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Technical Paper

Piston Secondary Dynamics Considering Elastohydrodynamic Lubrication

2007-04-16
2007-01-1251
An analytical method is presented in this paper for simulating piston secondary dynamics and piston-bore contact for an asymmetric half piston model including elastohydrodynamic (EHD) lubrication at the bore-skirt interface. A piston EHD analysis is used based on a finite-difference formulation. The oil film is discretized using a two-dimensional mesh. For improved computational efficiency without loss of accuracy, the Reynolds’ equation is solved using a perturbation approach which utilizes an “influence zone” concept, and a successive over-relaxation solver. The analysis includes several important physical attributes such as bore distortion effects due to mechanical and thermal deformation, inertia loading and piston barrelity and ovality. A Newmark-Beta time integration scheme combined with a Newton-Raphson linearization, calculates the piston secondary motion.
Technical Paper

A Comprehensive Method for Piston Secondary Dynamics and Piston-Bore Contact

2007-04-16
2007-01-1249
Low vibration and noise level in internal combustion engines has become an essential part of the design process. It is well known that the piston assembly can be a major source of engine mechanical friction and cold start noise, if not designed properly. The piston secondary motion and piston-bore contact pattern are critical in piston design because they affect the skirt-to-bore impact force and therefore, how the piston impact excitation energy is damped, transmitted and eventually radiated from the engine structure as noise. An analytical method is presented in this paper for simulating piston secondary dynamics and piston-bore contact for an asymmetric half piston model. The method includes several important physical attributes such as bore distortion effects due to mechanical and thermal deformation, inertia loading, piston barrelity and ovality, piston flexibility and skirt-to-bore clearance. The method accounts for piston kinematics, rigid-body dynamics and flexibility.
Technical Paper

Prediction of Tire-Snow Interaction Forces Using Metamodeling

2007-04-16
2007-01-1511
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.
Technical Paper

Optimal Engine Torque Management for Reducing Driveline Clunk Using Time - Dependent Metamodels

2007-05-15
2007-01-2236
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.
Technical Paper

An Efficient Re-Analysis Methodology for Vibration of Large-Scale Structures

2007-05-15
2007-01-2326
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.
Technical Paper

Modeling and Optimization of Vehicle Drivetrain Dynamic Performance Considering Uncertainty

2005-05-16
2005-01-2371
A vehicle drivetrain is designed to meet specific vehicle performance criteria which usually involve trade-offs among conflicting performance measures. This paper describes a methodology to optimize the drivetrain design including the axle ratio, transmission shift points and transmission shift ratios considering uncertainty. A complete vehicle dynamic model is developed using the bond graph method. The model includes the vehicle, engine, transmission, torque converter, driveline, and transmission controller. An equivalent MATLAB Simulink model is also developed in order to carry out the nonlinear dynamic analysis efficiently. A deterministic optimization is first performed to determine the optimum design in terms of fuel economy, without considering variations or uncertainties. Subsequently, a Reliability-Based Design Optimization is carried out to find the optimum design in the presence of uncertainty.
Technical Paper

Sensitivity Study of Probit and Two-Point Fatigue Testing Methods

2006-04-03
2006-01-0536
Fatigue strength mean and standard deviation may be estimated by the Probit and 2-Point test methods. In this paper, methodologies for conducting the tests are developed and results from Monte Carlo simulation are presented. The results are compared with those from concurrent testing with the staircase method. While the Probit and 2-Point methods are intuitively attractive, their results are significantly different from those from the staircase method. The latter remains the best of the three.
Technical Paper

Reliability Analysis Using Monte Carlo Simulation and Response Surface Methods

2004-03-08
2004-01-0431
An accurate and efficient Monte Carlo simulation (MCS) method is developed in this paper for limit state-based reliability analysis, especially at system levels, by using a response surface approximation of the failure indicator function. The Moving Least Squares (MLS) method is used to construct the response surface of the indicator function, along with an Optimum Symmetric Latin Hypercube (OSLH) as the sampling technique. Similar to MCS, the proposed method can easily handle implicit, highly nonlinear limit-state functions, with variables of any statistical distributions and correlations. However, the efficiency of MCS can be greatly improved. The method appears to be particularly efficient for multiple limit state and multiple design point problem. A mathematical example and a practical example are used to highlight the superior accuracy and efficiency of the proposed method over traditional reliability methods.
Technical Paper

Simulation-Based Reliability Analysis of Automotive Wind Noise Quality

2004-03-08
2004-01-0238
An efficient simulation-based method is proposed for the reliability analysis of a vehicle body-door subsystem with respect to an important quality issue -- wind noise. A nonlinear seal model is constructed for the automotive wind noise problem and the limit state function is evaluated using finite element analysis. Existing analytical as well as simulation-based methods are used to solve this problem. A multi-modal adaptive importance sampling method is then developed for reliability analysis at system level. It is demonstrated through this industrial application problem that the multi-modal adaptive importance sampling method is superior to existing methods in terms of efficiency and accuracy. The method can easily handle implicit limit-state functions, with variables of any statistical distributions.
Technical Paper

