SIMULATION OF NON-RIGID PRODUCTS: AN INDUSTRIAL APPLICATION RELATED TO CAR SOFT TOP DESIGN Benassi M., Colombo G., Cugini U., and Rizzi C. Dipartimento di Ingegneria Industriale Parco Area delle Scienze 181/A 43100 Parma Italy E-mail: [colombo, cugini, rizzi]@ied.unipr.it

KEYWORDS: Physically based modeling and simulation Mechanism analysis, Non-rigid parts.

ABSTRACT This paper addresses the problem of predicting the inservice behaviour of non-rigid product, i.e. the simulation of product functionalities under operating conditions within a Digital Mock-up. Think, for example, to the design of a car soft-top: while today, with the aid of common computerbased tools, it is rather simple to design and simulate the kinematic mechanism of opening/closure, it is not so easy to understand how it is influenced by the covering material. To this end we have used a commercial system for mechanism analysis and a tool, named SoftWorld, which permits to model and simulate the behaviour of non-rigid parts (sunroof fabric) taking into account material properties. SoftWorld adopts a particle-based model by which an object can be represented by a set of particles connected by forces describing the objects mechanical behaviour. Using the integrated environment we have studied and simulated the opening/closure mechanism of a convertible car soft-top integrated with covering materials behaviour. 1.

INTRODUCTION

In several industrial sectors, such as automotive, aerospace and textile, the design of system containing non-rigid materials is very important. In these contexts, modelling and simulation of systems with rigid and deformable parts are attracting more and more people, from both research and industrial communities. In this paper, we address the problem of predicting the in-service behaviour of non-rigid product, i.e., the simulation of product functionalities under operating conditions within a Digital Mock-up (DMU) referring to a car soft top as applicative example. We present the preliminary results of a research activity conducted within the framework of the European BriteProject DMU-FS (Digital Mock-Up – Functional Simulation (http://kaemart.unipr.it/dmu-fs). The consortium consisted of four end-users (Volkswagen-Project Leader, Alenia, Daimler Chrysler, and Renault), three IT Vendors (Dassault Systemes, LMS International, and Samtech) and two

research institutes (IGD-FhG, and Università di Parma). One objective has been the feasibility of models and techniques, independently developed and applied in different contexts, which can be appropriately integrated to study the considered mechanical system. Even if, with the aid of common computer-based tools, it is rather simple to design and simulate the kinematic mechanism of soft-top opening/closure, it is not so easy to understand how it is influenced by the covering material. In the following, we describe the approach adopted to perform the simulation of the sunroof fabric. First results of experimentation are presented as well as work in progress related to the integrated simulation with a commercial system for kinematic and dynamic analysis, named DADS (LMS International). 2.

TECHNIQUES AND TOOLS USED

In literature, different approaches can be found, and some models and techniques are well known and used to solve mentioned design problem. We considered multibody and physically based techniques the most suitable for our purposes. The first one can be adopted for the kinematics and dynamic analysis of the soft top mechanism, while the latter to model and simulate the fabric deformation when opening an closing the soft-top. In the following, multi-body and physically based modelling techniques are briefly introduced. 2.1 Multibody Techniques In the last decades, multibody techniques have been developed to implement software packages for the kinematics and dynamics of planar and spatial chains. The analytical model of a kinematic chain is defined by the generalised Cartesian coordinate of each body qi=[Ri, θI] for a planar motion. The joints among bodies and motion constraints (motion laws, imposed trajectories, etc.) are translated into constraint equations (1). Varying independent coordinates the numerical solution of (1) permits to determine the chain configuration.

[

]

Φ (q, t ) = Φ 1 (q, t ),...., Φ n (q, t )

T

=0

(1)

For what concerns velocity and acceleration analyses, (2) and (3), derived from (1), permit to solve the problem. © SCS

Φ q q& = − Φ t

d

(2)

iq

Φq && q = − Φq q& q& − 2 Φqt q& − Φtt

(3)

where Φ q is the Jacobian matrix. For what concerns the dynamics analysis of a system with constrained rigid bodies, we are interested in the study of the motion due to applied forces. Motion equations can be derived from the principle of virtual work. The approach is described in (Haug 1989) and constitues the theoretical basis on which DADS package (LMS International) has been developed. Figure 1 portrays the soft top mechanism modelled with DADS.

