dynamic modeling of car door weather seals: a first …...dynamic modeling of car door weather...

Dynamic modeling of car door weather seals: A first outline

A. Stenti, D. Moens, W. Desmet K.U.Leuven, Department of Mechanical Engineering, division PMA Celestijnenlaan 300 B, B-3001 Leuven, Belgium e-mail: [email protected]

Abstract Complex built-up mechanical structures can be made of panels and beams, which are connected via different types of joints, such as spot welds, bolted joints, seals, gaskets, glued connections etc. Two important issues concerning the dynamic modeling of joints involve the computational burden of including a detailed model of the joint into the system model and the possibility of including variability and uncertainty, typical for joints, in a full-scale model of the complete structure. In the general framework of developing engineering tools for virtual prototyping and product refinement, these two issues drive the need for the development of simplified equivalent joint models, to be readily included in full-scale NVH models at a reasonable computational cost. This paper concerns the structure-borne vibration transmission of a highly non-linear type of joint: a car door weather seal. A non-linear finite element model, which accounts for the amount of pre-stress of the seal, is used to identify an equivalent linearized seal model that can be included in a full-vehicle linear NVH model.

1. Introduction

When including joints in a Finite Element (FE) model, the typical levels of model refinement and subsequent computational burden required for sensitivity analysis, e.g. to investigate the joint effects on the overall structural dynamic behaviour, are very high. This makes it difficult to include a detailed description of the joint in a full-scale model of the complete structure. Therefore practical joint models usually involve parametric equivalent models. The type of equivalent model and its number of independent parameters usually depend on some specific requirements, on the type of application and of course on the specific joint considered. Complex built-up mechanical structures generally exhibit an important degree of uncertainty and variability. Typical design models of the complete structure are assumed to be representative for the entire manufactured ensemble of structures. Manufacturing variations and geometrical tolerances, material properties of components and connections, typically differ from one manufactured structure to the other. Measurements taken on a set of nominally identical structures in general exhibit an amount of variability, e.g. the same modes of vibration are found at slightly different frequencies. In addition, the properties of a single structure might vary with time due to environmental effects, such as changing temperature, ageing, wear and changes in operating conditions, e.g. load orientation. Measurements taken on a single structure at different times may result in some scatter on the measured responses. In this respect, joints are usually an important source of uncertainty and variability. Physical joint properties, such as stiffness, thickness, damping, often vary substantially from one structure to another. Uncertainties in these physical properties lead to significant uncertainties in the dynamic behaviour of the structure. It is therefore of practical interest to predict not one nominal baseline response, but to provide some statistics on the dynamic response of different realizations of the structure. The analysis of uncertain structures typically involve high computational efforts. In order to provide response statistics at a

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reasonable computational cost, various model evaluations are mandatory so that efficient models are required. Various approaches exist in literature [1]. The long-term aim of this research is to use a probabilistic approach to describe the joint uncertainties, and to derive the corresponding response statistics using a Monte Carlo simulation. In a Monte Carlo simulation, samples of the uncertain parameters are generated in accordance with the probability density function and the equations of motion are then solved for each realization of the uncertain parameter. This research concerns the structure-borne vibration transmission of a highly non-linear type of joint: a car door weather seal. In a first step, a detailed non-linear FE model of the seal is considered on component level. The second step focuses on the extraction of the seal linearized equivalent model, which accounts for the amount of pre-stress of the seal, while in the third step the equivalent model is included into a linear system level model. In the last step various runs of a cost-efficient system model are performed to provide the response statistics. This paper focuses on the first two steps and uses a simplified two-dimensional set-up to describe the car door weather seal.

2. Car door weather seal

2.1 Role of a seal in the NVH behaviour of a car

Automotive weather seals are typically dual extrusion bulbs of sponge and dense rubber that are attached to either the door or the car body in order to seal the passenger compartment. The seals can be held in place in several manners, e.g. intermittent pushpins, continuous carriers, etc., and have a vast variety of shapes with a height of approximately 10-30 mm. The seal wall thickness is typically a few millimetres to provide maximum sealing area at low compression force [2]. In a car door (fig.1), typically the seal strip runs all around the perimeter of the door. When closing the car door onto the door opening panel, the door remains in contact with the door opening panel through the hinges at the door front side, the lock mechanism at the door rear side and through the seal strip all around the door perimeter. The seal strip induces some residual stiffness and viscoelastic contribution to the door support conditions and play a role on the way exterior noise and vibration can be transmitted to the interior of the car.

