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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.

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.

Self-piercing riveting (SPR) has been used in production to join sheet materials since the early 1990s. A large amount of experimental trial work was required in order to determine an appropriate combination of rivet and anvil design to fulfill the required joint parameters. The presented study is describing the methodology of SPR joint design based on numerical simulation and experimental methods of defining required simulation input parameters. The required inputs are the stress-strain curves of sheet materials and rivets for the range of strains taking place in the SPR joining process, parameters required for a fracture model for all involved materials, and friction parameters for all interfaces of SPR process. In the current study, the normalized Cockroft-Latham fracture criterion was used for predicting fracture. Custom hole and tube expansion tests were used for predicting fracture of the riveted materials and the rivet, respectively.

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.

An approach for Probabilistic Reanalysis (PRA) of a system is presented. PRA calculates very efficiently the system reliability or the average value of an attribute of a design for many probability distributions of the input variables, by performing a single Monte Carlo simulation. In addition, PRA calculates the sensitivity derivatives of the reliability to the parameters of the probability distributions. The approach is useful for analysis problems where reliability bounds need to be calculated because the probability distribution of the input variables is uncertain or for design problems where the design variables are random. The accuracy and efficiency of PRA is demonstrated on vibration analysis of a car and on system reliability-based optimization (RBDO) of an internal combustion engine.

Scuffing is a failure mechanism which can occur in various engineering components, such as engine cylinder kits, gears and cam/followers. In this research, the scuffing behavior of 4140 steel and ductile iron was investigated and compared through ball-on-disk scuffing tests. A step load of 22.2 N every two minutes was applied with a light mineral oil as lubricant to determine the scuffing load. Both materials were heat treated to various hardness and tests were conducted to compare the scuffing behavior of the materials when the tempered hardness of each material was the same. Ductile iron was found to have a consistently high scuffing resistance before tempering and at tempering temperatures lower than 427°C (HRC ≻45). Above 427°C the scuffing resistance decreases. 4140 steel was found to have low scuffing resistance at low tempering temperatures, but as the tempering temperature increases, the scuffing resistance increased.

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.

One of the major problems that the automotive industry faces is reducing friction to increase efficiency. Researchers have shown that 30% of the fuel energy was consumed to overcome the friction forces between the moving parts of any automobile, Holmberg et al. [1]. The interface of the piston pin and pin bore is one of the areas that generate high friction under severe working conditions of high temperature and lack of lubrication. In this research, experimental investigation and theoretical simulation have been carried out to analyze the motion of the floating pin against pin bore. In the experimental study, the focus was on analyzing the floating pin motion by using a bench test rig to simulate the floating pin motion in an internal combustion engine. A motion data acquisition system was developed to capture and record the pin motion. Thousands of images were recorded and later analyzed by a code written by MATLAB.

In practice, the piston wrist pin is either fixed to the connecting rod or floats between the connecting rod and the piston. The tribological behavior of fixed wrist pins have been studied by several researchers, however there have been few studies done on the floating wrist pin. A new bench rig has been designed and constructed to investigate the tribological behavior between floating pins and pin bore bearings. The experiments were run using both fixed pins and floating pins under the same working conditions. It was found that for fixed pins there was severe damage on the pin bore in a very short time (5 minutes) and material transfer occurs between the wrist pin and pin bore; however, for the floating pin, even after a long testing time (60 minutes) there was minimal surface damage on either the pin bore or wrist pin.

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.

This paper describes a laboratory-based test system and procedure for determining the durability of RTV sealant with fretting movement. A test machine is described in which shear and tensile stress-generating displacements at room temperature and temperature of 100°C are produced to load an RTV seal. The test system utilizes an air pressurized hollow cylinder with a cap sealed by RTV sealant on a reciprocating test rig. An external air leakage monitoring system detects the health of the tested RTV seal. When air leakage occurs, the seal is determined to have failed. RTV sealant used in the test was fully cured at room temperature and then aged with engine oil. In the experiments, a total of 6 displacements were used to generate cycle/amplitude graphs for both shear and tensile modes. Failures were determined to be caused by the loss of adhesion in tensile mode, and by crack nucleation due to the special step design in shear mode.

Quality and performance are two important customer requirements in vehicle design. Driveline clunk negatively affects the perceived quality and must be therefore, minimized. This is usually achieved using engine torque management, which is part of engine calibration. During a tip-in event, the engine torque rate of rise is limited until all the driveline lash is taken up. However, the engine torque rise, and its rate can negatively affect the vehicle throttle response. Therefore, the engine torque management must be balanced against throttle response. In practice, the engine torque rate of rise is calibrated manually. This paper describes a methodology for calibrating the engine torque in order to minimize the clunk disturbance, while still meeting throttle response constraints. A set of predetermined engine torque profiles are calibrated in a vehicle and the transmission turbine speed is measured for each profile. The latter is used to quantify the clunk disturbance.

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.

This study examines the contributions and interactions of intake and exhaust tuning on a 4-stroke single-cylinder engine for various engine speeds and valve timings. The parametric study was performed using a 1-D engine simulation model, the combustion sub-model of which was calibrated based on experimental pressure data. Mechanisms by which tuning changes the volumetric efficiency of an engine were studied. Simulation results are compared with established empirical correlations which predict pipe lengths for maximum volumetric efficiency. It was found that intake tuning has a more dominant role in the breathing capability of the engine compared to exhaust tuning and that both are independent from each other. Valve timing was found to have no effect on intake tuning characteristics but to affect exhaust tuning.

This paper explores the trade-off between reliability-based design and robustness for an automotive under-hood thermal system using the iSIGHT-FD environment. The interaction between the engine cooling system and the heating, ventilating, and air-conditioning (HVAC) system is described. The engine cooling system performance is modeled using Flowmaster and a metamodel is developed in iSIGHT. The actual HVAC system performance is characterized using test bench data. A design of experiment procedure determines the dominant factors and the statistics of the HVAC performance is obtained using Monte Carlo simulation (MCS). The MCS results are used to build an overall system response metamodel in order to reduce the computational effort. A multi-objective optimization in iSIGHT maximizes the system mean performance and simultaneously minimizes its standard deviation subject to probabilistic constraints.

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.