Analytical Scheme of Stability Analysis for 4-DoF Mechanical System Subjected to Friction-Induced Vibrations

Abstract

Purpose: The stability problem for non-conservative multi-parameter dynamical system is usually associated with labor-intensive calculations, and numerical methods do not always allow one to obtain the desired information. The presence of circulatory forces often leads to the so-called ”destabilization effect” of the system under the influence of small dissipative forces. In this regard, it seems important to develop analytical approaches that make it possible to use a simplified scheme for checking the stability conditions. Methods: When obtaining and analyzing stability conditions, the algebra of polynomials and elements of mathematical analysis are applied. To obtain a simplified scheme for checking the stability conditions, an asymptotic method is used. Results and Conclusion: A mechanical system with four degrees of freedom which is under the action of dissipative, potential and non-conservative potential (circulatory) forces is considered. The stability problem of friction-induced vibrations is studying. In the case of weak damping an analytical approach is proposed that makes it possible to simplify the analysis of stability conditions, which, due to the presence of many uncertain parameters, are very cumbersome. With the help of numerical testing, the adequacy of the results obtained for the reduced conditions and full stability conditions was established. The results of the analysis make it possible to single out the ”advantageous” regions in the space of dimensionless parameters, which makes it possible to improve the design of the system to increase its reliability.