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

Goka, Edoh; Beaurepaire, Pierre; Homri, Lazhar; Dantan, Jean‐Yves

doi:10.1016/j.mechmachtheory.2019.04.020

Cited by 19 publications

(7 citation statements)

References 39 publications

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“…Worst-Case (also called deterministic) technique assigns the worst possible combination of each deviation among all the admissible assembly deviations combination of workpieces [19][20][21]. Statistical tolerance analysis enables to compute the rate that given individual tolerances can meet the requirements [9,10,[22][23][24].…”

Section: Tolerance Analysis Aimsmentioning

confidence: 99%

Evolutionary Cost-Tolerance Optimization for Complex Assembly Mechanisms Via Simulation and Surrogate Modeling Approaches: Application on Micro Gears

Khezri¹,

Schiller²,

Goka³

et al. 2023

Preprint

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With the introduction of new technologies, the scope of miniaturization has broadened. The conditions under which complicated products are designed, manufactured, and assembled ultimately influence how well they perform. The intricacy and crucial functionality of products are frequently only fulfilled through the use of high-precision components such as micro gears. In power transmission systems, gears are used in a variety of industries. Micro gears or gears with micro features, with tolerances of less than 5 m, are pushing manufacturing processes to their technological limits. Monte-Carlo simulation methods enable an accurate forecast of inaccuracies in compliance. The complexity of the micro gear's design, on the other hand, increases the simulation computation and runtime. An alternative method for simulation is to create a surrogate model to predict the behavior. This paper proposes a statistical surrogate model to predict the conformity of a pair of micro gears. Afterward, the advantage of the surrogate model enables the optimal tolerances assignment while taking gear functionality, and production cost into account.

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Section: Tolerance Analysis Aimsmentioning

confidence: 99%

Evolutionary Cost-Tolerance Optimization for Complex Assembly Mechanisms Via Simulation and Surrogate Modeling Approaches: Application on Micro Gears

Khezri¹,

Schiller²,

Goka³

et al. 2023

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Recently, a growing body of research has been done in the assembly tolerance allocation to define suitable values for various tolerance types. According to their focus, they could be approximately grouped into the propagation-based method [14,15] and nonpropagation method [16]. For example, in terms of the nonpropagation method, Lv et al [17] proposed a variation analysis method based on the deviation matrix in the assembly design.…”

Section: Related Workmentioning

confidence: 99%

A Data-Driven Methodology to Improve Tolerance Allocation Using Product Usage Data

Gao

Zheng

et al. 2021

Journal of Mechanical Design

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Industry 4.0 puts forward new requirements for the sustainable service of products. With the recent advances in measurement technologies, global and local deformations in inaccessible areas can be monitored. Product usage data such as geometric deviation, position deviation and angular deviation that lead to product functional performance degradation can be continuously collected during the product usage stage. These technologies provide opportunities to improve tolerance design by optimizing tolerance allocation using product usage data. The challenge lies in how to assess these deviations for identifying relevant field factors and reallocate the tolerance value. In this paper, a data-driven methodology based on the deviation for tolerance analysis is proposed to optimize the tolerance allocation. A feature graph of a mechanical assembly is established based on the assembly relationship. The node representation in the feature graph is defined based on the unified Jacobian-torsor model and the node label is calculated by a synthetic evaluation method. A novel algorithm based on the graph neural networks (GNNs) is proposed to investigate hidden relations between nodes in the feature graph and calculate labels of all nodes. A modification necessity index (MNI) is defined for each tolerance between two nodes based on their labels. A deviation difference matrix is constructed to calculate the MNI of each tolerance for identifying the to-be-modified tolerance value with high priorities for product improvement. The effectiveness of the proposed methodology is demonstrated through a case study for the optimal tolerance allocation of a press machine.

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“…The effectiveness of mathematical techniques depends on the coupling of the geometrical behavior modelling and the multiphysical behavior modelling (Deng et al 2017), usually in form of an analysis of component deformation. The most commonly used techniques are the Monte Carlo Simulation coupled with Finite Element Methods (Camelio, Hu, and Ceglarek 2003;Dahlström and Lindkvist 2004;Jareteg et al 2014;Söderberg et al 2012) and several probabilistic method (FORM, ...) (Goka et al 2019). In fact, Monte Carlo simulation remains the reference method but requires many mechanical computations that makes it very difficult to use in practice for industrial applications.…”

Section: Type 2 Tolerance Analysismentioning

confidence: 99%

Integrated uncertainty management in parametric design and tolerancing

Dantan

Eifler

2021

Journal of Engineering Design

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The key purpose of robust design and tolerancing approaches is the management of uncertainty. Against this background, it is not surprising that there is a large overlap between the basic ideas and concepts in both fields. However, while sharing the same objective, the focus of the corresponding development phases is quite different; that is (i) the determination of solutions that react insensitive, in other words robust, to n oise factors -Robust parametric design; and (ii) the limitation of the effects of manufacturing imprecision by the specification of optimal tolerances -Tolerancing. As a consequence, there also is a significant gap between both concepts. Focusing on the improvement of design solutions, robustness is often related to uncertainty of not known designs or manufacturing processes. Due to the complexity of a largely matured solution, tolerancing tasks are usually based on previously specified, key characteristics or behavior models that are supposed perfect. Therefore, an overview of robust design and tolerancing is used to highlight the deficiencies, and to formalize a new classification of tolerance analysis issues based on the type of uncertainty considered. The proposed framework is based on Dempster-Shafer evidence theory and allows to efficiently perform statistical tolerance analyses under model imprecision.

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

Cited by 19 publications

References 39 publications

Evolutionary Cost-Tolerance Optimization for Complex Assembly Mechanisms Via Simulation and Surrogate Modeling Approaches: Application on Micro Gears

Evolutionary Cost-Tolerance Optimization for Complex Assembly Mechanisms Via Simulation and Surrogate Modeling Approaches: Application on Micro Gears

A Data-Driven Methodology to Improve Tolerance Allocation Using Product Usage Data

Integrated uncertainty management in parametric design and tolerancing

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