Determination of inertia-stiffness parameters and motion modelling of three-mass vibratory system with crank excitation mechanism

Abstract

Vibratory technological equipment is widely used in various industries. The vast majority of existing vibratory machines are equipped by single-or double-mass oscillatory systems and inertial or electromagnetic vibration exciters. The novelty of the present study consists in development and investigation of the three-mass oscillatory system with crank excitation mechanism. Such a system can be effectively implemented in various designs of vibratory equipment, e.g., conveyers, separators, feeders, shakers, batchers, sieves, etc. Based on the mathematical model derived in the form of differential equations of the system's motion, there are deduced the analytical expressions for determining its inertia-stiffness parameters ensuring the energy-efficient resonance operation mode. Using the solid model of the vibratory conveyer-separator designed in SolidWorks software, there is determined the input data for calculating the parameters of the oscillatory system. Based on the results of calculations, the numerical modelling of the system's motion is carried out in MathCad software. In order to verify the correctness of the theoretical investigations, the simulation of the system's motion is carried out in SolidWorks Motion software. The comparative analysis of the results of numerical modelling and computer simulation is performed, and the prospects of their implementation are considered.

Kinematic and dynamic analysis of three-mass oscillatory system of vibro-impact plate compactor with crank excitation mechanism

“…The carried out analysis of the scientific publications dedicated to vibratory compacting machines [1]- [6] and self-propelled vibro-impact locomotion systems [7]- [9] has shown that the problems of the simultaneous implementation of the vibro-impact operational conditions and the self-propelling drives in the improved designs of the plate compactors are not thoroughly investigated. Therefore, the previous publications of the authors substantiated the optimal inertia-stiffness parameters of the three-mass vibratory system excited by the crank mechanism [10], considered the improved design of the crank excitation mechanism with controllable geometrical parameters [11], and studied the dynamic behavior of the three-mass vibro-impact system able to slide along a rough horizontal surface [12]. The novelty of the present paper consists in implementing the vibro-impact crank-type excitation mechanism for providing the self-propelling locomotion conditions of the vibratory plate compactor and reducing the extra pushing force that must be applied by the operator for setting the compactor into motion.…”

Determination of the first natural frequency of an elastic rod of a discrete-continuous vibratory system

“…The inaccuracy of the obtained results is scanty; therefore, it can be asserted that the rod-shaped continuous member is adequately in compliance with the discrete model (with the mass 𝑚 = 0.313 kg and the stiffness coefficient 𝑘 = 2.865•10 3 N/m) ensuring the first natural frequency of the three-mass vibratory system of approximately 15 Hz [9].…”

“…The advantage of such a fixation is the fact that there exists a cantilever with considerable inertness (as to its length); such a cantilever can be set in motion mechanically. This can be ensured if one of the supports is disturbed by an eccentric drive [9]. This enables us to a priori assert that the virtually separated mass and rigidity will be accepted by the two-mass oscillatory system as a third independent mass, and the three-mass discrete-continuous oscillatory system will be an inter-resonance one.…”

“…The analysis of numerous publications dedicated to oscillatory systems of various vibratory technological machines has shown that the problems of implementation of combined discrete-continuous three-mass systems are not thoroughly investigated. Therefore, in the previous publications of the authors, the optimal inertia and stiffness parameters of the three-mass discrete vibratory systems were substantiated [9], and the stress-strain state of the double-span elastic beam was analyzed [10]. The novelty of the present paper consists in determination of natural frequencies and substantiation of the possibilities of implementing the continuous rod-shaped members with distributed inertia and rigidity parameters for exciting the oscillations of the threemass discrete-continuous inter-resonance vibratory systems.…”

Mathematical modelling of forced oscillations of continuous members of resonance vibratory system

“…Despite the fact that numerous scientific publications are dedicated to discrete-continuous oscillatory systems, the problems of synthesizing the three-mass structures with rod-shaped elastic members excited by crank mechanisms are not thoroughly investigated. In the previous publications of the authors, there were considered the technique of calculation of the inertia-stiffness parameters of the three-mass discrete oscillatory system ensuring its operation in energy-efficient resonance mode [9], and the forced and free oscillations of an elastic rod considered as a disturbing body of the three-mass discrete-continuous oscillatory system [10,11]. The novelty of the present paper consists in deriving the mathematical model of the discrete-continuous vibratory system, in which the model of the discrete subsystem is combined with the model of the continuous subsystem by applying the reactions in the supports holding the uniform elastic rod.…”