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

Abstract

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.

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

“…modeled imperfections in good agreement with the imperfections observed on the manufactured components) to guarantee accurate results of the tolerance analysis. Globally, three models of surfaces are applicable: the nominal surface [11], the substitute surface [11], and the non-ideal surface represented by skin model concept [12]. Both, substitute and non-ideal surface, have an important role in the tolerance analysis method.…”

Tolerance analysis — Form defects modeling and simulation by modal decomposition and optimization

“…Here, the equations define the relations of displacements in the different loops of the joint graph, the relations of displacements represent the linear compatibility constraints between deviations and gaps in different loops, while the inequalities and equations define the interface constraints that characterize the non-interferences between surfaces that are nominally in contact with each other [32][33][34][35][36]. Nevertheless, considering positional deviations in a 3-dimensional context could lead to highly nonlinear functions which then have to be linearized piecewise [7,37].…”

“…The goal of such approaches is to estimate the probability of system conformity by simulation based methods (e.g., Monte Carlo Simulation) or point based method (e.g., FORM system), and optimization [36,37]. Further investigations for the computational problem of the function f have been proposed by Turner and Nigam [6], Guilford and Turner [48] and Zhang et al [49].…”

“…The approach is developed for a required parametrization of surfaces to deal with defect probability computation in an assembly simulation procedure. The assembly simulation is moreover, currently based on constrained optimization problems and defect probability assessment [4,47,58]. To add value to the existing research, the proposed MMD integrates form defects into simulation.…”

“…The tolerance analysis approach was further based on Monte Carlo simulation with 5000 examples of connectors that considered cylindrical surfaces as non-ideals. The aim of the model was to estimate the probability of assembly with respect to some previous works [37]. Globally, the probability of assembly was equal to 98.24% and the associated assembly simulation probabilities are given in Table 3.…”