Development and Analysis of a Simplified Nonlinear Model of a Hydraulic Engine Mount

Abstract

This paper concerns nonlinear modeling of a hydraulic engine mount, focusing on the decoupler action. The proposed model is a simple nonlinear function, which describes the flow resistance in terms of the decoupler plate displacement and speed. The flow resistance using this model increases dramatically as the decoupler plate approaches the top or bottom of the decoupler cage. The advantage of the proposed model over the existing ones is its simplicity. Numerical simulation results show the behavior of the model to be realistic. Approximate closed form solutions have been obtained for the system using the multiple scale perturbation method. Perturbation provides a solution for the mount response at resonance. These results match the intuitive and experimental results available in the literature. NOMENCLATURE a = A¡/Ad = area ratio A = cross-sectional area A p = equivalent piston area of rubber b = flow resistance factor B, = equivalent damping constant of rubber B = bA = flow resistance C = lumped compliance E = nonlinear resistance factor F = resistance force/nonlinear function H = dynamic stiffness transfer function K, = equivalent spring constant of rubber 1= L¡ / Ld = length ratio L = length m = Ml /Md = mass ratio M = p LA = mass of the passing fluid n = nonlinear exponent at Bobst Library, New York University on October 19, 2014 jvc.sagepub.com Downloaded from 496 P = static pressure ' . Q = flow s = Laplace transformation variable t = time x = absolute displacement y = x/0 -dimensionless displacement Y = amplitude of harmonic excitation A = gap distance a = turbulent exponent 3 = 0/ Y = dimensionless gap distance Q = detuning parameter (frequency of excitation) co = excitation frequency T = Qt = dimensionless time d = B/(MS2) f = Ap/(CAK) e = El (M dQ2) i = VF-1

Suspended Decoupler: A New Design of Hydraulic Engine Mount

“…Equations (28) are identical to the frequency response functions obtained in [13,16] for a floating decoupler mount if s is allowed to equal zero thereby validating the solution noting that the only difference mathematically between the two systems is the sy 3 d term. Figure 15 illustrates the frequency response function for both the supported decoupler introduced in this investigation and the unsupported decoupler model from [10].…”

“…Floating decoupler HEM is described in the literature very well [5][6][7][8][9][10][11][12][13][14][15][16]. To be compared with float type, here we describe a suspended decoupler HEM.…”

“…Additionally, the nonlinear damping term first introduced by Golnaraghi and Jazar is utilized [13,14]. However, to fully describe system dynamics, the inertia track momentum equation is needed along with the fluid continuity equations [10-14, 26, 27].…”

“…Whereas the surfaces contacting after sufficient decoupler deformation were treated as frictionless thereby allowing relative motion between the two bodies. To simplify the analysis and determine the effectiveness of the new design compared to floating decoupler design, we ignore the fluidsolid interaction as is done in modeling HEM [8][9][10][11][12][13][14][15][16].…”

“…Adiguna and coworkers determined dynamic behavior of HEMs in time domain [11] and frequency domain [5], utilizing linear and nonlinear lumped models [12]. The nonlinear function of the decoupler is successfully modeled, examined, and applied by Golnaraghi and Jazar [13,14] utilizing a third-degree equation to describe a nonlinear damping. Adapting their model, Christopherson and Jazar [15,16] optimized a sprung mass suspended by an HEM and provided a design method.…”