3D finite element analysis of a hydraulic engine mount including fluid-structure ... · 2014. 5. 16. · 3D finite element analysis of a hydraulic engine mount including fluid-structure

3D finite element analysis of a hydraulic engine mount including fluid-structure interaction

F. Daneshmand1, P. Saketi 1 & A. Khajepour2 1Mechanical Engineering Department, Shiraz University, Iran 2Mechanical Engineering Department, University of Waterloo, Canada

Abstract

The interaction between fluid and structure can, in many practical engineering problems, significantly affect the response of the structures and hence needs to be properly taken into account in the analysis. Fluid-structure coupling and the finite element method are used in this paper to propose a new strategy to analyze the dynamic behaviour of the hydraulic engine mount (HEM) that is now widely used as a highly effective vibration isolator in the automotive power-train. The work conducted in this paper demonstrates that the proposed method for estimating the system parameters using the FSI for modeling the HEM is effective and the dynamic characteristics of the HEM can be performed before its prototype development, and this can ensure its low cost and high quality for development. Keywords: hydraulic engine mount, fluid-structure interaction, finite element method.

1 Introduction

The fluid-structure interaction problems arise in many different areas of engineering where the system considered or some of its components are directly in contact with a fluid. Examples are aircraft, jet engines, ships, pipelines, nuclear and chemical reactors, offshore structures, bridges, etc. In these cases, the fluid often plays an important role in determining the behaviour of the structure of interest. To prevent the potential dramatic and expensive accidents, it is necessary to seek a reliable technique for the determination of the characteristics, in particular the natural frequencies of the structure in the presence of the fluid. It is usually not possible to obtain analytical solutions to

Fluid Structure Interaction and Moving Boundary Problems 165

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some of the fluid-structure interaction problems because of the material and kinematical complexity of the system modelled. As a result, numerical techniques have to be used for studying such problems. Numerical methods are not restricted to particular models and can be performed to any degree of precision desired. Among the different numerical techniques, the finite element method (FEM) is a highly systematized tool for the discretization of complex-shaped static and dynamic systems where the continuous problem is transformed into a solvable matrix problem. The various finite element methods used in the solution of fluid-structure interaction problems can be categorized into the four basic approaches, uncoupled approach, added mass approximation, Lagrangian formulation and Eulerian formulation [1]. Hydraulic engine mount (HEM) is now widely used as a highly effective vibration isolator in automotive power-train. It transmits the high frequency–low amplitude engine vibrations to the body, and the low frequency–high amplitude road disturbances to the engine. The increased use of hydraulic engine mounts in automobiles has created an interest in not only studying the structural motion but also in predicting fluid pressure levels and displacement fields to ensure passenger comfort. The vehicle engine mounting system, generally, consists of an engine (vibration source) and several mounts connected to the vehicle structure. The modern engine mounting systems have been successfully used to isolate the driver and passenger from both noise and vibration generated by the engine. A detailed discussion on engine vibration and desirable engine mount characteristics can be found in [2]. In this paper, a 3D fully coupled fluid–structure interaction (FSI) based on finite element method (FEM) using ANSYS software are used for modeling the dynamic performance of an HEM. The work conducted in this paper demonstrates that the proposed method for estimating the system parameters using the FSI for modeling HEM is effective and the dynamic characteristics of an HEM can be performed before its prototype development, and this can ensure its low cost and high quality for development. Finally, this paper shows that the inclusion of the bell system in the upper chamber can reduce the stiffness of the hydraulic mount.

2 Problem statement

The cross section of a typical engine mount is shown in Fig. 1. The model includes seven parts: mount to engine connector (Part #1), bell system (Part #2), upper chamber compliance (Part #3), inertia track (Part #4), decoupler (Part #5), lower chamber compliance (Part #6) and the fluid that fills the free space of chambers (Part #7). A lumped parameter (LP) model is a traditional model for modeling the dynamic characteristics of HEM, in which the system parameters are usually obtained by experiments [2]. The primary fluid variable may be a vector field of fluid particle displacements or a scalar field such as the pressure, displacement potential or the velocity potential. Pressure is used as the fluid variable in the present study. Multiplication of the wave equation by a test function w=w(x,y,z), integrating

166 Fluid Structure Interaction and Moving Boundary Problems


over the total fluid domain, using Green’s first formula and assuming absence of the body forces, leads to [3]

∫∫

∫∫∫

ΓΓ

ΓΩΩ

Γ∂∂

−Γ∂∂

+

Γ∂

∂−=Ω∇⋅∇+Ω

∂∂

42

1

2

22

2

2

022

2

2

)()(

dtpwcd

tpw

gc

dtu

wcdpwcdtpw sfρ

(1)

where Γ is the boundary of Ω, n is the outward normal of Γ and the fluid boundary is divided into four different parts according to their properties, namely 1. The wet surface or the fluid-structure interface, Γ1 2. A free surface with prescribed external pressure where we allow the

linearized (gravitational) waves, Γ2 3. Fixed surface with prescribed external pressure, Γ3 4. An energy absorbing surface, i.e., a surface able to transmit the incident

wave, Γ4.

Figure 1: Cross section of a typical hydraulic engine mount (The Magenta Lines are shown the FSI interface).

