Application of Differential Transformation Method for Nonlinear Cutting Tool Vibration

Abstract

This article aims to solve the mathematical model developed for machine tool vibrations by employing Differential Transformation Method (DTM). Multi-step differential transformation method is used as it has been shown to have good accuracy in physical applications. Nondimensionalization (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 (Multi-Step DTM) give very close results to Simulink® and DDE23.

Keywords

• Vibration
• Differential Transformation Method
• Delayed Differential Equation
• Chatter

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