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Experimental and numerical analysis of seat belt bunching phenomenon...

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Experimental and numerical analysis of seat belt bunching phenomenon...

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     International Journal of Impact Engineering 36 (2009) 763?C774

     Contents lists available at ScienceDirect

     International Journal of Impact Engineering

     journal homepage: www.elsevier.com/locate/ijimpeng

     Experimental and numerical analysis of seat belt bunching phenomenon

     David Dubois a, Harald Zellmer b, Eric Markiewicz c, *

     Autoliv France, Avenue de l??Europe, 76220 Gournay en Bray, France Autoliv Germany, Otto-Hahn-Strasse 4, P.O. Box 109, D-25333 Elmshorn, Germany c Laboratory of Industrial and Human Automation Control, Mechanical Engineering and Computer Science (LAMIH), UMR, CNRS 8530, University of Valenciennes, Le Mont Houy, Jonas 2, 59313 Valenciennes Cedex 9, France

     b a

     a r t i c l e i n f o

     Article history: Received 6 May 2008 Received in revised form 6 November 2008 Accepted 10 November 2008 Available online 24 November 2008 Keywords: Seat belt Bunching Finite element Correlation

     a b s t r a c t

     In current cars, loops are commonly used to redirect the webbing which reels out from the retractor to the passenger??s shoulder. Some types of pillar loops, also called D-rings, lead to a non-systematic instability. The webbing, which should scroll without hindrance through the D-ring, laterally shifts, bunches and produces the overturning of the ring. In this paper, this so-called seat belt bunching phenomenon is parsed during a ?rst step with sled test campaigns data. The results of designs of experiments are analysed and discussed. To expertize this instability issue, an innovative ?xture is exploited during a second step to reproduce the phenomenon in a fully controlled manner for dynamic and quasi-static loadings. To assess these subsystem tests, a Digital Images Correlation system is employed to evaluate the strain distribution of seat belt webbing during the bunching phase. Based on these local measurements, a correlation of a Finite Element model of seat belt bunching is achieved using a new shell element for webbing fabric, before proposing an explanation of the phenomenon. ?? 2008 Elsevier Ltd. All rights reserved.

     1. Introduction Automotive manufacturers and suppliers commonly conduct crash tests in order to assess the performance of safety systems on new vehicles. Crash scenarios are reproduced using dynamic tests. For instance, the EuroNCAP protocol; a 64 km/h frontal impact in a 40%

    offset deformable barrier, is used to simulate a car to car impact. An assessment protocol is then applied to achieve a rating for each body region. The head acceleration, the chest de?ection, the femurs loading, compression/extension/?exion of the neck are measured on crash test dummies and a star rating is given. The safest cars obtain a 5-star performance. During the vehicle deceleration, the dummies are subjected to the collision forces and in the case of a frontal impact, they move forward. To prevent severe contacts between the passenger and the car interior (dashboard, steering wheel), a three-point seat belt restrains the passenger??s motion. In parallel, the driver and the passenger airbags reduce the acceleration peak applied to the occupant and distribute the restraint loads on the upper part of the body. To take bene?t of their coupled actions, these restraint systems are developed in interaction. Nevertheless, although an airbag has a spectacular action during a collision, the belt, part of

     * Corresponding author. E-mail address:

    eric.markiewicz@univ-valenciennes.fr (E. Markiewicz). 0734-743X/$ ?C see front matter ?? 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijimpeng.2008.11.006

