Characterization and stability analysis of a multivariable milling tool by the enhanced multistage homotopy perturbation method

• Published in: International journal of machine tools & manufacture Vol. 57; pp. 27 - 33
• Main Authors: Compeán, F.I., Olvera, D., Campa, F.J., López de Lacalle, L.N., Elías-Zúñiga, A., Rodríguez, C.A.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01-06-2012; Elsevier
• Subjects: Applied sciences; Chatter; Cutting tools; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Homotopy; Mathematical models; Mechanical engineering. Machine design; Milling; Milling (machining); Multistage; Multivariable; Multivariable endmilling tool; Perturbation methods; Physics; Solid mechanics; Structural and continuum mechanics; Vibration; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Homotopy; Milling; Chatter; Multivariable endmilling tool; High performance; Vibration; Machining; Multistage apparatus; Contact angle; Stability criterion; Experimental study; Modeling; Rake angle; Perturbation method; Helical tooth; Cutting tool; Dynamic model; Variable pitch; Multivariable system; Cutting force
• ISSN: 0890-6955; 1879-2170
• DOI: 10.1016/j.ijmachtools.2012.01.010

This work deals with the characterization of a three stage multivariable tool used for high-performance milling and the modelling of its dynamic behaviour to predict the stability against chatter. The influence of the variable pitch, variable helix and variable rake angle on each cutting edge of the tool is modeled to calculate the stability lobes diagrams.
The proposed approach includes a mechanistic milling forces model and a cutting coefficients characterization procedure along with a modification of the Enhanced Multistage Homotopy Perturbation Method (EMHPM) to capture the multivariable phenomena of the tool in stability prediction, resulting in an accurate method to reproduce the regenerative vibration problem in end milling. Experimental data is provided to validate the followed approach for this new tool concept.
► A milling tool with variable pitch, helix and rake angle was modeled for cutting forces estimation. ► The forces on each tooth are characterized independently matching the experimental results. ► The enhanced multistage homotopy perturbation method has been used to solve the stability problem. ► The stability model captures the multi-variable nature of the tool with a low computational cost. ► The experimental tests and the stability lobes predicted show agreeable results.