Discretization of (1) is carried out by expanding the pressure p in terms of finite element basis functions or shape functions, each one associated with a unique nodal point. The shape functions in the fluid and solid domains are designated by the subscripts ‘f’ and ‘s’, respectively. The expressions for the pressure p and displacement u then take the form

)()(),(

)()(),(

tt

ttp

sss

f

UrHruPrHr

=

= (2)



where P is the pressure at the associated nodal points at time t. Using the standard Galerkin’s formulation with w∈{Hf}, the discretized form of (1) becomes

ebsfff LLLPKPCPM ++−=++ (3)

in which P is the matrix including the unknown nodal values of the pressure and

∫∫ΓΩ

Γ+Ω=2

2

dgcd f

Tff

Tff HHHHM ∫

Γ

Γ=4

dc fTff HHC (4)

∫Ω

Ω∇∇= dc fT

ff )()(2 HHK ∫

Γ

Γ=1

02 duc sf

Tfs HL ρ (5)

∫Ω

Ω∇= dc Tfb bHL )(02ρ ∫

Γ

Γ∂∂

=2

2

22

dtp

gc eT

fe HL (6)

In summary, the two sets of equations for the solid and fluid domains are

++−=++

+=++

ebsfff

fesssssss

LLLPKPCPM

LLUKUCUM (7)

It is seen that the finite element discretizations leads to a system of matrices for each domain and the link between these domains appears through the coupling terms Lf and Ls on the right-hand side. Here, Lf is a function of fluid pressure and Ls is a function of the structural displacement and really carry the interaction features of the model. All other terms on the right-hand side of the equations are true load vectors and can be evaluated as

scs UML = (8)

∫Γ

Γ⋅=1

02 dc s

Tfc nHHM ρ (9)

PKPnHHL cfsf d =

Γ⋅= ∫

Γ1

(10)

∫∫ΓΓ

Γ=Γ⋅=11

dd fTsfsc nHHnHHK (11)

Finally, the assembled system of equations leads to

+=

−+

+

eb

ess

f

css

f

ss

fc

s

LLL

PU

KKK

PU

CC

PU

MMM

0000

(12)

It may be noted that Tcc c KM 02ρ= and that the most elements in these matrices

are zero.



3 Results

The finite element meshes for different parts of a typical hydraulic engine mount are shown in Fig. 2. The decoupler and the inertia track system are shown in Fig.3. The lower and upper chambers are also shown in Fig. 4 and Fig 5, respectively. The problem specifications are given in Table 1.

Figure 2. Figure 3.

Figure 4. Figure 5. The 3D solid and fluid elements are used to model the HEM. The element specifications are shown in Fig. 8 and Fig. 9, respectively. To compare the effects of inclusion the bell system in HEM, two different models are considered in this paper. Each model also includes three different decoupler openings (Fully opened, 50% opening and fully closed). The models were considered for two different loadings: A) High Amplitude Low Frequency (10000 N, 100-200 Hz) and B) Low Amplitude High Frequency (1000 N, 1200-1300 Hz). All of these cases are shown in Table. 2.



Figure 6: Fluid Structure Absent.

Figure 7: Fluid structure present.

Table 1: Problem specifications (SI Unit).

Part No.

Material Young’s Modulus

Poisson’s Ratio

Density Sonic Velocity

1,2,4,5 Steel 200e9 0.3 7800 ------- 3,6 Rubber 200e5 0.42 800 ------- 7 Water ------- ----- 1000 1430



Figure 8: Solid 45 element.

Figure 9: Fluid 30 element.

The deflections of the models versus frequency are shown in the related figures as given in Table 2. Considering the maximum deflections of the models, it is clear that the inclusion of the bell system in the upper chamber can reduce the stiffness of the hydraulic mount.

4 Conclusion

The hydrodynamic response analysis of many practical engineering problems like hydraulic engine mounts (HEM) differs from that of any other ground



structure. It is because the hydrodynamic pressures modify the solid deformations, which in turn modify the hydrodynamic pressure causing them. It means that the fluid-structure interaction can significantly affect the response of the hydraulic engine mounts and need to be properly taken into account in the analysis.

Table 2: Loading conditions.

Fig. # 10 11 12 13 14 15 16 17 18 19 20 21 HA-LF * * * * * * LA-HF * * * * * *

Decoupler Fully Opened

*

*

Decoupler 50 % Opened

*

*

Bell System Included

Decoupler Fully Closed

*

*

Decoupler Fully Opened

*

*

Decoupler 50 % Opened

*

*

Bell System Excluded

Decoupler Fully Closed

*

*

The aim of the present study was to consider the fully coupled fluid structure interaction in investigation of the dynamic behavior of a hydraulic engine mount. This was included using a three-dimensional finite element modeling with pressure and displacement as unknowns in the fluid and solid domain, respectively. The advantages of the FSI model can be summarized as follows:

a. The static properties of the HEM can be estimated. b. The pressure distribution in the chambers and the velocity distribution

of the inertia track can be predicted. c. The shape and size optimization of the HEM can be performed.

Figure 10.

Figure 11.



Figure 12.

Figure 13.

Figure 14.

Figure 15.

Figure 16.

Figure 17.

Figure 18.

Figure 19.



Figure 20.

Figure 21.

The work presented in this paper demonstrated that the models created by using the FEM and fully coupled FSI are feasible and useful in analyzing and designing of hydraulic engine mounts. This modeling needs no mount prototype in the initial design stage and thus the time for mount design is greatly reduced.

References

[1] Daneshmand, F., Sharan, S. K. & Kadivar, M. H., Dynamic Analysis of a Gate-Fluid System, ASCE J. Engineering Mechanics, 2004.

[2] Geisberger, A., Khajepor, A. & Golnaraghi, F., Nonlinear modelling of hydraulic mounts: theory and experiment, Journal of sound and vibration, 249, 371-379, 2002.

[3] Daneshmand, F., Fluid-structure interaction problems and its application in dynamic analysis of radial gates, PhD Thesis, Mechanical Engineering Department, Shiraz University, Shiraz, Iran, 2000.



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3D finite element analysis of a hydraulic engine mount including fluid-structure ... · 2014. 5. 16. · 3D finite element analysis of a hydraulic engine mount including fluid-structure