Mathematical representation of Tolerance Zones

Giordano, Max; Pairel, Éric; Samper, Serge

doi:10.1007/978-94-017-1705-2_18

Cited by 40 publications

(15 citation statements)

References 1 publication

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“…This paper is based on convex hull techniques, such as DD (Giordano et al, 1999) or TMap R (Davidson et al, 2002), which represent a deviating geometrical element with an abstract deviation space. The models have a lot of similarities, although they differ in detail.…”

Section: Convex Hull Techniquesmentioning

confidence: 99%

A statistical method to identify main contributing tolerances in assemblability studies based on convex hull techniques

Ziegler

Wartzack²

2015

J. Zhejiang Univ. Sci. A

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Abstract:In tolerancing, it is important to obtain recommendations from tolerance simulation results for optimizing tolerance values or the tolerance scheme. For this purpose, sensitivity analysis identifies the importance of single input parameters for received simulation results. This paper presents a method to adopt global sensitivity analysis methods on convex hull based tolerancing techniques, such as deviation domains. The focus of this paper lies on assemblability studies, in which the simulation output is a clearance. A method to estimate the influence of single part tolerances on the assembly clearance is proposed and performed for a pin-hole connection.

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Section: Convex Hull Techniquesmentioning

confidence: 99%

A statistical method to identify main contributing tolerances in assemblability studies based on convex hull techniques

Ziegler

Wartzack²

2015

J. Zhejiang Univ. Sci. A

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“…that are not completely and univocally accepted (Polini, 2012). Those tolerance analysis models for rigid assemblies are the variation model (Gupta & Turner, 1993), the TTRS model (Desrochers, 2002), the matrix model (Desrochers & Rivière, 1997), the vector loop (Gao et al, 1998), the jacobian model (Laperrière & Lafond, 1999), the torsor model (Bourdet at al., 1996), the jacobian-torsor model (Ghie et al, 2003), the T-Map model (Davidson et al, 2002), the deviation domain model (Giordano et al, 1999). In the same time many commercial software packages, that are based on some of the previously cited models, are available for tolerance analysis of rigid assemblies, such as MECAMaster ® , Sigmund ® , 3DCS ® , VisVSA ® , CeTol ® and PolitoCAT ® (Prisco & Giorleo, 2002).…”

Section: Introductionmentioning

confidence: 99%

Free-body model for tolerance analysis of rigid parts with manufacturing signature and operating conditions

Polini¹,

Corrado²

2019

10.5267/j.esm

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This work shows a free-body model for tolerance analysis, that uses the force free-body diagrams and the functional equations' sensitivities, by simulating the geometrical tolerances together with the dimensional ones. The geometrical tolerances were related to the deviations due to the manufacturing process (i.e. the manufacturing signature). Moreover, weight and friction forces were simulated too. A sensitivity analysis on the developed free body model aimed to evaluate the number of points to discretize the circular bodies and how to calculate the point clouds barycentre in order to reduce the simulation time. A case study was used to exemplify the application of the proposed free-body method with and without considering the manufacturing signature. The results show that the free body model is able to solve assembly problems and the manufacturing signature significantly influences the values of the functional requirement on the product and, therefore, it is impossible to neglect it.

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“…The T-Maps model is one of several vector space models that map geometric manufacturing variations into a region of parametric space. Other authors have used other vector space models (Giordano et al, 1999;Roy and Li, 1999) to model the 3D variations of a planesegment (e.g., rectangular or circular) or the 4D variations of a line-segment. The conclusion of the comparison of models in (Mujezinović et al, 2004;Ameta et al, 2011) is that the other models contribute substantially to the science of representing geometric variations and tolerances, but that each model either is limited structurally from representing, or has not been developed to represent, one or more of the following aspects of the Standards: form tolerances, floating zones, Rule #1 tradeoff, bonus tolerance arising from material condition, and/or datum precedence.…”

Section: Introductionmentioning

confidence: 99%

Tolerance-Maps for line-profiles constructed from Boolean intersection of T-Map primitives for arc-segments

Davidson

Shah

2015

J. Zhejiang Univ. Sci. A

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For purposes of automating the assignment of tolerances during design, a math model, called the Tolerance-Map (T-Map), has been produced for most of the tolerance classes that are used by designers. Each T-Map is a hypothetical point-space that represents the geometric variations of a feature in its tolerance-zone. Of the six tolerance classes defined in the ASME/ANSI/ISO Standards, profile tolerances have received the least attention for representation in computer models. The objective of this paper is to describe a new method of construction, using computer-aided geometric design, which can produce the T-Map for any line-profile. The new method requires decomposing a profile into segments, creating a solid-model T-Map primitive for each, and then combining these by Boolean intersection to generate the T-Map for a complete line profile of any shape. To economize on length, the scope of this paper is limited to line-profiles formed from circular arc-segments. The parts containing the line-profile features are considered to be rigid.

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Mathematical representation of Tolerance Zones

Cited by 40 publications

References 1 publication

A statistical method to identify main contributing tolerances in assemblability studies based on convex hull techniques

A statistical method to identify main contributing tolerances in assemblability studies based on convex hull techniques

Free-body model for tolerance analysis of rigid parts with manufacturing signature and operating conditions

Tolerance-Maps for line-profiles constructed from Boolean intersection of T-Map primitives for arc-segments

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