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Using the total probability theorem, we propose a method to calculate the failure rate of a linear vibratory system with random parameters excited by stationary Gaussian processes. The response of such a system is non-stationary because of the randomness of the input parameters. A space-filling design, such as optimal symmetric Latin hypercube sampling or maximin, is first used to sample the input parameter space. For each design point, the output process is stationary and Gaussian. We present two approaches to calculate the corresponding conditional probability of failure. A Kriging metamodel is then created between the input parameters and the output conditional probabilities allowing us to estimate the conditional probabilities for any set of input parameters. The total probability theorem is finally applied to calculate the time-dependent probability of failure and the failure rate of the dynamic system. The proposed method is demonstrated using a vibratory system.

A twist beam rear suspension system is modeled, analyzed and optimized in this paper. An ADAMS model is established based on the REC (Rigid-Elastic Coupling) Theory, which is verified by FEM (Finite Element Method) approach, the effects of the geometric parameters on the twist beam suspension performance are investigated. In order to increase the calculation efficiency and improve the simulation accuracy, a neural network model and NSGA II (Non-dominated Sorting Genetic Algorithm II) are adopted to conduct a multi-objective optimization on a twist beam rear suspension system.

Weight reduction is very important in automotive design because of stringent demand on fuel economy. Structural optimization of dynamic systems using finite element (FE) analysis plays an important role in reducing weight while simultaneously delivering a product that meets all functional requirements for durability, crash and NVH. With advancing computer technology, the demand for solving large FE models has grown. Optimization is however costly due to repeated full-order analyses. Reanalysis methods can be used in structural vibrations to reduce the analysis cost from repeated eigenvalue analyses for both deterministic and probabilistic problems. Several reanalysis techniques have been introduced over the years including Parametric Reduced Order Modeling (PROM), Combined Approximations (CA) and the Epsilon algorithm, among others.

To improve fuel economy, there is a trend in automotive industry to use light weight, high strength materials. Automotive body structures are composed of several panels which must be downsized to reduce weight. Because this affects NVH (Noise, Vibration and Harshness) performance, engineers are challenged to recover the lost panel stiffness from down-gaging in order to improve the structure borne noise transmitted through the lightweight panels in the frequency range of 100-300 Hz where most of the booming and low medium frequency noise occurs. The loss in performance can be recovered by optimized panel geometry using beading or damping treatment. Topography optimization is a special class of shape optimization for changing sheet metal shapes by introducing beads. A large number of design variables can be handled and the process is easy to setup in commercial codes. However, optimization methods are computationally intensive because of repeated full-order analyses.

As vacuum suction cups are widely used in stamping plants, it becomes urgent and important to understand their performance and failure mode. Vacuum suction cups are employed to lift, move, and place sheet metal instead of human hands. Occasionally the vacuum cups would fail and drop parts, even it would cause expensive delays in the production line. In this research, several types of vacuum cups have been studies and compared experimentally. A new tensile device and test method was developed to measure the pulling force and deformation of vacuum cups. The digital image correlation technique has been adopted to capture and analyze the contour, deformation and strain of the cups under different working conditions. The experimental results revealed that the relevant influential parameters include cup type, pulling force angles, vacuum levels, sheet metal curvatures, etc.

Experimental studies of soot particles showed that the intensity ratio of amorphous and graphite layers measured by Raman spectroscopy correlates to soot oxidation reactivities, which is very important for regeneration of the diesel particulate filters and gasoline particulate filters. This physical mechanism is absent in all soot models. In the present paper, a novel two-layer soot model was proposed that considers the amorphous and graphite layers in the soot particles. The soot model considers soot inception, soot surface growth, soot oxidation by O2 and OH, and soot coagulation. It is assumed that amorphous-type soot forms from fullerene. No soot coagulation is considered in the model between the amorphous- and graphitic-types of soot. Benzene is taken as the soot precursor, which is formed from acetylene. The model was implemented into a commercial CFD software CONVERGE using user defined functions. A diesel engine case was simulated.

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.

