CYBERNETICS AND PHYSICS, VOL. 10, NO. 2, 2021, 106 –110 SLOW OSCILLATIONS IN DRIVES OF MACHINE ASSEMBLIES Nikolay P. Yaroshevich, Тetjana S. Yaroshevych, Оlexander V. Shovkomud Lutsk National Technical University Ukraine yaroshevichmp@gmail.com, t.yaroshevych@lntu.edu.ua, o.shovkomud@lntu.edu.ua Article history: Received 25.08.2021, Accepted 27.09.2021 Abstract Machine assembly with additional degrees of freedom is considered. The method of direct separation of motions was used for research. It was shown that the braking vibration moment occurring by the reason of resonance effects in the driven object can lead to excitation of rotor oscillations of the assembly with a frequency lower than the rotation frequency. Slow rotor oscillations represent a transient process to the stationary motion mode, which is established when an additional load torque occurs. Moreover, the maximum oscillation amplitudes will be relatively large. By the example of a vibration machine with an inertial drive, the occurrence of slow oscillations of the vibration exciter rotor is demonstrated. Key words Machine assembly, resonance oscillations, drive dynamics, vibration moment, slow oscillations, inner pendulum. 1 Introduction Oscillation of machine assemblies drives is an important engineering problem. Oscillations of drives are investigated in many publications on machine assemblies. First of all, we note the article [Kolovskii, 1985]. This paper investigates the dynamics of a machine assembly with an elastic transmission mechanism. It is shown by the method of a small parameter that when starting an assembly with a nonideal motor, a stationary mode of motion is possible, leading to the Sommerfeld effect. An expression is obtained for the additional average moment of resistance forces, driven to the motor rotor, caused by energy losses during oscillations. This moment is called vibrational in many works [Blekhman, 1971; Blekhman, 2018; Kolovskii, 1985]. A rigorous analytical study of the resonant dynamics of oscillatory systems with limited excitation was first performed by Ilya Izrailevich Blekhman [Blekhman, 1953]. Later, in his works devoted to this topic, a number of significant results were obtained, as well as new ideas for understanding the Sommerfeld effect were presented. In the book, which has already become a classic, "Vibration Mechanics" [Blekhman, 2000], it is shown that the regularities that occur during the manifestation of the Sommerfeld effect are quite simply explained from the standpoint of vibration mechanics. It should be noted that a significant contribution to the development of the theory of systems with limited excitation was made by works [Kononenko, 1969; Alifov and Frolov, 1990; Balthazar et al., 2003]. The book [Blekhman, 2000] indicates the expediency of using the concept and apparatus of vibration mechanics to solve problems of the dynamics of machine assemblies. In particular, it is shown that the dependence of the moment of the resistance forces and the driven moment of inertia of machine assembly on the rotor rotation angle, as well as the elasticity of links and nonideality of the motor, can lead to manifestation of the Sommerfeld effect. In the article [Blekhman and Kremer, 2017], the dynamics of a complex machine assembly with additional degrees of freedom is considered by the method of direct separation of motions. It is shown that these degrees of freedom modify the dynamics of the system with the basic degree of freedom; that when the frequency of the assembly rotor approaches one of the natural frequencies of the driven object, resonant braking of the rotor can take place; that the vibration moment arising from the resonance oscillations of the driven object can be significant. In addition, attention is drawn to the possibility of appearance in the systems under consideration, in addition to rapid oscillations of the rotor speed with the rotation frequency, also "semi-slow oscillations" (in some works called "slow oscillations")