Design and Simulation of a Car Soft Top - Semantic Scholar

XII ADM International Conference - Grand Hotel - Rimini – Italy - Sept. 5th-7th, 2001

Design and Simulation of a Car Soft Top Giorgio Colombo, Michele Prati, and Caterina Rizzi Dipartimento di Ingegneria Industriale, Università di Parma Parco Area delle Scienze 181/A – 43100 Parma

Abstract This paper addresses the problem of predicting the in-service behaviour of deformable product, i.e., the simulation of product functionalities under operating conditions within a Digital Mock-up. We have considered the design of a car soft-top; while today, with the aid of common computer-based tools, it is rather simple to design and simulate the kinematic mechanism of opening/closure, it is not so easy to understand how the covering material influences it. Moreover, the way the deformable material behaves may lead to malfunctions and damages of the overall structure. To this end we have used a tool, named SoftWorld that permits to model and simulate the behaviour of non-rigid materials, in our case the 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. 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 co-simulation with the commercial system DADS for kinematic analysis. 1.

INTRODUCTION

In the context of virtual prototyping, modelling and simulation of systems with rigid and deformable parts are attracting more and more people from both research and industrial communities. In literature, different approaches can be found, and some models and techniques are well known and used to solve such design problems. For example, in some cases, the effects of deformable parts on those rigid can be modelled by springs or dampers that apply forces exerted by deformable parts to rigid ones. However, for other categories of problems, this approach does not produce satisfying results, because it could be also necessary to study the deformation of non-rigid parts. The design of a car soft top is an interesting example of this problem. In this paper, we present preliminary results of a research activity whose main objective has been the feasibility of models and techniques, independently developed and applied in different context, which can be appropriately integrated to study the considered mechanical system. These are the multi-body and physically based techniques; 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.

A7-1


In the following, multi-body techniques and physically based modelling are briefly introduced. From the middle of 50’s, 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 co-ordinate of each body qi=[Ri, θI]. The kinematic pairs (joints) among the chain bodies and motion constraints (motion laws, imposed trajectories, etc.) are translated into constraint equations (1). Varying independent coordinates (degrees of freedom) the numerical solution of (1) permits to determine the chain configuration.

[

]

Φ (q, t ) = Φ 1 (q, t ),...., Φ n (q, t ) = 0 T

(1)

For what concerns velocity and acceleration analyses the (2) and (3), derived from (1), permit to solve the problem. Φ q q& = − Φ t (2)

d

iq

&& = − Φq q& q& − 2Φqt q& − Φtt Φq q

(3)

The dynamics analysis of a system with constrained rigid bodies is the study of the motion due to applied forces. Motion equations can be derived from the principle of virtual work. The approach briefly described is presented in [1] and constitues the theoretical basis on which DADS package, used in our research activity, has been developed. Regarding modelling and simulation of deformable objects, several techniques can be found in literature. They can be classified into three main categories: geometry-based, physically based, and hybrid [2]. Physically based approach seems to be the solution to our problem; within this category, discrete models are particularly interesting [3]. They describe a deformable object by combining very basic mechanical elements and behaviour simulation is carried out by computing the interaction laws among the elements. The discrete model, named particle-based, is the most known and used within research communities mainly for fabric modelling and simulation [4], [5], [6], [7], [8], [9], [10], [11], [12]. We can distinguish two techniques: energy based, and force based [13], [14]. The first technique cannot produce the dynamic response required for animation, therefore usually the force-based is the most suitable for modelling and simulating fabric [13]. Adopting the force-based version, an object is described as a set of particles with their mass, radius and other physical properties and the interaction laws among the particles are modelled by forces and constraints that determine the dynamic behaviour of the material. 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 ordinary differential equations, that can be reduced to a 1st order equivalent system and, therefore, solved step by step with numerical integration. However, most simulation tools, based on mentioned model, are mainly devoted to computer graphics or animation where main emphasis is on the production of images that look real. Cugini et al. developed a system [15], named SoftWorld, specifically targeted to industrial applications taking into account that in industrial sectors it is not sufficient to produce simulations that look real, but both physical accuracy and visual realism are required [16]. In this paper, we address the problem of predicting the in-service behaviour of nonrigid product, i.e., the simulation of product functionalities under operating conditions within a Digital Mock-up referring to a car soft-top as applicative example.

A7-2


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 co-simulation with the commercial system for kinematic and dynamic analysis, named DADS (LMS International). This research has been carried out within the framework of the European Brite-Project DMU-FS (Digital Mock-Up – Functional Simulation (http://kaemart.unipr.it/dmu-fs). 2.

