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http://hdl.handle.net/10985/6574
Mathematical issues in mechanical tolerance analysis
GAYTON, Nicolas; QURESHI, Ahmed Jawad; DUMAS, Antoine; DANTAN, Jean-Yves; ETIENNE, Alain
The aim of this paper is to provide an overview of tolerance analysis. Tolerancing decisions can profoundly impact the quality and cost of product. There is a strong need for increased attention to tolerance design to enable high-precision assemblies to be manufactured at lower costs. Indeed, tolerance analysis is a key element in industry for improving product quality. Designers want tight tolerances to assure product performance; manufacturers prefer loose tolerances to reduce cost. There is a critical need for a quantitative design tool for specifying tolerances. Tolerance analysis brings the engineering design requirements and manufacturing capabilities together in a common model, where the effects of tolerance specifications on both design and manufacturing requirements can be evaluated quantitatively. Significant amount of literature is related to tolerancing methods. Summaries of state of the art, the most recent developments, and the future trends in tolerancing research can be found. This paper provides a classification of the issues from a mathematical point of view.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/65742012-01-01T00:00:00ZGAYTON, NicolasQURESHI, Ahmed JawadDUMAS, AntoineDANTAN, Jean-YvesETIENNE, AlainThe aim of this paper is to provide an overview of tolerance analysis. Tolerancing decisions can profoundly impact the quality and cost of product. There is a strong need for increased attention to tolerance design to enable high-precision assemblies to be manufactured at lower costs. Indeed, tolerance analysis is a key element in industry for improving product quality. Designers want tight tolerances to assure product performance; manufacturers prefer loose tolerances to reduce cost. There is a critical need for a quantitative design tool for specifying tolerances. Tolerance analysis brings the engineering design requirements and manufacturing capabilities together in a common model, where the effects of tolerance specifications on both design and manufacturing requirements can be evaluated quantitatively. Significant amount of literature is related to tolerancing methods. Summaries of state of the art, the most recent developments, and the future trends in tolerancing research can be found. This paper provides a classification of the issues from a mathematical point of view.Impact of a behavior model linearization strategy on the tolerance analysis of over-constrained mechanisms
http://hdl.handle.net/10985/9291
Impact of a behavior model linearization strategy on the tolerance analysis of over-constrained mechanisms
DUMAS, Antoine; GAYTON, Nicolas; DANTAN, Jean-Yves
All manufactured products have geometrical variations which may impact their functional behavior. Tolerance analysis aims at analyzing the influence of these variations on product behavior, the goal being to evaluate the quality level of the product during its design stage. Analysis methods must verify whether specified tolerances enable the assembly and functional requirements. This paper first focuses on a literature overview of tolerance analysis methods which need to deal with a linearized model of the mechanical behavior. Secondly, the paper shows that the linearization impacts the computed quality level and thus may mislead the conclusion about the analysis. Different linearization strategies are considered, it is shown on an over-constrained mechanism in 3D that the strategy must be carefully chosen in order to not over-estimate the quality level. Finally, combining several strategies allows to define a confidence interval containing the true quality level.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/92912015-01-01T00:00:00ZDUMAS, AntoineGAYTON, NicolasDANTAN, Jean-YvesAll manufactured products have geometrical variations which may impact their functional behavior. Tolerance analysis aims at analyzing the influence of these variations on product behavior, the goal being to evaluate the quality level of the product during its design stage. Analysis methods must verify whether specified tolerances enable the assembly and functional requirements. This paper first focuses on a literature overview of tolerance analysis methods which need to deal with a linearized model of the mechanical behavior. Secondly, the paper shows that the linearization impacts the computed quality level and thus may mislead the conclusion about the analysis. Different linearization strategies are considered, it is shown on an over-constrained mechanism in 3D that the strategy must be carefully chosen in order to not over-estimate the quality level. Finally, combining several strategies allows to define a confidence interval containing the true quality level.AK-ILS: An Active learning method based on Kriging for the Inspection of Large Surfaces
