The Pim Maximum Lyapunov Index In The Process Of Mold Filling Characteristics Research

The injection process of powder injection molding is an incompressibl, non-Newtonian, non-isothermal, or unsteady flow process, which is a complex multiphase flow processes, while,it is a nonlinear dynamics system which be easily affected by many factors. The way defects occur during filling process has chaotic feature,so it is significant for us to inroduct the chaos theory to the the powder injection molding.At first, The filling process of powder injection molding can be regarded as two-phase flow system composed of power and binder when we ignore the gas affects. Through the analysis of two-phase flow and the appropriate dynamics equations, numerical simulation can be done by software ANSYS, in this process, velocity field, pressure field and the powder volume fraction contours can be intuitively observed,and the azimuth time series can ben extracted.Secondly, we can verify the effectiveness of small data algorithm through two typical nonlinear system.Then the azimuth time series is reconstructed by C-C method, thus,we can calculate largest Lyapunov exponents under different conditions from small data algorithm,all of the exponents are positive. So the existence of chaotic phenomenon in the process of Mold filling can be validated.At last, under the same injection velocity, we analyze the chaotic properties of different planes, The study results have shown that the largest Lyapunov exponents along x-axis direction of different planes have significant differences,but along y-axis and z-axis they almost have no difference; then we change the injection velocity and keep the same plane, The study results have shown that the largest Lyapunov exponents are significantly affected by injection velocity, both the largest Lyapunov exponents along x-axis direction and the the injection velocity have same variation law.