15 Mar.,2023

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**P. Kostka **, **R. Höhne **, **B. Maron **, **J. Ehlig **, **W. A. Hufenbach **

Institute of Lightweight Engineering and Polymer Technology, TU Dresden, Dresden, 01307, Germany

Correspondence to: P. Kostka , Institute of Lightweight Engineering and Polymer Technology, TU Dresden, Dresden, 01307, Germany.

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**Abstract**

Textile-reinforced plastics are of continuously rising interest for industrial applications due to their tailorable properties and large-scale production capability. The utilisation of this novel material group as components in multi-material structures for complex lightweight applications with a high degree of function integration is focussed within the research of the collaborative research centre (SFB) 639. Lightweight design and function integration potentials of these novel structures are examined using an adaptive, self-diagnosing leaf spring within the framework of a demonstrator vehicle. In this article, a concept for the leaf spring design and the actuation mechanism based on an internal pressure cavity for the realisation of a stiffness adaptation are presented. A multidisciplinary analysis concept was established including three sub-models - an analytical based Fast Design Tool, a Finite Element Model and a Multi-body simulation model. The investigations include the simulation of the leaf spring characteristics for different internal pressures and the influence on the static and dynamic behaviour of the demonstrator vehicle.

**Keywords: **
Textile-reinforced Thermoplastics, Adaptive Composite Structure, Multidisciplinary Analysis

**Cite this paper:** P. Kostka , R. Höhne , B. Maron , J. Ehlig , W. A. Hufenbach , Multidisciplinary Analysis Concept for the Development of a Composite Adaptive Leaf Spring, *International Journal of Composite Materials*, Vol. 3 No. 6B, 2013, pp. 10-16. doi: 10.5923/s.cmaterials.201310.02.

- The outstanding properties such as high strength and stiffness in combination with a low specific mass and the numerous possibilities of function integration make the still recent material group of textile-reinforced thermoplastics interesting for future lightweight applications in industry[1]. Textile-reinforced thermoplastic composites can be tailored to structural demands and combined in multi-material applications in a much more flexible manner than conventional materials. To comply with the current demands of industry, new design methods for these complex highly integrative thermoplastic hybrid yarn structures are developed within the research of the collaborative research centre (SFB) 639. Especially functionalised composite structures with integrated sensor networks appear to be suitable for these demands. Therefore, innovative sensor networks for data acquisition, storage and transmission[2] as well as embedded actuators, which distribution and electrical connection is realised using special functional layers[3], are in the focus of the current research. New complex material models to describe the nonlinear material behaviour of the focussed glass fibre polypropylene (GF-PP) hybrid-yarn-textile-thermoplastic (HYTT) composites are developed[4]. In order to show the lightweight potentials of this novel material group, a prototypical application of all investigated technologies by means of a generic demonstrator vehicle “FiF” - a transport vehicle for goods to be conveyed e.g. for construction sites or factories - is developed within the project. Thereby, a special subcomponent is represented by the vehicle leaf spring, which demonstrates the integration of adaptive functions by means of an actuation mechanism, sensors networks as well as the application of developed material models and novel modelling strategies.

- Within this research, lightweight design potentials of textile thermoplastic composites and new design methods are examined by developing an adaptive, self sensing textile-reinforced thermoplastic leaf spring within the framework of a demonstrator vehicle, Figure 1. One aim of the leaf spring development is to develop an actuating principle for varying the leaf spring stiffness, Figure 1. The adaption facilities self-levelling, body roll diminution in different situation, including cornering, accelerating and braking. Material-integrated sensors networks for measuring of loads and structural strain distribution deliver the input data for the control of these active functions.

- A multidisciplinary analysis concept consisting of 3 submodels was established in order to enable a comprehensive, though efficient development of the adaptive leaf spring, Figure 4. Using the concept, the static and dynamic behaviour of the adaptive leaf spring and of the generic vehicle can be simulated. This enables the consideration of the manifold requirements for the leaf spring design at an early stage in the development phase.In this study, a fast design tool based on analytical formulation was developed in order to estimate a preliminary design that fits the given requirements. Subsequently, a finite element (FE)-model based on the geometry resulting from the preliminary design was developed. The FE-model is used in order to accurately compute the mechanical strains as well as the spring characteristic for different internal cavity pressures. A multi-body simulation (MBS)-model of the whole vehicle was developed, whereas the calculated stiffnesses and spring characteristics are used as model parameters. The MBS-model simulates the static and dynamic behaviour of the “FiF” demonstrator for the given configuration. Based on the numerical results, the design of the composite leaf spring can be optimised using an iterative procedure including the FE-model and the MBS-model.

- Due to the very complex loading conditions, the design of the aspired inflatable composite structure is challenging. For the design identification, a realistic simulation using numerical methods is too extensive and time consuming. For that reason, analytical methods are used to describe the focussed problem. A fast design tool is proposed based on analytical formulas and an optimisation algorithm is used in order to identify the design that fits a specified objective. The identified preliminary design was used further for detailed analysis by means of the FE-Model.

- On the basis of the geometry and the loading conditions of the focussed adaptive leaf spring, two basic 2D-models were established for the derivation of the analytical formulas, Figure 5. The models represent the basic loading of the spring; namely the deflection due to a vertical load and the inflation due to a pressure inside the cavity. Since both loadings interact, the formulas of the 2D-models need to be combined in order to estimate the stresses and the deflection of the adaptive leaf spring at last.