     the passive restraint system, is the only protection against the ejection of the passenger away from his vehicle. A safety belt webbing is a fabric material using polyester threads woven on Jacquard weaving looms. The webbing of a width of 48 mm of the belt restraint system has to resist to dynamic loads up to 14 kN. Depending on the type of vehicle, about 3.5 m of webbing is used in the seat belt. The interactions between the warp and weft threads of the fabric control the behaviour of the seat belt during the crash event. Seat belt systems are usually combined with a load limiter retractor and also pre-tensioner integrated in the retractor, ?xed at the buckle or at the lower part of the B pillar (the pillar on which the rear doors are ?xed). A D-ring is used on the upper part of this pillar in order to redirect the seat belt, which reels out from the retractor to the passenger shoulder. It is designed to adapt its angular position according to the passenger??s motion. Numerous different kinds of D-rings (also called webbing guides) are used in current vehicles: most of them are made of a metal insert on which polymer part in nylon or in acetyl is moulded (see Fig. 1a). In some cases, the ring frame and the guidance surface are made of one piece of metal (see Fig. 1b). In the latest vehicles, the complete webbing guide assemblies are integrated into the trim panel, and only the diagonal belt portion appears (see Fig. 1c). For some belt geometries (the 3D position of the anchorage points of the seat belt on the vehicle), the use of certain D-rings has led to a non-systematic instability, which is very disadvantageous.

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     Fig. 1. Webbing guides (courtesy Autoliv).

     The webbing, which should scroll without hindrance through the webbing guide, laterally shifts, bunches and produces the overturning of the ring as shown on Fig. 2, where the D-ring has been masked for con?dentiality reasons. This phenomenon is an issue because it might prevent the restraint systems connected to the webbing from working in a normal manner (pre-tensioner, load limiter). In the face of such a problem, various studies [1?C4] have been carried out to control this phenomenon and needed to be pursued. 2. Analysis of the phenomenon based on sled tests To develop restraint systems, numerical simulations are conducted and to con?rm the airbag and the seat belt performances, dynamic sled tests are performed. A sled is a mechanical welded assembly developed to simulate the car interior. The anchorage points of the seat belt are positioned in accordance with the car project speci?cations. The dashboard geometry is reproduced using foams and seat prototypes are used. The bunching phenomenon was occasionally observed during these non-destructive sled tests. Previous studies [1] have shown that during this type of test, the plastic deformations of the crash frame are not reproduced and the corresponding absorbed energy is transferred to the webbing (no deformation of the B pillar on which the D-ring is ?xed, no deformation of the car ?oor on which the seat is ?xed, no dynamic pitch of the car body). The load applied to the seat belt webbing (measured locally by speci?c load cells) is thus often higher than the load measured during the corresponding complete vehicle crash tests. Sled tests are known to overload the webbing and to maximize the seat belt bunching likelihood. To expertize belt behaviours, frontal sled tests campaigns were performed. Based on this experimental approach, designs of experiments have permitted to point out that one of the major factors which in?uence the phenomenon is seat belt geometry [1]. Several risky seat belt geometries have been then de?ned but no generic assessment has been developed to explain the seat belt bunching phenomenon. To pursue the research, a critical analysis of the design of experiments results was proposed. It appears that two consecutive and supposed identical tests may result in two different local behaviours of the ring (bunching for the ?rst one and no bunching

     for the second one). For instance, sled tests performed with two seats on the same platform (and thus the same pulse, the same dummies, the same belt geometries) gave different results: bunching on one side and no bunching on the other side (see Fig. 3). This status questioned the initial condition of the seat belt webbing and D-ring interactions. An analysis of the initial lateral position of the webbing on the D-ring was then conducted (see Fig. 4, where the D-ring has been masked for

