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The main aim of the present work is to study the effect of axial preload on the durability of aerospace fastened joints. For that purpose, experimental and numerical approaches are adopted to demonstrate the beneficial effect of axial preload on the fatigue life of representative aerospace fastened joints. In the experimental approach, an innovative tightening technique, based on iterative tightening, is used to reduce the scatter habitually induced on preload when the conventional torque tightening technique is employed. The main benefit, besides the use of this alternative tightening technique, is to allow an accurate preload to be introduced without geometry or stiffness modification, thus enabling the preload effect to be determined precisely. The results show the effect of preload on the static resistance, fatigue life and failure mode of fastened joints. In the numerical approach, a 3D finite element model is developed and the analysis of its behavior confirms and explains experimental observations. Analysis of longitudinal stresses through critical paths shows that the effect of high preload is beneficial because it reduces hydrostatic pressure and shear stress amplitude, thus leading to longer fatigue lives. The correlation between experimental observations and the numerical results is studied using SWT and Crossland multiaxial fatigue criteria.

International audience; This article is devoted to the development of a calculation macro-model for the sizing of aircraft wheel fasteners. By their design, airliners tires are too rigid to be mounted on the wheel like car or motorcycle tires. Therefore, it is necessary to design a wheel in two separate parts so as to plug the tire on a first half-wheel and then “close” the assembly with the second. Therefore, the two half-wheels must be held together. Inmost cases, a bolted joint plays this essential role. The aim of this work is to develop a methodology related to the generation of semi-analytical model representative of the assembly. The tool is designed with a local approach that models an angular wheel sector including the most solicited bolt. It makes possible to evaluate tensile and bending stresses in the bolt, taking into account the roundness effect of the wheel. The objective is to obtain results close to finite element 3D modeling but with a very limited computation time. To achieve this goal, the principle of this model is to represent all parts of the wheel by 1D axisymmetric elements such as plate and shell elements, beam, tube, and spring elements (to model the contact) ensuring a description close to the actual wheel. Contact between the two half-wheels is also taken into account in order to detect the location of any unsticking after application of external loads. Different cases will be simulated (inflation case, straight line, and cornering case). The mechanical strength of the most solicited bolt will be analyzed for these different configurations. The results in tensile and bending stresses will be observed at the screwlevel.Acomparison of the results from the proposed digital macro-model and the 3D digital simulations will be analyzed. The developed tool will be used in the early design phase which allows the design engineer to define the mechanical and geometric properties of the wheel and bolts to find the optimal assembly.

International audience; The paper examines the static behavior of the inverted planetary roller screw (PRS) through numerical and experimental studies. The numerical analysis of the inverted PRS is first presented to capture the global and local deformations in different configurations. Using a three-dimensional finite element (3D FE) method, a sectorial model of the mechanism is built involving an entire roller. The model describes the static behavior of the system under a heavy load and shows the state of the contacts and the in-depth stress zones. The current work also investigates the axial stiffness (AS) and the load distribution (LD) under both compressive and tensile loadings. It is shown that the LDs are not the same at each contact interface of the roller and that they depend on the configuration of the system. Also, the nut is less stressed than the screw shaft because of their contact curvatures. In parallel, complementary experiments are carried out to measure the axial deflection of the screw shaft and the rollers in five cases with different numbers of rollers. In each situation, the mechanism is under the same equivalent axial and static load. The tests reveal that rollers do not have the same behavior, the difference certainly being due to manufacturing and positioning errors that directly affect the number of effective contacts in the device. This stresses the fact that the external load is unequally shared over rollers and contacting threads. By introducing the notion of an equivalent roller, the results are used to validate the previous numerical model of an inverted PRS. As they provide a better understanding of the inverted PRS, these investigations are useful to improve the existing analytical models of the device.

