathematical formulation of tolerance analysis which integrates the notion of quantifier: ‘‘For all acceptable deviations (deviations which are inside tolerances), there exists a gap configuration such as the assembly requirements and the behavior constraints are verified’’ & ‘‘For all acceptable deviations (deviations which are inside tolerances), and for all admissible gap configurations, the assembly and functional requirements and the behavior constraints are verified’’. The quantifiers provide a univocal expression of the condition corresponding to a geometrical product requirement. This opens a wide area for research in tolerance analysis. To solve the mechanical problem, an approach based on optimization is proposed. Monte Carlo simulation is implemented for the statistical analysis. The proposed approach is tested on an over-constrained mechanism

Application of reliable methods to the analysis and synthesis of tolerances

En conception de systèmes mécaniques, la phase de cotation fonctionnelle consiste à affecter des cotes, constituées d’une valeur nominale et d’un intervalle de tolérance, à des dimensions de pièces. En particulier, l’analyse des tolérances consiste à vérifier que les intervalles de tolérance choisis permettent le respect de la fonctionnalité du mécanisme. A l’inverse, la synthèse des tolérances vise à déterminer ces intervalles de tolérance, si possible de manière optimale, permettant le respect des exigences fonctionnelles. Les approches statistiques traditionnelles, bien que très utiles en phase de préconception, ne sont pas capables d’estimer avec précision le risque de non qualité. Cette thèse aborde ces problèmes selon un angle de vue différent, non plus pour garantir le respect d’exigences fonctionnelles, mais pour garantir le Taux de Non-Conformité (TNC) du mécanisme. Il s’agit de la probabilité que l’exigence fonctionnelle ne soit pas respectée. Les méthodes fiabilistes, s’appuyant sur la théorie des probabilités, permettent un calcul précis et efficace de cet indicateur. L’objectif de cette thèse est d’explorer le domaine de l’analyse et de la synthèse des tolérances afin d’identifier et d’exposer les apports des méthodes fiabilistes sur ces problématiques. Dans ces travaux de thèse, différents outils fiabilistes sont mis à disposition permettant l’analyse des tolérances de tous types de mécanismes avec ou sans jeu. La théorie probabiliste permet une modélisation très complète des dimensions des pièces. En particulier, l’approche APTA (Advanced Probability-based Tolerance Analysis of products) est développée afin de prendre en compte l’évolution aléatoire de certains paramètres de modélisation, notamment les décalages de moyenne, responsables de fortes variations du TNC. L’analyse des tolérances étant plus complexe pour les mécanismes avec jeux, une méthodologie spécifique a été développée basée sur une décomposition en situations de points de contacts et l’utilisation d’une méthode fiabiliste système. Différents indices de sensibilité sont aussi proposés afin d’aider à identifier les cotes ayant le plus d’influence sur le TNC d’un mécanisme. Enfin, l’optimisation du coût de production, sous contrainte de TNC, permet une synthèse des tolérances optimale. Les gains potentiels en termes de coût dépassent 50% par rapport aux conceptions initiales tout en maitrisant le niveau de qualité du produit. Les sociétés RADIALL SA et VALEO Système d’Essuyages, concepteurs et fabricants de produits pour l’automobile et l’aéronautique, ont proposé des cas d’études sur lesquels est démontrée la pertinence des travaux effectués. Sur la base de ces travaux, Phimeca Engineering, spécialisée dans l’ingénierie des incertitudes, développe et commercialise un outil informatique professionnel.To design mechanical systems, functional dimensioning and tolerancing consists in allocating a target value and a tolerance to part dimensions. More precisely, tolerance analysis consists in checking that chosen tolerances allow the mechanism to be functional. In the opposite, the tolerance synthesis goal is to determine those tolerances, optimaly if possible, such as functional requirements are respected. Traditional statistical approaches are very useful in pre-design phases, but are incapable of estimating precisely non-quality risks. This PhD thesis adresses this problem from a different point of view. The objective is no longer to respect functional requirements but to guarantee the Non-Conformity Rate (NCR) of the mechanism. It is the probability that the functional requirement is not respected. Reliability methods, based on probabilistic theory, allow a precise and efficient calculation of the NCR. The main goal of this thesis is to explore tolerance analysis and synthesis domains in order to identify potential contributions of reliability methods to these issues. In this work, different reliability tools are provided enabling tolerance analysis of all kind of mechanisms with or without gaps. The probability theory allows a detailed modeling of parts dimensions. In particular, the APTA (Advanced Probability-based Tolerance Analysis of products) approach is designed to take into account random variations of some parameters such as mean shifts which influence highly the NCR. As tolerance analysis is more complex for mechanisms with gaps, a specific method is designed based on a decomposition of contact points situations and the use of a reliability system method. Several sensitivity indexes are also proposed to identify the leading dimensions on the NCR. The optimization of the production cost, under a NCR constraint, enables an optimal tolerance synthesis. The potential benefits in terms of costs exceed 50% compared to initial designs while keeping under control quality levels of products. Companies RADIALL SA and VALEO Wiping Systems, designers and manufacturers of products for the automotive and aeronautic industries, have provided case studies on which is demonstrated the relevance of the presented work. Based on this work, the company Phimeca Engineering, specialized in uncertainties, is developing and commercializing a professional computer tool

