Variation Simulation of Fixtured Assembly Processes for Compliant Structures Using Piecewise-Linear Analysis

Stewart, Michael; Chase, Kenneth W.

doi:10.1115/imece2005-82371

Cited by 22 publications

(17 citation statements)

References 8 publications

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“…According to (21), this polytope is determined as follows: Respect of functional condition FC in this second configuration is illustrated in Figure 20 and defined by equation (40)…”

Section: Simulating Respect Of a Functional Requirementmentioning

confidence: 99%

“…Many studies have been developed using a parametric approach where distortion in the parts is taken into account. Some models can simulate the geometric variations of an aeronautical structure 20,21 or an automobile structure 22,23 by seeking to minimise strains caused in the parts by the assembly process. Maciej et al have proposed a tolerance analysis platform incorporating the strain caused in parts by the assembly process and the dynamic behaviour of a mechanical system.…”

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confidence: 99%

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Analysis of tolerances and thermo-mechanical strains by operations on polytopes for hyperstatic mechanism architecture

Teissandier¹,

Ledoux

Pierre³

2019

AAOAJ

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simulate system compliance with functional requirements (stator rotor clearance, flush, etc.). The tolerance optimization is a critical point to address since the mechanisms most of time corresponds to hyperstatic architectures. In such cases, the contact between surfaces of parts induced by these architectures considerably increases the complexity of the problems to be solved. More to this, the parts are generally assumed to have an infinitely rigid behaviour. This limitation should be overcome in case of flexible parts of the mechanisms subject to thermal expansion and external mechanical loads.Studies introduced by Fleming in 1988 provided the foundation for a variational approach to tolerance analysis, based on operations by sets of geometric constraints. 1 A set of geometric constraints defines all the possible positions of a surface within a tolerance zone 2 which can be generated by offsets of the nominal model of the part. 3 In this way the geometric variations of a part that are compliant with ISO specifications for orientation or position tolerances can be characterised. [4][5][6][7] In the same way, a set of geometric constraints can also be used to characterise all relative positions between two distinct surfaces that are potentially in contact. 8 Fleming established the correlation between cumulative defect limits on parts in contact and the Minkowski sum of finite sets of geometric constraints. 1 A detailed synthesis of this is given in. 9 Algorithms of Minkowski sums applied to the problem of tolerance analysis have also been developed. 10,11 Giordano showed that modelling the relative positions of two parts resulting from several potential contacts can be formalised by an operation involving the intersection of sets of geometric constraints. 12 More generally, the variational approach to tolerancing consists of characterising the relative position of two surfaces from any two parts of a system by intersections and Minkowski sums of sets of geometric constraints derived from ISO specifications for the parts and specifications formulated specifically for two parts potentially in contact. 13 The variational approach to geometric tolerancing differs from parametric approaches. 14 Parametric approaches, especially those used in the various commercial tools, formalise the relative position of any two surfaces of a mechanism at a specific point by a simple relation (linear or non-linear) between parameters of position (translation and/or rotation). This relation is obtained using either an analytical method 15-18 or a Monte Carlo method. 19 This type of approach does not support the redundancy of suppressing degrees of freedom between two parts. In addition, it is generally necessary to generate several equations to simulate the relative position of two surfaces. Historically the procedures for tolerance analysis using a variational or parametric approach are based on the following physical hypotheses: no defect in the shape of the real surfaces, no local strain on surfaces in contact, and no flexible pa...

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“…According to (21), this polytope is determined as follows: Respect of functional condition FC in this second configuration is illustrated in Figure 20 and defined by equation (40)…”

Section: Simulating Respect Of a Functional Requirementmentioning

confidence: 99%

mentioning

confidence: 99%

Analysis of tolerances and thermo-mechanical strains by operations on polytopes for hyperstatic mechanism architecture

Teissandier¹,

Ledoux

Pierre³

2019

AAOAJ

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show abstract

“…Mortensen (2002) presented the general methodology of the FASTA method based on different ways to model geometric covariance. Stewart (2004) presented a new method to statistically analyse flexible part assembly processes using fixtures. The proposed Piecewise-Linear Elastic Analysis method has been developed for predicting the residual stress, deformation and spring-back variation in compliant assemblies, by performing separated FEA for each PCFR assembly phase, and combining linearly their results.…”

Section: Related Workmentioning

confidence: 99%

Statistical variation analysis of multi-station compliant assemblies based on sensitivity matrix

Gerbino

Patalano

Franciosa

2008

IJCAT

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A new method for tolerance/variation analysis of multi-station assemblies of compliant parts is presented. Based mainly on the 'unit displacement' and 'sensitivity matrix' method, it allows for the use of statistical variations in key points to predict the final shape variation of multi-station assemblies. 'Linear contacts' between parts are included to avoid part-to-part intersections. The evaluation of what happens at the end of the assembly process enables users to analyse different assembly configurations in the early design phase. Implemented in the Matlab environment, it requires two linear FEA runs for each assembly station. Two case studies are presented and discussed.

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“…Several studies have been carried out to manage compliant structure [1][2][3][4]. These works take into account geometric variations induced by the assembly process and manufacturing dispersions.…”

Section: Introductionmentioning

confidence: 99%

Integration of thermomechanical strains into tolerancing analysis

Pierre

Teissandier

Nadeau

2009

Int J Interact Des Manuf

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To improve the performance of a helicopter turboshaft engine requires optimising the energy yield of the different components, and more particularly controlling clearance between the tips of the high pressure turbine blades and the stator. Dimension-chain tools take into account the manufacturing dispersion of the parts and assembly defects. This ensures the interchangeability of the different components and guarantees that a turbine can carry out different service functions, as the turbine is modelled in infinitely rigid solids. However, this approach does not take thermomechanical effects into account. And yet, the different operating regimes of a helicopter engine make it indispensable that the effects caused by the thermodynamic cycle should be integrated. The aim of this article is to show how using dimension chain and thermomechanical tools can contribute to controlling clearances at the tip of a high pressure turbine blade.

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Variation Simulation of Fixtured Assembly Processes for Compliant Structures Using Piecewise-Linear Analysis

Cited by 22 publications

References 8 publications

Analysis of tolerances and thermo-mechanical strains by operations on polytopes for hyperstatic mechanism architecture

Analysis of tolerances and thermo-mechanical strains by operations on polytopes for hyperstatic mechanism architecture

Statistical variation analysis of multi-station compliant assemblies based on sensitivity matrix

Integration of thermomechanical strains into tolerancing analysis

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