Study And Simplify On The Mathematical Model Of The Bubble Growth Process Of Extrusion Foam Molding

The mathematical model of the growth process of the bubble in the foaming mold of polymers is of great importance to studying the growth behave of the bubble. However, the complexity of it in practical engineering poses excessive restrictions on its applications. Therefore, apart from a careful study of the mathematical model, the simplification of it, which has been of the utmost concern of many experts, is also given emphatic attention in this dissertationThe first of the five chapters presents a general introduction of the background and the current situation of the study of the mathematical model of the growth process of the bubble in the foaming mold of polymers, adding a comprehensive account of the work that has been done by seniors in this field and the writer's comments.Two physical models, which have been relatively influential, in the studies of the growth process of the bubble since the 1980s, are analyzed and contrasted in Chapter Two. One of the two physical models, the cell model, is thus chosen as the physical model of the foaming system on which the mathematical model is based. In the process of establishing the mathematical model, the DeWitt constitutive equation is employed to describe the relationship between the stress of melt and the deformation rate. Some mathematical model have been established by the seniors in studying the growth mechanism of the bubble, but, because the physical model they had chosen and their constitutive equation do not totally agree, those mathematical model differ in many ways, and some serious calculation errors can even be found in them. Therefore, this dissertation has relevantly derived the mathematical model of governing growth process of the bubble, located the calculation errors in the senior'works, pointed out the problems resulting from those errors and drawn a conclusion that the theory applied by the seniors to explain the effect of the initial stress on the bubble radius is insufficient, and consequently the theoretical explanation of the effect of the initial stress on the bubble radius still remains an unsolved problem. Furthermore, in order to make it more convenient for the derived mathematical model to be applied, it is simplified to a great...