PurposeThis paper seeks to deal with a new modelization method which aims at fatigue sizing of preloaded bolted joints. Industrial design offices indeed need new models which, on the one hand, take bending of the bolts and geometrical non‐linearity into account and, on the other hand, run fast enough to be used for preliminary design stages. Usual sizing procedures derive from VDI recommendations, which makes them inaccurate. On the contrary, classical finite element methods are revealed to be very costly.Design/methodology/approachThe first task lies in reducing the physical problem down and model the structure using axisymmetrical elements. Then, the core of the method lies in modifying the stiffness matrix of a tube element, in order to modify the axial compression stiffness to the one used by preloaded assembly classical computations. Eventually, a 2D finite element model is programmed which takes advantage of the modified element. A mounting was built to reproduce the typical loading of a slewing bearing. Experimental tests were carried out in order to help analyse the problem and to check finite element simulation results.FindingsSample experimental results are presented which confirm the need for new models and validate the 2D model that was developed.Research limitations/implicationsThe new finite element, as well as the set of hypotheses that are used, appear to be usable for other bolted joints.Practical implicationsA software was produced for the industrial partners, which is usable by non FE‐specialists.Originality/valueThis work may serve as a basis for building fast and accurate finite element models of other types of bolted joints.

International audience; The cold expansion process is a technology that is widely used to enhance the fatigue resistance of aircraft metallic parts. The issue analysed in this paper concerns the case when the expansion is carried out through an assembly composed of several sheets. The numerical work conducted was intended to understand the phenomenology of the process within a stiff assembly. In particular, it aimed to analyse the deformation of the sheets and the residual stress fields generated by the process. For this purpose, an axisymmetric finite element model of the split sleeve process was developed, simulating a single expansion performed through a stack of two titanium holes (Ti-6Al-4V). The sheets to be expanded were positioned between two steel plates to simulate the assembly. The model could predict the shape and intensities of the fields within the expanded sections and their global outer shapes. We particularly focused on the phenomena prevailing between sheets. The simulation showed that deformations at the interface were greatly reduced when the stack was stiffened axially. Moreover, high circumferential and axial residual stresses were generated in the sheets. Results were compared with a single hole expanded without axial stiffening.

International audience; The cold expansion process is a technology that is widely used to enhance the fatigue resistance of aircraft metallic parts. The issue analysed in this paper concerns the case when the expansion is carried out through an assembly composed of several sheets. The numerical work conducted was intended to understand the phenomenology of the process within a stiff assembly. In particular, it aimed to analyse the deformation of the sheets and the residual stress fields generated by the process. For this purpose, an axisymmetric finite element model of the split sleeve process was developed, simulating a single expansion performed through a stack of two titanium holes (Ti-6Al-4V). The sheets to be expanded were positioned between two steel plates to simulate the assembly. The model could predict the shape and intensities of the fields within the expanded sections and their global outer shapes. We particularly focused on the phenomena prevailing between sheets. The simulation showed that deformations at the interface were greatly reduced when the stack was stiffened axially. Moreover, high circumferential and axial residual stresses were generated in the sheets. Results were compared with a single hole expanded without axial stiffening.

International audience; In this paper, an original approach is proposed to calculate the static load distribution and the axial stiffness of a planetary roller screw (PRS) mechanism. Assuming that the external loading is shared equally over an arbitrary number of rollers, only a sector of the system is represented to save on computing time. The approach consists in using a structure of bars, beams, and nonlinear springs to model the different components of the mechanism and their interactions. This nonlinear model describes the details of the mechanism and captures the shape of the nut as well as the bending deformation of the roller. All materials are assumed to operate in the elastic range. The load distribution and the axial stiffness are determined in three specific configurations of the system for both compressive and tensile loads. Further, the influence of the shape of the nut is studied in the case of the inverted PRS. The results obtained from this approach are also compared to those computed with a three-dimensional finite-element (3D FE) model. Finally, since the calculations appear to be very accurate, a parametric study is conducted to show the impact of the bending of the roller on the load distribution.

International audience; Bolted joints are essential elements of mechanical structures and metal constructions. Although their static behaviour is fairly well known, their dynamic behaviour due to shocks and vibrations has been less studied, because of the large size of the finite element models needed for a detailed simulation. This work presents four different simplified models suitable for studying the dynamic behaviour of an elementary bolted joint. Three of them include contact elements to allow sliding of the screw head and the nut on the assembled parts, and the last one allows rotation between screw and nut. A penalty approach based on the Coulomb friction model is used to model contact. The results show that these models effectively represent the dynamic behaviour, with different accuracy depending on the model details. The last model simulates the self loosening of a bolt subjected to transversal vibrations.