Fig. (1): A typical car door profile [2]. Fig (2): A typical seal section [4].

Initial use of seals in automotive applications was aimed at accommodating for construction variations. Lately the isolation issue became important, and the design was oriented to better isolate the passenger compartment from dust, water and air leakage. Nowadays the general trend in seal design is mainly oriented on the isolation of the passenger compartment from noise and vibration. For automotive applications the material requirements aspect, such as resilience, weather resistance (including ultraviolet radiation effects), bonding strength, tear, abrasion resistance, etc. also need to be considered when designing for optimal weather seals.

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In references [2,3] guidelines are given on some aspects of the seal connectivity problem that need to be taken mostly into account when designing for an optimal car door weather seal. They define some factors which characterize the seal static and dynamic performances, namely: the compression load deflection behaviour (CLD), the shape of the seal during compression, the contact pressure distribution, the aspiration condition and the sound transmission loss (STL) characteristic of the seal. When closing a car door on the door opening panel energy is spent to overcome the resistance of the lock mechanism at the door rear side, and to compress the seal strip that runs around the perimeter of the door. The CLD curve gives information on the amount of energy spent to compress the seal strip, which can represent up to 50% of the total energy needed to close the door [2]. It is influenced mainly by the seal material characteristic and by the seal shape. The change of contact pressure distribution during compression gives information on the likelihood of air and water leakage through the seal [2]. The deformed shape during compression gives information on the stress distribution in the seal [2]. The aspiration condition is defined as the condition of loss of contact between the seal and the facing metal surface of the door. At a certain driving speed the pressure difference between the interior and the exterior of the car pushes the seal outward. If the resultant pressure is higher than the frictional forces at the contact area, separation occurs. The occurrence of separation is influenced by the compression rate and the friction coefficient of the rubber to metal contact area. When separation occurs, an open path for direct noise is created and turbulence at the door edge is generated. The turbulence is due to the interaction between the escaping air fluxes from the passenger compartment, encountering the air fluxes at the exterior of the car [2]. The airborne noise generated at the exterior of the car is mainly due to wind noise, exhaust noise, engine noise and tire noise [3,4]. Wind noise is generated mainly on the side glass windows of the doors by the turbulent flow of air around the A pillar structures and other recesses and projections in the body surface and is transmitted into the vehicle interior through body panels, side window glass and the seal gap between the door and the door opening panel. In reference [5] it is emphasized that the side glass windows and the car door seals are the two main mechanisms of sound transmission from the exterior to the interior of the passenger cabin. Seals are usually considered acoustically transparent, i.e. zero STL, at frequencies in the vicinity of a critical mass-air-mass resonance frequency. The noise entering the car cavity through the car door weather seals is then comparable in level to the broadband noise generated by the window panel vibrations. From a general NVH perspective, the interest turns on how the seal characteristic, i.e. the geometry (2D seal shape and 3D section variation along the door perimeter), the constitutive material (dense and sponge rubber seal parts), the damping (typically high values and frequency dependent), the stiffness (frequency dependent and pre-stress dependent), and the mass distribution (the frequency range of the seal dynamics), influence the car door vibration levels and the mechanism of energy transmission from the door to the car body. The support and isolation characteristic of the seal become important performance factors that should be taken into account in seal design and are the present and future interest of this research. In the general frame of developing engineering tools for virtual prototyping and product refinement a complete characterization of the seal connectivity problem in terms of the aforementioned performance factors will provide a profound insight into the problem and provide design evaluations before any prototype hardware is developed.

2.2 Non-linear FE model of a car door weather seal

2.2.1 FE modeling of rubber components

Modeling a car door weather seal is a highly non-linear problem. The non-linearities include geometrical non-linearities, due to large displacements and large strains, material non-linearities, due to a non-linear stress-strain behaviour together with hysteretic phenomena and viscoelastic behaviour, contact and self-contact problems involved with the compression of the car door weather seal, etc. Special purpose finite element formulations are needed to handle this class of problems. In addition, the contact problem requires a finite element formulation capable of treating varying contact conditions between deformable bodies.

