Abstract
The study investigates vibrations of a screen box with its flat translational motion being excited by a ball auto-balancer. The CAD system Solidworks is used to develop a 3D model of a vibration machine and a dual-frequency vibroexciter in the form of a ball auto-balancer. The 3D modeling has helped establish the law of motion of the center of mass of the box. The trajectory of its motion is studied, and the tests have shown that the motion is the sum of two circular motions: – a slow circular motion at an angular velocity of the balls’ rotation; – a fast circular motion at an angular velocity of the rotor rotation. The motion trajectory of the center of mass of the box is an epitrochoid. The projections of the center of mass of the box onto the coordinate axes in the motion plane allegedly change under the law of dual-frequency vibrations. Under the assumption that the projections of the center of mass of the box produce dual-frequency vibrations, the software package Statistica for statistical analysis was used to choose the coefficients under a relevant law. Eventually, it has been established that: – the process of determining the values of the coefficients is steady (robust), and the coefficients practically do not change with changes in the time interval; – the amplitude of slow vibrations is directly proportional to the total mass of the balls; – the amplitude of fast vibrations is directly proportional to the unbalance on the auto-balancer body. For both short and long intervals of time (during several slow vibrations of the box), the discrepancy between the law of vibrations of the center of mass of the box that was found through the 3D modeling and the law of dual-frequency of vibrations found by the method of statistical analysis does not exceed 1 %. The results of the study show that the auto-balancer works as two independent inertial vibroexciters. The first vibroexciter is formed by the balls that are closely pressed to each other. They rotate around the longitudinal axis of the shaft at the frequency of the box’s own vibrations. It generates its slow resonant circular vibrations. The second vibroexciter is formed by the unbalanced mass on the auto-balancer body. It excites a fast circular motion of the box at the speed of the shaft rotation.
Highlights
The most potentially productive are mechanisms that combine in themselves advantages of resonant and dual-frequency vibration machines [1,2,3,4]
It is essential to check the possibility of exciting dual-frequency vibrations by a passive auto-balancer at such kinematics of the box motion
The results of studies [9,10,11,12,13,14] prove that passive auto-balancers in principle can excite vibrations that are close to a dual frequency of a screen box making a flat translational motion
Summary
The most potentially productive are mechanisms that combine in themselves advantages of resonant and dual-frequency vibration machines [1,2,3,4]. It should be noted that the effects of corrective weights being jammed in auto-balancers at one of the resonant velocities of the rigid rotor rotation with isotropic support have been investigated in many studies [8,9,10,11,12,13,14]. Equations of the motion of the auto-balanced rotor have been worked out Their numerical integration has revealed the effect of the pendulums’ jamming at the (only) resonant velocity of the rotor rotation. The results of studies [9,10,11,12,13,14] prove that passive auto-balancers (pendular, ball, or roller) in principle can excite vibrations that are close to a dual frequency of a screen box making a flat translational motion. The present study is focused on researching steady vibrations of a screen box with a flat translational motion of the box excited by a ball auto-balancer, as well as the law of vibrations and its parameters
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