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Abstract: This work investigates dynamics of a two-stage gear system involving backlash and time-dependent mesh stiffness. This paper mainly consists to develop a 12 degree of freedom gear dynamic model. The model consists of a two-stage spur gear, three shafts, and two inertias representing load and prime mover and three bearings. Gear contact is characterised by a periodically changing stiffness and a backlash which can lead to loss of the contact. The nonlinear dynamic response of the system is studied thanks to a technique of linearization which decomposes the nonlinear system into some linear systems satisfying some conditions. Each system is solved thanks to the Newmark iterative algorithm. The results obtained appear to be the phenomenon of loss of teeth contact because of the discontinuity of the kinematic movement between the motives and receiving components of the system.

Abstract: La formation des cellules (FC) de production se traduit par le groupement des produits en familles et le partage des machines en sous groupes. Le traitement de ce problème devient plus complexe en présence de gammes alternatives. Dans ce contexte, nous proposons une nouvelle approche qui traite ce problème en deux niveaux. Le premier niveau porte sur l’application de la méthode des plans d’expériences. L’objectif étant de choisir, pour chaque produit, la gamme préférentielle permettant l’optimisation des indicateurs de performance de FC. En plus, ce niveau de traitement permet une analyse de la sensibilité de la solution finale ignorée par les techniques antérieures de la FC. Nous avons proposé et justifié un nouvel indice de la FC défini par le pourcentage de conservation des données de la matrice d’incidence initiale. Le second niveau de traitement consiste à appliquer la méthode de la FC basée sur l’analyse des corrélations statistiques entre les différents produits et machines. Pour expliquer l’approche proposée, nous avons détaillé deux exemples numériques. Les résultats d’une analyse comparative appliquée à des problèmes reconnus en littérature, ont permis de valider l’approche proposée.

Abstract: In this work, the dynamic behaviour of misaligned rotor is presented. The rotor is mounted in two hydrodynamic journal bearings and has two degrees of freedom. Reynolds’ equation is obtained by considering the effect of mass transfer across the fluid film. This is discretized by means of the finite difference method and solved numerically. By integrating the oil pressure distribution, the hydrodynamic forces are calculated. The elasticity of the fluid film is modelled by stiffness and damping matrices. The motion equations have been established for the rotor bearings system and simulated with Newmark method. The effect of bearings geometry on the dynamic coefficients is presented. A theoretical model describing the angular misalignment defect is analysed in order to survey the vibratory response of the misaligned rotor. Numerical simulation results are presented and discussed.

Abstract: Due to excessive service load, inappropriate operating conditions or simply end of life fatigue, damage can occur in gears. When a fault, either distributed or localised, is incurred by gears, the stiffness and consequently vibration characteristics of the damaged tooth will change. In this work an analytical formulation of the time varying gearmesh stiffness was derived. An original analytical modelling of tooth cracks is presented and the gearmesh stiffness reduction due to this fault is quantified. A comparison with finite element model is presented in order to validate the analytical formulation.

Abstract: Cellular Manufacturing (CM) system has been recognized as an efficient and effective way to improve productivity in a factory. In recent years, there have been continuous research efforts to study different facet of CM system. They are developed to satisfy only one or limited functional requirements of the CM system design. The literature does not contain much published research on CM design which includes all design aspects. In this paper we provide a framework for the complete CM system design. It combines Axiomatic Design (AD) and Experimental Design (ED) to generate several feasible and potentially profitable designs. The AD approach is used as the basis for establishing a systematic CM systems design structure. ED has been a very useful tool to design and analyze complicated industrial design problems. AD helps secure valid input-factors to the ED. An element of the proposed framework is desmontrate through a numerical example for a cell formation problem with alternative process.

