# A Study on the Dynamic Behavior of a Sieve in an Industrial Sifter
## 2 Multi-Frequency Vibrating Screens
### Linear-Elliptical Double-Frequency Sifter  
Obtaining intensive segregation of feed grains is possible thanks to the use of, among others, two-frequency screens, which give better process indicators compared to classic screens, currently used, for example, in the mining industry. The sieve movement paths obtainable with a two-speed screen favour the intensive course of the process of mixing the granular layer on the sieve. Dual frequency screens feature two different rotational speed vibrators that drive these machines. Sifters belonging to this group have at least two rotary vibrators.  
The diagram of the exemplary configuration of the double-frequency screen is shown in Figure 1. It shows a horizontally supported variant, but the machine can also be inclined to the horizontal at an angle \(\alpha\) of up to 300, as well as freely suspended from the spring suspension. To drive such a screen, two rotary vibrators with identical or different static moments of inertia are used.  
An important parameter characterizing the operation of a double-frequency screen is the speed transmission coefficient defined by Equation (1).  
\[\xi\ =\ \frac{\omega_{1}}{\omega_{2}}\ =\ \frac{n_{1}}{n_{2}}, \tag{1}\]  
Such a parameter quantity determines how much the angular velocities \(\omega_{1}\) and \(\omega_{2}\) (or rotational \(n_{1}\) and \(n_{2}\)) of two rotary vibrators differ from each other. Depending on the applied speed transmission coefficient, different paths of motion of the vibrating machine can be obtained. In the case of double-frequency screens, it is important to properly configure the drive system, understood as the appropriate selection of dimensions: \(l_{1}\) and \(l_{2}\), as well as \(h_{1}\) and \(h_{2}\) (Figure 1). Too large values of distances \(l_{1}\) and \(l_{2}\) mean that in the movement of the riddle, the torsional movement around the center of gravity \(S_{0}\) is important, resulting in large amplitudes at the beginning and end of the screen. In this case, the screen center amplitudes are small. The screening material layer will then be rolled upwithin the central part of the screen. Such a course of the screening process is unacceptable, as excess material may spill through the sidewalls of the screen. As a partial solution to this problem, an additional increased horizontal inclination of the screen can be made.  
The axis perpendicular to the line connecting the centers of masses of both vibrators is the so-called kinematic axis of the machine. It can be vertical, e.g., OK\({}_{1}\), in the case of vibrators placed extremely and symmetrically at both ends of the riddle, or inclined at any angle \(\beta\), e.g., OK\({}_{2}\), in the case of shifting the vibrators relative to each other by the appropriate values \(h_{1}\) and \(h_{2}\) as well as \(l_{1}\) and \(l_{2}\). The angle \(\beta\) is called the screen path fluctuation angle because, in the case of counter-rotating and equal frequency of excitations on both vibrators, it allows to obtain straight-line vibrations inclined at this angle. In the case of concurrent synchronization at the same frequencies, we usually get an elliptical motion in which the main axis of the ellipse is tilted to the horizontal at the angle \(\beta\).