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An analytical load distribution solution for calculation of the loads exerted by the rolling elements on the outer raceway in cylindrical roller bearings under radial loading is proposed in this paper. The loads exerted by the rolling elements are obtained based on an assumption that the profile of the maximum contact pressures of rolling elements resemble the profile of the contact pressure of the corresponding lumped cylinder. Based on this assumption, an analytical load distribution solution which gives the loads exerted by the rolling elements on the outer raceway is derived based on the non-conforming contact solution of Hertz and the conforming contact solution of Persson. These loads can be calculated from the analytical solution with the total applied load and the normalized contact pressure profile of the corresponding lumped cylinder. Two-dimensional finite element analysis was conducted to validate the proposed analytical solutions.

This paper presents an investigation into the behavior of spot-welded steel connections based on a DOE approach. This work is a part of spot-weld modeling methodology development work being performed at Ford. Control factors such as material, coating, gage size, and noise factors such as loading direction (angle), and speed are considered in this study. Different levels of each variable are included to cover a wide range of practical applications. The test methodology used to generate the responses for the spot-weld coupons have been discussed in a companion paper [1]. From the force-displacement curves obtained from the test, the responses such as peak force, displacement at peak force, and rupture displacement are identified. These responses are then statistically analyzed to identify the relative importance and effect of the design factors. Finally, response surface models are developed to determine responses across different levels of each variable.

In this paper, analytical stress intensity factor solutions for spot welds with ideal geometry in lap-shear specimens of different materials and thicknesses are presented as functions of the applied load, the elastic material property parameters, and the geometric parameters of the weld and specimen. The analytical stress intensity factor solutions are selectively validated by the results of a three-dimensional finite element analysis for a dissimilar spot weld with ideal geometry in a lap-shear specimen. Finally, selected stress intensity factor solutions at the critical locations of spot welds in lap-shear specimens of dissimilar magnesium, aluminum and steel sheets with equal and different thicknesses are presented in the normalized forms as functions of the ratio of the specimen width to weld diameter.

There are a wide variety of approaches to model the automotive seat and occupant interaction. This paper traces the studies conducted for simulating the occupant to seat interaction in frontal and/or rear crash events. Starting with an initial MADYMO model, a MADYMO-LS/DYNA coupled model was developed. Subsequently, a full Finite Element Analysis model using LS/DYNA was studied. The main objective of the studies was to improve the accuracy and efficiency of CAE models for predicting the dummy kinematics and structural deformations at the restraint attachment locations in laboratory tests. The occupant and seat interaction was identified as one of the important factors that needed to be accurately simulated. Quasi-static and dynamic component tests were conducted to obtain the foam properties that were input into the model. Foam specimens and the test setup are discussed. Different material models in LS/DYNA were evaluated for simulating automotive seat foam.

Closed-form structural stress solutions are investigated for fatigue life estimations of flow drill screw (FDS) joints in lap-shear specimens of aluminum 6082-T6 sheets with and without clearance hole based on three-dimensional finite element analyses. The closed-form structural stress solutions for rigid inclusions under counter bending, central bending, in-plane shear and in-plane tension are first presented. Three-dimensional finite element analyses of the lap-shear specimens with FDS joints without and with gap (with and without clearance hole) are then presented. The results of the finite element analyses indicate that the closed-form structural stress solutions are quite accurate at the critical locations near the FDS joints in lap-shear specimens without and with gap (with and without clearance hole) for fatigue life predictions.

A new closed-form structural stress solution for a spot weld in a square thin plate under central bending conditions is derived based on the thin plate theory. The spot weld is treated as a rigid inclusion and the plate is treated as a thin plate. The boundary conditions follow those of the published solution for a rigid inclusion in a square plate under counter bending conditions. The new closed-form solution indicates that structural stress solution near the rigid inclusion on the surface of the plate along the symmetry plane is larger than those for a rigid inclusion in an infinite plate and a finite circular plate with pinned and clamped outer boundaries under central bending conditions. When the radius distance becomes large and approaches to the outer boundary, the new analytical stress solution approaches to the reference stress whereas the other analytical solutions do not.

