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

Abstract

is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. Tolerance analysis aims on checking whether specified tolerances enable functional and assembly requirements. The tolerance analysis approaches discussed in literature are generally assumed without the consideration of parts' form defects. This paper presents a new model to consider the form defects in an assembly simulation. A Metric Modal Decomposition (MMD) method is henceforth, developed to model the form defects of various parts in a mechanism. The assemblies including form defects are further assessed using mathematical optimization. The optimization involves two models of surfaces: real model and difference surface-base method, and introduces the concept of signed distance. The optimization algorithms are then compared in terms of time consumption and accuracy. To illustrate the methods and their respective applications, a simplified over-constrained industrial mechanism in three dimensions is also used as a case study.

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

“…The non-ideal surface is built by adding form defects to the substitute surface. The method used to build the non-ideal surface has been explained in [17,18]. The vector F used throughout this paper, represents the set of form defects amplitudes of the surfaces defined in correlation with the discretization of the surfaces.…”

“…To perform the computation of these two probabilities, a Monte Carlo simulation combined with a constrained optimization is employed. This method has been introduced by Qureshi et al [10] considering only size, position and orientation defects; and further extended to integrate parts' form defects [17,18] and to consider different contact types [20]. The overall tolerance analysis technique of an over-constrained mechanical system is explained in Algorithm 1.…”

“…Moreover, some others researchers proposed to study the floating contacts by means of a regularized closure function and a constrained optimization problem [31], Virtual Work Principle and a contact model of joints to determine the displacements at each node and relative displacements/rotations of the kinematic pairs [32], constrained registration techniques and difference surface in a sequential positioning problem [33], Tooth Contact Analysis algorithm [2,34], the Gap Hull estimation [35]. Among all the previous methods, the Signed Distance Approach [17,18,20,23] combined with an optimization technique is selected to characterize the fixed and sliding contacts assembly in the mechanical system. Thus, this subsection presents this local simulation on the gap components of a fixed or sliding contact added to the classical tolerance analysis approach.…”

“…Thus, this subsection presents this local simulation on the gap components of a fixed or sliding contact added to the classical tolerance analysis approach. Based on the SDT approach [15,17,18], the clearance torsor g of a contact can be written as follows:…”

Influence on machinability and form tolerance of Inconel 718 in Edm using different diameter multi hole Cu electrodes

“…Tolerances are specified generally by two methods; unilateral tolerance and the bilateral tolerance. Unilateral tolerance allows the variance for a nominal measure in one direction only, whereas the bilateral tolerance allows the dimensional variation in both the directions from the specified value [2,17,18].…”