Operations on polytopes: application to tolerance analysis

Teissandier, Denis; Delos, Vincent; Couétard, Yves

doi:10.1007/978-94-017-1705-2_43

Cited by 45 publications

(25 citation statements)

References 2 publications

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“…Pertaining to technical solutions, a rich overview of tolerance analysis models of over-constrained mechanisms is also given in [3,6,7,34,38,41,[51][52][53][54][55][56][57]. Globally, the main shortcomings of the tolerance analysis approaches are their insufficient consideration of parts' form defects in the respective systems.…”

Section: Technical Solutions and Analysis Approachesmentioning

confidence: 99%

Tolerance analysis — Form defects modeling and simulation by modal decomposition and optimization

Homri

Goka

Levasseur

et al. 2017

Computer-Aided Design

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. Tolerance analysis aims on checking whether specified tolerances enable functional and assembly requirements. The tolerance analysis approaches discussed in literature are generally assumed without the consideration of parts' form defects. This paper presents a new model to consider the form defects in an assembly simulation. A Metric Modal Decomposition (MMD) method is henceforth, developed to model the form defects of various parts in a mechanism. The assemblies including form defects are further assessed using mathematical optimization. The optimization involves two models of surfaces: real model and difference surface-base method, and introduces the concept of signed distance. The optimization algorithms are then compared in terms of time consumption and accuracy. To illustrate the methods and their respective applications, a simplified over-constrained industrial mechanism in three dimensions is also used as a case study.

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Section: Technical Solutions and Analysis Approachesmentioning

confidence: 99%

Tolerance analysis — Form defects modeling and simulation by modal decomposition and optimization

Homri

Goka

Levasseur

et al. 2017

Computer-Aided Design

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“…In the case of positioning subassemblies in contact, a transfer of the assembly requirements must be applied to each part. Various mathematical models allow calculating dimensioning chains like analysis lines method (8), the behaviour laws (11) and assembly conditions with polytopes (12). Finally, to define the functional tolerancing, the designer needs to specify the operating conditions of the mechanism.…”

Section: Tolerancing Approach Of Rigid Partsmentioning

confidence: 99%

ISO Tolerancing of hyperstatic mechanical systems with deformation control

Rouetbi

Pierre

Anselmetti

et al. 2016

Lecture Notes in Mechanical Engineering

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The functional tolerancing of hyperstatic mechanisms provides contractual documents established following the ISO tolerancing. The tolerancing methodologies consider that the mechanism is infinitely rigid. These mechanisms impose tight clearances to ensure the functional requirements and parts fittability. The proposed methodology consists in developing a mechanical model relating the tolerances obtained by traditional methods of geometrical tolerancing and the parts deformability to define the tolerance values of the geometrical specifications. The first step is to define the geometrical specifications with ISO tolerancing. The fittability between two parts in contact requires maximum material conditions. The functional requirements employ least material condition. The second step consists in defining the capacity of parts to deform taking the tolerance values into account. A mechanical model is described relating the parts deformability to the tolerances to guaranty the conformity of the functional requirements and assembly parts fittability. As a validation example, the proposed methodology is used on a hyperstatic mechanism composed of two subassemblies: an outer tube and a shaft made of several assembled sections.

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“…A functional condition expressed between any two surfaces of a mechanism is characterised by a functional polytope. Respecting a functional condition is simulated by including a calculated polytope in the functional polytope [1], [11] and [12]. The calculated polytope is the result of operations (Minkowski sums and intersections) between geometric polytopes and contact polytopes.…”

Section: Variability Due To Manufacturing and Assembly Processesmentioning

confidence: 99%

“…The calculated polytopes 1,1/3,1 D resulting from the Minkowski sums defined by equation (29) are shown in figure 16, where max J represents clearance in the five ball and cylinder pair contacts and 1,1 t the dimension of the tolerance zone for the location specification of surface 1,1. From figure 16 we can determine the values of the location deviation between surfaces 1,1 and 3,1.…”

Section: 31mentioning

confidence: 99%

“…In this article we propose a model which will define clearance between blade tips and stator for different turbine architectures, taking the following variabilities into account: -processes for obtaining parts, -processes for assembling parts, -thermomechanical behaviour of the turbine. The model described in this article is based on a variational approach, manipulating sets of geometric constraints that formalise polytopes [1]. A polytope is the bounded intersection of a finite set of closed half-spaces of n  of which the boundaries are hyperplanes of 1 n  [2].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Variational tolerancing analysis taking thermomechanical strains into account: Application to a high pressure turbine

Pierre¹,

Teissandier²,

Nadeau³

2014

Mechanism and Machine Theory

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. Abstract:The aim of this study is to propose a variational method of tolerancing analysis using a multiphysical approach. This method is based on operations on polytopes (Minkowski sum and intersection) and can be used to validate geometric specifications, contact specifications and thermomechanical specifications. The first part describes how thermomechanical strains are integrated into a tolerancing analysis tool, based on operations on polytopes. In the second part correlations are defined between two turbine performance criteria, leakage section and risk of touching, and two geometric conditions respectively. In the third part, the influence of design choices is described, in particular the influence of the shape of the parts and the behaviour of the joints on the thermomechanical operating regime of the turbine. Two turbine architectures are considered in relation to the same two performance criteria, and lastly the main turbine architecture results are discussed and future developments described.

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Operations on polytopes: application to tolerance analysis

Cited by 45 publications

References 2 publications

Tolerance analysis — Form defects modeling and simulation by modal decomposition and optimization

Tolerance analysis — Form defects modeling and simulation by modal decomposition and optimization

ISO Tolerancing of hyperstatic mechanical systems with deformation control

Variational tolerancing analysis taking thermomechanical strains into account: Application to a high pressure turbine

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