Optimized Packing of 3D Objects Bounded by Spherical and Conical Surfaces

Abstract

Introduction. Optimizing the packing of arbitrary geometric objects in additive manufacturing opens up new possibilities for increasing the efficiency of additive manufacturing of parts of a complex configuration due to the saving of energy, material and time resources. Additive manufacturing, a cornerstone in fields such as space engineering, medicine, mechanical engineering, and energy, has its efficiency hinging on the optimization of the 3D printing process. Given its widespread application, refining this process is of utmost importance. The purpose of the paper. The paper aims to develop an approach for packing assembled parts of complex geometry in the working area of a 3D printer, while adhering to the standards of 3D printing. Results. For the analytical description of the complex shaped industrial products, a, so called, “composed spherical cone” is used. This generates a family of such objects as spheres, cylinders, spherical cylinders, cones, truncated cones and spherical discs. Using the normalized quasi-phi-function of composed spherical cones, a mathematical model of the problem is presented in the form of a nonlinear programming problem. A solution strategy is developed, encompassing three primary stages: generation of feasible starting points, search of local minima and search of a better local minimum. Numerical examples of packing various industrial products in a 3D printer chamber is provided. 3D-parts are approximated by composed spherical cones with different metric parameters. Conclusions. The conducted numerical simulation confirms the effectiveness of the proposed optimization approach. This study emphasizes the importance of further research and innovation in the field of 3D printing and its optimization, and also demonstrates the potential of using mathematical models to solve practical problems in a production environment. Keywords: packing, assembled spherical cone, mathematical modeling, optimization, additive manufacturing.