Elastic Clearance Domain and Use Rate Concept Applications to Ball Bearings and Gears

Samper, Serge; Petit, Jean-Philippe; Giordano, Max

doi:10.1007/1-4020-5438-6_33

Cited by 5 publications

(4 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Functional decomposition and multi-level approaches have been developed to provide a systematic approach for mapping functional requirements into geometrical characteristics [31]. These approaches cover different design stages starting from conceptual design [82,249,77] and from the axiomatic design perspective [277], in are also used in the context of concurrent engineering [90], and considering the influence of contacts and assembly sequence [10,252].…”

Section: Detail Tolerance Specificationmentioning

confidence: 99%

Tolerancing: Managing uncertainty from conceptual design to final product

et al. 2018

View full text Add to dashboard Cite

Section: Detail Tolerance Specificationmentioning

confidence: 99%

Tolerancing: Managing uncertainty from conceptual design to final product

et al. 2018

View full text Add to dashboard Cite

“…Bourdet [1]and Clement [2] proposed a method using Small Displacement Torsor to describe part error; Desrochers [3] studied the error transferred between assembly parts with Jacobi method. Samper [4][5] proposed the theory of convex hull to analyze the bearing accuracy and stiffness. Harris [6] gived the reallocation of tolerance based on simple configuration; Noguchi [6] studied the influence of waviness and deviation of ball diameter on the non-repetitive of ball bearings.…”

Section: Introductionmentioning

confidence: 99%

Research of the influence of geometrical factors on rotary accuracy of high-precision spindle

Zhu

Zhang

Guo

2013

2013 IEEE International Symposium on Assembly and Manufacturing (ISAM)

View full text Add to dashboard Cite

As an important component of machine tools, spindle is the end part directly determining the quality of machined surfaces. It is essential to guarantee the spindle rotary accuracy for improving the machining quality. Spindle rotary accuracy is determined by bearing accuracy and other components' geometric error. Firstly, a 5-DOF bearing model is applied to describe the position and orientation deviations between inner ring and outer ring. It is also used to describe bearings' rotational error. Secondly, the distance of curvature centers of inside and outside raceways is calculated when the position and orientation of inner ring changes, in consideration of the dimensioned and form errors of the inner, outer rings and balls. Small Displacements Torsor (SDT) is used to describe machining error of spindle. Finally, geometric factors such as shaft machining error, bearing's preload and the assembly angle are discussed.

show abstract

“…24 In a variational approach using domains, Giordano et al have incorporated local strains in surfaces in contact in a ball bearing and in a cylindrical gear transmission. 25 The aim of this study is to propose a multiphysical approach, able to take into account variability's due to the processes involved in obtaining and assembling the parts, as well as variations due the thermo-mechanical behaviour of the parts. This multiphysical approach uses a variational method based on operations on polytopes.…”

mentioning

confidence: 99%

“…There are two possibilities:a. The intersection between the halfspaces defined by(25) generates a polytope, b. The intersection between the halfspaces defined by(26) generates an empty set.…”

mentioning

confidence: 99%

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

Teissandier¹,

Ledoux

Pierre³

2019

AAOAJ

View full text Add to dashboard Cite

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...

show abstract

Elastic Clearance Domain and Use Rate Concept Applications to Ball Bearings and Gears

Cited by 5 publications

References 4 publications

Tolerancing: Managing uncertainty from conceptual design to final product

Tolerancing: Managing uncertainty from conceptual design to final product

Research of the influence of geometrical factors on rotary accuracy of high-precision spindle

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

Contact Info

Product

Resources

About