    con?dentiality reasons). This critical analysis underlined an unexpected factor which in?uences the bunching likelihood, the initial position of the webbing according to the D-ring slot corners. A tiny variation of the webbing position can modify or delay the bunching phenomenon. The initial positioning of the webbing on the D-ring was not known at ?rst as being an in?uential factor on the crash test results because it is usually not a factor under control. Several points can explain this insuf?ciency: ?C The initial position of the webbing on the D-ring is a consequence of the belt geometry. Moreover, the size of the dummy (Hybrid III 05, 50 or 95%ile) and the seat position (slide position, height adjustment position) also vary the webbing/D-ring boundary conditions. ?C It is also controlled by component speci?cation, the friction level between the D-ring and the webbing, the friction value between the webbing and the dummy, the spring strength inside the retractor and the webbing slack resulting from the manual buckling of the seat belt on the dummy??s body. ?C The dynamic ring technology has also an in?uence on the webbing positioning on the D-ring. In a case of a direct crash test (sled decelerated using deformable bumpers), the initial webbing position is often modi?ed by the tiny sways of the dummy during the acceleration phase. These perturbations can potentially be reduced by the use on an inversed crash sled (sled accelerated using hydraulic valves), but as the seat belt bunching phenomenon is an instability problem, small variations of the sled pulse can also interfere with the webbing behaviour. The critical analysis of the results of various designs of experiments shows that experimental studies based on sled tests are helpful to investigate the phenomenon but do not lead to a ?nal solution to the instability of D-rings. They enable listing of several important in?uential factors and show tendencies. Detailed analysis proved that sled dynamics tests are not adapted to the study of the webbing/D-ring interactions, because this test method provokes local dispersions which have an effect on the ?nal result of the experiments. Numerous sled tests would be necessary to evaluate the trends according to the initial position of the webbing on the D-ring, but the high cost of these sled tests does not enable such methods to be pursued.

     Fig. 2. Seat belt bunching phenomenon.

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     Fig. 3. Sled test with two Hybrid III 95%ile dummies.

     3. Analysis of the phenomenon based on global sub-system tests To complete the analysis of the seat belt bunching phenomenon, a global sub-system test, called the Webbing Guide Drop Test (WGDT) has been used [5]. The principle of this bench is: a half cylinder drop

    weight, ?xed to the sled of a drop test, impacts a horizontal webbing portion between a set of rods (see Fig. 5). The horizontal webbing portion is then pulled and the shoulder belt reels out. The D-ring is screwed on a vertical column. Its column is oriented at 45 to facilitate the shoulder belt orientation. The total energy applied to the system is controlled by the mass and the speed of the impactor. Experimental campaigns showed that the WGDT is a consistent method to test D-ring in dynamic loading conditions. With this device, the D-ring??s instability can be easily reproduced (see Fig. 6) with loading levels and scrolling speeds equivalent to those observed during R16 sled tests [6]. The advantage of this test method compared to the sled test is that results are completely repeatable and the cost per experiment is low compared to dynamic sled tests. The use of the WGDT to investigate the seat belt bunching phenomenon enables us to complete the global understanding of the webbing behaviour. It con?rms that the initial position of the webbing in?uences the global stability of the ring. Nevertheless to assess and to solve the ring??s instability; a local analysis of the webbing has been carried out. 4. Analysis of the phenomenon based on local sub-system tests Based on sled test results and the WGDT results, the need for a local sub-system test has emerged [7]. 4.1. Sub-system test To reduce the variance of designs of experiment based on sled test and to focus the study on the behaviour of D-rings, a sub-system

     test method is required. Thus, an innovative experimental bench was developed by Autoliv of North Germany [8,9]. 4.2. Experimental set-up This innovative experiment called WGRAT (Webbing Guide Rotative Arm Test), consists in two main parts (see Fig. 7) ?xed on a quasi-static tensile test machine: ?C Part 1: a support structure with a rotating arm on which the Dring is ?xed. ?C Part 2: a ?xture on which the retractor and a load cell are mounted. This mechanism has a multi-angle rotative arm, which allows reproduction of all the belt orientations seen in an automotive vehicle. It is usually ?xed to the lower jaw of a tensile test machine. For each test, a retractor is mounted on the device, the D-ring is ?xed on its axle and the webbing is set through the ring. Then the free end of the webbing is ?xed to the upper jaw of the tensile test machine. The experimental ?xture (see Fig. 8) enables loading of the D-ring in similar loading conditions to a sled test. The use of two devices of angle variation allows re-creation of the seat belt curvature through the D-ring. Compared to a real car set-up, the loading conditions are varied as follows: ?C The position of the retractor and the position of the loading webbing end are reversed. ?C The loading direction is constant (during a sled test, the dummy is moving forward and the loading direction is varying). ?C The speed of loading is limited by the pulling device speci?cation (it can reach up to several metres

    per second during a sled test). No deceleration pulse is applied to the D-ring and to the webbing.