Abstract: The important step in the design of a cellular manufacturing (CM) system is to identify the part families and machine groups and consequently to form manufacturing cells. The scope of this article is to formulate a multivariate approach based on a correlation analysis for solving cell formation problem. The proposed approach is carried out in three phases. In the first phase, the correlation matrix is used as similarity coefficient matrix. In the second phase, Principal Component Analysis (PCA) is applied to find the eigenvalues and eigenvectors on the correlation similarity matrix. A scatter plot analysis as a cluster analysis is applied to make simultaneously machine groups and part families while maximizing correlation between elements. In the third stage, an algorithm is improved to assign exceptional machines and exceptional parts using respectively angle measure and Euclidian distance. The proposed approach is also applied to the general Group Technology (GT) problem in which exceptional machines and part are considered. Furthermore, the proposed approach has the flexibility to consider the number of cells as a dependent or independent variable. Two numerical examples for the design of cell structures are provided in order to illustrate the three phases of proposed approach. The results of a comparative study based on multiple performance criteria show that the present approach is very effective, efficient and practical.

Abstract: Gearbox power transmissions are widely used in the automotive industry. They have a complex vibro-acoustic behaviour that is influenced by the various acoustic–structural interaction mechanisms. This paper concentrates on modelling these systems using a three-dimensional finite-element (FE) approach for the structure combined with a Rayleigh integral (RI) method for the acoustic radiation process. A modal analysis method is used to evaluate the elasto-acoustic modal characteristics for the coupled system. Effect of the fluid inside the gearbox on the vibration response is discussed. The combined use of this FE/RI model enables evaluation of the acoustic response. A case study of a simplified gearbox internally excited with gear mesh stiffness fluctuation is presented. Vibratory analysis allows concluding that the vibro-acoustic coupling between elastic housing, air-cavity and free acoustic field have not to be neglected.

Abstract: Cellular manufacturing (CM) is an important application of group technology (GT) that can be used to enhance both flexibility and efficiency in today’s small-to-medium lot production environment. The crucial step in the design of a CM system is the cell formation (CF) problem which involves grouping parts into families and machines into cells. The CF problem are increasingly complicated if parts are assigned with alternative routings (known as generalized Group Technology problem). In most of the previous works, the route selection problem and CF problem were formulated in a single model which is not practical for solving large-scale problems. We suggest that better solution could be obtained by formulating and solving them separately in two different problems. The aim of this case study is to apply Taguchi method for the route selection problem as an optimization technique to get back to the simple CF problem which can be solved by any of the numerous CF procedures. In addition the main effect of each part and analysis of variance (ANOVA) are introduced as a sensitivity analysis aspect that is completely ignored in previous research. The case study results provided a better CF solution compared with Kusiak’s solution.

Abstract: Tooth faults affecting gear transmission are always accompanied by a stiffness reduction. In this article an analytical method is proposed to quantify the reduction of gearmesh stiffness due to two common tooth faults: spalling and breakage. Bending, fillet-foundation and contact deflection are taken into account. The dynamic response of a single stage spur gear transmission is computed by using analytical gearmesh issued from analytical modelling and the vibration signatures of each tooth fault is identified.

Abstract: Free vibration and damping characteristics of a sandwich plate with elastic facings and visco-elastic core have been studied using a finite-element method. The present method considers a linear variation in the in-plane displacement through the thickness in the faces and a quadratic variation in the core. Quadrilateral finite elements were developed and a dynamic equation was derived. Damping has been introduced by considering a complex shear model of the visco-elastic material, which accounts for the phase difference between strain and stress. Eigenvalue problems are then solved, and the natural frequencies and modal loss factors of the sandwich plate are extracted. Effects of geometrical and material property parameters are discussed.

Abstract: This paper presents the structural shape optimization with linear elastic material, large displacement and small strains. The whole shape optimization process is carried out by coupling a closed geometric shape in R2 with boundaries defined by B-splines curves, automatic mesh generation at each iteration, exact sensitivity analysis and mathematical programming method (SQP: Sequential Quadratic Programming). The design variables are the control point's coordinates which minimize the Von-Mises criteria, with a constraint that the total material volume of the structure remains constant. In this work the sensitivity analysis is performed using two methods: numerically by an efficient finite difference scheme and by the new method called exact Jacobian method. The feasibility of the proposed method is carried out for two numerical examples. Dans ce travail, nous nous sommes intéressés à l'optimisation de forme des structures en présence de non-linéarités géométriques (grands déplacements). Les variables d'optimisation sont les coordonnées des points de contrôle avec une paramétrisation par les courbes de B-splines. Le critère d'optimisation (fonction objectif à minimiser) est défini à partir du critère de Von Mises avec conservation du volume de la structure le long du processus d'optimisation. La résolution du problème mécanique est faite par la méthode des éléments-finis. L'algorithme d'optimisation utilisé est (S.Q.P.: séquential quadratic programming). Cet article présente une description détaillée du calcul de la sensibilité par la méthode exacte et la méthode différence finie pour un matériau à comportement élastique isotrope. Deux exemples numériques seront réalisés.

