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It is challenging to perform probabilistic analysis and design of large-scale structures because probabilistic analysis requires repeated finite element analyses of large models and each analysis is expensive. This paper presents a methodology for probabilistic analysis and reliability based design optimization of large scale structures that consists of two re-analysis methods; one for estimating the deterministic vibratory response and another for estimating the probability of the response exceeding a certain level. The deterministic re-analysis method can analyze efficiently large-scale finite element models consisting of tens or hundreds of thousand degrees of freedom and large numbers of design variables that vary in a wide range. The probabilistic re-analysis method calculates very efficiently the system reliability for many probability distributions of the design variables by performing a single Monte Carlo simulation.

The performance of Gasoline Direct Injection (GDI) engines is governed by multiple physical processes such as the internal nozzle flow and the mixing of the liquid stream with the gaseous ambient environment. A detailed knowledge of these processes even for complex injectors is very important for improving the design and performance of combustion engines all the way to pollutant formation and emissions. However, many processes are still not completely understood, which is partly caused by their restricted experimental accessibility. Thus, high-fidelity simulations can be helpful to obtain further understanding of GDI injectors. In this work, advanced simulation and experimental methods are combined in order to study the spray characteristics of two different 3-hole GDI injectors.

High-fidelity finite element (FE) tire-snow interaction models have the advantage of better understanding the physics of the tire-snow system. They can be used to develop semi-analytical models for vehicle design as well as to design and interpret field test results. For off-terrain conditions, there is a high level of uncertainties inherent in the system. The FE models are computationally intensive even when uncertainties of the system are not taken into account. On the other hand, field tests of tire-snow interaction are very costly. In this paper, dynamic metamodels are established to interpret interaction forces from FE simulation and to predict those forces by using part of the FE data as training data and part as validation data. Two metamodels are built based upon the Krieging principle: one has principal component analysis (PCA) taken into account and the other does not.

Styrene-Butadiene Rubber (SBR) is a copolymer of butadiene and styrene. It has a wide range of applications in the automotive industry due to its high durability, resistance to abrasion, oils and oxidation. SBR applications vary from tires to vibration isolators and gaskets. SBR is also used in tuned dampers which aim to reduce and control the angular vibrations of crankshafts, acting as an isolator and energy absorber between the tune damper's hub and the inertia ring. The dynamic properties of this polymer are therefore, very important in developing an appropriate analytical model. This paper presents the results of a series of experiments performed to determine the dynamic stiffness and damping properties of SBR. The frequency, temperature and displacement dependent properties are determined in a low frequency range from 0.4 to 150 Hz, and in a mid frequency range from 150 to 550 Hz. The most interesting property of SBR is its frequency dependent behavior.

Most previous measurements of diesel sprays have yielded few details regarding the near-nozzle structure of the sprays. X-ray radiography measurements have provided quantitative, time-resolved measurements of spray behavior, but the radiography data are projections of the actual fuel distribution. In this study, diesel sprays from two axial, single-hole nozzles are measured using x-ray radiography from several viewing angles. A model-based reconstruction is used to determine the actual density distribution from the projected data. The spray from the hydroground nozzle is eccentric and relatively dense, while the spray from the non-hydroground nozzle is asymmetric and far less dense. Even several mm from the nozzles, the calculated density values are high enough to call into question the assumptions underlying many standard CFD spray models.

By taking advantage of high-intensity and high-brilliance x-ray beams available at the Advanced Photon Source (APS), ultrafast (150 ps) propagation-based phase-enhanced imaging was developed to visualize high-pressure high-speed diesel sprays in the optically dense near-nozzle region. The sub-ns temporal and μm spatial resolution allows us to capture the morphology of the high-speed fuel sprays traveling at 500 m/s with a negligible motion blur. Both quality and quantitative information about the spray feature can be readily obtained. In the experiment, two types of single-hole nozzles have been used, one with a hydroground orifice inlet and the other with a sharp one. Within 3 mm from the nozzle, the sprays from these nozzles behave differently, ranging from laminar flow with surface instability waves to turbulent flow. The sprays are correlated with the nozzle internal geometry, which provides practical information for both nozzle design and supporting numerical simulation models.