     Fig. 4. Initial lateral positions of the webbing on the D-ring.

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     Fig. 5. WGDT principle.

     5. Experimental analysis based on WGRAT The local assessment on the seat belt bunching phenomenon based on experimental tests has been pursued in two steps: ?C For dynamic loadings, using a hydraulic jack and a high speed video camera. ?C For quasi-static loadings, using a tensile test machine and a Digital Images Correlation for strain distribution measurement.

     initially in a central position, slides laterally and bunches in the left corner of the ring at 22 ms (see Fig. 10). These dynamic tests enable visualization of the deformation of the vertical belt portion. Initially ?at, the webbing deforms and several weaves appear on the surface close to the ring. In parallel, the analyses of horizontal lines drawn on the belt show discontinued local perturbations which grow until bunching. 5.3. Quasi-static WGRAT test set up During a second step, the WGRAT device was used for quasistatic loadings to evaluate the strain distribution through the webbing (see Fig. 11). To complete the assessment of the seat belt bunching phenomenon, an analysis of the strain distribution through the webbing during the instability issue was carried out. In order to study the strain ?eld distribution over the seat belt webbing during the bunching phenomenon, tensile tests, performed on an INSTRON? tensile test machine, were undertaken and postanalysed by GOM/ARAMIS? Digital Images Correlation system [10]. To enable the strain measurement, the specimens needed preparation. For this purpose, a very thin layer of white ?exible silicon was spread on the surface of the vertical portion of webbing. A black colour spray was next applied to obtain an irregular contrast pattern. During these quasi-static tests, the following set-up was used: ?C Retractor without load limiter (to reduce the reel-out distance of the webbing through D-ring and to focus on the analysis area). ?C 45 /45 belt geometry. ?C The webbing was positioned in the middle of the D-ring.

     5.1. Dynamic WGRAT test set-up The WGRAT device was adapted to dynamic loadings to obtain the same outlet speed of the webbing through the webbing guide as the speed measured during dynamic sled tests (see Fig. 9). Thus, the ?xture was mounted on a high-speed hydraulic jack at ONERA Lab. Centre, Lille (The French Aerospace Laboratory). The frame is made of two vertical columns ?xed on the ground (2.5 ? 2.5 m2). This is ?xed to a 40 ton seismic mass suspended and damped. The columns are connected by a horizontal crosspiece to two degrees of freedom, on the

    middle of which the hydraulic jack is mounted. Its loading capacity is 50 kN in dynamic. Its maximal speed is close to 10 m/s. The cylinder travel exceeds 250 mm. Its guidance is obtained by hydrostatic bearings and allows radial loadings. 5.2. Dynamic WGRAT test result For a 200 mm jaw displacement at 3.5 m/s and a 45 /45 angle between the vertical belt and the diagonal belt, the webbing,

     Fig. 6. Bunching phenomenon generated with the WGDT.

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     Fig. 7. Components of the WGRAT.

     ?C The loading speed was ?xed at 100 mm/min. ?C The camera frame was ?xed to one frame per second. ?C A 1240 ? 1240 pixels resolution digital video camera was used. The sample was installed in the tensile testing machine and the ARAMIS system was calibrated and positioned in front of the sample (see Fig. 12). During the tensile tests, a camera recorded the 2D displacements of the splash pattern. At the same time, the displacement of the jaw, the tensile load and the retractor load were recorded. A Digital Images Correlation of the movie pictures was performed to measure the longitudinal and transversal strain distributions. This method enabled quantitative capture of the development of an unbalanced strain ?eld of the webbing before and during the bunching phenomenon. 5.4. Quasi-static WGRAT test results Three repeatable tensile tests were performed. During these tests, left bunching phenomena occurred. The two main directions