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The MSC/MARC finite element code can handle most of these specifications and has been used to perform the reported non-linear analysis. Seals are made of elastomers, which are polymers that behave as natural rubber at room temperature. Rubber can be stretched up to several hundreds of strain percentages without reaching failure. Rubber stress-strain behaviour is significantly non-linear and almost fully elastic. Rubber can be nearly incompressible (dense rubber) or very compressible (foam or sponge rubber). Rubber usually exhibits significant damping properties, and its behaviour is time, temperature and frequency dependent. Large deformation analysis of non-linear materials, such as elastomers, requires convenient measures of stress and strain. Most non-linear FE codes, such as MSC/MARC, use measures such as the so-called Green-Lagrange strain measure and the corresponding work conjugate stress called the 2nd Piola Kirchhoff stress measure or the Cauchy (true) stress with the energetically conjugate measure of strain logarithmic (true) strain [6-8]. Those are convenient alternatives to the more familiar engineering stress and engineering strain. At small strains, the differences between various measures of stresses and strains are negligible. The non-linear behaviour of rubber also requires specific constitutive material formulations, namely hyper elastic material models. Finite element codes for this class of non-linear problems are generally provided with a wide range of material models, capable of describing the material behaviour under different strain conditions, temperatures and including the material characteristic behaviour dependency on the excitation frequency content. In finite element codes, such as MSC/MARC, different forms of strain energy density functions W may characterize elastomeric materials. The strain energy density functions are in general represented in terms of a weighted summation of strain invariants. The strain invariants 1I , 2I and 3I are functions of the stretch ratios and expressed as:

23

22

211 λλλ ++=I 2

123

23

22

22

212 λλλλλλ ++=I 2

322

213 λλλ=I

where the stretch ratios are defined as:

ii

iii L

LLελ +=

∆+= 1 ; 3,2,1=i

Fig. (3): Stretch ratios.

where iii LL∆=ε is the engineering strain. In case of perfectly incompressible materials, the third invariant equals one, i.e. 13 =I . The simplest model of rubber elasticity is the Neo-Hookean model represented as:

( )3110 −= ICW

L1

L3

L2

λ1L1

λ2L2

λ3L3

t3

t1

t2


This model exhibits a constant shear modulus, and gives a good correlation with experimental data up to 40% strain in uniaxial tension and up to 90% strain in simple shear [7]. The constant 10C is obtained by curve fitting material test data under various strain conditions, depending on the application requirements. Other more phenomenological theories lead to the generalized Mooney-Rivlin model, which is in the form of a weighted summation of strain invariants and results in a better agreement with test data for both unfilled and filled rubbers. The model used in this paper is the five term generalized Mooney-Rivlin model also know as the James-Green-Simpson model, which takes the form:

( ) ( ) ( )( ) ( ) ( )31302

1202111201110 333333 −+−+−−+−+−= ICICIICICICW

Other material models exist in literature, such as the Arruda Boyce model, the Odgen model or the Blatz-Ko’s model (used to model foam and sponge rubber), etc. and are present in most of the commercial codes for non-linear finite element calculations. Each model has its own stability characteristics and strain range of applications, the agreement with test data being the main issue [9]. The simulation of contact behaviour requires the motion tracking of bodies before, during and after contact, including the friction and heat transfer simulation between contact surfaces. The numerical objective is to detect the motion of the bodies, apply a constraint to avoid penetration, and apply appropriate boundary conditions to simulate the frictional behaviour and heat transfer. Several procedures have been developed to treat these problems such as the Perturbed or Augmented Lagrangian methods, penalty methods, etc. MSC/MARC allows contact analysis to be performed automatically without the use of special contact elements, e.g. gap elements, and is implemented with the Direct Constraint method. It is out of the scope of this paper to give an exhaustive treatment of those arguments. The reader is referred to technical books such as references [6-9].

2.2.2 The FE model of the car door weather seal

The simplified two-dimensional car door seal mechanism is modelled as shown in figure 4. A slice of the door seal is cut and plain strain approximation is assumed. The door is pinned on the right (light violet arrows) and is in contact with the seal on the left side. The seal (fig. 5) is glued to the ground, which represents the car body. An incremental force is applied to close the door (yellow arrow). The seal gradually compresses by closing the door. At different closure gaps, the door is dynamically excited with a harmonic force, and the seal pre-stress effect on the door dynamics is investigated. The door is 1 m long, has a thickness of 0.01 m, and it is made of isotropic and homogeneous steel, with the following modulus of elasticity, Poisson coefficient and mass density:

211101.2

mNE ∗= , 33.0=υ , 37850

mkg

=ρ

Fig. (4): Section view of the two-dimensional door-seal configuration.

