Mathematical Description Design Process of Plastic Details

It is known that the strength and precision factors are the most important indicators of the quality for plastic parts. At the same time, the precision depends on the magnitude of shrinkage strain. Тherefore, it is possible to establish a direct analytical relationship between quality, strength and shrinkage strain factors, which is a function of the difference between the thermal stresses and other physical process. Currently, the difference in thermal stresses (residual stress) is not controlled due to the lack of reliable methods to determine and control their magnitude and direction. However, the magnitude of the volumetric or linear strain of finished products can be controlled by manipulating other quality factors.Determination of the link between volumetric strain and strength is possible by controlling the cooling process of the polymer components under normal operating conditions. Then it’s possible to analytically find the change in volumetric strain of the parts and the change in the difference of thermal stresses during cooling.Thus, the volumetric strain is a linear thermal shrinkage, i.e. the change of dimension and geometric shapes in all three directions (x, y, z) and is controlled by the quality criterion.On the other hand, the cooling process of plastic parts due to their low thermal conductivity is characterized by the cooling gradient of cross section. This leads to the formation of thermo-elastic stresses. The greater the temperature difference between the center and the surface layers, the more stress should be expected. For each infinitesimal layer the difference in the free thermal and total shrinkage rate will be compensated by a different strain.At first, the cooling rate of the outer layers despite the poor thermal conductivity greater than the internal. Further cooling results in a state where the cooling rate of the inner regions is greater than that of the outer. As a result, of this more intensive volume reduction begins in parts of the inner layers. The outer layers prevent this kind of decrease. The resistance of some layers of plastic parts to the shrinkage than that of the others causes thermal stresses, which at high temperatures can cause destruction of the components, if the value of any stress exceeds the tensile strength of the material.After cooling tangential compressive stresses are fixed in the outer layers of plastics and in the internal – tensile. Residual stresses are the greater, the greater the temperature difference over the cross section, the higher the rate of cooling and the lower part of the stresses succeed to relax, the greater are be residual stresses.Therefore, more detailed look shall be given to the distribution patterns of the thermal stresses drop for cylindrical plastic parts when they are cooled (fig.1).