Theoretical study of the interactions between vibrations of large numbers of FDM 3D printers

It is known that the vibrations of machine tools-and 3D printers taken as a specific example-can be transmitted through the floor on which they are mounted. Each printer can be represented as an oscillator, and there is some transmission through the floor even though isolators are usually used to combat that. Here we present a theoretical dynamic analysis of a system of such oscillators, either in line or distributed in a square pattern. It is assumed that the interactions between printers decrease as the square of the distance between them while is proportional to the square of the propagation wave speed. An analysis of the system shows that even though the natural frequency spectrum broadens with the number of the oscillators, its upper and lower limits can be predicted. Correlations were found to estimate the ratio of the upper bound limits of the natural frequency between 2D and 1D array configurations. A study regarding the Fuse Deposition Modeling (FDM) 3D printers is performed using characteristic nominal data for such polymer material extrusion systems. Then, a simple experimental set up consisting of two small-size FDM printers was implemented to record the frequency bin spectra of each printer separately and their interaction when placed over a wood or a concrete floor. From the latter theoretical model, it is concluded that as the number of printer units and the order of arrangement is increased, the critical propagation wave speed decreases indicating that the floor foundation stiffness can be reduced without the risk of achieving resonance conditions. On the opposite, as the mass of the printing units is increased the propagation wave speed increases, requiring a stiffer floor foundation as an adequate substrate support to place the printers. From the preliminary experimental results, interaction between two printers was observed when operating over a wood floor, while when over a concrete floor no interaction was detected. This analysis helps designing systems of polymer material extrusion 3D printers to have little interference between them.