# A Study on the Dynamic Behavior of a Sieve in an Industrial Sifter
## 1 Introduction  
Vibrating screens, conveyors, rammers, and other bulk material processing machines are often applied in mining, metallurgical, construction, and other industries [1]. It is widely known that the shape of the trajectory of the screen during its vibrations strongly affects reaching the best processing properties of the machine. For example, in the case of vibrating screens used for coal preparation, the screen motion can be circular, elliptical, or in a straight line. The linear one is used on horizontal, high-frequency, and banana screens. An elliptical one can also be applied on horizontal and banana screens [2]. To explain, the banana screen utilizes a curved banana-shaped deck instead of a flat deck fitted with a horizontal screen [2]. The elliptical motion is claimed to allow higher capacities and efficiencies over both linear and circular motion machines [3]. The trajectories of vibrational motion leading to the intense segregation of the grain layer moving on the sieve have been investigated for a long time. Using the stationary grain these elaborated, [PERSON] and [PERSON] [4] investigated grain separation and cleaning efficiency distribution of the cleaning unit, fractionated by sieve and horizontal air stream, along the sieve length. They studied the effect of feed rate, air speed, and sieve oscillation frequency on the cleaning efficiency of sorghum. They found that cleaning efficiency weakened with the enhancement of sieve oscillations frequency and feed rate. Simultaneously, cleaning loss was enhanced with the rise of such frequency, feed rate, and air speed. According to [5], the more complicated the kinematic of oscillating sieves, the more the agents influence the efficacy of the screening process. Their negative effect becomes more severe with the wear and ageing of their mechanical components [6, 7, 8]. The drive of the various vibrating machines presented in [9; 10; 11; 12; 13] was based on a traditional scheme with a converter of rotating motion into a reciprocating one. The complicated kinematic scheme of such a drive enhanced the cost of the machine, simultaneously weakening energy efficacy and reliability due to many rubbing and wearing surfaces engaged. [PERSON] et al. [14] found that in such type of drive the metal consumption and energy losses were enhanced because inertial flywheels were introduced to alleviate periodic force pulses. [PERSON] et al. [15] elaborated on the vibrator with the regulated frequency and amplitude of oscillations using counterbalances. In this paper, the regulation is suggested to be realized at the cost of even more complex kinematics, i.e., the use of supplementary spring-loaded counterbalances. [PERSON] et al. [16] realized the complex oscillation using the normal force of a plane linear asynchronous motor (LAM). They elaborated an adaptive LAM control system allowing stabilizing of the vibrational parameters of the sieve mill. LAM allowed direct receiving movement of the operating body and an energy-effective electric drive of vibrations with their regulated parameters together with the elastic components. Despite LAMs, the other electric drives can force reciprocating motion. [PERSON] et al. [17] elaborated on a linear reciprocating pulse jet engine and proposed its application in cooling compressors. According to [18], linear electromagnetic transducers are often applied in vibration devices. The authors mathematically modelled an electromechanical structure with reciprocating motion of bodies linked by spring bonds and stimulated by a drive coil. [PERSON] and [PERSON] [19], proposed changing the resistance of the secondary LAM component and controlling the speed with starting and traction forces. The resistance was modified via a movable element shorting a various number of windings in each groove. According to [5], the adjustable linear induction motors (LINs) are applicable as traction machines for magnetic levitation transport.