W2A-033 Rotational moulding-0.txt
COMPUTER SIMULATION OF THE ROTATIONAL MOULDING PROCESS

Liang Xu R. J. Crawford

School of Mechanical and Manufacturing Engineering, The Queen's University of Belfast, Ashby Building, Stranmillis Road, Belfast, Northern Ireland, UK, BT9 5 AH
Abstract: In recent years, with the increasing demands being placed on the rotational moulding process, particularly with regard to thick-wall moulding, the need for an accurate computer simulation has become very apparent. Rotational moulding is a difficult process to model due to the complexities caused by the biaxial rotation of the mould, the physical and phase changes which take place in the plastic and the dynamic nature of the boundaries within the mould. In this paper, a new unsteady-state, non-linear heat transfer model of the rotational moulding process has been developed, together with an efficient numerical formulation for the simulation of heat transfer during the whole moulding cycle. The procedure uses modified boundary conditions for the solution of the internal air temperature field. The heat transfer between the inner mould surface and the internal air and the internal air temperature change due to the air mass changing during the moulding cycle have been analysed. This has resulted in a computer program which can predict accurately the internal air temperature profile through the cycle. This enables prediction of the heating time, cooling time and hence the overall cycle time for the process.
1 Introduction

Rotational moulding is a processing technique which is primarily utilized in the manufacture of hollow articles from thermoplastic and, to a limited extent, thermosetting materials. Rotational moulding is generally regarded as a slow processing method because the plastic must be heated from room temperature, up to its melting temperature and back to room temperature when it is inside the mould. Initially, the material in the form of powder or liquid is placed in a shell-like metal mould. The closed mould is then rotated biaxially by the rotational moulding machine and indexed into an oven. The heat supplied by the oven melts the thermoplastic powder which then partially fuses together and the biaxial rotation causes a porous skin to be laid up on the mould inner surface. This gradually melts to form a polymeric shell attached to the internal surface of the mould. Sufficient time must be allowed in the oven for the material to completely distribute, fuse and consolidate. Subsequently, the mould is rotated to a cooling chamber, where it is quenched to the demoulding temperature. The cooling may be carried out by a fan which blows air over the mould, water spray, or a combination of both. When the mould is cold, it is opened and the solidified part is removed. Thereupon, the mould is recharged and the cycle repeated.

In the past, technological advancement and understanding of the rotational moulding process has depended largely upon the experience of the moulders and the establishment of process conditions has been achieved on a trial and error basis. Early work helped to fill gaps in the understanding of the heat transfer which occurs during the rotational moulding process. Recent research has also resulted in improvements in direct real time process control so that the trial and error aspects of the process have to a large extent been overcome.

However, there are still difficulties in producing rotomoulded articles with very large wall thickness (i.e. greater than 15 mm). Current heat transfer analysis methods have proved to be unstable, in accurate and/or extremely demanding in computer time due to the complex thermal conditions within the multi-layer porous powder mass within the mould. It is evident that there is a need for thick wall rotomoulded products in, for example, the pipe industry. In this case, mouldings up to 40 mm thick are required and it is extremely expensive to optimize the process conditions for such products by trial and error. Hence there is a need for an accurate computer simulation of the process which will enable these types of thick wall products to be analysed.

The development of such a simulation has been carried out at the Rotational Moulding Research Centre at the Queen's University of Belfast. Previously two programs were developed in an initial attempt at this problem. These proved to be extremely valuable in streamlining experimental research programs. However, a problem with the two existing programs is that they cannot predict the oven time, cooling time and cycle time for moulding part thicknesses over 12 mm. Above this thickness the analysis tends to become unstable. Also, they cannot accurately predict the internal air temperature profile which is now known to be so critical to the process. This is because at the time they were developed it did not appear necessary to address the complex problem of the moving boundary between the internal air and the melting, fusing, consolidating plastic adhering to the mould.

The initial program developed was called 'ROTOSIM' and has been described in detail elsewhere. This model examined the biaxial motion of a hollow mould containing a powder mass with a series of superimposed heat transfer models. The shape of the mould was defined by a grid of points in 3-D space. The grid was rotated according to a defined ratio of plate to arm rotational speeds. During this rotation, the relative motion of the powder pool was calculated to determine the region of mould/powder contact and the temperature profiles through the mould. The computer model calculated the rise in temperature of the mould and powder as heat is transferred from the oven environment. This program provided very accurate predictions of cycle times for wall thickness up to 12 mm.