The bolt as an element which integrates several small parts to a united big structure had been used since a long time ago. This type of impermanent joint holds many advantages in the engineering field such as facilitating the maintenance, particularly at the change of defected part, and also making the delivery of many parts composing a huge structure more sensible by transporting them in diverse modes of transport. One of problems using this type of joint is sometimes it is difficult to assure holes position between parts to be aligned just as designed, in order to facilitate positioning of parts during assembly we could possibly use parts with slotted hole. However, a slotted hole will result in a reduced contact surface between the bolt and parts assembled, therefore the behavior of this type will be clearly different compared to the assembly with normal hole. The research will be conducted with assistance of a finite elements software ABAQUS® for simulating the model along with its parameters and mathematical software Matlab® for interpolating data obtained from the simulation. Firstly, the model will be validated by comparing it to experimental result of research conducted by Bakhiet[1], then its boundary conditions and mesh will be used to next model simulations. Secondly, the parameters of the assembly will be varied such as bolt positions on the part and the modulus Young ratio of bolt and parts. Finally, both assemblies are to be compared (e.g. with normal and slotted hole) and then the assembly’s critical value is to be found by using dimensionless parameters developed by Turgeon and Vadean[2]. From research conducted, we could conclude that the behavior of the assembly, particularly at its fatigue stress produced at the bolt, changes significantly with the variation of the bolt position and also the modulus Young ratio of the bolt and part. A reduced value of fatigue stress produced will be achieved while the bolt position is the nearest possible with respect to the point where load applied. Whereas, a higher modulus Young ratio will convict a higher fatigue stress produced at the bolt

International audience; A number of experimental studies have demonstrated that pre-tensioning fasteners significantly increases the fatigue life of shear joints. Fatigue life prediction for clamped joints is still a complex and unresolved issue because of the mixed nature of load transfer, which partly occurs by frictional forces. This article presents a calculation method based on a multiaxial-type critical-plane criterion, which determines the fatigue life and fatigue crack initiation site. For this purpose, the values of hydrostatic pressure and amplitude of maximum alternating shear stress on a critical octahedral plane are determined at each point of the structure and for each loading increment, and are used to predict the fatigue life of the joint. A dedicated experimental study was conducted within materials & processes airbus laboratory to validate the numerical results. In addition, a dimensionless parameter Rs is introduced to quantify the proportion of load transferred by friction and by bearing of the bolt, and allows the optimal preload to be approximated, above which value more clamping should not give further improvement. This value characterizes the shift of the crack location from the net section to the outside of the compressed area.

Bolted joints used in aeronautical structures are subject to vibrations, which can result in critical damage either from self-loosening or from fatigue. This study is devoted to the examination of the dynamic behavior of a simple bolted joint assembly subjected to quickly varying transverse load, which induces bending of the jointed plates. The adopted approach is based on finite element method, with a coupled bolt model and a penalty friction model, and implicit time simulation. Numerical result sets are presented and discussed.

International audience; In aeronautical structures, assemblies with thin laminates are becoming increasingly usual, especially for fuselage design. In these structures, out-of-plane loads can appear in bolted joints and can lead to progressive punching of the fastener’s head in the laminate resulting, in some cases, in a failure mode called pull-through [1]. This complex phenomenon, which occurs in assemblies, was studied firstly by using a simplified ‘‘circular’’ pull-through test method. Qualitative micrographic examinations showed damage very similar to that observed in impacted specimens. The research presented here extends the Discrete Ply Model Method (DPM) developed by Bouvet et al. [2] to this case. The finite elements model is based on a particular mesh taking ply orientations into account. Cohesive elements are placed at the interfaces between solid elements to represent matrix cracks and delamination, thus allowing the natural coupling between these two damage modes to be represented. The model shows good correlation with test results, in terms of load/displacement curve, and correct prediction of the damage map until failure, including the splitting phenomenon.