     Fig. 9. Experimental ?xture mounted on a high-speed hydraulic jack at ONERA-Lille.

     of the strain tensor were calculated and they showed different behaviours. The measurement ?eld, size about 10 ? 4 cm2, was located in the centre of the specimen where the largest deformation was expected. Finally, the deformation behaviour in the whole measuring area was observed in real time until bunching. By eliminating the jaw movement of the specimen, the local deformation of the specimen surface can be made visible. By a mathematical derivation of these images, the strains were determined and displayed as a whole ?eld distribution (isolines of equal strains). The distribution epsilon X and epsilon Y was calculated and graphically shown by plotting strain curves variation exported to a speci?c ASCII-format. Thus, the behaviour of the sample during the test was able to be evaluated and displayed graphically. 5.4.1. Transversal strain The analysis of the deformation of the seat belt webbing (in the weft direction) shows a homogeneous and a strain distribution close to zero of the webbing before the bunching phenomenon. As soon as the webbing begins to bunch, the out-of-plane deformation of the samples disturbs the measurement. 5.4.2. Longitudinal strain

    The analysis of the longitudinal strain of webbing shows that its behaviour varies in several stages. ?C From 0 to 34 mm, a homogeneous distribution of the longitudinal strain can be seen on the webbing sample (see Fig. 13). ?C At 34 mm, a dissymmetry of the longitudinal strain appears and this dissymmetry increases from 34 to 67 mm. At that stage, the difference between the strain values calculated on the right edge and the ones calculated on the left edge of the webbing sample reaches 30% (see Fig. 14). This phenomenon was computed along several sections of the webbing (see sections 1?C5, Fig. 14). An increasing difference reaching more than 2% of longitudinal strain value (a variation of 30% between

     Fig. 8. WGRAT mounted on a quasi-static tensile test machine.

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     Fig. 10. Experimental case of bunching with the WGRAT.

     each edge, see Fig. 15) was measured between the two edges of the webbing before the overturning of the D-ring. ?C At 68 mm, the bunching phenomenon begins, and 15 mm later the bunching phenomenon is completely achieved (see Fig. 16). ?C After bunching, at 83 mm, the out-of-plane deformation of the sample disturbs the measurement in the centre of the specimen but the edges deformation can be assessed. For each edge, the longitudinal strain reaches the same average value: 9% (see Fig. 17). Judging from the results obtained by the Digital Image Correlation method, the phenomenology of the seat belt bunching phenomenon can be discussed. At the beginning of the test, the belt is uniformly loaded, thus the system is in equilibrium. As disequilibrium appears, the longitudinal strain distribution becomes inhomogeneous along the width of the webbing. That unbalanced strain distribution grows up to reach a 30% variation between each edge of the webbing and leads to the instability of the system by the overturning of the Dring. The system has reached a new stable state with a symmetric strain distribution. At that stage, the dissymmetry of the strain distribution and the D-ring rotation appear to be synchronized. To complete the results obtained with the Digital Image Correlation method and to pursue the assessment of the bunching phenomenon, a ?nite element (FE) numerical model of D-ring/seat belt interactions has been developed. The use of this numerical tool aims towards organizing into hierarchy the factors in?uencing the stability of D-rings.

     6. Numerical analysis based on WGRAT tests To complete the experimental analysis of the seat belt bunching phenomenon based on the WGRAT dynamic and quasi-static test results, a numerical analysis is proposed. A speci?c FE model of seat belt webbing is developed. Based on the numerical innovation, the experimental tests described in the