The process of spray atomization has typically been understood in terms of the Rayleigh-Taylor instability theory. However, this mechanism has failed to fully explain much of the measured data. For this reason a number of new atomization mechanisms have been proposed. The present study intends to gain an understanding of the spray dynamics and breakup processes in the near-nozzle region of heavy-duty diesel injector sprays. As this region is optically dense, synchrotron x-rays were used to gain new insights. This spray study was performed using a prototype common-rail injection system, by injecting a blend of diesel fuel and cerium-containing organometalic compound into a chamber filled with nitrogen at 1 atm. The x-rays were able to probe the dense region of the spray as close as 0.2 mm from the nozzle. These x-ray images showed two interesting features. The first was a breakup of the high density region about 22 μs After the Start Of Injection (ASOI).

This paper presents the utilization of alternative correlation functions in the Kriging method for generating surrogate models (metamodels) for the performance of the bearings in an internal combustion engine. Originally, in the Kriging method an anisotropic exponential covariance function is developed by selecting optimal correlation parameters through optimization. In this paper an alternative nonparametric isotropic covariance approach is employed instead for generating the correlation functions. In this manner the covariance for spatial data is evaluated in a more straightforward manner. The metamodels are developed based on results from a simulation solver computed at a limited number of sample points, which sample the design space.

This paper presents the development of surrogate models (metamodels) for evaluating the bearing performance in an internal combustion engine. The metamodels are employed for performing probabilistic analyses for the engine bearings. The metamodels are developed based on results from a simulation solver computed at a limited number of sample points, which sample the design space. An integrated system-level engine simulation model, consisting of a flexible crankshaft dynamics model and a flexible engine block model connected by a detailed hydrodynamic lubrication model, is employed in this paper for generating information necessary to construct the metamodels. An optimal symmetric latin hypercube algorithm is utilized for identifying the sampling points based on the number and the range of the variables that are considered to vary in the design space.

A quantitative and time-resolved technique has been developed to probe the fuel distribution very near the nozzle of a high-pressure diesel injector. This technique uses the absorption of synchrotron x-rays to measure the fuel mass with good time and position resolution. The penetrating power of x-rays allows measurements that are difficult with other techniques, such as quantitative measurements of the mass and penetration measurements of the trailing edge of the spray. Line-of-sight measurements were used to determine the fuel density as a function of time. The high time resolution and quantitative nature of the measurement also permit an accurate measure of the instantaneous mass flow rate through the nozzle.

A time-resolved x-radiographic technique has been employed for measuring the fuel distribution close to a single-hole nozzle fitted in a high-pressure diesel injector. Using a monochromatic synchrotron x-ray beam, it is possible to perform quantitative x-ray absorption measurements and obtain two-dimensional projections of the mass of the fuel spray. We have completed a series of spray measurements in the optically dense, near-nozzle region (< 15 mm from the nozzle orifice) under ambient pressures of 1, 2, and 5.2 bar N2 and 1 bar SF6 at room temperature with injection pressures of 500 and 1000 bar. The focus of the measurements is on the dynamical behaviors of the fuel jets with an emphasis on their penetration in the near-nozzle region. Careful analysis of the time-resolved x-radiographic data revealed that the spray penetration in this near nozzle region was not significantly affected by the limited change of the ambient pressure.

Using synchrotron x-radiography and mass deconvolution techniques, this work reveals strikingly interesting structural and dynamic characteristics of the direct injection (DI) gasoline hollow-cone sprays in the near-nozzle region. Employed to measure the sprays, x-radiography allows quantitative determination of the fuel distribution in this optically impenetrable region with a time resolution of better than 1 μs, revealing the most detailed near-nozzle mass distribution of a DI gasoline fuel spray ever detected. Based on the x-radiographs of the spray collected from four different perspectives, enhanced mathematical and numerical analyses were developed to deconvolute the mass density of the gasoline hollow-cone spray. This leads to efficient and accurate regression curve fitting of the measured experimental data to obtain essential parameters of the density distribution that are then used in reconstructing the cross-sectional density distribution at various times and locations.

A fast and accurate journal bearing elastohydrodynamic analysis is presented based on a finite difference formulation. The governing equations for the oil film pressure, stiffness and damping are solved using a finite difference approach. The oil film domain is discretized using a rectangular two-dimensional finite difference mesh. In this new formulation, it is not necessary to generate a global fluidity matrix similar to a finite element based solution. The finite difference equations are solved using a successive over relaxation (SOR) algorithm. The concept of “Influence Zone,” for computing the dynamic characteristics is introduced. The SOR algorithm and the “Influence Zone” concept significantly improve the computational efficiency without loss of accuracy. The new algorithms are validated with numerical results from the literature and their numerical efficiency is demonstrated.