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Abstract: This paper describes a clutch model having eleven degrees of freedom and three types of nonlinearity introduced by dry friction, double-stage stiffness, and spline clearances. The Coulomb friction formulations and spline clearance functions are smoothed before they are applied to the nonlinear system. The calculation of the dynamic response of the clutch is done by the Runge Kutta method. The dynamic behavior of both a healthy clutch system and clutch system containing an eccentricity defect is compared in the time and frequency domains. The effects of a harmonically varying load on the dynamic response of the defective clutch system with nonlinear dry friction and under sinusoidal torque excitation are also reported.

Abstract: In this work, we present a model of a three-dimensional manufacturing tolerancement by the use of a tensorial approach. We are interested in the study of the influence of the fixture errors of a workpiece on a machined surface. The orientation variation of a workpiece is caused by the fixture errors. Consequently three-dimensional geometric defaults are generated when the workpiece is machined. Using a tensorial approach, these defaults are modelled by the positional variations of a set of surface points. By a numerical simulation, we validate the developed model and show the influence of the fixture errors on the geometric orientation specifications. We also show that the choice of the fixture location can be verified by the 3D influence of the geometric fixture errors on the generated defaults of machined surfaces.

Abstract: Cell Formation (CF) problem involves grouping the parts into part families and machines into manufacturing cells, so that parts with similar processing requirements are manufactured within the same cell. Many researches have suggested methods for CF. Few of these methods; have addressed the possible existence of exceptional elements (EE) in the solution and the effect of correspondent intercellular movement, which cause lack of segregation among the cells. This paper presents a simulation-based methodology, which takes into consideration the stochastic aspect in the cellular manufacturing (CM) system, to create better cell configurations. An initial solution is developed using any of the numerous CF procedures. The objective of the proposed method which provides performances ratings and cost-effective consist in determine how best to deal with the remaining EE. It considers and compares two strategies (1) permitting intercellular transfer and (2) exceptional machine duplication. The process is demonstrated with a numerical example.

Abstract: The crucial step in the design of a Cellular Manufacturing (CM) system is the Cell Formation (CF) problem. This problem consists of identifying the part families and the machine groups and, consequently, forming manufacturing cells. The aim of this paper is to formulate a new multivariate approach based on a correlation analysis for solving CF problem. The proposed approach is carried out in two phases. In the first phase, the correlation matrix is used as similarity coefficient matrix. In the second phase, Principal Component Analysis (PCA) is applied as a cluster analysis to make simultaneously machine groups and part families. This approach integrates significant production data such as processing time and part type production volume in the early stages of grouping decisions for CM. The objective is to minimise the total processing time outside the cells. Two illustrative examples and numerical results are provided.

Abstract: The dynamic equation of a sandwich plate is presented under the hypothesis of linear longitudinal displacement fields in each layer and an hysteretic structural damping of the viscoelastic core. A modal approach is adopted to investigate sandwich plate dynamical behaviour. First, the elastic eigenmodes are used in the characterisation of the modal damping. Then, the dynamical analysis is established using the modal dynamic recombination method and the result of modal damping characterisation. The numerical results obtained show that the eigenmodes are not orthogonal with respect to the damping matrix but are only weakly coupled. Besides, the modal damping matrix coefficients vary according to the ratio of the core thickness to the total thickness of the sandwich plate following a second order polynomial function. The modal approach with hysteretic modal damping characterisation is proposed in establishing dynamical responses. The results show that dynamical responses due to the use of a hysteretic diagonal modal damping matrix are in good agreement with those obtained when a full modal damping matrix is considered.