A proportional damping with 510,0 −== βα is considered. The door is modelled with 562 nodes and 582 elements. The door is meshed in two different manners: away from the door-seal contact area, a

door

seal

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coarse mesh of isoparametric four-node plain strain elements, with a characteristic length of 0.01 m, is used.

Fig. (5): Zoom view of the seal.

In the proximity of the contact area, the mesh is refined with isoparametric tri-node plain strain elements, with a characteristic length of 0.001 m. In the contact area, the door and the seal have similar mesh refinements, which guarantees a better convergence in the contact simulation. The conventional isoparametric four-node and tri-node plain strain elements are modified with the Assumed Strain formulation, to better represent door bending vibrations [8]. The seal has an omega shape of 100 =D mm, 60 =d mm (fig. 5), and is made of EPDM dense rubber material. A five term generalized Mooney-Rivlin hyper elastic material model is used. The material coefficients are taken from literature [2,3]:

0932811.010 =C MPa, 0902353.001 =C MPa, 0063716.020 =C MPa, 0062266.011 =C MPa, 0003311.030 =C MPa.

The material density is 31200 m

kg=ρ . Since the seal in this application is not highly confined, the rubber bulk modulus is considered infinite. The temperature, time and frequency dependency issues of rubber behaviour are not considered in this work. The seal is modelled with 443 nodes and 354 elements. The seal is meshed with isoparametric four-node plain strain elements with Herman formulation, and have a characteristic length of 0.001m (fig. 5). The MSC/MARC finite elements with Herman formulation are a special group of elements, capable of handling large deformation effects and incompressible material behaviour [8]. The door-seal contact area is modelled with a deformable-to-deformable contact condition. Both for the door-seal contact and the seal-seal self contact, the friction coefficient is 0.4 and the friction mechanism is defined via a Coulomb model [8]. The seal is clamped to the ground.

2.3 Non-linear quasi-static analysis of the seal

A non-linear quasi-static analysis is performed first to define the compressed seal configuration due to the applied force. A point force of 1300 N is imposed incrementally at the edge of the door (fig. 4, yellow arrow). A Lagrangian Formulation, an Eulerian Formulation or an Arbitrary Lagrangian-Eulerian Formulation (AEL) can be used to describe the kinematics of deformation. The choice of one over the other is generally dictated by the convenience of modelling the physics of the problem and the integration of the constitutive equations. In the Lagrangian formulation, the finite element mesh is attached to the material and moves through space along with the material. A Lagrangian Formulation is generally suited for structural problems. In analysis of fluid flow processes, the Lagrangian approach results in highly distorted meshes since mesh convects with the material. Hence, an alternative formulation, namely Eulerian, is used to describe the motion of the body. In this method the element mesh is fixed in space and

ground

D0 d0


the material flows through the mesh. In the AEL formulation the mesh moves independently from the material [8].

Fig. (6): step 0 – 0 % CR. Fig. (7): step 4 – 18 % CR.



In case of the large deformation of rubber, a Lagrangian Formulation is generally adopted, although severe mesh distortion can lead to premature termination of the analysis. These problems are generally solved with adaptive meshing and rezoning. The Lagrangian approach can be classified in two categories: the total Lagrangian method and the updated Lagrangian method. In the former the equilibrium is expressed with the original undeformed state as a reference; in the latter the current configuration acts as a reference state [8]. Depending on which option is used the stress and strain results are given in different form as discussed previously.

