Mathematical modeling of controlled vibration mechanisms

The article presents the results of the development and improvement of the theoretical foundations of mathematical modeling of controlled vibration mechanisms of the following three types: a scanner, a reversible mechanism, and mechanisms based on external physical fields – the electrorheological and magnetorheological effects. An analysis and generalization of existing studies and designs of vibration systems with controlled parameters and kinematic relations are carried out, and an updated classification of control methods is proposed. A unified mathematical model is formulated based on the principles of precision vibromechanics and modern vibration theory. Numerical calculations and qualitative analysis of the differential equations were performed using modern computational methods. The reliability of the results is confirmed by experimental tests of a new vibration mechanism design, demonstrating improved dynamic accuracy and control efficiency.