Figure 1: Mechanism model 2.2

Physically based Techniques

Regarding modelling and simulation of deformable parts, several techniques can be found in literature: geometrybased, physically based, and hybrid (Cugini et al. 1999). Physically based models, in particular discrete ones, seem to be the solution to our problem (Witkin 1992). Among the discrete models, the particle-based one, force-based version, is the most known and used within research communities for fabric modelling and simulation (Breen and House 1994) (Carignan et al. 1992) (Eberhardt and Weber 1996) (Hing and Grimsdale 1996) (Siggraph 1998) (Volino and Thalmann 1997) (House and Breen 1998). By this approach, an object is described as a set of particles with mass, volume and other physical properties. The material behavior is modelled by forces acting on the particles and depending on material properties. The simulation is carried out using the Newton law: f = ma. The resulting mathematical model of a particle system is a system of 2nd order ODE, that can be reduced to a 1st order equivalent system and, therefore, solved step by step with numerical integration. Most of simulation tools, based on this model, are mainly oriented to computer graphics or animation, and their main goal is to produce images that look real. Cugini et al. developed a system (Frugoli et al. 2000), named SoftWorld,

specifically targeted to industrial applications taking into account that in industrial sectors both physical accuracy and visual realism are required (Rizzi et al. 2000). Therefore, we decided to use SoftWorld to model and simulate the behavior of sunroof fabric. SoftWorld is based on the particle-based model, force-based version. However, to simulate the behaviour of a deformable part, like sunroof fabric, we must also manage interactions between the sunroof and surrounding environment and constraints that the deformable part must respect (e.g., fixed positions as connections point to the mechanism and mechanism trajectory). Therefore, SoftWorld has been extended to fulfill project objectives. Our modelling and simulation system take into considerations external forces, constraints and collisions with obstacles. External forces, such as gravity and aerodynamics forces, are treated as the internal ones. Constraints restrict the movements of a part; they are conditions that must be respected by the object during its motion. To handle constraints, the dynamic constraints technique (Platt and Barr 1988) has been implemented. It permits to apply multiple constraints to the same particle and ensures the respect of all the constraints at each step of the simulation. Collisions with obstacles occur when a flexible object hits a rigid object or penetrates itself (self-collision). Collision management involves two aspects: collision detection and collision response (Cugini et al. 1999). The first is often the bottleneck of deformable objects simulation systems handling highly discretised objects. The high number of particles and surface elements forces the simulator to execute a continuous check of the possible situations of collision and takes a great part of the simulation time. To speed up the searching process, we employed the method of bounding boxes, a good compromise between simplicity and efficiency (Provot 1997). 3.

CAR SOFT TOP MODEL

As previously mentioned, we used two tools: SoftWorld, developed at University of Parma for physically based modelling and simulation, and, DADS, a commercial system for multibody analysis. In the following we describe the particle based model generated for the sunroof. 3.1

Physically based model of the sunroof

For the sunroof simulation, it is necessary to generate the particle-based model of the sunroof. Following steps have been performed: § § § §

from the PMU (Physical Digital Mock-Up), the 2D panels composing the sunroof have been defined; 2D panels have been discretised according to the adopted model; forces among particles have been defined and physically characterised; 2D panels have been sewed around the mechanism.

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2D panels definition We derived the geometry of the 2D panels composing the sunroof from the sunroof PMU provided by Karmann. Figure 2 shows the derived 2D panels.

1980) (Breen and House 1994). In this case, it was not possible to use such a system because of sunroof fabric thickness and main tests (e.g., bending) could not be carried out. Therefore, we decided to extrapolate necessary data from those acquired for multi-layered fabric; for a more precise model, it should be necessary to perform proper experimentations. Sewing 2D patterns To sew a pair of panels, the edges identified as seaming lines must have the same number of polygon segments with the same length. The discretisation algorithm, above mentioned, takes into account this problem and two panels can be sewed welding them along the seaming line. The particles on the border of first panel are deleted and replaced with particles on the border of the second panel. Spatial positions and assembly rules of the 2D patterns have been derived from the 3D model (.stl file) of the sunroof provided by project partners. Figure 3 summarises the procedure followed to generate th 3D assembled physical model of the sunroof, where particles have been highlighted.

