Stability analysis by the EMHPM for regular and multivariable cutting tools in milling operations

Abstract

Machining is a process by which a cutting tool removes material from a workpiece through relative movements between to achieve the desired shape. Milling is a common form of machining using rotary cutters to remove material by advancing a cutter into a work piece. The milling process requires a milling machine, workpiece, fixture, and cutter. When milling vibrations occur, they are usually produced by the impact of the vibration of the previous cut on the current one, this type of vibrations is known as self-excited vibration (chatter) since it occurs between the workpiece and the cutting tool. In this thesis we predict unwanted vibrations during the material removal process in milling using stability lobes. Since milling can be studied using a dynamic equation, a new method for solving a delay differential equation (DDE) is presented by using second- and third-order polynomials to approximate the delayed term using the Enhanced Homotopy Perturbation Method (EMHPM). Different simulations are performed first with regular and later with multivariable tools. To study the proposed method performance in terms of convergency and computational cost in comparison with the first-order EMHPM, Semi-Discretization and Full-Discretization Methods, a delay differential equation that model cutting milling operation process was used. To further assess the accuracy of the proposed method, a milling process with a multivariable cutter is examined to find the stability boundaries. Then, theoretical predictions are computed from the corresponding DDE finding uncharted stable zones at high axial depths of cut. Time-domain simulations based on Continuous Wavelet Transform (CWT) scalograms, Power Spectral Density (PSD) charts and Poincaré Maps (PM) were employed to validate the stability lobes found by using the third-order EMHPM for the multivariable tool and they were compared with experimental results.