Comparative Analysis of Digital Modeling Methods: The Example of Additive Manufacturing Processes

Abstract

The paper presents the methods of digital modeling of dynamic objects used for additive manufacturing processes. The digital modeling methods of direct Euler differences, inverse Euler differences, the Tustin transform, and the structural-parametric identification method were used to develop digital models of the transient characteristic of a dynamic object describing the position of a 3D laser printer beam. The structural-parametric identification method is based on the use of a consistent Z-transformation and the apparatus of continuous fractions. The study proved the advantage of the structural-parametric identification method, which leads to the construction of a digital model isomorphic to the continuous model, since this method allows determining the values of the finite-difference equation that coincide with the values of the transient characteristic of the object. The other methods proposed in the paper lead to finite-difference equations that successfully approximate the transient response at a small discretization step. Yet, increasing the discretization step to the limits determined by the structural-parametric identification method leads either to a significant loss of approximation accuracy or to a change in the properties of the digital model. Thus, the use of the structural-parametric identification method in modeling additive manufacturing processes will improve the quality of finished products, the accuracy and mobility of production, and save raw materials.