The modeling of plastic fuel tank systems for crash safety applications has been very challenging. The major challenges include the prediction of fuel sloshing in high speed impact conditions, the modeling of multilayer thermoplastic fuel tanks with post-forming (non-uniform) material properties, and the modeling of tank straps with pre-tensions. Extensive studies can be found in the literature to improve the prediction of fuel sloshing. However, little research had been conducted to model the post-forming fuel tank and to address the tension between the fuel tank and the tank straps for crash safety simulations. Hoping to help improve the modeling of fuel systems, the authors made the first attempt to tackle these major challenges all at once in this study by dividing the modeling of the fuel tank into eight stages. An ALE (Arbitrary Lagrangian-Eulerian) method was adopted to simulate the interaction between the fuel and the tank.

Finite element models of cast aluminum and stamped steel lower control arms (LCAs) were created to simulate subsystem tests of LCA with bushings and brackets. Several modeling methods were used to simulate the dynamic responses of cast aluminum LCAs, and the advantages and disadvantages of each method are discussed. Factors that are essential for modeling stamped steel components found in previous studies [1, 2] including strain rate, forming, and welding effects are incorporated in the stamped steel LCA models. Difficulties in modeling LCAs subsystem, possible remedies, and further improvements are also discussed in this paper.

To achieve optimal axial and bending crush performance using dual phase steels for components designed for crash energy absorption and/or intrusion resistance applications, the cross sections of the components need to be optimized. In this study, Altair HyperMorph™ and HyperStudy® optimization software were used in defining the shape design variables and the optimization problem setup, and non-linear finite element code LS-DYNA® software was used in crush simulations. Correlated crash simulation models were utilized and the square cross-section was selected as the baseline. The optimized cross-sections for bending and axial crush performance resulted in significant mass and cost savings, particularly with the application of dual phase steels.

Strain rate effects have been identified as one of the most critical factors for the modeling of vehicle components in many previous investigations. The strain rate data available to the authors have been processed to obtain the input decks of a required material law in prior investigations. With the application of strain rate modeling, the strain rate database needs to be expanded. In order to continuously improve the safety CAE quality and efficiency, especially the prediction of a vehicle's pulse in a crash event, the effort has been made to include more strain rate data and extend the material database for safety CAE applications. In this study, strain rate data provided by Ispat Inland Inc. for AISI/DOE Technology Roadmap Program are processed. The material processed in this study include HSS590-CR, 440W-GA, BH300-GI, HSLA350-GI, DP600-HR, TRIP590-EG, TRIP600-CR, TRIP780-CR.

In this paper, an analytical method is proposed for determining the stress distributions in steering knuckle/tapered stud assemblies. The method is based on solutions of the plane stress thick cylinder interference fit problem with modifications to account for the effects of stud taper and dissimilar component materials. The analytical solutions are applied to knuckle/tapered stud assemblies. The results from the analytical solutions are compared to those from a finite element analysis. It is shown that the analytical and FEA results are in good agreement for several load and frictional conditions, and the hoop and radial stress solutions presented in this paper are good engineering solutions to the knuckle/tapered stud problem where the draw distance is provided.

The authors have proposed a new formulation to characterize the mechanical properties of spot welds under dynamic loadings including separation. In this paper, the authors primarily discuss a systematic procedure to determine the parameters of the proposed spot weld model from test data using a Design of Experiment (DOE) approach and statistical analyses. All analysis pertaining to the spot weld modeling under impact loading has been performed using RADIOSS, a commercially available explicit FE crash solver. In this study, the spot weld connection was modeled using a two-node beam-type spring element with 6 DOF at each node, and the sheet metal was modeled using a four-node shell element. The main objective was to develop a spot weld modeling methodology that is accurate and robust enough to be used in a full vehicle model which is composed of hundreds of different parts and will be crashed under different test conditions.

The objective of this study is to verify the performance of a target vehicle model in vehicle-to-vehicle impact applications. In some vehicle-to-vehicle tests, the target vehicle stays the same and the bullet vehicle changes from test to test depending on the programs under evaluation. To obtain reasonable crash pulse predictions in vehicle-to-vehicle impacts, it was decided to develop an accurate and robust target vehicle model first. The development of the target vehicle model was divided into two phases, rigid barrier and vehicle-to-vehicle impacts. Twelve rigid barrier tests, including full rigid barriers, angular rigid barriers, offset rigid barriers, and fixed rigid poles were adopted in the first phase of the study to calibrate the target vehicle model. The results of the study have been reported [1]. This paper focuses on the verification of vehicle-to-vehicle impacts.

