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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.

Early in the engineering design cycle, it is difficult to quantify product reliability or compliance to performance targets due to insufficient data or information for modeling the uncertainties. Design decisions are therefore, based on fuzzy information that is vague, imprecise qualitative, linguistic or incomplete. The uncertain information is usually available as intervals with lower and upper limits. In this work, the possibility theory is used to assess design reliability with incomplete information. The possibility theory can be viewed as a variant of fuzzy set theory. A possibility-based design optimization method is proposed where all design constraints are expressed possibilistically. It is shown that the method gives a conservative solution compared with all conventional reliability-based designs obtained with different probability distributions.

A reliability analysis method is presented for time-dependent systems under uncertainty. A level-crossing problem is considered where the system fails if its maximum response exceeds a specified threshold. The proposed method uses a double-loop optimization algorithm. The inner loop calculates the maximum response in time for a given set of random variables, and transforms a time-dependent problem into a time-independent one. A time integration method is used to calculate the response at discrete times. For each sample function of the response random process, the maximum response is found using a global-local search method consisting of a genetic algorithm (GA), and a gradient-based optimizer. This dynamic response usually exhibits multiple peaks and crosses the allowable response level to form a set of complex limit states, which lead to multiple most probable points (MPPs).

High vibration levels at the rear bearing cap and oil pump were observed in dyno tests for a particular design of a V6 engine at a rated speed of 4800 r/min. It was found experimentally that the crankshaft-flywheel assembly had a bending resonance at 240 Hz which was excited at around 4800 r/min by 3rd order forces on the crankshaft. A newly developed crankshaft system model (CRANKSYM) was used to analytically verify the above finding and propose possible solutions to the problem. CRANKSYM can perform a coupled analysis among the crankshaft structural dynamics, main bearing hydrodynamics and engine block flexibility. It considers the flywheel dynamics (including the gyroscopic effect), belt loads, crankshaft “bent” and block misboring, and the anisotropy of the block flexibility as seen from a rotating crankshaft. It can also calculate the dynamic stresses on the crankshaft throughout the whole engine cycle. A brief description of CRANKSYM is given in the paper.

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.

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.

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.

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.

Early in the engineering design cycle, it is difficult to quantify product reliability due to insufficient data or information to model uncertainties. Probability theory can not be therefore, used. Design decisions are usually, based on fuzzy information which is imprecise and incomplete. Recently, evidence theory has been proposed to handle uncertainty with limited information. In this paper, a computationally efficient design optimization method is proposed based on evidence theory, which can handle a mixture of epistemic and random uncertainties. It quickly identifies the vicinity of the optimal point and the active constraints by moving a hyper-ellipse in the original design space, using a reliability-based design optimization (RBDO) algorithm. Subsequently, a derivative-free optimizer calculates the evidence-based optimum, starting from the close-by RBDO optimum, considering only the identified active constraints.

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.

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.

A complete probabilistic model of uncertainty in probabilistic analysis and design problems is the joint probability distribution of the random variables. Often, it is impractical to estimate this joint probability distribution because the mechanism of the dependence of the variables is not completely understood. This paper proposes modeling dependence by using copulas and demonstrates their representational power. It also compares this representation with a Monte-Carlo simulation using dispersive sampling.

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.

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.

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.

The system response of many engineering systems depends on time. A random process approach is therefore, needed to quantify variation or uncertainty. The system input may consist of a combination of random variables and random processes. In this case, a time-dependent reliability analysis must be performed to calculate the probability of failure within a specified time interval. This is known as cumulative probability of failure which is in general, different from the instantaneous probability of failure. Failure occurs if the limit state function becomes negative at least at one instance within a specified time interval. Time-dependent reliability problems appear if for example, the material properties deteriorate in time or if random loading is involved which is modeled by a random process. Existing methods to calculate the cumulative probability of failure provide an upper bound which may grossly overestimate the true value.

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.

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.

Piston design is a challenging engineering problem which involves complex physics and requires satisfying multiple performance objectives. Uncertainty in piston operating conditions and variability in piston design variables are inevitable and must be accounted for. The piston assembly can be a major source of engine mechanical friction and cold start noise, if not designed properly. In this paper, an analytical piston model is used in a deterministic and probabilistic (reliability-based) multi-objective design optimization process to obtain an optimal piston design. The model predicts piston performance in terms of scuffing, friction and noise, In order to keep the computational cost low, efficient and accurate metamodels of the piston performance metrics are used. The Pareto set of all optimal solutions is calculated allowing the designer to choose the “best” solution according to trade-offs among the multiple objectives.

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.