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Because of the density mismatch between the decoupler and surrounding fluid, the decoupler of all hydraulic engine mounts (HEM) might float, sink, or stick to the cage bounds, assuming static conditions. The problem appears in the transient response of a bottomed-up floating decoupler hydraulic engine mount. To overcome the bottomed-up problem, a suspended decoupler design for improved decoupler control is introduced. The new design does not noticeably affect the mechanism's steady-state behavior, but improves start-up and transient response. Additionally, the decoupler mechanism is incorporated into a smaller, lighter, yet more tunable and hence more effective hydraulic mount design. The steady-state response of a dimensionless model of the mount is examined utilizing the averaging perturbation method applied to a set of second-order nonlinear ordinary differential equations. It is shown that the frequency responses of the floating and suspended decoupled designs are similar and functional. To have a more realistic modeling, utilizing nonlinear finite elements in conjunction with a lumped parameter modeling approach, we evaluate the nonlinear resorting characteristics of the components and implement them in the equations of motion.

Modern vehicles illustrate a trend toward lighter, higher performance, aluminum-based engines thereby increasing the potential for vibration. The engine is the largest concentrated mass in a vehicle and causes vibration if it is not properly isolated and constrained. The trend for many years to isolate vibrations was to simply connect the engine and frame by means of an engine mount made of elastomeric materials such as rubber [

Because there is a need for a vibration isolator that can exhibit a dual damping ratio that is dependent upon frequency the hydraulic engine mount was introduced. The hydraulic engine mount is a device that approximately provides the desired damping characteristics via the implementation of a mechanical switching mechanism known as the decoupler in conjunction with a narrow, highly restrictive fluid path known as the inertia track [

Figure

(a) Typical hydraulic engine mount. (b) Typical decoupler mechanism.

The decoupler and its housing are shown in Figure

This system works quite well and is in place on the large majority of automotive applications to date. It is analyzed, and modeled by researchers since 1980 from different viewpoints. Adiguna and coworkers determined dynamic behavior of HEMs in time domain [

In the present investigation we study two common assumptions and explore their effects in modeling and dynamics of hydraulic engine mounts. First assumption is that in lumped model of the system, the nonlinearities involved in elastomechanical parts are usually ignored and a linear behavior is assumed. Second assumption is that either in transient or steady-state responses it is assumed that the decoupler is settled down in its neutral position exactly in the middle of the gap of decoupler duct. Therefore, two questions arise as to what are the effects of nonlinearities involved in elastomechanical parts, and what happens on initial start up if the decoupler is bottomed up.

This investigation will utilize finite element analysis to determine the mechanical behavior of the components, and will employ perturbation analysis to determine transient and steady-state behaviors of the mount.

Because of the density mismatch between the decoupler and surrounding fluid, the decoupler will float, sink, twist, or stick to the cage bounds, assuming static conditions. The problem is what happens if the decoupler is in a nonoptimum location for a given random or initial excitation to provide either low damping by being open or closed to allow for high damping.

We introduce a supported decoupler mechanism illustrated in Figure

New decoupler mechanism.

Up to the present, very few researchers have looked at the start-up or transient behavior of the hydraulic mount with Adiguna et al. being among the few [

Floating decoupler HEM is described in the literature very well [

Figure

Proposed hydraulic engine mount design.

Figure

Model of the proposed hydraulic mount.

Decoupler geometry.

Decoupler plate

Housing of decoupler plate

In every HEM there are two rubber-type components in upper and lower chambers to collect the moving fluid. These rubbery components produce compliances of the system which appear in the equations of motion. Besides the two chambers, the suspended decoupler also show an elastic behavior. Utilizing FEM we show how to determine the elastic behavior of the decoupler, upper bellow, and lower collector compliances.

To begin the analysis of the engine mount it is paramount that the necessary geometric and material parameters are identified. To accomplish such, finite element analysis is utilized as a tool to provide knowledge of component load-deflection relationships, volumetric expansion properties, and so forth. By creating a finite element model based upon the geometry illustrated in Figure

Discretized finite element model.

To simulate the impact condition between the decoupler and the surrounding cage bounds Lagrangian type-contact elements were imposed upon potential impacting surfaces (see Figure

Contact element surfaces (not in scale).

Because the decoupler is to be made of an elastomeric material the three-parameter Mooney-Rivlin model, illustrated in (

Mooney-Rivlin constants.