    previous section are modelled. 6.1. FE modeldnew shell ?nite element model for webbing To improve the ?nite element model of seat belt webbing fabric, an innovative shell ?nite element is developed using Pam-Crash? packages [11]. This shell element takes into account the low but effective bending stiffness of the seat belt webbing by the use of a plate bending element with a decoupled and orthotropic bending stiffness. According to the results of tests on seat belt webbing, a method to simulate its behaviour was studied. To evaluate its stability, it is applied to realistic belt geometries and loadings. The global behaviour of seat belt webbings corresponds to the behaviour of a fabric. Fabrics are usually modelled with membrane elements, which do not take the bending stiffness into account. This method has proved to be satisfactory for the simulation of thin fabrics, such as fabrics used for airbags, but cannot be extrapolated to the case of seat belt webbing because the bending stiffness cannot be neglected during the bunching phenomenon. Thus a new simulation method was used to model the behaviour of seat belt webbings. It consists in the superposition of two layers of shell ?nite elements (see Fig. 18.). The two layers are

     Fig. 11. Sample with splash pattern during a tensile test.

     Fig. 12. Camera of the ARAMIS measuring system and lights.

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     Sections S1 Long. Strain

     S2 2 S3

     S4

     S5

     Fig. 13. Variation of the longitudinal strain distribution at 16 mm.

     de?ned with the same nodes and the density of each layer corresponds to half the density of seat belt webbings. The ?rst layer is a membrane element usually used for fabric element; it de?nes the membrane behaviour. The ?rst part of this model corresponds to the membrane stiffness. Its main use in the ?eld of dynamics is the simulation of airbag fabric. This material corresponds to a linear elastic membrane material which consists in two families of ?bres, running at given angles in two directions, embedded in an isotropic matrix. The following general relationship between membrane stresses and strains describes the general isotropic case.

     fabric 2 3 0

     t

     isotropic matrix layer 2 at 90 2

     t 3

     layer 1 at 0 2 3

     s11 0 E1 0 0 1 n 5t4 0 0 0 5 4 s22 5 ? @ Em 4 n 1 0 1 ?? n2 0 0 e1 ?? nT=2 s12 0 0 G1 2 312 3 311 0 0 0 t 4 0 E2 0 5A4 322 5 g12 0 0 G2

     (1)

     Where Em is the Young??s modulus of the isotropic matrix, E1 and E2 are Young??s tension/compression moduli of the threads, G1 and G2 are shear moduli and n is Poisson??s coef?cient. This element is formulated in a total Lagrangian approach, in which the Green?CLagrange strains (3GL ? 1/2(L2 ?? L2)/L2) and the 0 0 second Piola?CKirchhoff stresses are used (sPK ? (L/L0) E 3GL). This element is completely integrated by four Gaussian points. The second part of the model corresponds to a bending plate stiffness based on a Mindlin shell element [12]. This plate bending element [11] is usually used in the ?eld of non-linear dynamic loadings to simulate the behaviour of composite ply made of two components, the ?bres and a matrix. Then, the behaviour of uni-directional continuous ?bres reinforced composites is modelled with this shell using the superposition of plies composed of two phases: a uni-directional ?bres phase and an orthotropic matrix phase (see Fig. 19). The original aspect of this numerical model is the distinction of these two phases. Each phase of each ply is de?ned independently in tension and in compression. For each ply, the stiffness is calculated by superposing the effects of the orthotropic elastic matrix (matrix minus ?bres) and of the one-dimensional elastic ?bres (see Fig. 20).

     Sections S1 Long. Strain 8 7 S3 6 S4

     S2

     S5

     Fig. 14. Variation of the longitudinal strain distribution at 67 mm.

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     Sections Strain

     11 10 9 Longitudinal Strain (%) 8 7 6 5 4 3 2 1 0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 S1 S2 S3 S4 S5

     Webbing width (mm)

     Fig. 15. Longitudinal strain distributions for different sections of the webbing at 67 mm.

     Sections S1 Long. Strain 10 9 S3 8 S4

     S2

     S5

     Fig. 16. Variation of the longitudinal strain distribution at 83 mm.

     11 10 9 Longitudinal Strain (%) 8 7 6 5 4 3 2 1 0 0 2 4 6 8 S1

     Sections Strain

     S2

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