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The finite element formulation generally ends up with a non-linear set of equations, which must be solved incrementally. The governing equation of the linearized system can be expressed, in an incremental form as:

ruK =∂

where u∂ and r are, respectively, the correction to the incremental displacements and residual force vectors. There are several solution procedures available in MSC/MARC for the solution of non-linear equations, such as: the Full Newton-Rahpson Algorithm, the Modified Newton-Rahpson Algorithm, the Secant Method, the Arc-Length Method, etc. Again, an exhaustive treatment of those methods is widely presented in literature [6-9]. In this work, a total Lagrangian Formulation is adopted and a Full Newton-Rahpson method with a fixed step scheme strategy is used. The point force is split in 22 increments. Convergence is reached in 52.74 seconds (wall time) with 61 iterations, on a workstation HP-UX, B2000, 400 MHz, 512 MB RAM. The compression ratio (CR) is defined as: ( ) 00 DDDCR i −= where 0D is the initial seal diameter and

iD the seal diameter at increment i . Figures 6 to 11 show the seal deformed shape and a contour plot of the normal contact pressure distribution during compression. In general, these plots give information on the distribution of stresses and strains in the seal and information on the likelihood of air and water leakage, by looking at how the contact area varies during compression. In this application, the geometry of the door-seal contact area initially is quite simple and flat. However, due to the seal omega shape, the contact pressure subsequently splits into two contact areas. In a real case where the geometry of the door-seal contact area is more complex, wrapping around sharp corners can also occur increasing the likelihood of air and water leakage through the seal. The force-displacement curve (fig. 12) shows the non-linear nature of the problem. A linear material model would have definitely underestimated the stiffness hardening occurring above increment 6 (fig. 12). During compression the seal first softens and then, after increment 6, its stiffness increases again. The seal can be considered as a non-linear spring with a spring coefficient varying with the amount of seal compression. The omega shape performs well in terms of STL [3] but leads in general to high peak forces in the CLD curves and therefore to high levels of the energy needed to close the door [2].

Fig. (12): Force vs. Displacement curve. Fig. (13): Point Receptances at different CR.

2.4 Dynamic analysis of the car door

The theory of small amplitude vibrations in deformed viscoelastic solids [10] is implemented in MSC/MARC. This theory is generally applicable to the analysis of rubber support mounts, vibration isolation gaskets and automotive door seals.

N/m * (1000)

m * (0.001)


At various increments, i.e. at various CR values and gap closures, the sensitivity of the door dynamics to the pre-stress levels of the seal is investigated. The Direct Stiffness method is applied and the linearized dynamic stiffness matrix of the complete structure is solved for each frequency in the band of interest. At five different pre-stressed configurations, i.e. increment 0 (CR = 0 %), 4 (CR = 18 %), 10 (CR = 54 %), 15 (CR = 74 %) and 21 (CR = 91 %), a point force of 1 N harmonically excites the structure up to 500 Hz. The door remains pinned at the right end and free at the left end, where it remains in contact with the compressed seal only.

Mode Table 1 I II III IV V 0 % 9 Hz 40 Hz 126 Hz 262 Hz 446 Hz 18 % 12 Hz 41 Hz 126 Hz 262 Hz 446 Hz 54 % 15 Hz 43 Hz 127 Hz 262 Hz 446 Hz 74 % 21 Hz 56 Hz 130 Hz 263 Hz 447 Hz

CR

91 % 24 Hz 77 Hz 140 Hz 268 Hz 449 Hz MSC/MARC linearizes the problem around the last equilibrium state of interest. If the equilibrium state is a non-linear, statically pre-stressed situation, MSC/MARC considers all effects of the non-linear deformation on the dynamic solution. These effects include: initial stress, change of geometry and influence of constitutive law. The vibration problem can be solved as a linear problem using complex arithmetic [8]. Figure 13 shows the point receptances (node 200, yellow arrow in fig. 4) at the different seal CR values. At zero Hertz, a shifting of 28 dB can be observed; the response gets stiffer as the sealing is compressed. The seal pre-stress levels mainly affect the door low-frequency region. A shifting on the first few door bending peaks can be observed in figures 13 and 18. Table 1 summarizes the results. Figure 18 shows a frequency shift of respectively 155%, 74%, 9% and 2%, of the first four bending modes of the door. As the frequency increases the seal influence gradually decreases.

Fig. (14): inc. 4, mode 1. Fig. (15): inc. 4, mode 3.

Fig. (16): inc. 21, mode 1. Fig. (17): inc. 21, mode 3.

