Application of Differential Transformation Method for Nonlinear Cutting Tool Vibration

Authors : İbrahim DEMİR, M. M. Fatih KARAHAN, Nizami AKTÜRK

Pages : 109-122

View : 14 | Download : 7

Publication Date : 2021-03-29

Article Type : Research Paper

Abstract :This article aims to solve the mathematical model developed for machine tool vibrations by employing Differential Transformation Method insert ignore into journalissuearticles values(DTM);. Multi-step differential transformation method is used as it has been shown to have good accuracy in physical applications. Nondimensionalization insert ignore into journalissuearticles values(scaling); technique is used in order to fully understand the physical effects of each varying parameter. Transformed function of delayed nonlinear velocity terms are explained. MatLab® software is used for DTM solutions. The equation of motion is solved with the DDE23 function in MatLab® software as well as with MatLab®/Simulink® software to compare the results. The solution of the fundamental DTM which is obtained by using the constant transformed function values which differ from other methods after a certain time period. However, the results obtained with the transformed functions for different values at each sampling time insert ignore into journalissuearticles values(Multi-Step DTM); give very close results to Simulink® and DDE23.
Keywords : Vibration, Differential Transformation Method, Delayed Differential Equation, Chatter