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Tolerance analysis of a product coupling geometric and architectural specifications in a probabilistic approach

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Abstract

This article describes tolerance analysis using a reliability-based approach to ensuring that a functional condition is satisfied. A particular feature of this procedure is that it defines the combined effects of geometric and dimensional ISO specifications for product parts, and the architectural parameters that define the relative positions of parts in contact. In the first part, we describe configuring the product parameters by geometric deviations, and from this, a global model is produced to characterise the variation in rotor/stator clearance in a turboshaft engine turbine. This model relies on tolerance zone dimensions, dimensional tolerances and architectural parameters. When clearance is examined using the reliability-based approach, links emerge between the turbine’s architectural parameters and its geometric and dimensional specifications. Indicators can then be deduced which guide the designer in selecting the optimum turbine architectures.

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Abbreviations

i, j :

Surface j of part i

i, 0:

Nominal model of part i

D i,jn :

Nominal diameter D of i, j (case of cylindrical surface)

d i,j :

Dimension deviation of diameter of i, j (case of cylindrical surface)

t i,j :

Dimension of the tolerance zone of i, j

α i,j/i,0, β i,j/i,0 and γ i,j/i,0 :

Orientation deviations of i, j with respect to i, 0

A i,j/i,0, B i,j/i,0 and Γ i,j/i,0 :

Degrees of invariance in rotation of i, j with respect to i, 0

u T_i,j/i,0, v T_i,j/i,0 and w T_i,j/i,0 :

Translation deviations of i, j with respect to i, 0 at point T

U T_i,j/i,0, V T_i,j/i,0 and W T_i,j/i,0 :

Degrees of invariance in translation of i, j with respect to i, 0 at point T

\( \left[ {d_{i,j/i,0} } \right] = \left[ {\begin{array}{*{20}c} {{\varvec{\rho}}_{i,j/i,0} } \\ {{\mathbf{\varepsilon }}_{T - i,j/i,0} } \\ \end{array} } \right] \) :

Small displacement torsor (SDT) of surface i, j with respect to i, 0

\( {\varvec{\rho}}_{i,j/i,0} = \left( {\begin{array}{*{20}c} {\alpha_{i,j/i,0} \quad {\text{or}}\quad {\rm A}_{i,j/i,0} } \\ {\beta_{i,j/i,0} \quad {\text{or}}\quad {\rm B}_{i,j/i,0} } \\ {\gamma_{i,j/i,0} \quad {\text{or}}\quad \Upgamma_{i,j/i,0} } \\ \end{array} } \right) \) :

Rotation vector

\( {\mathbf{\varepsilon }}_{T\_i,j/i,0} = \left( {\begin{array}{*{20}c} {u_{T\_i,j/i,0} \quad {\text{or}}\quad U_{T\_i,j/i,0} } \\ {v_{T\_i,j/i,0} \quad {\text{or}}\quad V_{T\_i,j/i,0} } \\ {w_{T\_i,j/i,0} \quad {\text{or}}\quad W_{T\_i,j/i,0} } \\ \end{array} } \right) \) :

Translation vector expressed at point T

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  1. University of Bordeaux, I2M, UMR 5295, Talence, France

    Yann Ledoux & Denis Teissandier

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  1. Yann Ledoux
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  2. Denis Teissandier
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Correspondence to Yann Ledoux.

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Ledoux, Y., Teissandier, D. Tolerance analysis of a product coupling geometric and architectural specifications in a probabilistic approach. Res Eng Design 24, 297–311 (2013). https://doi.org/10.1007/s00163-012-0146-9

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