In this paper, the development of random vibration testing schedules for durability design verification of engine mounted products is presented, based on the equivalent fatigue damage concept and the 95th-percentile customer engine usage data for 150,000 miles. Development of the 95th-percentile customer usage profile is first discussed. Following that, the field engine excitation and engine duty cycle definition is introduced. By using a simplified transfer function of a single degree-of-freedom (SDOF) system subjected to a base excitation, the response acceleration and stress PSDs are related to the input excitation in PSD, which is the equivalent fatigue damage concept. Also, the narrow-band fatigue damage spectrum (FDS) is calculated in terms of the input excitation PSD based on the Miner linear damage rule, the Rayleigh statistical distribution for stress amplitude, a material's S-N curve, and the Miles approximate solution.

Design of sheet metal drawing processes requires accurate information about the distribution of restraining forces, which is usually accomplished by a set of drawbeads positioned along the perimeter of the die cavity. This study is targeting bringing together the results of finite element analysis and experimental data in order to understand the most critical factors influencing the restraining force. The experimental study of the restraining force was performed using drawbead simulator tool installed into a tensile testing machine. Based upon the experimental results, it was observed that the restraining force of the given drawbead configuration is dependent upon the depth of bead penetration, friction between the drawbead surfaces as well as the clearance between the flanges of the drawbead simulator. This clearance is often adjusted during stamping operations to increase or decrease material inflow into the die cavity without any modification in the die.

In this study, a unique multi-camera three-dimensional digital image correlation (3D-DIC) system was designed and applied to an engine dynamometer cell to measure the displacement and strain of the exhaust manifold while an engine was running in a durability test. In the engine dynamometer cell, the ambient temperature varies from 25°C to 80°C~100°C cyclically and the exhaust manifold experiences high temperatures up to 900°C with high frequency vibrations. In order to obtain reliable data under such conditions, two 3D-DIC systems were designed and set up in the engine dynamometer. One is a high-speed 3D-DIC system, consisting of cameras with a sampling rate of 1250 frames per second. It was used to measure the local displacement of the bolted joint in the exhaust manifold. The high-speed measurement system is able to record the behavior of the bolt during the thermal cycles.

Experiments were carried out on a straight pipe extension of an exhaust port of a multi-cylinder, spark-ignition engine to investigate the axial variation of the steady-state surface heat transfer. Local, steady-state, surface heat flux measurements were made at five different stations on the test section. Based on an optimization procedure developed in this study, the heat-flux measurements obtained for axial distances x / D > 2, were found to be correlated very well (R2 = 0.95) by an equation in the form of an entrance length correction, which is a function solely of x / D, multiplied by the Sieder-Tate convective heat transfer correlation; a correlation valid for fully-developed, steady-state, turbulent, pipe flows. Most importantly, this paper provides strong evidence that the observed heat transfer augmentation in the engine exhaust system is due solely to entrance effects and not due to flow fluctuations, which was the accepted cause.

Finite element analysis is a well-established methodology in structural dynamics. However, optimization and/or probabilistic studies can be prohibitively expensive because they require repeated FE analyses of large models. Various reanalysis methods have been proposed in order to calculate efficiently the dynamic response of a structure after a baseline design has been modified, without recalculating the new response. The parametric reduced-order modeling (PROM) and the combined approximation (CA) methods are two re-analysis methods, which can handle large model parameter changes in a relatively efficient manner. Although both methods are promising by themselves, they can not handle large FE models with large numbers of DOF (e.g. 100,000) with a large number of design parameters (e.g. 50), which are common in practice. In this paper, the advantages and disadvantages of the PROM and CA methods are first discussed in detail.

An optimal idle speed control (ISC) system for an automotive engine is introduced in this paper. The system is based on a non-linear model including time delay. This model is linearized at the nominal operating point. The effect of the time delay on control is compensated by prediction. This methodology is applied to a Chrysler 2.0 liter 4-cylinder SOHC (Single Overhead Cam) engine. All of the unknown parameters of the model are identified by using the normal operating data from the test engine. Based on these identified parameters, an optimal controller was designed and implemented using a rapid prototyping system. Numerous experiments of the optimal controller were carried out at the Chrysler Technology Center in Auburn Hills, Michigan. The performance was compared to that of the existing controller. The results showed that the optimal controller has the capability to effectively control the engine idle speed under a variety of accessory loads and disturbances.