A comprehensive formulation is presented for the dynamics of a rotating flexible crankshaft coupled with the dynamics of an engine block through a finite difference elastohydrodynamic main bearing lubrication algorithm. The coupling is based on detailed equilibrium conditions at the bearings. The component mode synthesis is employed for modeling the crankshaft and block dynamic behavior. A specialized algorithm for coupling the rigid and flexible body dynamics of the crankshaft within the framework of the component mode synthesis has been developed. A finite difference lubrication algorithm is used for computing the oil film elastohydrodynamic characteristics. A computationally accurate and efficient mapping algorithm has been developed for transferring information between a high - density computational grid for the elastohydrodynamic bearing solver and a low - density structural grid utilized in computing the crankshaft and block structural dynamic response.

This paper presents the development of surrogate models (metamodels) for evaluating the bearing performance in an internal combustion engine without performing time consuming analyses. The metamodels are developed based on results from actual simulation solvers computed at a limited number of sample points, which sample the design space. A finite difference bearing solver is employed in this paper for generating information necessary to construct the metamodels. An optimal symmetric Latin hypercube algorithm is utilized for identifying the sampling points based on the number and the range of the variables that are considered to vary in the design space. The development of the metamodels is validated by comparing results from the metamodels with results from the actual bearing performance solver over a large number of evaluation points. Once the metamodels are established they are employed for performing probabilistic analyses.

As applications in aerospace, transportation and data centers are faced with increased electric power consumption, their dc operating voltages have increased to reduce cable weight and to improve efficiency. Electric arcs in these systems still cause dangerous fault conditions and have garnered more attention in recent years. Arcs can be classified as either low impedance or high impedance arcs and both can cause insulation damage and fires. Low impedance arcs release lots of energy when high voltage becomes nearly shorted to ground. High impedance arcs can occur when two current-carrying electrodes are separated, either by vibration of a loose connection or by cables snapping. The high impedance arc decreases load current due to a higher equivalent load impedance seen by the source. This complicates the differentiation of a high impedance arc fault from normal operation.

The fuel spray behavior in the near nozzle region of a gasoline injector is challenging to predict due to existing pressure gradients and turbulences of the internal flow and in-nozzle cavitation. Therefore, statistical parameters for spray characterization through experiments must be considered. The characterization of spray velocity fields in the near-nozzle region is of particular importance as the velocity information is crucial in understanding the hydrodynamic processes which take place further downstream during fuel atomization and mixture formation. This knowledge is needed in order to optimize injector nozzles for future requirements. In this study, the results of three experimental approaches for determination of spray velocity in the near-nozzle region are presented. Two different injector nozzle types were measured through high-speed shadowgraph imaging, Laser Doppler Anemometry (LDA) and X-ray imaging.

Multi-hole DI injectors are being adopted in the advanced downsized DISI ICE powertrain in the automotive industry worldwide because of their robustness and cost-performance. Although their injector design and spray resembles those of DI diesel injectors, there are many basic but distinct differences due to different injection pressure and fuel properties, the sac design, lower L/D aspect ratios in the nozzle hole, closer spray-to-spray angle and hense interactions. This paper used Phase-Contrast X ray techniques to visualize the spray near a 3-hole DI gasoline research model injector exit and compared to the visible light visualization and the internal flow predictions using with multi-dimensional multi-phase CFD simulations. The results show that strong interactions of the vortex strings, cavitation, and turbulence in and near the nozzles make the multi-phase turbulent flow very complicated and dominate the near nozzle breakup mechanisms quite unlike those of diesel injections.

The overstress probe fatigue testing method, although codified to characterize fatigue strength, is poorly understood. While it yields data confirming whether minimum fatigue strength may be met, it does not directly reveal the mean fatigue strength. Procedures for conducting the test are somewhat arbitrary and rely on fitting a 3-parameter Weibull model. In this paper, a Monte Carlo procedure is developed to simulate the overstress probe test. The effect of various parameters used in the test is also discussed. A comparison is made between Weibull and Gaussian models. Suggestions for conducting the overstress probe test are provided.

In this paper, an efficient method for the reliability analysis of systems with nonlinear limit states is described. It combines optimization-based and simulation-based approaches and is particularly applicable for problems with highly nonlinear and implicit limit state functions, which are difficult to solve by conventional reliability methods. The proposed method consists of two major parts. In the first part, an optimization-based method is used to search for the most probable point (MPP) on the limit state. This is achieved by using adaptive response surface approximations. In the second part, a multi-modal adaptive importance sampling method is proposed using the MPP information from the first part as the starting point. The proposed method is applied to the reliability estimation of a vehicle body-door subsystem with respect to one of the important quality issues -- the door closing effort.