A CAR SOFT-TOP MODEL

For our application, two tools have been considered: SoftWorld, developed at University of Parma for physically based modelling and simulation, and, DADS, a commercial system for multibody analysis. Before describing sunroof model, we briefly introduce the system. 2.1

SoftWorld

SoftWorld has been specifically developed to model non-rigid objects and to simulate their behaviour for industrial applications [15] [16]. It adopts the particle-based model, forcebased version. Simulating the behaviour of a deformable object, like sunroof fabric, is not sufficient to consider only internal forces, we must also manage interactions between the object (the sunroof) and surrounding environment and constraints that the object must respect (e.g., fixed positions as connections point to the mechanism and mechanism trajectory). Therefore, SoftWorld has been extended in order to be able to simulate sunroof behaviour and interaction with the mechanism. We have taken into considerations: § External forces, such as gravity and aerodynamics forces, treated as the internal ones; § Constraints that restrict the movements of a part (conditions that must be respected by the object during its motion); § Collisions with obstacles, for example, when a flexible object hits a rigid object or penetrates itself (self-collision). To handle constraints, the dynamic constraints method has been implemented since it permits to apply multiple constraints to the same particle and ensures the respect of all the constraints at each step of the simulation [17]. The main drawbacks of this approach are the high computational cost and the numerical problems when the linear system becomes ill conditioned. Collision management involves two aspects: collision detection and collision response [2]. 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 [18]. The collision test between two objects can be safely skipped when their bounding boxes do not intersect. This method must be improved in some way because a soft object could self-collide. We approach this problem by splitting objects into regions and considering the bounding box of each region. Another aspect is the possible collision with a rigid part of the opening/closure mechanism with fixed position. There are two possible approaches to rigid objects collisions: integration with particles or ad hoc solution. We adopted the second solution by which it is not necessary to solve the linear system required by the dynamic constraints, thus saving a lot of time. The rigid objects keep fixed position or trajectory so it is very easy to compute directly the correct collision response.

A7-3


2.2

Physically based model of the sunroof

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

Derive from the PMU (Physical Digital Mock-Up) the 2D panels composing the sunroof; Discretise 2D panels according to the adopted model; Define forces distribution; Sew the 2D panels around the mechanism.

2D panels definition This activity was performed because of the geometry of the 2D panels was not available from the partners of the project. We derived them from the sunroof PMU provided by Karmann and from the 3D STL model to get information regarding position and assembly rules of the 2D patterns. Fig. 3 shows the derived 2D panels.

Fig. 3 – Sunroof 2D panels 2D panels discretisation Even if the sunroof fabric is a three-layered material, we decided, for the first tests, to adopt a simplified model. We modelled the fabric as composed by a single equivalent layer. We discretised each 2D panel with a regular grid of particles (Figure 4) connected by a set of forces describing the fabric mechanical properties. When dealing with fabric-like material, as in this case, the two directions of the grid model the warp and weft directions and it is possible to simulate material anisotropy by characterising differently the forces along the two directions. Particle j

Fig. 4 – Fabric discretisation rule

A7-4


The edges of the 2D panel constituting the sunroof require particular attention. First, we place a particle at each vertex of the 2D pattern contour; then we add 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 characterise the mechanical behaviour of material. Because of experience carried out in other industrial contexts (e.g., clothing) following forces have been used to model the mechanical behaviour: § 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 within 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 [4]. 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 couple 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. Fig. 5 shows the assembled physical model of the sunroof, where particles have been highlighted.

Fig. 5 - 3D sunroof physical model

A7-5


3.

EXPERIMENTATION

The simulation has been carried out into two steps: off-line simulation and co-simulation DADS-SoftWorld. 3.1

Off-line simulation

In this case, the simulation of the opening/closure mechanism integrated with covering material behaviour has 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 (see § 2.2), we proceeded as follows: 1. Mechanism kinematic analysis using DADS has been carried out in order to get data on the trajectories of connecting points; 2. Generation of the input file containing the trajectories of the mechanism connecting points; 3. Execution of the simulation using SoftWorld and visual verification of the capote behaviour. Concerning the first step, the 3D model of the mechanism 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. Fig. 6 shows some step of the simulation.

