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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.

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.

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.

An efficient reliability estimation method is presented for engineering systems with multiple failure regions and potentially multiple most probable points. The method can handle implicit, nonlinear limit-state functions, with correlated or non-correlated random variables, which can be described by any probabilistic distribution. It uses a combination of approximate or “accurate-on-demand,” global and local metamodels which serve as indicators to determine the failure and safe regions. Samples close to limit states define transition regions between safe and failure domains. A clustering technique identifies all transition regions which can be in general disjoint, and local metamodels of the actual limit states are generated for each transition region.

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.

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.

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.

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.

There are two sorts of uncertainty inherent in engineering design, the random and the epistemic. Random, or stochastic, uncertainty deals with the randomness or predictability of an event. It is well understood, easily modeled using classical probability, and ideal for such uncertainties as variations in manufacturing processes or material properties. Epistemic uncertainty deals with our lack of knowledge, our lack of information, and our own and others' subjectivity concerning design parameters. Epistemic uncertainty plays a particularly important role in the early stages of engineering design, when a lack of information about nominal values of parameters is much more important than potential variations in those parameters. Design reuse, or the design of product platforms, is an example in which epistemic uncertainty can play a crucial role in early design.

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 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.

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.

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.

A theoretical analysis is presented for calculating the trajectory of a ringless piston within the cylinder clearance of an I.C. engine with a crosshead design. The flexible polytope unconstrained minimization method is used to find the equilibrium between the piston rod structural elasticity and the gas-film hydrodynamics at the piston-cylinder interface. It was found that even when the crosshead bearing is not concentric with the cylinder (i.e., there is an initial eccentricity between the piston and cylinder centerlines), the piston does not touch the cylinder wall during an engine cycle. However, this happens only when a carefully designed piston skirt profile and piston rod length and diameter are used.