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

Pierre, Laurent; Teissandier, Denis; Nadeau, Jean-Pierre

doi:10.1016/j.mechmachtheory.2013.11.014

Cited by 19 publications

(10 citation statements)

References 21 publications

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“…If (11) has no real solutions, this range of 2 is empty. (b) The intersection of these ranges of 2 in (a) is calculated as D 2 .…”

Section: Formulation Of Assembly Requirementmentioning

confidence: 99%

“…Furthermore, tolerance analysis of over-constrained assembly is subject to many nongeometrical factors involved in an assembly process, such as thermal flux, contact force, gravity, etc. Pierre et al [11] integrated thermomechanical strains into variational tolerance analysis. Gouyou et al [2] discussed the part deformation subject to contact forces which allow the parts to be assembled when the interference happens.…”

Section: Introductionmentioning

confidence: 99%

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Tolerance Analysis of Over-Constrained Assembly Considering Gravity Influence: Constraints of Multiple Planar Hole-Pin-Hole Pairs

Liu

Wang

et al. 2018

Mathematical Problems in Engineering

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Over-constrained assembly of rigid parts is widely adopted in aircraft assembly to yield higher stiffness and accuracy of assembly. Unfortunately, the quantitative tolerance analysis of over-constrained assembly is challenging, subject to the coupling effect of geometrical and physical factors. Especially, gravity will affect the geometrical gaps in mechanical joints between different parts, and thus influence the deviations of assembled product. In the existing studies, the influence of gravity is not considered in the tolerance analysis of over-constrained assembly. This paper proposes a novel tolerance analysis method for over-constrained assembly of rigid parts, considering the gravity influence. This method is applied to a typical over-constrained assembly with constraints of multiple planar hole-pin-hole pairs. This type of constraints is non-linear, which makes the tolerance analysis more challenging. Firstly, the deviation propagation analysis of an over-constrained assembly is conducted. The feasibility of assembly is predicted, and for a feasible assembly, the assembly deviations are determined with the principle of minimum potential energy. Then, the statistical tolerance analysis is performed. The probabilities of assembly feasibility and quality feasibility are computed, and the distribution of assembly deviations is estimated. Two case studies are presented to show the applicability of the proposed method.

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“…If (11) has no real solutions, this range of 2 is empty. (b) The intersection of these ranges of 2 in (a) is calculated as D 2 .…”

Section: Formulation Of Assembly Requirementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Tolerance Analysis of Over-Constrained Assembly Considering Gravity Influence: Constraints of Multiple Planar Hole-Pin-Hole Pairs

Liu

Wang

et al. 2018

Mathematical Problems in Engineering

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“…In the studies by Chevassus et al (2006), Breteau et al (2007) and Mounaud et al (2007), part deformations are introduced for overconstrained applications. Domain computation modeling the stiffness of mechanical joints has been proposed by Samper and Giordano (2003) and Pierre et al (2014). Some authors have included deformation in polytope computations.…”

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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“…The transfer of functional requirements is carried out using the same tools as for the transfer of assembly requirements. The tolerancing analysis will provide mathematical relations resolved by the analysis lines in Quick GPS (13), polytopes (14), deviation domains (15), T-map (16)... These conditions generate geometrical specifications with reference systems at least material requirements (10).…”

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

Cited by 19 publications

References 21 publications

Tolerance Analysis of Over-Constrained Assembly Considering Gravity Influence: Constraints of Multiple Planar Hole-Pin-Hole Pairs

Tolerance Analysis of Over-Constrained Assembly Considering Gravity Influence: Constraints of Multiple Planar Hole-Pin-Hole Pairs

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

ISO Tolerancing of hyperstatic mechanical systems with deformation control

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