Fig. 6 – Some simulation steps 3.2

Co-simulation DADS-SofWorld

Second step, currently in progress, considers the co-execution of the sunroof simulation; this required the integration between DADS and SoftWorld. In order to simulate the mutual interaction between the structural moving parts of the soft-top sunroof and the fabric, data must be passed from DADS to SoftWorld and vice versa at each integration time step. This means that DADS transfers to SoftWorld the changed

A7-6


boundary conditions (position of the points where the fabric is connected to the structural parts). The results of SoftWorld calculation, the forces acting on the fabric connection points, are applied to the structure in DADS. To implement this data transfer, the solver for DADS is extended, so that it writes out the position and velocity 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. Up to now, 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.

4.

CONCLUSIONS

New software tools are essential for modeling 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 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 prototype and the approach are 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. ACKNOWLEDGEMENTS 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. REFERENCES [1] [2]

[3] [4]

[5]

Haugh E.J., Computer Aided Kinematics and Dynamics of Mechanical Systems, Allyn and Bacon, Boston, 1989. Cugini U., Bordegoni M., Rizzi C., F. De Angelis, Prati M., Modelling and haptic interaction with non rigid materials, in State of the Art Reports, Eurographics 99, Ed. Eurographics Associations, Eds. B. Falcidieno e J. Rossignac, Milano, 7-11 settembre 1999, pp. 1-20 (invited paper). Witkin A., Particle System Dynamics, Proc. 19th International Conference on Computer Graphics and Interactive Techniques, ACM Siggraph 92, Chicago, July, 1992. Breen D., House D., Wozny M.J., A Particle-based model for Simulating the Draping Behaviour of Woven Cloth, Textile Research Journal, Vol. 64, N0. 11, November 1994, pp. 663-685. Carignan M., Yang Y., Magnenat Thalmann N., and Thalmann D., Dressing animated synthetic actors with complex deformable clothes, Computer Graphics (Proc. Siggraph), vol. 26, n. 2, July 1992, pp. 99-104.

A7-7


[6]

[7]

[8] [9] [10] [11]

[12] [13] [14] [15]

[16]

[17] [18]

Eberhardt B. and Weber A., A Fast Flexible, Particle – System Model for Cloth Draping, Computer Graphics in Textiles and apparel, IEEE Computer Graphics and Applications, vol. 16, n.5, September 1996, pp. 52-59. Hing N. N.g., and Grimsdale L., Computer Graphics Techniques for Modeling cloth, Computer Graphics in Textiles and apparel, IEEE Computer Graphics and Applications, vol. 16, n.5, September 1996, pp. 28-41. Provot X., Animation realiste de vetements, PhD Thesis, Université René Descartes, Paris V, Matematiques et Informatiques. Siggraph 1998, Cloth and Clothing in Computer Graphics, Course Note n. 31. Volino P., Courchesne M. and Thalmann N.M., Versatile and Efficient Techniques for Simulating Cloth and Other Deformable Objects, Computer Graphics, vol. 29, pp. 137-144. Volino P., Thalmann N. M., Jianhua S., and Thalmann D., An evolving system for simulating clothes on virtual actors,Computer Graphics in Textiles and apparel, IEEE Computer Graphics and Applications, vol. 16, n.5, September 1996, pp. 42-51. Volino P. and Thalmann N., Developing Simulation Techniques for an Interactive Clothing System, Proc. VSMM 97, IEEE Computer Society, pp. 109-118. House D. H., Breen D. E., Representation of Woven Fabrics, Course Notes n. 31 Siggraph 98. Witkin, Particle System Dynamics, Proc. 19th International Conference on Computer Graphics and Interactive Techniques, ACM Siggraph 92, Chicago, July, 1992. Frugoli G., Galimberti A., Rizzi C.,and Bordegoni M., Discrete Element Approach for NonRigid Material Modelling, Robot Manipulation of Deformable Objects, Eds. Dominik Henrich Heinz Worn, Advanced Manufacturing Series - Springer 2000, pp. 29-42. Rizzi C.,and Bordegoni M., and Frugoli G., Simulation of Non-Rigid Materials Handling, Robot Manipulation of Deformable Objects, Eds. Dominik Henrich Heinz Worn, Advanced Manufacturing Series - Springer 2000, pp. 199-210. J. Platt, A. H. Barr, Constraint Methods for Flexible Models, Computer Graphics, vol. 22, n.4, 1988, pp. 279-288. X. Provot, Collision and self-collision handling in cloth model dedicated to design garments, Proc. Graphics Interface 97, 1997, pp. 177-189.

A7-8