The first peak at increment 4 is a bouncing mode; the door is rigidly rotating around the pinned end and compresses the seal (fig. 14). This peak is driven primarily by the stiffness of the seal and the inertia of the door, and its numerical value can be estimated by the formula:

HzLMxK

d

34.932

24

1 =≈ω

where dM is the door mass, L the door length, x the seal distance from the pinned door end and 4K is the seal stiffness value at increment 4, i.e. the slope of the CLD curve at increment 4. The other peaks are the door proper bending peaks. As the CR increases this formula tends to overestimate the first peak since also the door flexibility start to contribute to the peak frequency. At increment 21 the first peak is shifted up to 24 Hz and the bouncing mode is coupled with the first bending mode of the door (fig. 16). As the CR increases, the resonance

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frequencies of the seal itself are also shifted up in frequency (fig. 19, red line with circles). Below 500 Hz there is no inertial effect of the seal on the door and the seal acts as a complex stiffness support.

Fig. (18): Modes Shifts. Fig. (19): Seal first resonance.

Fig. (20): left-free door dynamics. Fig. (21): left-supported door dynamics.

3. The seal equivalent model

The above results show that the seal influence on the door dynamics up to 500 Hz is stiffness dominated. Even though the viscoelastic effects were not investigated, these results already suggest that the seal influence can be divided in three main contributions: a damping, a resonant, and a stiffness contribution. The damping contribution covers the complete door dynamic range and it has not been investigated at this stage. The resonant behaviour of the seal itself generally occurs at higher frequencies, well above the stiffness influence region. The stiffness contribution is indeed mainly present in the low frequency range; only the first few door bending peaks are shifted. An equivalent model is formulated in terms of a linear equivalent mass-spring-dashpot system, each component taking into account the relative contribution. This paper focuses on the seal stiffness contribution. In the range up to 500 Hz, the stiffness contribution can be simply modelled by an equivalent spring (fig. 22).

Fig. (22): schematic view of the equivalent spring.

equiv. spring


Fig. (23): the seal only shape. Fig. (24): CLD curves.

By evaluating the slope of the CLD curve at the increment of interest one can choose the value of the equivalent stiffness. Increment of interest means a specific CR value and a specific closure gap value. The location of the equivalent spring can be chosen by looking at the normal contact pressure distribution plots during compression as to reproduce the actual contact conditions. Figure 20 shows the door point receptances when the seal is not considered, i.e. a door pinned to the right and free at the left end side (green curve), versus the increment 4 curve (blue curve). The green curve misses the seal driven bouncing mode, and represents the lower boundary value for the stiffness interval to be considered for the equivalent spring. Figure 21 shows the transfer receptance curves when the seal is substituted with a simply supported boundary condition (green curve), versus increment 21 curve (blue curve). The green curve represents the upper boundary value for the stiffness interval, which then spans from a left-free end to a simply supported end condition. Superimposing dynamic analyses on non-linear analyses is generally time consuming. A full 3D detailed model of the car door together with a detailed model of the seal strip would involve impractical solution times. The idea is to extrapolate as much information to be readily used in the equivalent mass-spring-dashpot system as possible from the seal shape without considering the door. By reproducing exactly the geometry of the door-seal contact area with rigid bodies in MSC/MARC, it is possible, by conveniently rotating these bodies, to compress the seal as it is compressed in the real case (fig 23). The CLD curves are very similar (fig 24). By doing a modal analysis on the seal alone, the dynamic behavior of the seal can be retrieved (fig 19, blue line with triangles) and the mass, stiffness and damping contribution evaluated. Remaining focused on the stiffness contribution, the CLD curve can be curve-fitted and numerically differentiated in order to retrieve the full stiffness interval. Obviously one can obtain only information regarding the static stiffness since this plot cannot predict the dependency of the complex modulus on frequency. Figure 25 shows the Matlab curve fit of the CLD curve, while figure 26 shows the inverse of the CLD slopes evaluated by different numerical techniques. The green curve is the numerical derivative of the Matlab fitted curve and gives the closest results to the curve representing the zero Hertz values of the point receptances at the different increments (fig 26, black curve with triangles). The discrepancies at increments 13 and 15 can be associated with numerical stability problems. By choosing a certain increment value, figure 26 gives directly the corresponding stiffness value to be used in the equivalent spring. In figures 27 and 28, at increments 4 and 21 respectively, a comparison between the door resonances evaluated with the seal modelled in detail and with the seal equivalent model, shows a good agreement. Figure 29 represents the relative error in percent between the numerical derivative of the Matlab fitted curve (fig 26, green curve) and the curve representing the zero Hertz values of the point receptances at the different increments (fig 26, black curve with triangles). Figure 30 represents the effect that these errors have on the door resonances. Figure 30 shows the relative error in percent between the door resonances evaluated with the seal modelled in detail, and the door resonances evaluated on the equivalent model. This error is always below 10% for all the modes.