http://hdl.handle.net/10985/9294
AK-ILS: An Active learning method based on Kriging for the Inspection of Large Surfaces
DUMAS, Antoine; ECHARD, Benjamin; GAYTON, Nicolas; ROCHAT, Olivier; VAN DER VEEN, Sjoerd; DANTAN, Jean-Yves
Tolerance verification permits to check the product conformity and to verify assumptions made by the designer. For conformity assessment, the uncertainty associated with the values of the measurands must be known. In fact, to evaluate form characteristics of large aircraft structure workpieces, sampling is required, so a measurement error is present: exact estimation of form characteristics would require complete knowledge of the surface. To minimise this measurement error, this paper presents a Krigingbased procedure to identify the minimum of measured points to check the conformity with a given confidence level. The proposed method is validated on a simple example of orientation tolerance and then performed to inspect the form defect on three large aircraft workpieces.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/92942013-01-01T00:00:00ZDUMAS, AntoineECHARD, BenjaminGAYTON, NicolasROCHAT, OlivierVAN DER VEEN, SjoerdDANTAN, Jean-YvesTolerance verification permits to check the product conformity and to verify assumptions made by the designer. For conformity assessment, the uncertainty associated with the values of the measurands must be known. In fact, to evaluate form characteristics of large aircraft structure workpieces, sampling is required, so a measurement error is present: exact estimation of form characteristics would require complete knowledge of the surface. To minimise this measurement error, this paper presents a Krigingbased procedure to identify the minimum of measured points to check the conformity with a given confidence level. The proposed method is validated on a simple example of orientation tolerance and then performed to inspect the form defect on three large aircraft workpieces.Statistical tolerance analysis of over-constrained mechanisms with gaps using system reliability methods
http://hdl.handle.net/10985/9295
Statistical tolerance analysis of over-constrained mechanisms with gaps using system reliability methods
BEAUCAIRE, Paul; GAYTON, Nicolas; DUC, Emmanuel; DANTAN, Jean-Yves
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.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/92952013-01-01T00:00:00ZBEAUCAIRE, PaulGAYTON, NicolasDUC, EmmanuelDANTAN, Jean-YvesOne 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.A statistical tolerance analysis approach for over-constrained mechanism based on optimization and Monte Carlo simulation
http://hdl.handle.net/10985/9296
A statistical tolerance analysis approach for over-constrained mechanism based on optimization and Monte Carlo simulation
QURESHI, Ahmed Jawad; SABRI, Vahid; BEAUCAIRE, Paul; GAYTON, Nicolas; DANTAN, Jean-Yves
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.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/92962012-01-01T00:00:00ZQURESHI, Ahmed JawadSABRI, VahidBEAUCAIRE, PaulGAYTON, NicolasDANTAN, Jean-YvesTolerancing 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 a mechanism with gaps based on system reliability methods
http://hdl.handle.net/10985/9297
Statistical tolerance analysis of a mechanism with gaps based on system reliability methods
BEAUCAIRE, Paul; GAYTON, Nicolas; DUC, Emmanuel; DANTAN, Jean-Yves
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.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/92972013-01-01T00:00:00ZBEAUCAIRE, PaulGAYTON, NicolasDUC, EmmanuelDANTAN, Jean-YvesOne 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
http://hdl.handle.net/10985/9282
Statistical tolerance analysis of a hyperstatic mechanism, using system reliability methods
BEAUCAIRE, Paul; GAYTON, Nicolas; DUC, Emmanuel; LEMAIRE, Maurice; DANTAN, Jean-Yves
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.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/92822012-01-01T00:00:00ZBEAUCAIRE, PaulGAYTON, NicolasDUC, EmmanuelLEMAIRE, MauriceDANTAN, Jean-YvesThe 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 new system formulation for the tolerance analysis of overconstrained mechanisms
http://hdl.handle.net/10985/17421
A new system formulation for the tolerance analysis of overconstrained mechanisms
DUMAS, Antoine; GAYTON, Nicolas; SUDRET, Bruno; DANTAN, Jean-Yves