Simulation of Tire-Snow Interfacial Forces for a Range of Snow Densities with Uncertainty

2006-04-03
2006-01-0497
The objective of this paper is to assess the effect of snow density on tire-snow interaction in the presence of uncertainty. The snow-depth dependent finite element analysis (FEA) and semi-analytical models we have developed recently can predict tire-snow interfacial forces at a given density under combined slip conditions. One drawback of the models is that they are only applicable for fresh, low-density snow due to the unavailability of a density-dependent snow model. In reality, the snow density on the ground can vary between that of fresh snow to heavily compacted snow that is similar to ice. Even for fresh snow on the ground, as a vehicle moves forward, the rear wheels experience higher snow densities than the front wheels. In addition, being a natural material, snow's physical properties vary significantly even for the same density.
Journal Article

Prediction of Automotive Side Swing Door Closing Effort

2009-04-20
2009-01-0084
The door closing effort is a quality issue concerning both automobile designers and customers. This paper describes an Excel based mathematical model for predicting the side door closing effort in terms of the required minimum energy or velocity, to close the door from a small open position when the check-link ceases to function. A simplified but comprehensive model is developed which includes the cabin pressure (air bind), seal compression, door weight, latch effort, and hinge friction effects. The flexibility of the door and car body is ignored. Because the model simplification introduces errors, we calibrate it using measured data. Calibration is also necessary because some input parameters are difficult to obtain directly. In this work, we provide the option to calibrate the hinge model, the latch model, the seal compression model, and the air bind model. The door weight effect is geometrically exact, and does not need calibration.
Technical Paper

Probabilistic Analysis for the Performance Characteristics of Engine Bearings due to Variability in Bearing Properties

2003-05-05
2003-01-1733
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.
Technical Paper

Structural Vibration of an Engine Block and a Rotating Crankshaft Coupled Through Elastohydrodynamic Bearings

2003-05-05
2003-01-1724
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.
Technical Paper

Oil Film Dynamic Characteristics for Journal Bearing Elastohydrodynamic Analysis Based on a Finite Difference Formulation

2003-05-05
2003-01-1669
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.
Journal Article

Probabilistic Reanalysis Using Monte Carlo Simulation

2008-04-14
2008-01-0215
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.
Journal Article

Efficient Re-Analysis Methodology for Probabilistic Vibration of Large-Scale Structures

2008-04-14
2008-01-0216
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.
Journal Article

An RBDO Method for Multiple Failure Region Problems using Probabilistic Reanalysis and Approximate Metamodels

2009-04-20
2009-01-0204
A Reliability-Based Design Optimization (RBDO) method for multiple failure regions is presented. The method uses a Probabilistic Re-Analysis (PRRA) approach in conjunction with an approximate global metamodel with local refinements. The latter serves as an indicator to determine the failure and safe regions. PRRA calculates very efficiently the system reliability of a design by performing a single Monte Carlo (MC) simulation. Although PRRA is based on MC simulation, it calculates “smooth” sensitivity derivatives, allowing therefore, the use of a gradient-based optimizer. An “accurate-on-demand” metamodel is used in the PRRA that allows us to handle problems with multiple disjoint failure regions and potentially multiple most-probable points (MPP). The multiple failure regions are identified by using a clustering technique. A maximin “space-filling” sampling technique is used to construct the metamodel. A vibration absorber example highlights the potential of the proposed method.
Technical Paper

Imprecise Reliability Assessment When the Type of the Probability Distribution of the Random Variables is Unknown

2009-04-20
2009-01-0199
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.
Technical Paper

Reliability Estimation of Large-Scale Dynamic Systems by using Re-analysis and Tail Modeling

2009-04-20
2009-01-0200
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.
Journal Article

Optimal and Robust Design of the PEM Fuel Cell Cathode Gas Diffusion Layer

2008-04-14
2008-01-1217
The cathode gas diffusion layer (GDL) is an important component of polymer electrolyte membrane (PEM) fuel cell. Its design parameters, including thickness, porosity and permeability, significantly affect the reactant transport and water management, thus impacting the fuel cell performance. This paper presents an optimization study of the GDL design parameters with the objective of maximizing the current density under a given voltage. A two-dimensional single-phase PEM fuel cell model is used. A multivariable optimization problem is formed to maximize the current density at the cathode under a given electrode voltage with respect to the GDL parameters. In order to reduce the computational effort and find the global optimum among the potential multiple optima, a global metamodel of the actual CFD-based fuel cell simulation, is adaptively generated using radial basis function approximations.
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