Rigid and Elastic Precision Domains of Ball Bearings

Samper, Serge; Adragna, Pierre‐Antoine; Favreliere, Hughes; Pairel, Éric; Hernandez, Pascal

doi:10.1115/1.3615686

Cited by 2 publications

(3 citation statements)

References 10 publications

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“…For tolerance accumulation, in order to compute the accumulated domains, Minkowski sums or the intersection of domains must be applied. These operations require dealing with linear domains to be applied [11,22,23]. Based on these two reasons, we chose to linearize the non-linear equations of the behavior model.…”

Section: Resultsmentioning

confidence: 99%

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Impact of a behavior model linearization strategy on the tolerance analysis of over-constrained mechanisms

Dumas

Dantan²,

Gayton³

2015

Computer-Aided Design

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h i g h l i g h t s • A tolerance analysis approaches overview is proposed. • A linearization procedure of the behavior model is required for both approaches. • Some linearization strategies provide conservative probability of failure results. • A confidence interval is obtained using two different linearization strategies. • The order of magnitude of the probability has an effect on the convergence speed. All manufactured products have geometrical variations which may impact their functional behavior. Tolerance analysis aims at analyzing the influence of these variations on product behavior, the goal being to evaluate the quality level of the product during its design stage. Analysis methods must verify whether specified tolerances enable the assembly and functional requirements. This paper first focuses on a literature overview of tolerance analysis methods which need to deal with a linearized model of the mechanical behavior. Secondly, the paper shows that the linearization impacts the computed quality level and thus may mislead the conclusion about the analysis. Different linearization strategies are considered, it is shown on an over-constrained mechanism in 3D that the strategy must be carefully chosen in order to not overestimate the quality level. Finally, combining several strategies allows to define a confidence interval containing the true quality level.

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Section: Resultsmentioning

confidence: 99%

“…• Mathematical tools: In order to be able to apply Minkowski sums or intersections to compute accumulated hypervolumes, domains have to be linear. A cylinder type joint in a mechanism leads to the definition of a non-linear clearance domain, so it has to be linearized in several facets [22,23].…”

Section: Displacement Accumulation Tolerance Accumulationmentioning

confidence: 99%

Impact of a behavior model linearization strategy on the tolerance analysis of over-constrained mechanisms

Dumas

Dantan²,

Gayton³

2015

Computer-Aided Design

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“…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)

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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.

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Rigid and Elastic Precision Domains of Ball Bearings

Cited by 2 publications

References 10 publications

Impact of a behavior model linearization strategy on the tolerance analysis of over-constrained mechanisms

Impact of a behavior model linearization strategy on the tolerance analysis of over-constrained mechanisms

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

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