A new system formulation for the tolerance analysis of overconstrained mechanisms

Abstract

International audienceThe goal of tolerance analysis is to verify whether design tolerances enable amechanism to be functional. The current method consists in computing a probabilityof failure using Monte Carlo simulation combined with an optimizationscheme called at each iteration. This time consuming technique is not appropriatefor complex overconstrained systems. This paper proposes a transformationof the current tolerance analysis problem formulation into a parallel systemprobability assessment problem using the Lagrange dual form of the optimizationproblem. The number of events being very large, a preliminary selectivesearch algorithm is used to identify the most contributing events to the probabilityof failure value. The First Order Reliability Method (FORM) for systemsis eventually applied to compute the probability of failure at low cost. Theproposed method is tested on an overconstrained mechanism modeled in threedimensions. Results are consistent with those obtained with the Monte Carlosimulation and the computing time is significantly reduced

Probabilistic-based approach using Kernel Density Estimation for gap modeling in a statistical tolerance analysis

“… The use of the KDE method enables one to use another method than the MCS to study the tolerance analysis of over-constrained mechanical systems. This other method can be the First Order Reliability Method (FORM) for systems applied in [6] to compute the probabilities of failure. The use of this FORM method in not compatible with the classical statistical tolerance analysis method presented in Section 2.…”

“…The contact 1a/2a is sliding because body is bolted to the shaft and this assembly technique allows slight displacement in the direction of the contact plane. Thus, three clearance parameters are identified as shown in the following clearance g*: (6) where α, β are components of the rotations around the x-and y-axes, and w is the translation in the z-axes. These components of g* are not trivial and are dependent on form defects.…”

“…One of the current challenges in tolerancing is the consideration of the over-constrained mechanical systems with gaps. The assembly of such mechanical systems is possible because of the gaps [6], even though the parts exhibit geometric imperfections. Consequently, the study of over-constrained mechanical systems is more complex than the iso-constrained mechanical systems.…”

“…Moreover, these methods are not able to consider parts' form defects and are globally applied on 2D cases. Furthermore, to overcome these previous limitations, a new method based on the Lagrange dual form of the optimization problem and FORM method has been proposed to compute the probability of failure with reduced computational efforts and carrying out a preliminary selective search algorithm to identify the configurations which contribute mostly to this probability of failure [6]. Though this work considers 3D over-constrained mechanical systems with multi-configuration of gaps, it has not considered the form defects nor the different types of contacts in the tolerance analysis procedure.…”

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

“…The gaps in mechanical joints between different parts, coupled with the manufacturing deviations, impact the functionality of an assembly system. The manufacturing deviations are assumed to be independent random variables defined by their tolerance zones and the probability distributions with respect to manufacturing process, while the gaps are characteristic of epistemic uncertainty which makes the tolerance analysis complex [1]. The gaps are seldom considered in iso-constrained assembly, but in over-constrained assembly they allow the parts to be assembled without deformation and interference, and cannot be ignored.…”