International audience; This paper presents a 3D finite element (FE) model of a thread forming screw assembly process based on the ABAQUS 6.5.4 Explicit software program. The model consists of two principal elements: an M10×12 thread forming screw and a lower 4 mm plate into which the screw taps its threads. The aim was to develop a robust industrial dimensioning tool; the model can be extended to establish the preload and investigate other types of assemblies. A 45 deg sector, which represents 1/8 of the joint, was modeled to maintain a good compromise between calculation time and an accurate representation of the thread forming process. The intent of the study was to analyze the material flow throughout the thread forming process; a parametrical study was also conducted to identify the most influential process parameters. To validate the model, FE numerical simulation results are compared with published experimental results. The study shows that the lead hole diameter has an important influence on the screwing torque.

International audience; This paper deals with the dimensioning of two-bolted assemblies made up from joint prismatic subassemblies subjected to fatigue compressive loads coplanar with the screw axis. The presented study is complementary to a previous study relative to tension loading [A. Daidie, J. Chakhari, A. Zghal, Numerical model for bolted T-stubs with two bolt rows, Struct. Eng. Mech. 26 (3) (2007) 343–361]. However, one should note that the two loading cases are not similar since an additional influential corner contact problem occurs in the case of compressive loading. The main development in this paper relative to the previous study [A. Daidie, J. Chakhari, A. Zghal, Numerical model for bolted T-stubs with two bolt rows, Struct. Eng. Mech. 26 (3) (2007) 343–361] is taking into consideration this complex corner contact problem. In this framework, the local deformation between the subassemblies and the corner of the supporting structure is formulated and a non-linear expression of a constrained displacement is established. Moreover, the evolution of the contact zone under the compressive loading, which is not similar in the case of tension loading, is taken into consideration. Consequently, a new extended numerical model for compressive loading is established from unidirectional finite elements and validated by 3D finite element simulations. An algorithm which updates the contact stiffness matrix and sets out forces and displacements at each node of the subassembly is developed using C language program. Finally, a statistical software method is used as in the case of tensile loading. It is important to note that in the case of compressive loading, this statistical software method is not only used to establish the effect of the joint parameters, but also to identify and tune up parameters relative to the complex problem of the corner contact.

International audience; Bolted bearing connections are one of the most important connections in some industrial structures, and manufacturers are always looking for a quick calculation model for a safe design. In this context, all the analytical and numerical models reduce the global study to the study of the most critical sector. Therefore, the main inputs for these models are the maximal equivalent contact load and the corresponding contact angle. Thus, a load distribution calculation model that takes all the important parameters, such as the stiffness of the supporting structure and the variation in the contact angle, into consideration is needed. This paper presents a 3D finite element (FE) simplified analysis of load distribution and contact angle variation in a slewing ball bearing. The key element of this methodology, which is based on the Hertz theory, is modeling the rolling elements under compression by nonlinear traction springs between the centers of curvature of the raceways. The contact zones are modeled by rigid shells to avoid numerical singularities. Each raceway curvature center is coupled to the corresponding contact zone by rigid shells. The main contribution of this method is not only the evaluation of the contact loads with a relatively reduced calculation time but also the variation in the contact angle from the deformed coordinates of the curvature centers. Results are presented for several loading cases: axial loading, turnover moment, and a combined loading of axial force and turnover moment. The influence of the most important parameters such as the contact angle, the stiffness of the bearings, and the supporting structure is discussed. Finally, a preliminary experimental validation is conducted on a standard ball bearing. The results presented in this paper seem encouraging. The FE study shows an important influence of several parameters and a good correlation with experimental results. Consequently, this model can be extended to other types of slewing bearings such as roller bearings. Moreover, it can be implemented in complex industrial structures such as cranes and lifting devices to determine the corresponding load distributions and contact angles and, consequently, the most critical sector.

