Theoretical investigations into the capabilities of a coaxial inertial drive with various operating modes for vibratory conveyors and screens are conducted in the paper. The coaxial inertial exciter is designed with one asynchronous electric motor and the kinematically synchronized rotation of two unbalanced masses. Three variants of angular speeds ratios, namely ω₂/ω₁ = 1, ω₂/ω₁ = –1, and ω₂/ω₁ = 2, are considered. Based on these relations, the circular, elliptical, and complex motion trajectories of the working members are implemented. In the first two cases, single-frequency harmonic oscillations take place. In the latter case, the double-frequency periodic oscillations are excited. The dynamic behavior of the motor’s shaft during its running-up and running-out is considered. The influence of the inertial parameters of the unbalanced rotors and the relative phase shift angle between them on the elliptical trajectories of the vibratory system’s mass center motion is investigated. The use of forced kinematic synchronization provides the motion stability of the vibratory system for all considered working regimes.

Vibratory equipment is widely used for performing various finishing processes, machining and forcing of different parts and materials. Numerous researchers and technologists pay specific attention to the possibilities of implementing vibration-driven machinery for conducting the lapping and polishing operations on flat surfaces. The present paper is dedicated to studying the laps kinematic parameters of the vibratory finishing machine actuated by six electromagnets. The paper’s scientific novelty consists in the experimental verification of the previously modelled and simulated circular trajectories of the laps under different operational conditions. The methodology of research contains two basic stages: changing the excitation frequency at the constant traction force and changing the traction force at the constant excitation frequency. The improved 3D-design of the vibratory finishing machine was developed in the SolidWorks software. The experimental prototype was implemented in practice, and full-scale tests were carried out using the WitMotion sensors and software. Based on the obtained experimental data, the trajectories of the machine’s laps were constructed and analyzed in the MathCad software. The research results substantiate the possibilities of providing circular oscillations of the laps at different operational conditions. The results can be used by technologists and engineers while choosing the appropriate design and control parameters for similar vibratory equipment intended for lapping and polishing of flat surfaces.

The general design of the wheeled vibration-driven robot is developed in the SolidWorks software (Dassault Systèmes SolidWorks Corporation, Premium 2022, Waltham, MA, USA) on the basis of a double-mass semidefinite oscillatory system. The idea of implementing the vibro-impact working regimes of the internal (disturbing) body is considered. The corresponding mathematical model describing the robot motion conditions is derived using Euler-Lagrange equations. The numerical modeling is carried out by solving the obtained system of differential equations with the help of the Runge-Kutta methods in the Mathematica software (Wolfram Research, Inc., 13.0, Champaign, IL, USA). The computer simulation of the robot motion is conducted in the MapleSim (Waterloo Maple Inc., 2019.1., Waterloo, ON, Canada) and SolidWorks software under different robot design parameters and friction conditions. The experimental prototype of the wheeled vibration-driven robot is developed at the Vibroengineering Laboratory of Lviv Polytechnic National University. The corresponding experimental investigations are carried out in order to verify the correctness of the obtained results of the numerical modeling and computer simulation. All the results are presented in the form of time dependencies of the robot’s basic kinematic characteristics: displacements, velocities, accelerations of the wheeled platform and disturbing body. The influence of the impact gap value on the average translational speed of the robot’s wheeled platform is studied, and the corresponding recommendations for designers and researchers of similar robotic systems are stated. The prospective directions of further investigations on the subject of the present paper and similar vibration-driven locomotion systems are considered.

The improved design of a vibratory lapping machine is developed in the SolidWorks software on the basis of a suspended double-mass oscillatory system. The system is set into motion by three pairs of electromagnets generating periodic excitation forces applied between the upper and lower laps. By adopting the same forced frequencies and the specific phase shifts of the excitation forces, we aim to produce antiphase translational (circular) oscillations of the laps. In such a case, the best accuracy and operational efficiency of the lapping (polishing) process can be reached. The present research is aimed at analyzing the dynamic behavior of the lapping machine’s oscillatory system. In particular, the motion trajectories of the laps, as well as their kinematic characteristics (displacements, velocities, and accelerations) are considered. The mathematical model of the oscillatory system is developed using the Euler–Lagrange equations. The numerical modelling of the system motion is performed in the Mathematica software using the Runge–Kutta methods. The computer simulation of the laps oscillations is conducted in the SolidWorks software under different friction conditions. The experimental prototype of the vibratory lapping machine was tested in the Vibroengineering Laboratory of Lviv Polytechnic National University. The possibility of generating controllable translational (circular) oscillations of the laps is theoretically studied and experimentally confirmed. Further investigations on the subject of the present paper could focus on the physical-mechanical and technological parameters (surface flatness, roughness, hardness, wear resistance, etc.) obtained through the lapping and polishing processes using the proposed vibratory finishing machine.