Keywords: hydraulically damped rubber mount, engine mount, fluid-structure interaction, finite element, static elastic characteristic, dynamic characteristic.

Hydraulically damped rubber mounts (HDMs) are widely equipped in vehicle powertrain mounting systems (PMS) and they play an important role in noise, vibration and harshness (NVH) control. Understanding the HDM working process is fundamental to the HDM performance design in order to meet the vibration isolation requirements of the PMS. Characteristic simulation of HDMs is usually explored using a lumped-parameter model [1,2], in which fully fluid-rubber interactions (FRI) are not considered. In this paper, the HDM working process simulation is studied based on the use of finite element (FE) analysis of fluid-structure interaction (FSI).

Firstly, key technologies in the FE analysis of FSI, such as the arbitrary-Lagrangian-Eulerian (ALE) mesh control, stable algorithms for fluid FE computation, a numerical method for coupled FE formulation of the FSI and meshing methods for a fluid-structure interface, are introduced [3,4]. Theories of fluid FE formulation in ALE coordinates, the FE method with mixed displacement-pressure elements for an incompressible rubber material and constitutive laws for rubber hyperelasticity are presented.

A type of HDM composed of a rubber spring, two fluid chambers, a fluid track and a decoupler membrane is selected to investigate the FE modeling technology of the HDM by using the commercial codes ADNIA and ADINA-F. An axisymmetric FE model of the HDM with a simplified fluid track into an orifice is developed. The fluid domain is defined by three-node triangular elements (all apex variables and one center velocity) in ALE coordinates; rubber components are defined by four-node mixed displacement-pressure elements (one pressure degree of freedom) for the incompressible media in Lagrangian coordinates; and other structures are modeled by four-node displacement elements. To save computation, a compatible mesh is set up along the fluid-structure interface. The constitutive laws of rubber materials in the HDM are identified by adopting a FE method for hyperelasticity in the commercial software ABAQUS [5]. Nodes on the bottom face of lower body are fixed. A vertical loading displacement is given at nodes on the top surface of the upper connector. A direct computing solution is used to calculate the coupled FRI FE formulations. Fluid velocity-pressure and structural displacement-pressure are obtained simultaneously. Large-scale deformation of the fluid-rubber interface and element distortion in the fluid field are overcome by a proportional mesh control approach.

A kind of quasi-static working process of the HDM is carried out with a slow vertical displacement loading on the top surface of the upper connector. The predicted static elasticity agrees well with the experimental result, which verifies the effectiveness of the modeling approach of the HDM presented. This static working process simulation can be used to evaluate the carrying capacity, to identify chamber volumetric characteristics, such as volumetric elasticity, equivalent piston area used in lumped-parameter models of HDMs [6].

The dynamic working process simulation is performed by adding harmonic vertical displacement on the deformed HDM. Fluid pressure-velocity fields and deformation-stress fields of the rubber spring and their dynamic responses under typical working conditions are analyzed, which is helpful to determine volumetric characteristics and to the structural design of the HDM. However, more accurate three-dimensional FE models of the HDM should be investigated to predict dynamic characteristics of the HDM, especially the tuned isolator damper effect of the fluid track. The FE based model presented and the simulation approach of the HDM can be applied to other kinds of HDM to predict and reanalyze characteristics in development of the computer aided technology of HDMs. The success of a strongly coupled FE method in solving the fluid-large deformation rubber interaction of the HDM reveals a promise for the solution of many other engineering FSI problems when using the FE method.

1

R. Singh, G. Kim, P.V. Ravindra, "Linear Analysis of Automotive Hydro-Mechanical Mount With Emphasis on Decoupler Characteristics", Journal of Sound & Vibration, 158, 219-243, 1992. doi:10.1016/0022-460X(92)90047-2

2

G. Kern, T. Grobmann, D. Gohilich, "Computerunterstutzte Auslegung von Hydraulisch Gedampften Gummilagern", ATZ, 94, 462-472, 1992.

3

C. Nitikitpaiboon, K.J. Bathe, "An Arbitrary Lagrangian-Eulerian Velocity Potential Formulation for Fluid-Structure Interaction", Computer & Structures, 47, 871-891, 1993. doi:10.1016/0045-7949(93)90364-J

4

A.N. Brooks, T.J.R. Hughes, "Streamline Upwind/Petro-Galerkin Formulations for Convection Dominated Flows with Particular Emphasis on The Incompressible Navier-Stokes Equations", Computer Methods in Applied Mechanics and Engineering, 32, 199-259, 1982. doi:10.1016/0045-7825(82)90071-8

5

L.R. Wang, Z.H. Lu, "Finite Element Simulation Based Modeling Method for Constitutive Law of Rubber Hyperelasticity", Rubber Chemistry Technology, 76, 270-284, 2003.

6

L.R. Wang, "Study of Theory and Methods for Simulation of Nonlinear Characteristics of Hydraulically Damped Rubber Mount", PhD thesis, Tsinghua University, Beijing, P. R. China, 2002.

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