N/m * (1000)

m * (0.001)

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Fig. (25): Matlab curve fit. Fig. (26): inverse CLD slopes.

Fig. (27): inc. 4 vs. equiv. spring. Fig. (28): inc. 21 vs. equiv. spring.

Fig. (29): slopes relative error. Fig. (30): frequency error.

The equivalent values obtained in this way are reliable for a particular section of the seal. In real applications the seal runs all around the perimeter of the car door and its section generally changes in shape. It is therefore important to repeat those calculations at each section of interest in order to get the right distribution of equivalent springs to be distributed around the perimeter of the door.

4. Concluding remarks

This paper analyses the structure-borne vibration transmission of a car door weather seal. A simplified two-dimensional set-up is used to describe a car door weather seal. A non-linear finite element model is developed to investigate the role of the seal pre-stress on the door dynamic response. The seal influence on the door dynamic response is divided in three main contributions: a damping, a resonant and a stiffness contribution. The results are used to extract an equivalent linearized seal model, in the form of a mass-spring-dashpot system, to include in a full-vehicle linear NVH model.


Superimposing dynamic analyses on non-linear analyses is generally time consuming. The idea was to extrapolate as much information to be readily used in the equivalent mass-spring-dashpot system as possible from the seal shape without considering the door. This paper focuses on the seal stiffness contribution, which is modelled by an equivalent spring only. The seal resonant and damping contribution, together with the modelling of its viscoelastic characteristic, and the experimental validations of the presented results, are next steps of research. When a complete seal equivalent model will be established, typical uncertainty and variability levels for the joint will be introduced, and various Monte Carlo runs of a cost-efficient system model will be performed to provide the response statistics.

5. Acknowledgements

This research is part of the Belgian program on Interuniversity Poles of Attraction initiated by the Belgian State, Prime Minister's Office, Science Policy Programming.

Bibliography

[1]: R.S.Langley, The Dynamic Analysis of Uncertain Structures, Proceedings of the 7th International Conference on Recent Advances in Structural Dynamics, Univ. of Southampton, UK, July 2000, keynote paper. [2]: D. A. Wagner, K. N. Morman, Jr., Y. Gur, M. R. Koka, Nonlinear analysis of automotive door weatherstrip seals, Finite Elements in Analysis and Design, Vol. 28 (1997), pp 33-50. [3]: Y. Gur, and K. N. Morman, Sound transmission analysis of vehicle door sealing system, 1999 Proceedings of the SAE Noise & Vibration Conference, Traverse City, Michigan, Paper No. 1999-01-1804, pp 1187-1196. [4]: J. Park, L. Mongeau, and T. Siegmund, Effects of Geometric Parameters on the Sound Transmission Characteristic of Bulb Seals, 2003 Proceedings of the SAE Noise & Vibration Conference, Traverse City, Michigan, May 2003. [5]: G.S. Strumolo, The Wind Noise Modeller, 1997 Proceedings of the SAE Noise & Vibration Conference, Traverse City, Michigan, Paper No. 971921, pp 417-425. [6]: NAFEMS - Introduction to Nonlinear Finite Element Analysis, edited by E. Hinton, NAFEMS, Glasgow, 1992. [7]: MSC.Software Corporation, Nonlinear Finite Element Analysis of Elastomers, www.marc.com/Support/Library. [8]: MSC/MARC Volume A, Theory and User Information, Version 2003. [9]: S. Cescotto, Grandes Deformations De Materiaux Hyperelastiques En Etat Plan De Contraintes Par La Methode Des Elements Finis, Extrait de la Collection des Publications de la Faculté des Sciences Appliquées de l’Université de Liège, No. 64-1977. [10]: K.N Morman, Jr., and J.C. Nagtegaal, Finite Element Analysis of Sinusoidal Small-Amplitude Vibrations in Deformed Viscoelastic Solids. PART I: Theoretical Development, International Journal for Numerical Methods in Engineering, Vol. 19 (1983), pp 1079-1103.

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