Espoch

Introduction
This paper presents a probabilistic analysis of the main bearing lubrication performance of an operating internal combustion engine. Surrogate models or metamodels are developed for critical lubrication performance measure based on a detailed dynamic engine simulation solver which couples the structural dynamics of the crankshaft and block with detailed main bearingelastohydrodynamic behavior. The Kriging method [1, 2] is used to generate the metamodels based on a limited number of sample points.
Probabilistic analyses are first performed to calculate the main bearing statistical performance in terms of the mean, standard deviation, and probability density function of defined bearing performance measures. Subsequently, a probabilistic sensitivity analysis is described foridentifying the important random variables. Finally, a reliability-based design optimization (RE DO) [3-6] study is conducted for optimizing the main bearing performance under uncertainty and results from a V6 engine are presented.
A significant amount of work in the area of elastohydrodynamic analysis of connecting rod bearings has been reported in the literature. An integrated system leveloperating V6 engine simulation model, consisting of flexible crankshaft and engine block dynamics model coupled by an efficient elastohydrodynamic bearing lubrication solver has been presented in Refs. [7,8]. A detailed coupling of the crankshaft rigid and flexible body dynamics [9] was used. The work in Refs [7,8] is employed in this paper for calculating the performance measures used in themetamodel generation. In the past, the impact of variability has not been considered in engine dynamic simulations.
A great deal of research has been done on metamodel development. Polynomials, interpolating and smoothing splines [10], neural network [11, 12] radial basis functions [13], and wavelets [14] have been investigated in the past. Also, the concept of the Kriging method has been introduced[1,2] The Kriging method provides an efficient predictor for problems with limited available samples. It treats the deterministic output as the realization of a stochastic process and provides a statistical basis for efficient prediction. The maximum likelihood estimation [2] is used for estimating the optimal Kriging parameters.
A metamodel (or surrogate model) replaces the actual simulation modelwith a computationally efficient interpolation model. It is developed using actual simulations performed at a group of sample points. Different methods can be employed for selecting the sample points. The Latin hypercube sampling [15] is commonly used. However, the Latin hypercube randomly generated samples may demonstrate low accuracy since they may not exhibit "space-filling" properties. Moreaccurate sampling methods, based on criteria such as entropy [16], integrated mean squared error [2], and minimum intersite distance [17], are computationally expensive. An optimal Latin hypercube algorithm has been reported in Ref. [18] which combines good projection properties and computational efficiency. An optimal symmetric Latin hypercube (OSLH) algorithm with good space-filling properties andcomputational efficiency is described in Ref. [19]. The OSLH sampling method is employed in this paper. Metamodels are developed based on OSLH samples.
An operating V6 engine represents a complicated nonlinear system which is affected by variation in manufacturing processes, operating conditions, material properties, etc. In this paper, Variability is introduced in some engine design variablesand a probabilistic analysis is preformed for the main bearing performance.
The clearance at each main bearing and the oil viscosity comprise the random variables. All random variables are assumed normally distributed. The maximum oil film pressure and the percentage of time (the time ratio) within each cycle that a bearing operates with film thickness lower than a user defined threshold value...