A Generic Method for the Worst Case and Statistical Tridimensional Tolerancing Analysis

Mansuy, Mathieu; Giordano, Max; Hernandez, Pascal

doi:10.1016/j.procir.2013.08.042

Cited by 17 publications

(5 citation statements)

References 8 publications

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“…For tolerance accumulation, in order to compute the accumulated domains, Minkowski sums or the intersection of domains must be applied. These operations require dealing with linear domains to be applied [11,22,23]. Based on these two reasons, we chose to linearize the non-linear equations of the behavior model.…”

Section: Resultsmentioning

confidence: 99%

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Impact of a behavior model linearization strategy on the tolerance analysis of over-constrained mechanisms

Dumas

Dantan²,

Gayton³

2015

Computer-Aided Design

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h i g h l i g h t s • A tolerance analysis approaches overview is proposed. • A linearization procedure of the behavior model is required for both approaches. • Some linearization strategies provide conservative probability of failure results. • A confidence interval is obtained using two different linearization strategies. • The order of magnitude of the probability has an effect on the convergence speed. 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 overestimate the quality level. Finally, combining several strategies allows to define a confidence interval containing the true quality level.

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Section: Resultsmentioning

confidence: 99%

“…• Mathematical tools: In order to be able to apply Minkowski sums or intersections to compute accumulated hypervolumes, domains have to be linear. A cylinder type joint in a mechanism leads to the definition of a non-linear clearance domain, so it has to be linearized in several facets [22,23].…”

Section: Displacement Accumulation Tolerance Accumulationmentioning

confidence: 99%

Impact of a behavior model linearization strategy on the tolerance analysis of over-constrained mechanisms

Dumas

Dantan²,

Gayton³

2015

Computer-Aided Design

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“…There are also articles comparing some of these tolerance analyses (Mansuy et al, 2013a;Ameta et al, 2011). T-Maps and domains can be used in worst case or statistical approaches Mansuy et al, 2013b). Constraint satisfaction approaches have been developed based on simulated populations of parts using the Monte Carlo method.…”

Section: Tolerance Study Of Overconstrained Assemblymentioning

confidence: 99%

Tolerance analysis of overconstrained and flexible assemblies by polytopes and finite element computations: application to a flange

et al. 2017

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In industrial contexts, overconstrained assemblies are often used to ensure sufficient stiffness and accuracy of assembly. Such architectures are quite usual, however, analysis and synthesis of the tolerance are not easy to define and quantify. In these cases, the compliance of the assembly is not automatic and deformations may often occur, requiring a particular and difficult analysis of the assembly from scientific and computing points of view. The present work addresses such overconstrained mechanisms through a general and a sequential approach. Based on this, it is possible to determine the final assembly condition (with or without interference) as a function of part defects. First, the assembly procedure is performed based on polytope computations, assuming a rigid part behavior. From this, a stochastic simulation is performed and some non-compliant assemblies (assemblies with interferences) are identified. For these assemblies, the rigid behavior of parts is then overcome by means of finite element simulations and a typical procedure is set up to introduce part defects. We then deduce whether the assembly can be made from the load needed to assemble the parts. This procedure is applied to a flange composed of five pin / hole pairs, as this is a highly overconstrained mechanism. Nomenclature• t M−1,i/2,i : translation vector of surface i of part 1 in relation to surface i of part 2 at point M. If i = 0, we are considering the translation of the nominal geometry of part 1 in relation to the nominal geometry of part 2 at point M.• r 1,i/2,i : rotation vector of surface i of part 1 in relation to surface i of part 2. If i = 0, we are considering the rotation of the nominal geometry of part 1 in relation to the nominal geometry of part 2,• e M−1,i/1,0 : location defect vector of surface i of part 1 in relation to its nominal geometry at point M,• e M−2,i/2,0 : location defect vector of surface i of part 2 in relation to its nominal geometry at point M, 1• D n , D 1,i and D 2,i : the diameter of the nominal surface, the diameters of surface i of part 1 and surface i of part 2 respectively,• H − i, j : half-space of the contact constraint derived from the j th discretization point between surface i of part 1 and surface i of part 2,• P i : contact polytope of surface i of part 1 in relation to surface i of part 2,• P R : resulting contact polytope of part 1 in relation to part 2.

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“…3 The T-Map represents all possible variations in size, position, form, and orientation for a target feature by means of a hypothetical Euclidean point-space. 4 Mansuy et al 5 applied deviation domain to perform both worst case and statistical tolerancing analysis. Similar to T-Map and deviation domain, the polytope represents geometrical deviations on mechanical parts by sets of half-spaces coming from the restriction of the position of a finite set of points of a toleranced feature.…”

Section: Introductionmentioning

confidence: 99%

A novel tolerance analysis method for three-dimensional assembly

Cao

Liu

Yang

et al. 2018

Proceedings of the Institution of Mechanical Engineers, Part B:

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Three-dimensional tolerance analysis is increasingly becoming an innovative method for computer-aided tolerancing. Its aim is to support the design, manufacturing, and inspection by providing a quantitative analysis of the effects of multi-tolerances on final functional key characteristics and predict the quality level. This article proposes a novel approach for three-dimensional assembly analysis—a hybridization of vector loop and quasi-Monte Carlo method. The former is used to establish the three-dimensional assembly chain and obtain the assembly function. The latter is adopted to generate n sets of dimensional values according to the distribution of each dimension in chain. The new method is shown to inherit many of the best features of classical vector loop and quasi-Monte Carlo, combining easy-to-obtain assembly function with accurate statistical analysis. For every set of dimensional values, one sample value of a functional requirement can be computed with the Newton–Raphson iterative procedure. A crank slider mechanical assembly is shown as an example to illustrate the proposed method.

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A Generic Method for the Worst Case and Statistical Tridimensional Tolerancing Analysis

Cited by 17 publications

References 8 publications

Impact of a behavior model linearization strategy on the tolerance analysis of over-constrained mechanisms

Impact of a behavior model linearization strategy on the tolerance analysis of over-constrained mechanisms

Tolerance analysis of overconstrained and flexible assemblies by polytopes and finite element computations: application to a flange

A novel tolerance analysis method for three-dimensional assembly

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