Parameter | Value (MPa) |
---|---|

To solve the finite element model an applied numerical solution method must be employed. Such an approach was required due primarily to two factors. First, the material for the decoupler is nonlinear and requires full geometric nonlinearity options to be utilized. Second, the contact between the rubber and metallic cage bounds is asymmetric noting the differences in material responses between the two structures; therefore, the full Newton-Raphson approach must be employed to deal with the unsymmetrical nature of the assembled matrices [

The fluid is assumed to be incompressible compared to elastic and flexible parts. To simulate fluid-induced pressure an evenly distributed pressure of 20 kPa was assumed to one side of the entire exposed surface of the decoupler. To constrain the entire assembly from motion the lower surface of the cage was fixed in all degrees of freedom. In order to obtain information regarding the load-deflection relationship of the supported decoupler the applied pressure was resolved into a force component by multiplying the area upon which the pressure was applied. The corresponding deflection measurement was taken in the vertical direction from the center node (exposed due to symmetry conditions) of the decoupler disk. The results of the finite element analysis are illustrated in Figure

Decoupler load-deflection relationship.

Notice from Figure

Consider the upper structure of the engine mount with material properties shown in Table

Material properties.

Component | Young’s modulus (GPa) | Poisson’s ratio |
---|---|---|

Spring | 207 | 0.30 |

Upper structure | 71 | 0.33 |

Spring support | 71 | 0.33 |

Upper structure model and meshed geometry.

The finite element model was constrained on the lower surface with load being applied in the form of a specified displacement in the axial direction on the opposing surface. In addition, fixed constraints were applied to the lower and outer surfaces of the surrounding rubber component as illustrated in Figure

To solve the finite element model a nonlinear simulation was utilized allowing for finite strains. Figure

Load-deflection relationship.

Next, consider the upper bellows and its corresponding volumetric compliance. The corresponding finite element model is illustrated in Figure

Upper compliance model and meshed geometry.

Figure ^{5}/N, which corresponds to the volumetric compliance of the upper bellows structure.

Volume-pressure relationship (upper compliance).

Determination of the lower chamber volumetric compliance is accomplished much the same as for the upper chamber. Figure

Lower compliance model and meshed geometry.

Volume-pressure relationship (lower compliance).

Notice the behavior of the lower compliance illustrated in Figure

Hydraulic mount parameters.

Property | Value | Unit |
---|---|---|

m^{2} | ||

m^{2} | ||

m^{2} | ||

Ns/m | ||

3.257 | Ns/m | |

Ns/m | ||

m^{5}/N | ||

m^{5}/N | ||

5.2605 | N/mm^{3} | |

−32.344 | N/mm^{2} | |

334.22 | N/mm | |

kg | ||

kg | ||

0.50 | — | |

8.0246 | N | |

0.5 | mm | |

1.0 | mm |

By introducing the support to the decoupler the momentum balance equation for the decoupler exhibits a restoring force term. Additionally, the nonlinear damping term first introduced by Golnaraghi and Jazar is utilized [

Equations (

To obtain a solution in the frequency domain for (

Expressing the first derivatives as in (

In order for equations (

Figure

Decoupler frequency response.

Figure

Inertia track frequency response.

Noting that the supported decoupler design is based on the initial transient response of the system, consider the force transmitted through the engine mount due to a 1 mm pulse input held for a period of 0.1 seconds. To calculate the force transmitted through the engine mount, consider the following equation developed in [

Determining the solution to the equations of motion in (

Figure

Transmitted force.

This study has introduced a decoupler design motivated by the desire to improve upon the current floating-decoupler design. Using nonlinear finite elements, information in regards to the structural elastic behavior was obtained. This information was then readily utilized by the lumped parameter modeling approach utilized by practically all researchers investigating hydraulic engine mounts. Using the lumped parameter model, the frequency response of the system was investigated utilizing averaging method and compared to previously published results describing floating-decoupler-type mounts with excellent agreement. The agreement between the two models indicated that by supporting the decoupler on thin, low-stiffness tabs, the overall steady-state response of the system is practically unaffected. Additionally, by using numerical analysis to determine the transient response of the system, the supported decoupler substantially improves the engine mounts’ response to sudden excitations. Future work must be about optimizing the supported decoupler design illustrated in this investigation utilizing the RMS optimization method.

Area

Equivalent viscous damping coefficient

Volumetric compliance

Nonlinear decoupler damping coefficient

Nonlinear decoupler force coefficient

Force

Inverse sum of compliances

Upper rubber load-deflection coefficient

Upper rubber load-deflection coefficient

Upper rubber equivalent stiffness

Mass

Pressure

Flow rate

RMS of acceleration transmissibility

Time

Position

Excitation

Gap size

Excitation frequency

Damping ratio

Natural frequency

Nondimensional amplitude

Nondimensional frequency

Tensor invariants

Material constants

Strain energy density.

Inertia track

Decoupler

Piston

Rubber

Upper chamber

Lower chamber

Atmosphere

Transmitted.