Subsequently, in an attempt to examine the effect of internal air temperature, a program called 'ROHEAT' was developed. In this case the internal air temperature was considered as a constant value. This assumption made the programming much simpler and it allowed the effects of internal heating and cooling to be explored. However, this assumption does not reflect the real rotational moulding situation. From rotational moulding experiments, it has been found that the internal air temperature changes with time during the whole moulding cycle and this temperature profile provides important quality control information for the moulding technique. Additionally, the important part of the heat transfer between the inner surface of the metal mould and the internal air mass at the initial stage of the rotational moulding process, i.e. before the plastic powder adhered to the inner metal mould wall, was not taken into account in the 'ROHEAT' and 'ROTOSIM' programs. Additionally, both of these programs required a considerable amount of computing time. This limits their usefulness on personal computers - particularly when the wall thickness of the moulded product is large.

In this paper, a new unsteady-state, non-linear rotational moulding heat transfer model has been proposed and has been analysed in detail. The heat transfer mechanism used in this model have been developed to enable computation of the internal air temperature profile and it is possible therefore to provide estimates for the oven time, cooling time and the overall cycle time for various resins and for various thicknesses of mouldings, including very thick wall products. Based on this model, a more powerful rotational moulding computer simulation system with greatly reduced computing times has been developed. It is ideally suited for use on a PC. This has provided the opportunity to optimize the rotational moulding process conditions for rotomoulded products. It is anticipated that in the near future this information will be utilized in real-time control system for rotational moulding machines.

2 Modelling and numerical simulation of heat transfer during rotational moulding

2.1 General

The heat transfer process which occurs during the rotational moulding process reflects the unique nature of this moulding technique. Understanding this process in an important and essential step in the understanding of rotational moulding. It is also very important with regard to product quality control and the economics of the process.

The theories of heat transfer are well established but their application to the rotational moulding process is rare. This is because, on the one hand, the apparent simplicity of rotational moulding did not require detailed analysis and, on the other hand, those who recognized the need were put off by the complexity of the moving powder inside a rotating mould. This complexity arises from the interactions between the various heat transfer processes, the variation in conditions from one part of the system to another, the inherent complication of the tumbling powder, and the interaction of the thermal properties of plastics (i.e. thermal conductivity, thermal diffusivity, latent heat of fusion). Physical properties, mould shape, mould material, mould thickness, oven efficiency, part wall thickness and biaxial rotational speeds also have an important effect.

By tradition, the process of heat transfer is classified into three basic distinct modes: conduction, convection and radiation. The basic laws of heat transfer are simple, but their application to real situations is usually a very complicated matter. The heat transfer models developed for the rotational moulding process have become more and more complex as the models become increasingly sophisticated.

For the purpose of developing this new computer simulation system for the rotational moulding process, the following approach was used. Firstly the heat transfer mechanism occurring during the process were defined. Next, mathematical models were developed to describe these heat transfer mechanisms and the necessary data was measured for several polymers. Then the numerical analysis methods were established. This was followed by the computer programming. Finally the predictions obtained from the program were compared with the experimental data measured using the ROTOLOG process controller.

2.2 Heat transfer analysis
Heat transfer in the rotational moulding process involves unsteady-state heat flow. In theory, during rotational moulding the heat is transferred from an oven, through a metal mould, then through a plastic bed and into the internal air space. The heat transfer can be broken down into a series of modules as follows:
(1) Transition of heat from the air in the oven to the outer surface of the mould - boundary condition 1. (2) Heat transfer through the mould wall. (3) Heat transfer between the inner surface of the mould and the plastic bed - boundary condition 2. (4) Heat transfer through the plastic bed. (5) Transmission of heat from the plastic bed to internal air - boundary condition 3. (6) Heat transfer of the internal air mass.

These six stages will be analysed in detail below.

The true mathematical description of the heat transfer in the rotational moulding process is complex because of the movement of the powder inside the mould and the variation of the physical and thermal properties of the material. The simulation of the physical problem that corresponds to the actual rotational moulding process conditions is also complex. Though in principle such a simulation may be feasible, it may be of little use to industry if it is very expensive due to the extremely intensive computations involved. Therefore, it is necessary to make appropriate simplifications in the simulation. During this research, the following initial assumptions were made for the purpose of simplification: (a) Initially the powder is assumed to be in the bottom of the mould and so the internal air is heated through the mould wall by the oven. Recent video evidence has shown that the powder pool does remain essentially static with a slow 'crawling' motion over the inside surface of the mould. (b) Once the polymer melt temperature is reached the powder is assumed to be in static contact with all parts of the internal surface of the mould. (c)	The heat transfer is one-dimensional, i.e. what happens at one point on the wall is the same at all other points. This is reasonable because under normal circumstances the surface of the mould will be at a uniform temperature and heat transfer is towards its centre. (d) The mould shape is cylindrical. This assumption is made (i) to keep the analysis within reasonable bounds and (ii) because many thick wall products are cylindrical, e.g. pipes.

The fundamental laws of heat conduction and convection take the form of a set of differential equations for temperature T. In this model, a more general finite difference approximation has been used for the solution of the partial heat transfer equations. During the numerical analysis of the model, both explicit and implicit methods have been used to solve the heat transfer equations.