Figure 2: Sunroof 2D models 2D panels discretisation Even if the sunroof fabric is a three-layered material, we adopted, for the first tests, a simplified model representing the fabric as composed by a single equivalent layer. We discretised each 2D panel with a rectangular grid of particles having a grid step of 25 mm. When dealing with fabric-like material, as in this case, the two directions of the grid model the warp and weft directions. Material anisotropy can be simulated by characterising differently the forces along the two directions. The edges of the 2D panel constituting the sunroof have required particular attention. The implemented algorith, first, places a particle at each vertex of the 2D pattern contour; then adds other particles along the pattern edges to have roughly the same resolution presents in the inner part. The algorithm splits edges recursively based on the grid step. Forces distribution The internal forces model the mechanical behaviour of material. Because of experience carried out in other industrial contexts (e.g., clothing) (Cugini et al. 1999) (Rizzi et al. 2000), following forces have been: § Stretching and repelling forces applied between pairs of particles that tend to keep particles at the rest distance; § Bending forces applied to a line of three particles that keep them aligned; § Trellising (shear) forces that acts over squared cells of four particles and contrast deformations on the plane. Springs and bending forces have different characterisation in warp and in weft directions. Usually fabric parameters characterizing the dynamic behaviour are derived from KES (fabric Kawabata Evaluation System) measurements or similar (Kawabata

Figure 3: Procedure to generate sunroof particle model Figure 4 and 5 show other two views of the sunroof initial configuration. 4.

EXPERIMENTATION

The simulation has been carried following two different approaches: off-line simulation and integrated simulation DADS-SoftWorld.

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Figure 4: Sunroof initial configuration (wire-frame)

data must be passed from DADS to SoftWorld and vice versa at each integration time step (Figure 7). DADS transfers to SoftWorld the calculated boundary conditions (position of the points where the fabric is connected to the mechanism bodies). Forces acting on the fabric connection points calculated by SofWorld, are applied to the mechanism model in DADS. To implement this data transfer, the DADS solver is extended, so that it writes out the kinematics data and reads in the corresponding reaction forces at each time step. Similarly, a new version of the SoftWorld, named NetSoft, has been implemented by using sockets. This activity is currently in progress and simple tests have been carried out in order to verify the communication between the two packages. Results have been considered encouraging even if some problems related to the determination and synchronisation of the time step are still open.

Figure 5: Sunroof initial configuration (shaded) 4.1

Off-line simulation

Off-line simulation means that the simulation of the opening/closure mechanism and the covering material have been carried out using independently DADS and SoftWorld. The main objective has been to verify the feasibility of our approach. Once the physical model has been defined, we proceeded as follows: § using DADS, the mechanism kinematic analysis has been performed to get data on the trajectories of connecting points; § the input file for SoftWorld containing the trajectories of the mechanism connecting points has been generated; § the simulation has been executed using SoftWorld and visual verification of the capote behaviour. Concerning the first step, the 3D model of the mechanism (Figure 1) has been provided by the partners of the project and, as mentioned above, we used it to recover trajectories and points where the soft-top fabric is connected to the mechanism parts. Figure 6 portrays some steps of the simulation.

Figure 6: Some steps of the simulation

Constraints at n Integration step

Multi Body Code

Sun roof particle model

NetSoft Forces at connecting points

Sun roof Simulation

Mechanism Simulation

Car soft top Simulation

Figure 7: DADS-SoftWorld integration CONCLUSIONS

4.2

Integrated simulation DADS-SofWorld

In this case, we integrated the multibody code DADS with SoftWorld. In fact, to simulate the mutual interaction between the mechanism of the car soft-top and the fabric,

New software tools are essential for modelling and simulate product functionalities under operating conditions within a Digital Mock-up. They must integrate some tools now independent and self-contained. In this paper, we described © SCS

preliminary results related to the simulation of a car soft top carried out using a prototype developed at the University of Parma, Department of Industrial Engineering and a commercial system for kinematic and dynamic analysis. The tests allow us to verify the approach adopted (i.e., the particle-based model) and potential of the system. The results are encouraging and they demonstrate that the approach is effective for representing and evaluating the behavior of system with non-rigid parts. Future activities will concern the execution of experimental tests in order to get mechanical data of the sunroof fabric and to go on experimenting the integration with a commercial system and execute the co-simulation.

Siggraph 1998. 1998. “Cloth and Clothing in Computer Graphics,”. Course Note No. 31. Volino P. and N. Thalmann, 1997. “Developing Simulation Techniques for an Interactive Clothing System”. In Proceeding VSMM 97, IEEE Computer Society, 109-118. Witkin A. 1992. “Particle System Dynamics”. In Proceeding 19th International Conference on Computer Graphics and Interactive Techniques, ACM Siggraph 92 (Chicago, Il, July).

AKNOWLEDGEMENTS The authors would like to thank the EU Commission for funding our projects in this area, and our colleagues that participated to the research projects on non-rigid materials modelling and simulation.

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