An efficient approach for series system reliability-based design optimization (RBDO) is presented. The key idea is to apportion optimally the system reliability among the failure modes by considering the target values of the failure probabilities of the modes as design variables. Critical failure modes that contribute the most to the overall system reliability are identified. This paper proposes a computationally efficient, system RBDO approach using a single-loop method where the searches for the optimum design and for the most probable failure points proceed simultaneously. Specifically, at each iteration the optimizer uses approximated most probable failure points from the previous iteration to search for the optimum. A second-order Ditlevsen upper bound is used for the joint failure probability of failure modes. Also, an easy to implement active strategy set is employed to improve algorithmic stability.

Reliability-based design optimization accounts for variation. However, it assumes that statistical information is available in the form of fully defined probabilistic distributions. This is not true for a variety of engineering problems where uncertainty is usually given in terms of interval ranges. In this case, interval analysis or possibility theory can be used instead of probability theory. This paper shows how possibility theory can be used in design and presents a computationally efficient sequential optimization algorithm. The algorithm handles problems with only uncertain or a combination of random and uncertain design variables and parameters. It consists of a sequence of cycles composed of a deterministic design optimization followed by a set of worst-case reliability evaluation loops. A crank-slider mechanism example demonstrates the accuracy and efficiency of the proposed sequential algorithm.

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.

The advantages of having higher stiffness to weight ratio and strength to weigh ratio that composite materials have resulted in an increased interest in them. In automotive engineering, the weight savings has positive impacts on other attributes like fuel economy and possible noise, vibration and harshness (NVH). The driveline of an automotive system can be a target for possible use of composite materials. The design of the driveshaft of an automotive system is primarily driven by its natural frequency. This paper presents an exact solution for the vibration of a composite driveshaft with intermediate joints. The joint is modeled as a frictionless internal hinge. The Euler-Bernoulli beam theory is used. Lumped masses are placed on each side of the joint to represent the joint mass. Equations of motion are developed using the appropriate boundary conditions and then solved exactly.

Probabilistic studies can be prohibitively expensive because they require repeated finite element analyses of large models. Re-analysis methods have been proposed with the premise to estimate accurately the dynamic response of a structure after a baseline design has been modified, without recalculating the new response. Although these methods increase computational efficiency, they are still not efficient enough for probabilistic analysis of large-scale dynamic systems with low failure probabilities (less or equal to 10-3). This paper presents a methodology that uses deterministic and probabilistic re-analysis methods to generate sample points of the response. Subsequently, tail modeling is used to estimate the right tail of the response PDF and the probability of failure a highly reliable system. The methodology is demonstrated on probabilistic vibration analysis of a realistic vehicle FE model.

In reliability design, often, there is scarce data for constructing probabilistic models. It is particularly challenging to model uncertainty in variables when the type of their probability distribution is unknown. Moreover, it is expensive to estimate the upper and lower bounds of the reliability of a system involving such variables. A method for modeling uncertainty by using Polynomial Chaos Expansion is presented. The method requires specifying bounds for statistical summaries such as the first four moments and credible intervals. A constrained optimization problem, in which decision variables are the coefficients of the Polynomial Chaos Expansion approximation, is formulated and solved in order to estimate the minimum and maximum values of a system’s reliability. This problem is solved efficiently by employing a probabilistic re-analysis approach to approximate the system reliability as a function of the moments of the random variables.

The paper studies the distributions of residual stresses in auto components after induction hardening. Three prototype parts are analyzed in this paper. Firstly, the temperature fields of the analyzed parts are quantitatively simulated during quenching by simulating surface heating to the austenitization temperature of the material. Secondly, the formation and states of the residual stresses are predicted. Therefore the distribution of residual stress is simulated and shows compressive stresses on the surface of components so that the strength can be improved. The simulated results by computer are compared with experimental results. The good comparison indicates that the results obtained by the FEA analysis are reliable. Thus, it can be concluded that the FEA (Finite element analysis) program is effectively developed to simulate heating and quenching processes and residual stresses distribution.