Static and dynamic mathematical modeling of an USM rack

Abstract

Abstract Ultrasonic machines (USM) are increasingly used in the technology of processing products made from composite and especially hard and brittle materials. The study of the static and dynamic of USM is essential. The high dynamic quality and precision of machine tools is largely determined by their rigidity. Rigidity determines the vibration resistance of the tool head, which affects the stability of the process and the accuracy of processing. In the present paper, dynamic and static model of the USM is used and a mathematical model of the USM has been developed, which makes it possible to identify parameters in computer experiments that increase the accuracy of hole processing by improving the dynamic quality of the structure using a material with high damping capability such as synthetic granite. As a result, the mathematical relationship between the parameters of stiffness and damping and the vibration amplitude of the working tool is developed, which allows to assess constructive solutions in terms of achieving minimize frequency oscillations of the working tool. It was found that, using synthetic granite decreased the maximum value of the amplitude of the rack oscillations from 77 μm to 13 μm.