Optimisation of location and dimension of SMC precharge in compression moulding process
Introduction
The compression moulding process is a manufacturing process in which precharges containing chopped fibres are compressed in a mould. In many cases, SMC (Sheet Moulding Compound) in the form of a thin sheet is used. At the design step, the fibre state of the structure to produce is assumed to have a homogeneous fibre volume fraction and an isotropic fibre orientation at anywhere on the structure. This fibre’s state changes due to the flow characteristics produced during the filling process. The mechanical properties of the final product are determined dominantly by this fibre state. Consequently, this non-uniform distribution of the fibre state induced by the fibre separation or the change of fibre orientation during the compression moulding process generates non-uniform mechanical properties of the final product.
Some principal process parameters, such as the cure time, the mould closing speed, the moulding pressure and the precharge specification (geometry, placement and size of precharge) affect the quality of the final product. Among them, the precharge specification is considered as direct parameter because it induces various flow patterns during the process. In the case of arbitrary loading conditions, the fibre state with a homogeneous fibre volume fraction and an isotropic fibre orientation may be optimal for the mechanical performance. To realise a homogeneous and isotropic fibre state, a precharge covering the entire mould surface must be placed in the mould. If the mould has a complex shape, making the precharge shape becomes complicated. Generally, in the compression moulding process, the shape of the precharge is supposed as simple as possible and a rectangular one is preferred.
In this study, both manufacturing process simulation and structural analysis were coupled to perform multi-objective optimisation. And the location and dimensions of a rectangular-shaped precharge are considered as design variables to maximise the structural performance.
The first part of the study was dedicated to the understanding of the compression moulding process and the mechanical properties of the produced materials. The generalised Hele-Shaw (GHS) model proposed by Folgar and Tucker [1] is taken for the flow analysis of the compression moulding process. Regarding the change of fibre volume fraction during the manufacturing process, the fibre separation due to matrix–matrix and fibre–fibre interactions was proposed by Yoo [2] and Hojo et al. [3], [4]. They modelled the fibre separation from the equilibrium between the drag force and the network force on fibres so as to predict fibre fraction. Moreover, the non-uniform fibre orientation distribution is one of the main causes for non-uniform mechanical properties in the product. As for the method to determine the state of fibre orientation, Jackson et al. [5] suggested the fibre orientation distribution function and Advani and Tucker [6], [7], [8] predicted fibre orientation by using orientation tensors. Also, Park et al. [9] suggested a fibre orientation model considering the fibre separation effect. In order to predict the mechanical properties of a short-fibre composite based on the fibre state, the properties of a unidirectional composite should be estimated first. Halpin–Tsai equation is the most popular model for predicting the properties of short-fibre composites and is used to estimate the mechanical properties of unidirectional composites [10]. And the final fibre orientation tensors obtained from the simulation of compression moulding processing are used for obtaining the average orientation on any point in the product [6]. For the structural analysis of plate, a DST (Discrete Shear Triangle) element [11] and a DRM (Discrete Reissner–Mindlin) element [12] are used for thin and thick plate based on Reissner–Mindlin assumptions.
Till now, the most of research works for compression moulding process are separately dealt with the flow simulation, the prediction of fibre state or the structural properties induced by the fibre state. There are some works on other manufacturing processes for the optimisation of processing conditions or the structural design to obtain optimal structural properties. The structural optimisation considering manufacturing process for autoclave moulding was studied [13], [14], [15]. Park et al. performed a simultaneous optimisation considering structural and process constraints for RTM process [16], [17], [18]. Some studies suggested the optimal processing conditions as melt temperature and filling time for injection moulding process to improve mechanical properties [19], [20]. For compression moulding process, some works were done on the optimisation of mould heating design or precharge shape in order to minimise surface temperature variation and keep uniform flow to prevent weld-line without considering fibre states or structural properties [21], [22], [23]. Kim et al. [24] performed the optimal thickness design considering compression moulding process effects coupled with the structural design.
In this work, to maximise structural properties of the final product manufactured by compression moulding process, the processing conditions such as the location and dimension of precharge are considered as design variables in optimisation problem.
This paper presents at first a numerical simulation approach of the compression moulding process using SMC precharge linked with the structural analysis. After that, an optimisation process to find optimal precharge conditions such as its location and dimension is presented. As optimisation method, a genetic algorithm (GA) is implemented. Furthermore, the method to define the precharge location and dimension using a GA is presented. As technique for handling the constraints, a penalty function method and a repair algorithm, modified for optimisation problems, are proposed.
Section snippets
Flow modelling
For the GHS model used to analyse the compression moulding process, it is assumed that the material is incompressible and the inertia is negligible because the flow in the thickness direction is negligible. The flow of filling process is assumed to be two-dimensional. Due to the small thickness, only the variation of the shear stress in the thickness direction is taken into account in the momentum equation. The flow velocity is defined as the average in-plane velocity in the thickness direction
Optimisation of location and dimension of precharge
As previously mentioned, the precharge location and dimension can give significant effects directly on the fibre state according to various flow patterns. Therefore, the precharge location and dimension can be considered as design variables of optimisation problem to maximise the structural properties. It is assumed that the precharge has a simple shape, e.g. rectangular shape, and that the precharge size is given so as to keep a constant weight after filling. GA is implemented as optimisation
Example and results
The optimisation of precharge conditions is applied to a symmetric structure and an arbitrary and unsymmetrical shaped structure in 3D. In fact, as well as precharge conditions, other constraints should be also considered such as air-void or weld-line formation during the manufacturing process. However, in these examples, it is assumed that air-void can be removed through the vent and the fibre orientation represents the weld-line characteristics. The material properties of the precharge and
Conclusions
The optimisation of precharge conditions in compression moulding process was studied. To define the location and dimension of the precharge as a design vector, the grids were implemented to determine its location and size. To treat this optimisation, the whole search field of the design vector was divided into two spaces, the feasible and infeasible search spaces, because of the correlations of the design variables and constraints. To handle these constraints, penalty function method and repair
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