Optimal design of an engine mount using an enhanced genetic algorithm with simplex method

Abstract

This study provides an analysis of the applications of optimization routines for designing fluid mounts. After summarizing the concept of fluid mounts and their dynamic characteristics, we review the importance of the notch and resonance peak that occur in dynamic stiffness of fluid mounts. Fluid mounts are tuned for specific application so that their notch frequency coincides with the disturbance frequency, by selecting the proper parameters for the mount. Additionally, the mount parameters are selected such that the notch remains as deep (close to zero) as possible and the resonance peak is kept as short as possible. The notch depth and resonance peak present opposing requirements for the selection of mount parameters in the sense that lowering one will result in increasing the other. Using a bond graph model, this study will evaluate the effect of various parameters on the mount notch depth and resonance peak height characteristics. The results show that different parameters can have a varying effect on the notch frequency and depth, as well as the resonance frequency and peak height. The results of the study are extended by examining the effectiveness of two different optimization methods-namely, the Enhanced Genetic Algorithm (EGA) and Sequential Quadratic Programming (SQP)-for selecting the combination of parameters that can yield the deepest notch and shortest resonance peak. Using two different design cases, the study shows that SQP exhibits much more sensitivity to the initial conditions that are selected for the mount parameters than EGA. Both methods, however, are able to converge to an optimal solution within the constraints that are selected for the parameters. For both cases, EGA is able to converge to the set of parameters that provide a deep notch and a short resonance peak.

Computational model of conventional engine mounts for commercial vehicles: validation and application

“…Equations (25)-(30) together with Equations (14), (19), (21), (23) and (24) constitute the mathematical model of conventional mounts. The model parameters should be determined from the measurement data for the real mount.…”

“…To conduct this constrained optimisation problem, Matlab subroutine fmincon is used. With known model parameters (k e , F fmax , x 2 , k 1 , c 1 , k 2 , c 2 ) obtained by the above-described optimisation algorithm, Equations (25)-(30) together with Equations (14), (19), (21), (23) and (24) constitute the computational model of conventional mount. Using the developed computational model, stiffness and damping of the mount can be calculated for different amplitudes and frequencies of the harmonic excitation.…”

“…Moreover, various research works on modelling and analysis of engine mounts have been presented [15][16][17]. Also, Foumani et al [18], Alkhatib et al [19], Arzanpour et al [20], Ahn et al [21], Vahid et al [22] have carried out research on optimisation of the passive engine mount models. Although there is a substantial body of published literature in the area of vibration isolation, most of it focuses on the isolation problems in cars, trains and aircraft applications.…”

Development of integrated evolutionary optimization algorithm and its application to optimum design of ship structures

“…This results in a large search space and huge memory requirements for the computation. To overcome these demerits, many researchers have studied developing many hybrid genetic algorithms which combine the genetic algorithm with other ones [3][4][5][6]. These can save computation time and find the global solution as far as it goes.…”

A Critical Review of Optimization Methods for Road Vehicles Design

“…The majority of engineering problems involve a constrained optimization formulation, that is, the task of minimizing (or maximizing) a vector of objective functions subject to different types of constraints. Objective functions and constraints must be quantifiably expressed as functions (f, g) of the design variables x, i.e., find x such that (1) where f is the objective function vector, x is the vector of the design variables, X is the definition domain of x, and h j , g j are equality and inequality constraints, respectively. The set X can represent certain ranges of real values or certain types, such as integer or "standard" values, which are very often used in design specifications.…”