Research on the Problem of Equal Circle Packing within a Rectangular Boundary Based on Motion Simulation

_ In the manufacturing industry, the problem of circle plate packing processing is common and important. In this study, an innovative algorithm is proposed to transform the packing of a circle in a rectangular container into the motion of a disturbed object group. First, the discrete element method (DEM) is used to construct the mathematical model of equal circle motion. By establishing the time domain and complex frequency domain models, the internal stability of the motion system and the feasibility of the algorithm implementation are confirmed. Second, the sweep and prune method and the quadtree method are introduced for collision detection, and the continuous collision detection is used to deal with the tunneling phenomenon caused by high-speed motion. Then, based on the impulse method, the collision circle is processed, and the impulse size is accurately calculated from the two aspects of velocity change and position constraint. The error compensation is introduced to reduce the calculation error, and the calculated impulse updates the circular velocity and position in real time. Finally, the feasibility of the algorithm is verified by an example test, which provides a new direction for solving the circle packing problem. Keywords two-dimensional packing, equal circle packing, stability analysis, collision detection, collision response