Application des méthodes fiabilistes à l'analyse et à la synthèse des tolérances

To design mechanical systems, functional dimensioning and tolerancing consists in allocating a target value and a tolerance to part dimensions. More precisely, tolerance analysis consists in checking that chosen tolerances allow the mechanism to be functional. In the opposite, the tolerance synthesis goal is to determine those tolerances, optimaly if possible, such as functional requirements are respected. Traditional statistical approaches are very useful in pre-design phases, but are incapable of estimating precisely non-quality risks. This PhD thesis adresses this problem from a different point of view. The objective is no longer to respect functional requirements but to guarantee the Non-Conformity Rate (NCR) of the mechanism. It is the probability that the functional requirement is not respected. Reliability methods, based on probabilistic theory, allow a precise and efficient calculation of the NCR. The main goal of this thesis is to explore tolerance analysis and synthesis domains in order to identify potential contributions of reliability methods to these issues. In this work, different reliability tools are provided enabling tolerance analysis of all kind of mechanisms with or without gaps. The probability theory allows a detailed modeling of parts dimensions. In particular, the APTA (Advanced Probability-based Tolerance Analysis of products) approach is designed to take into account random variations of some parameters such as mean shifts which influence highly the NCR. As tolerance analysis is more complex for mechanisms with gaps, a specific method is designed based on a decomposition of contact points situations and the use of a reliability system method. Several sensitivity indexes are also proposed to identify the leading dimensions on the NCR. The optimization of the production cost, under a NCR constraint, enables an optimal tolerance synthesis. The potential benefits in terms of costs exceed 50% compared to initial designs while keeping under control quality levels of products. Companies RADIALL SA and VALEO Wiping Systems, designers and manufacturers of products for the automotive and aeronautic industries, have provided case studies on which is demonstrated the relevance of the presented work. Based on this work, the company Phimeca Engineering, specialized in uncertainties, is developing and commercializing a professional computer tool.En conception de systèmes mécaniques, la phase de cotation fonctionnelle consiste à affecter des cotes, constituées d’une valeur nominale et d’un intervalle de tolérance, à des dimensions de pièces. En particulier, l’analyse des tolérances consiste à vérifier que les intervalles de tolérance choisis permettent le respect de la fonctionnalité du mécanisme. A l’inverse, la synthèse des tolérances vise à déterminer ces intervalles de tolérance, si possible de manière optimale, permettant le respect des exigences fonctionnelles. Les approches statistiques traditionnelles, bien que très utiles en phase de préconception, ne sont pas capables d’estimer avec précision le risque de non qualité. Cette thèse aborde ces problèmes selon un angle de vue différent, non plus pour garantir le respect d’exigences fonctionnelles, mais pour garantir le Taux de Non-Conformité (TNC) du mécanisme. Il s’agit de la probabilité que l’exigence fonctionnelle ne soit pas respectée. Les méthodes fiabilistes, s’appuyant sur la théorie des probabilités, permettent un calcul précis et efficace de cet indicateur. L’objectif de cette thèse est d’explorer le domaine de l’analyse et de la synthèse des tolérances afin d’identifier et d’exposer les apports des méthodes fiabilistes sur ces problématiques. Dans ces travaux de thèse, différents outils fiabilistes sont mis à disposition permettant l’analyse des tolérances de tous types de mécanismes avec ou sans jeu. La théorie probabiliste permet une modélisation très complète des dimensions des pièces. En particulier, l’approche APTA (Advanced Probability-based Tolerance Analysis of products) est développée afin de prendre en compte l’évolution aléatoire de certains paramètres de modélisation, notamment les décalages de moyenne, responsables de fortes variations du TNC. L’analyse des tolérances étant plus complexe pour les mécanismes avec jeux, une méthodologie spécifique a été développée basée sur une décomposition en situations de points de contacts et l’utilisation d’une méthode fiabiliste système. Différents indices de sensibilité sont aussi proposés afin d’aider à identifier les cotes ayant le plus d’influence sur le TNC d’un mécanisme. Enfin, l’optimisation du coût de production, sous contrainte de TNC, permet une synthèse des tolérances optimale. Les gains potentiels en termes de coût dépassent 50% par rapport aux conceptions initiales tout en maitrisant le niveau de qualité du produit. Les sociétés RADIALL SA et VALEO Système d’Essuyages, concepteurs et fabricants de produits pour l’automobile et l’aéronautique, ont proposé des cas d’études sur lesquels est démontrée la pertinence des travaux effectués. Sur la base de ces travaux, Phimeca Engineering, spécialisée dans l’ingénierie des incertitudes, développe et commercialise un outil informatique professionnel

