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Journals / Gazi University Journal of Science Part A: Engineering and Innovation / 2026 / Volume: 8 Issue: 1

Application of Differential Transformation Method for Nonlinear Cutting Tool Vibration

İbrahim Demir(MANİSA CELÂL BAYAR ÜNİVERSİTESİ, MÜHENDİSLİK FAKÜLTESİ, MAKİNE MÜHENDİSLİĞİ BÖLÜMÜ)0000-0002-2128-3949
M. M. Fatih Karahan(MANİSA CELÂL BAYAR ÜNİVERSİTESİ, MÜHENDİSLİK FAKÜLTESİ, MAKİNE MÜHENDİSLİĞİ BÖLÜMÜ)0000-0001-9040-5041
Nizami Aktürk(GAZİ ÜNİVERSİTESİ, MÜHENDİSLİK FAKÜLTESİ, MAKİNE MÜHENDİSLİĞİ BÖLÜMÜ)0000-0003-1398-8145
Pages
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Publication Date
2021-03-29
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This article aims to solve the mathematical model developed for machine tool vibrations by employing Differential Transformation Method (DTM).
📊
Key Findings & Data:The equation of motion is solved with the DDE23 function in MatLab® software as well as with MatLab®/Simulink® software to compare the results.
💡
Conclusion & Impact: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.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Vibration · Differential Transformation Method · Delayed Differential Equation

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.

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Cite This Article

Demir, İ., Karahan, M. M. F., Aktürk, N. (2021). Application of Differential Transformation Method for Nonlinear Cutting Tool Vibration. Gazi University Journal of Science Part A: Engineering and Innovation, Volume: 8 Issue: 1. https://ajindex.com/articles/1398646

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