Abstract: La modélisation d'une transmission par engrenages simple étage en mouvement permanent par un système à 2 degrés de liberté a permis de mettre en évidence un mode de corps rigide et un mode élastique. Le mode de corps rigide traduit la condition cinématique de roulement sans glissement et la condition de transmission de mouvement. Le mode élastique est la conséquence directe de l'élasticité des dents qui est à l'origine de l'erreur de transmission. La variation périodique de la raideur d'engrènement lors de la rotation constitue une source d'excitation interne pour la transmission. La détérioration d'une ou de plusieurs dents affecte la raideur d'engrènement et influe par conséquent sur le comportement dynamique de la transmission. Le but de cette étude est de simuler un type de défaut localisé sur une ou plusieurs dents ou bien réparti sur toutes les dents de façon à décrire approximativement un début de fissure, un écaillage, ... L'analyse de la réponse dynamique a permis alors de déterminer qualitativement l'influence de ce défaut. Des méthodes de détection appropriées au type de défaut sont utilisées. Il s'est avéré que pour les défauts localisés, la méthode du cepstre est très utile tandis que la méthode spectrale reste valable pour les défauts répartis. Numerical simulation of the dynamical behavior of a gear transmission set with tooth faults. The modeling of a one-stage spur gear transmission in permanent movement by a two-DOF system show us two modes: rigid body mode and elastic mode. Rigid body mode expresses the kinematics condition of rolling without slip and the state of transmission of movement. Elastic mode is the outcome of tooth elasticity, which is the origin of the static transmission error. The time varying Meshing stiffness is the main internal excitation source for the transmission. Deterioration of one or several teeth affects the gearmesh stiffness and consequently the dynamic behavior of the transmission. The purpose of this survey is to simulate a localized and distributed tooth faults in order to describe a beginning of crack, a scaling, ... Dynamic responses show that cepstrum analysis is very efficient for localized faults and spectrum analysis remains valid for distributed faults.

Abstract: This paper presents a two node finite element with six degrees of freedom per node, able to model the behaviour of a three-dimensional isotropic helical beam with two constant radii of curvature (curvature and torsion radii). The formulation, which includes the shear strain effects, is based on the assumed resultant forces hybrid approach. The resulting forces approximation verifies exactly the equilibrium equations. Numerical results of samples and distribution of generalized forces along the helical beam are presented. Comparison with other models indicates that the presented element gives exact solutions.

Abstract: This paper presents an efficient two nodes finite element with six degrees of freedom per node, capable to model the total behaviour of a helical spring. The formulation, which includes the shear deformation effects, is based on the assumed forces hybrid approach. The resultant forces approximation verifies exactly the resultant equilibrium equations. The developed model proves its accuracy compared with other elements. This element permits to get the distribution of different stresses along the spring and through the wire surface by only one element.

Abstract: Design and modelization of a storeyed cutting tool for the grinding of plastics. This study deals with a storeyed cutting tool intended to plastic grinder. In manufacturing industries, cutting tools used nowadays induce vibrations and noises owing to cutting edge shape which increases cutting efforts with a limited rhythm of grinding plastics. The conceived tools should resolve those problems. Il s'agit d'une étude détaillée d'un nouvel outil de coupe étagé destinée aux broyeurs de matières plastiques. La technologie actuelle des outils de coupe utilisés provoque des vibrations du fait des formes des arêtes tranchantes qui augmentent les efforts de coupe avec une cadence limitée de matière broyée. Cette étude permet donc de résoudre ces problèmes.

Abstract: This paper deals with the vibro-acoustic behaviour of two vibrating plates coupled to a viscothermal fluid cavity. The acousto-elastic model is established in dimensionless appropriate form including the effects of viscosity and thermal conductivity of fluid and taking into account the fluid–structure interaction. The finite element method is used for the discretization of the functional of energy, which gives after minimization a symmetrical coupled matrix system in which the acoustic matrices are frequency dependent. For this purpose, an iterative procedure is derived to determine the eigenmodes of the coupled system. The modal approach is adopted to determine the vibro-acoustic system's response which the numerical results show the importance of the viscothermal effects in the case of thin fluid layers.