An accurate and robust target vehicle model was developed for vehicle compatibility applications. Although vehicle compatibility simulation involves a bullet vehicle hitting a target vehicle, the focus of this paper is to develop a target vehicle model. To ensure the robustness, the target vehicle model needs to provide reasonable responses under different impact conditions. This can be achieved by calibrating the model against different physical tests. Significant effort was taken to improve the accuracy of the target vehicle model. In the calibration process, some components were found to have significant effects on the global responses. These components play different roles in different crash modes. To improve the overall correlation with test, different component tests were also designed and conducted to understand the characteristics and improve the modeling of these critical components.

The objective of this study is to develop a target vehicle model for vehicle-to-vehicle impact applications. In order to provide reasonable predictions for crash pulses in vehicle-to-vehicle impacts, an accurate and robust target vehicle model was developed first. An ideal target vehicle model should be able to provide reasonable results when hit by different bullet vehicles at different impact speeds and under different impact conditions. This was achieved by calibrating the target vehicle model against different vehicle crash tests, which include full rigid barriers, angular rigid barriers, offset rigid barriers, and fixed rigid poles. Twelve rigid barrier tests were adopted in this study to calibrate the target vehicle model. During the calibration process, some of the vehicle structures were examined and remodeled carefully for their properties and mesh quality.

This study is a systematic investigation of the body mounts' dynamic characteristics in component, sub-system and full system levels and its application in the frontal impact analysis of a body-on-frame (BOF) vehicle. Concluded from the component study, the body mount is modeled by non-linear spring with built-in damage and rupture properties. The sub-system study reveals the importance of modeling the interaction between the body mount and its surrounding structure. A general-purpose interaction modeling is developed to provide a realistic CAE simulation of this interaction behavior. The full system is mainly for methodology validation. Four 90-degree frontal and the one IIHS offset frontal crash tests are used to evaluate the performance of the body mount in low and high speeds and its capability of predicting the body mount and the floor pan failures.

This study summarizes the latest development of the methodologies for testing and CAE modeling of the engine mount. A systematic approach is used in this study with detailed component, subsystem and full system level investigations. The component level study reveals the entangling phenomenon of the inertial and rate effects in the engine mount dynamic characteristics. In the subsystem, the interaction between the engine mount and its surrounding structure is explored. The full system study is primarily used to validate the CAE methodology for engine mounts developed in the component and subsystem level studies. Four full vehicle barrier crash tests, with different crash modes and speeds, are employed in this validation phase to evaluate the performance of the engine mount CAE methodology.

The frontal rail is one of the most important components of a vehicle in determining crash performance, especially for a body on frame vehicle. Prior research [1] has shown that the frontal rail absorbs a significant amount of impact energy in a crash condition. In order to optimize crash performance, a component level sensitivity study was conducted to determine the effect different types of triggers would have on the performance of the frontal rail. The objective of this study is to determine the sensitivity of trigger size, trigger shape, and trigger orientation as well as to improve corresponding trigger modeling methodology by comparing crushed components to crushed CAE models. In this sensitivity study, the location of the triggers was held fixed, while the size, shape, and orientation were varied. The metric that will be used to compare the performance of these different trigger shapes is the overall stiffness of the frontal rail.

In this paper, the differences of the residual stresses due to rolling in a finite elastic-plastic plate by rigid and elastic deformable rollers at very high rolling loads are investigated by two-dimensional plane strain finite element analyses using ABAQUS. In the finite element analyses, the rollers are modeled both as rigid and linear elastic, and have frictionless contact with the elastic-plastic finite plate. The plate material is modeled as an elastic-plastic power-law strain hardening material with a non-linear kinematic hardening rule for loading and unloading. Two new numerical schemes are developed to represent the elastic roller to model the indentation and rolling. The results of the contact pressure and subsurface stress distributions from the two numerical schemes are almost identical.

In this paper, the evolution equation for the active yield surface during the unloading/reloading process based on the pressure-sensitive Drucker-Prager yield function and a recently developed anisotropic hardening rule with a non-associated flow rule is first presented. A user material subroutine based on the anisotropic hardening rule and the constitutive relation was written and implemented into the commercial finite element program ABAQUS. A two-dimensional plane strain finite element analysis of a crankshaft section under fillet rolling was conducted. After the release of the roller, the magnitude of the compressive residual hoop stress for the material with consideration of pressure sensitivity typically for cast irons is smaller than that without consideration of pressure sensitivity. In addition, the magnitude of the compressive residual hoop stress for the pressure-sensitive material with the non-associated flow rule is smaller than that with the associated flow rule.