- In general, the optimal design of an adaptive leaf spring for lightweight applications features a maximum stiffness adaption and a minimised weight under consideration of the prescribed material strength and available space. A well known principle to achieve a lightweight structure is to fully utilise the material strength throughout the supporting structure. This principle is adopted for the design identification taking the interaction of the combined loadings, by means of the given equations (1) to (6), into account. In order to predict failure in the composite belts of the adaptive leaf spring, a physically based Failure Mode Concept (FMC) according to Cuntze[7] was used. The FMC distinguishes between five failure modes, representing one theoretically independent failure mechanism in multidirectional laminates. The main advantage of the FMC is the strict allocation of a strength criterion to one failure mode and to one associated basic strength. For each failure mode, a mode reserve factor can be calculated, describing the material stain. In this study, the fibre tensile failure and matrix tensile failure are relevant due to the biaxial stress state in the belts. The corresponding mode reserve factors can be expressed as(7)where and are the tensile strengths, , are the load induced stresses parallel and transverse to the fibre direction and

The Generalized Reduced Gradient Algorithm is used in order to solve the nonlinear identification problem. Totally, seven equally-spaced crosssections were evaluated for the design identification. The identified preliminary design for the identified adaptive leaf spring is shown in Figure 6.

- The pre-identified leaf spring design was modelled using Abaqus (version11.2). The FEmodel can be used for extensive studies regarding the optimal design identification, taking the complex 3d-stress states as well as the nonlinear geometrical and material effects into account. In order to provide basic data for the multi-body simulation, the determination of the spring characteristic of the pre-identified leaf spring was focussed first. The symmetrical modelling technique was used in order to reduce the computational efforts significantly. The existing geometry, material properties as well as the boundary conditions and the loading allows modelling only a fourth of the leaf spring, Figure 7. The finite element mesh consists of approx. 12000 cubic elements with linear displacement approach (Abaqus element type C3D8I), which feature an improved representation of the shear behaviour compared to standard cubic elements[8]. In order to avoid rigid body movements, displacement constraints were defined. Furthermore, the connection between the metal bars and the composite belts is assumed as ideal and remains unconsidered. For the further simplification of the modelling, a linear material model is used with material parameters experimentally determined within the SFB 639 subprojects C1 and C4, Table 2.

A reliable simulation of the spring characteristic requires the consideration of the coupling effects of the fluid filled cavity with the surrounding composite structure. In order to represent the hydrostatic fluid and to simulate the fluid-structure interaction, hydrostatic fluid elements provided in Abaqus were used. With these elements, the fluid-structure interaction assuming either constant pressure or constant volume of the fluid can be modelled[9]. In this study, the characteristics of a leaf spring with a fully enclosed cavity filled with oil, whereas the volume of the oil remains constant, are simulated. The simulation was performed for several inner pressures up to 1.0 bar and a vertical load of 6 kN, which is applied via Multiple-Point-Constraints (MPC) to the structure. The deflection and the applied point load were extracted at the reference point and the spring characteristics were retrieved finally, Figure 8. The results illustrate the stiffness adaptation of the leaf spring due to the expanding cross-section of the leaf spring. The progressive curvature is due to buckling of the belts, once a critical load is exceeded. This problem needs to be addressed in following studies, for example through the integration of local stiffeners. Aside from that, the adaptability of the analytical Fast Design Tool is justified, since the occurring stresses are within the allowable range. For further analysis purposes, the spring characteristics and the leaf spring dimensions are transferred to the multi-body simulation software.

- The multi-body simulation model (build with SimulationX version 3.5) of the vehicle “FiF” presented in[9], was extended by two leaf springs with adaptive stiffness and with additional single-wheel suspension details. The leaf springs are part of the rear suspension system and were modelled by a predefined 3D-spring model provided by SimulationX. Their location as a part of the rear suspension kinematics and the vehicle coordinate system is illustrated by the 2D-view of the 3D-model in Figure 9 (a). The simplified suspension kinematics are shown in Figure 9 (b).

- The potentials of textile-fibre reinforced thermoplastics as components in an adaptive leaf spring made in multi-material design are investigated numerically. In order to realise the adaptation of the spring characteristic, an actuation mechanism by means of a fluid filled cavity inside the leaf spring was proposed. A multidisciplinary analysis concept was established, which allows the consideration of the manifold requirements, e.g. the static behaviour of the leaf spring and the dynamic behaviour of the vehicle, at an early stage of the development phase. According to the concept, a preliminary design of the adaptive leaf spring was identified by means of an analytical Fast Design Tool. Subsequently, a FE-simulation confirmed the functionality of the proposed actuation mechanism by means of the leaf spring adaptation capabilities. A multi-body simulation demonstrated that for static applications, e.g. levelling the platform, the adaptive leaf spring considerably influences the vehicles behaviour. However, the effect on the dynamic behaviour of the vehicle is limited. In order to extend the controlled stiffness range of the leaf spring, an optimal design identification using an iterative procedure based on the established multidisciplinary analysis concept is planned. Therefore, previously identified nonlinear material behaviour of the HYTT will be considered. In order to experimentally validate the used concepts and models, the manufacturing of the identified leaf spring and basic tests are intended.

- The authors would like to express their gratitude towards the Deutsche Forschungsgemeinschaft (DFG), for funding the research in the scope of the subprojects E1 and C1 of the Collaborative Research Centre SFB 639 “Textile-Reinforced Composite Components in Function-Integration Multi-Material Design for Complex Lightweight Applications” and the whole research community of the SFB 639.

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