Clearance vs. tolerance for rigid overconstrained assemblies

Abstract

In order to manage quality, companies need to predict performance variations of products due to the manufacturing components deviations. Usually, to enable the assembly of overconstrained mechanical structure, engineers introduce clearance inside joints. We call mechanical assembly, a set of undeformable components connected together by mechanical joints. This paper presents a solution: firstly, to compute the minimum value of clearance for any given components sizes, and, secondly, to simulate variation of the minimum clearance value when the components dimensions vary between two limits. To achieve this goal, a regularized closure function G is defined. It depends on dimensional parameters, u, representing components dimensions, on positional parameters, p, representing components positions and on clearance parameters, j, representing mechanical joints clearance. A constrained optimization problem is solved to determine the minimum clearance value. An imaginative solution based on numerical integration of an ordinary differential equation is proposed to show the clearance variation. The method is designed to be used during the preliminary phase of overcontrained assemblies design. An advantage is the small number of input data unlike the tolerance analysis dedicated software.

An Approach for the Inclusion of Loading Conditions in a Polyhedral-Based Method for Early Variation Management

“…In a floating contact, the tangential and normal displacements are allowed, meaning that it has all the possible degrees of freedom (DoF) of a mechanical joint. There are works that study this contact configuration in over constraint systems using the virtual work principle or regularized closure functions G (Cammarata, 2017;Rameau et al, 2018). A fixed contact is represented in Fig.…”

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

“…Some researchers have proposed numerical optimization approaches with several objective functions (convex hull volume, Euclidean distance, weighted unsigned distance, weighted signed distance) [23], experimental and theoretical investigations using the SDT and clearance domain (gap hull) models [24], the Fast Fourier Transform and the Conjugate Gradient Method in case of elastic contact of rough surfaces [25,26], development of an optimization algorithm and geometric interference relationships [27] and some other methods in [28][29][30]. 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.…”

Research on assembly clearance of precision spherical coupling parts by point cloud analysis

“…Therefore, it is important to measure the assembly clearance. Franciosa et al [1] predicted the gap between the two connectors during welding with the assumption that the position of the welding torch is known. Mao et al [2] established an improved quasi dynamic model to study the effect of annular deformation on the assembly clearance between roller bearing and shell.…”