Application des méthodes fiabilistes à l'analyse et à la synthèse des tolérances

En conception de systèmes mécaniques, la phase de cotation fonctionnelle consiste à affecter des cotes, constituées d une valeur nominale et d un intervalle de tolérance, à des dimensions de pièces. En particulier, l analyse des tolérances consiste à vérifier que les intervalles de tolérance choisis permettent le respect de la fonctionnalité du mécanisme. A l inverse, la synthèse des tolérances vise à déterminer ces intervalles de tolérance, si possible de manière optimale, permettant le respect des exigences fonctionnelles. Les approches statistiques traditionnelles, bien que très utiles en phase de préconception, ne sont pas capables d estimer avec précision le risque de non qualité. Cette thèse aborde ces problèmes selon un angle de vue différent, non plus pour garantir le respect d exigences fonctionnelles, mais pour garantir le Taux de Non-Conformité (TNC) du mécanisme. Il s agit de la probabilité que l exigence fonctionnelle ne soit pas respectée. Les méthodes fiabilistes, s appuyant sur la théorie des probabilités, permettent un calcul précis et efficace de cet indicateur. L objectif de cette thèse est d explorer le domaine de l analyse et de la synthèse des tolérances afin d identifier et d exposer les apports des méthodes fiabilistes sur ces problématiques. Dans ces travaux de thèse, différents outils fiabilistes sont mis à disposition permettant l analyse des tolérances de tous types de mécanismes avec ou sans jeu. La théorie probabiliste permet une modélisation très complète des dimensions des pièces. En particulier, l approche APTA (Advanced Probability-based Tolerance Analysis of products) est développée afin de prendre en compte l évolution aléatoire de certains paramètres de modélisation, notamment les décalages de moyenne, responsables de fortes variations du TNC. L analyse des tolérances étant plus complexe pour les mécanismes avec jeux, une méthodologie spécifique a été développée basée sur une décomposition en situations de points de contacts et l utilisation d une méthode fiabiliste système. Différents indices de sensibilité sont aussi proposés afin d aider à identifier les cotes ayant le plus d influence sur le TNC d un mécanisme. Enfin, l optimisation du coût de production, sous contrainte de TNC, permet une synthèse des tolérances optimale. Les gains potentiels en termes de coût dépassent 50% par rapport aux conceptions initiales tout en maitrisant le niveau de qualité du produit. Les sociétés RADIALL SA et VALEO Système d Essuyages, concepteurs et fabricants de produits pour l automobile et l aéronautique, ont proposé des cas d études sur lesquels est démontrée la pertinence des travaux effectués. Sur la base de ces travaux, Phimeca Engineering, spécialisée dans l ingénierie des incertitudes, développe et commercialise un outil informatique professionnel.To design mechanical systems, functional dimensioning and tolerancing consists in allocating a target value and a tolerance to part dimensions. More precisely, tolerance analysis consists in checking that chosen tolerances allow the mechanism to be functional. In the opposite, the tolerance synthesis goal is to determine those tolerances, optimaly if possible, such as functional requirements are respected. Traditional statistical approaches are very useful in pre-design phases, but are incapable of estimating precisely non-quality risks. This PhD thesis adresses this problem from a different point of view. The objective is no longer to respect functional requirements but to guarantee the Non-Conformity Rate (NCR) of the mechanism. It is the probability that the functional requirement is not respected. Reliability methods, based on probabilistic theory, allow a precise and efficient calculation of the NCR. The main goal of this thesis is to explore tolerance analysis and synthesis domains in order to identify potential contributions of reliability methods to these issues. In this work, different reliability tools are provided enabling tolerance analysis of all kind of mechanisms with or without gaps. The probability theory allows a detailed modeling of parts dimensions. In particular, the APTA (Advanced Probability-based Tolerance Analysis of products) approach is designed to take into account random variations of some parameters such as mean shifts which influence highly the NCR. As tolerance analysis is more complex for mechanisms with gaps, a specific method is designed based on a decomposition of contact points situations and the use of a reliability system method. Several sensitivity indexes are also proposed to identify the leading dimensions on the NCR. The optimization of the production cost, under a NCR constraint, enables an optimal tolerance synthesis. The potential benefits in terms of costs exceed 50% compared to initial designs while keeping under control quality levels of products. Companies RADIALL SA and VALEO Wiping Systems, designers and manufacturers of products for the automotive and aeronautic industries, have provided case studies on which is demonstrated the relevance of the presented work. Based on this work, the company Phimeca Engineering, specialized in uncertainties, is developing and commercializing a professional computer tool.CLERMONT FD-Bib.électronique (631139902) / SudocSudocFranceF