International audience; Self-loosening of bolts is a problem encountered in many industrial fields, and especially in aviation. The purpose of this paper is to study the self-loosening phenomenon numerically through an assembly consisting of two plates assembled by a bolt and subjected to a transversal dynamic load. First, a 3D finite element model is developed, with contact elements and all geometrical details, including the real thread geometry with its helix angle. This leads to many degrees of freedom and long calculation time. Then a 1D simulation is made, based on a simplified model with only 4 degrees of freedom and few contact conditions. Calculation is nearly instantaneous. Both models describe the succession of sticking and slipping on contact surfaces and predict loosening of the assembly. They provide close results. The next step will be to compare their behaviour with an experimental approach, in order to validate and fit the models.

International audience; This article presents a numerical tool for dimensioning two-threaded fasteners connecting prismatic parts subjected to fatigue tension loads that are coplanar with the screw axis. A simplified numerical model is developed from unidirectional finite elements, modeling the connected parts and screws with bent elements and the elastic contact layer between the parts with springs. An algorithm updating the contact stiffness matrix, calculating forces and displacements at each node of the structure and thus normal stresses in the screws in both static and fatigue is further developed using C language. An experimental study is also conducted in parallel with the numerical approach to validate the developed model assumptions, the numerical model and the 3D finite element results. Since stiffness values for the compressive zones in the parts are analytically difficult to determine, a statistical software method is used, from which a tuning factor is derived for identifying these stiffness values. The method is also applied to set out the influence of each parameter on the fatigue behaviour of each screw. Finally, the developed model will be used to establish a new, sophisticated, fast and accurate tool for dimensioning bolted mechanical structures.

International audience; Managing the axial stiffness of various components in a bolted joint is a major industrial concern for modelling different tightening processes and for accurate fatigue dimensioning. This paper presents a new approach for calculating the axial stiffness of the several elements of a bolt (the head and the engaged part), the nut and the fastened plates. Finite element modelling based on deformation energy improves the existing models and take in to account the type of materials and coefficients of friction of various elements in contact. From these corrections, approaches for axial stiffness calculation based on empirical formulas are proposed for easier application and for future FE modelling bolted joints using beam elements. Finally, the theoretical study is validated by an original experimental approach.

International audience; This paper investigates the behavior of large diameter bearing bolted joint in order to evaluate fatigue resistance of the screws. Based on experimental results, a sector of a slewing bearing is modeled using 3D finite elements. The model is built via hypothesis of sine-distributed efforts on the roller tracks. The simulations are carried out for the most loaded screw, which is located in the symmetry plane. Experimental measures on equipped screws are checked against numerical 3D simulations. This validates the numerical modeling method. Then the numerical model is used to evaluate the influence of several geometrical and physical parameters. The preload intensity reveals to be the major parameter. The bushes’ height affects load filtering and improves fatigue strength of the screws. The height of the mounting tubes smoothes potential stiff points. The friction coefficient between the ring and the mounting is investigated as well. Eventually, several observations are made which lead to design recommendations for fatigue sizing of the slewing bearing screwed joints.

this article deals with bolted assemblies subjected to transverse loading The design of experiments (DOE) method is applied to this type of assembly in order to analyse the behaviour of the various design parameters. The results of observation come from a finite elements model which was preliminarily validated by an experimental study. A factorial design with six factors and three levels, makes it possible to draw interesting conclusions about the various factors likely to influence the design of this type of connection

Fatigue failure is a common problem with bolted joints. Preloading can often offer great advantage, in that it reduces the intensity of the alternative part of strains. Although it is more and more usual to carry out very precise finite element calculations, it should be highlighted that the error arising from simulations or experiments may be surprisingly great when looking at supplements of strain, i.e. alternative strain. That is one of the reasons why designing preloaded bolted joints requires great care, and sometimes turns out to be impractical. A partnership has been established for several years with a group of industrial manufacturers and users of slewing bearings. The objective is to model a parameterised bolt-assembled slewing bearing system and to develop a simulation tool that • allows us to check resistance of the bolts for maximum load as well as fatigue load • runs much faster than a three-dimensional simulation in order to enable us to compare multiple configurations, in order to be used in early design stages.