The goal of tolerance analysis is to verify whether design tolerances enable a mechanism to be functional. The current method consists in computing a probability of failure using Monte Carlo simulation combined with an optimization scheme called at each iteration. This time consuming technique is not appropriate for complex overconstrained systems. This paper proposes a transformation of the current tolerance analysis problem formulation into a parallel system probability assessment problem using the Lagrange dual form of the optimization problem. The number of events being very large, a preliminary selective search algorithm is used to identify the most contributing events to the probability of failure value. The First Order Reliability Method (FORM) for systems is eventually applied to compute the probability of failure at low cost. The proposed method is tested on an overconstrained mechanism modeled in three dimensions. Results are consistent with those obtained with the Monte Carlo simulation and the computing time is significantly reduced.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/174212015-01-01T00:00:00ZDUMAS, AntoineGAYTON, NicolasSUDRET, BrunoDANTAN, Jean-YvesThe goal of tolerance analysis is to verify whether design tolerances enable a mechanism to be functional. The current method consists in computing a probability of failure using Monte Carlo simulation combined with an optimization scheme called at each iteration. This time consuming technique is not appropriate for complex overconstrained systems. This paper proposes a transformation of the current tolerance analysis problem formulation into a parallel system probability assessment problem using the Lagrange dual form of the optimization problem. The number of events being very large, a preliminary selective search algorithm is used to identify the most contributing events to the probability of failure value. The First Order Reliability Method (FORM) for systems is eventually applied to compute the probability of failure at low cost. The proposed method is tested on an overconstrained mechanism modeled in three dimensions. Results are consistent with those obtained with the Monte Carlo simulation and the computing time is significantly reduced.Key Characteristics identification by global sensitivity analysis
http://hdl.handle.net/10985/17468
Key Characteristics identification by global sensitivity analysis
IDRISS, Dana; BEAUREPAIRE, Pierre; GAYTON, Nicolas; HOMRI, Lazhar
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.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10985/174682019-01-01T00:00:00ZIDRISS, DanaBEAUREPAIRE, PierreGAYTON, NicolasHOMRI, LazharDuring 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.An iterative statistical tolerance analysis procedure to deal with linearized behavior models
http://hdl.handle.net/10985/17422
An iterative statistical tolerance analysis procedure to deal with linearized behavior models
DUMAS, Antoine; GAYTON, Nicolas; BLES, Thomas; LOEBL, Robin; DANTAN, Jean-Yves
Tolerance analysis consists of analyzing the impact of variations on the mechanism behavior due to the manufacturing process. The goal is to predict its quality level at the design stage. The technique involves computing probabilities of failure of the mechanism in a mass production process. The various analysis methods have to consider the component’s variations as random variables and the worst configuration of gaps for over-constrained systems. This consideration varies in function by the type of mechanism behavior and is realized by an optimization scheme combined with a Monte Carlo simulation. To simplify the optimization step, it is necessary to linearize the mechanism behavior into several parts. This study aims at analyzing the impact of the linearization strategy on the probability of failure estimation; a highly over-constrained mechanism with two pins and five cotters is used as an illustration for this study. The purpose is to strike a balance among model error caused by the linearization, computing time, and result accuracy. In addition, an iterative procedure is proposed for the assembly requirement to provide accurate results without using the entire Monte Carlo simulation.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/174222015-01-01T00:00:00ZDUMAS, AntoineGAYTON, NicolasBLES, ThomasLOEBL, RobinDANTAN, Jean-YvesTolerance analysis consists of analyzing the impact of variations on the mechanism behavior due to the manufacturing process. The goal is to predict its quality level at the design stage. The technique involves computing probabilities of failure of the mechanism in a mass production process. The various analysis methods have to consider the component’s variations as random variables and the worst configuration of gaps for over-constrained systems. This consideration varies in function by the type of mechanism behavior and is realized by an optimization scheme combined with a Monte Carlo simulation. To simplify the optimization step, it is necessary to linearize the mechanism behavior into several parts. This study aims at analyzing the impact of the linearization strategy on the probability of failure estimation; a highly over-constrained mechanism with two pins and five cotters is used as an illustration for this study. The purpose is to strike a balance among model error caused by the linearization, computing time, and result accuracy. In addition, an iterative procedure is proposed for the assembly requirement to provide accurate results without using the entire Monte Carlo simulation.