Multi-frequency vibrators have advantages in bulk materials processing but their design is usually complicated. This article presents the synthesis of design parameters of a two-frequency inertial vibrator according to the specified power characteristics. Based on the developed mathematical model, the parameters of variable periodic force is derived for two angular velocities 157, 314 rad/s and their ratios 0.5 and 2. In the case of the 0.5 ratio, the instant angular velocity of the resulting force vector is 2.0–3.5 times greater than for ratio 2. A dynamical model of vibrating screen with the synthesized inertial drive is considered. It was found that at the ratio of angular velocities 0.5, the second harmonic of acceleration prevails at 50 Hz, while at the ratio of 2, the first harmonic has a greater amplitude at 25 Hz. For the first variant, the power does not depend on the initial angle between unbalances, and at the second variant, it can vary. The angle of rotation of unbalances affects the trajectory of the centre of mass and the phases of the harmonics but does not affect their amplitude. Due to such dynamical features, the two-motor inertial drive allows the vibrating machines to operate at a wider range of frequencies and amplitudes.

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.

Introduction: The paper considers the improved design of the wheeled vibration-driven robot equipped with an inertial exciter (unbalanced rotor) and enhanced pantograph-type suspension. The primary purpose and objectives of the study are focused on mathematical modeling, computer simulation, and experimental testing of locomotion conditions of the novel robot prototype. The primary scientific novelty of the present research consists in substantiating the possibilities of implementing the enhanced pantograph-type suspension in order to improve the robot’s kinematic characteristics, particularly the average translational speed.Methods: The simplified dynamic diagram of the robot’s oscillatory system is developed, and the mathematical model describing its locomotion conditions is derived using the Euler-Lagrange differential equations. The numerical modeling is carried out in the Mathematica software with the help of the Runge-Kutta methods. Computer simulation of the robot motion is performed in the SolidWorks Motion software using the variable step integration method (Gear’s method). The experimental investigations of the robot prototype operating conditions are conducted at the Vibroengineering Laboratory of Lviv Polytechnic National University using the WitMotion accelerometers and software. The experimental data is processed in the MathCad software.Results and discussion: The obtained results show the time dependencies of the robot body’s basic kinematic parameters (accelerations, velocities, displacements) under different operating conditions, particularly the angular frequencies of the unbalanced rotor. The numerical modeling, computer simulation, and experimental investigations present almost similar results: the smallest horizontal speed of about 1 mm/s is observed at the supplied voltage of 3.47 V when the forced frequency is equal to 500 rpm; the largest locomotion speed is approximately 40 mm/s at the supplied voltage of 10 V and forced frequency of 1,500 rpm. The paper may be interesting for designers and researchers of similar vibration-driven robotic systems based on wheeled chassis, and the results may be used while implementing the experimental and industrial prototypes of vibration-driven robots for various purposes, particularly, for inspecting and cleaning the pipelines. Further investigation on the subject of the paper should be focused on analyzing the relations between the power consumption, average translational speed, and working efficiency of the considerer robot under various operating conditions.