Machines 2022, 10, 130. https://doi.org/10.3390/machines10020130 www.mdpi.com/journal/machines Article Dynamic Analysis of an Enhanced Multi‐Frequency Inertial Exciter for Industrial Vibrating Machines Volodymyr Gursky 1 , Pavlo Krot 2, *, Vitaliy Korendiy 1 and Radosław Zimroz 2 1 Institute of Mechanical Engineering and Transport, Lviv Polytechnic National University, 79013 Lviv, Ukraine; vol.gursky@gmail.com (V.G.); vitalii.m.korendii@lpnu.ua (V.K.) 2 Faculty of Geoengineering, Mining and Geology, Wroclaw University of Science and Technology, 50‐370 Wroclaw, Poland; radoslaw.zimroz@pwr.edu.pl * Correspondence: pavlo.krot@pwr.edu.pl Abstract: 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 mathe‐ matical 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 vi‐ brating machines to operate at a wider range of frequencies and amplitudes. Keywords: inertial exciters; vibrating machines; dynamical model; multi‐frequency vibrators; design parameters 1. Introduction Most vibrating screens, bulk materials conveyors and feeders use inertial vibrating exciters, which are designed taking into account the specified trajectory (linear, circular, elliptical) and direction of the corresponding working element movement (vibrating sieve, transport tray, etc.) [1]. Such trajectories can be realized with one electric motor and a different number of unbalances that rotate synchronously due to forced kinematic or dynamic synchronization [2]. The different means of kinematic synchronization can be used, e.g., gears [3], belt transmissions, or elastic links with nonlinear stiffness [4]. Various cases of dynamic synchronization of rotating unbalanced rotors require appropriate methods of stability analysis based on the theory of nonlinear oscillations [4,5]. Research is not limited to single‐mass systems but is also used for two‐mass sys‐ tems [6], and systems with different numbers of vibrators and unbalanced masses [7]. The stability of vibration systems is particularly affected by the elastic and damping characteristics of support springs [8], the durability of which is significantly limited. Condition monitoring of vibrating machines requires new methods of cyclically per‐ turbed signals processing, which are also significantly affected by the impulsive non‐Gaussian noise from the falling and vibrating pieces of bulk material [9,10]. Appropriate kinematic synchronization of unbalances allows for eliminating one of the components of oscillating motion, such as the vertical component [11], if this is re‐ quired by the technology. Depending on the working conditions, controlling the move‐ Citation: Gursky, V.; Krot, P.; Korendiy, V.; Zimroz, R. Dynamic Analysis of an Enhanced Multi‐Frequency Inertial Exciter for Industrial Vibrating Machines. Machines 2022, 10, 130. https:// doi.org/10.3390/machines10020130 Academic Editor: César M. A. Vasques Received: 29 December 2021 Accepted: 9 February 2022 Published: 11 February 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/license s/by/4.0/).