Improving Stability Prediction in Peripheral Milling of Al7075T6

Chatter is an old enemy to machinists but, even today, is far from being defeated. Current requirements around aerospace components call for stronger and thinner workpieces which are more prone to vibrations. This study presents the stability analysis for a single degree of freedom down-milling operation in a thin-walled workpiece. The stability charts were computed by means of the enhanced multistage homotopy perturbation (EMHP) method, which includes the helix angle but also, most importantly, the runout and cutting speed effects. Our experimental validation shows the importance of this kind of analysis through a comparison with a common analysis without them, especially when machining aluminum alloys. The proposed analysis demands more computation time, since it includes the calculation of cutting forces for each combination of axial depth of cut and spindle speed. This EMHP algorithm is compared with the semi-discretization, Chebyshev collocation, and full-discretization methods in terms of convergence and computation efficiency, and ultimately proves to be the most efficient method among the ones studied.The authors wish to acknowledge the financial support received from HAZITEK program, from the Department of Economic Development and Infrastructures of the Basque Government and from FEDER funds. Additional support was provided by the Tecnologico de Monterrey, through the Research Group in Nanomaterials and Devices Design

On the effect of distributed regenerative delay on the stability lobe diagrams of milling processes

Regenerative machine tool chatter is investigated for milling operations with helical tools. The stability of a two-degrees-of-freedom milling model is analyzed, where the cutting-force is modeled as a force system distributed along the rake face of the tool. Introducing a distributed force system instead of a concentrated cutting-force results in an additional short, peri-odically varying distributed delay in the governing equations of the system. It is shown that the additional delay significantly affects the stability of the machining operation, especially at low spindle speeds. This phenomenon is referred to as the short regenerative effect, and is studied by computing the stability lobe diagrams of milling operations via the semi-discretization technique. The sensitivity of the stability charts to the shape of the force distribution and the contact length between the chip and tool is investigated. Keywords milling, stability, machine tool chatter, regenerative delay, cutting-force distribution

On the stability of high-speed milling with spindle speed variation

Spindle speed variation is a well-known technique to suppress regenerative machine tool vibrations, but it is usually considered to be effective only for low spindle speeds. In this paper, the effect of spindle speed variation is analyzed in the high-speed domain for spindle speeds corresponding to the first flip (period doubling) and to the first Hopf lobes. The optimal amplitudes and frequencies of the speed modulations are computed using the semidiscre- tization method. It is shown that period doubling chatter can effectively be suppressed by spindle speed variation, although, the technique is not effective for the quasiperiodic chatter above the Hopf lobe. The results are verified by cutting tests. Some special cases are also discussed where the practical behavior of the system differs from the predicted one in some ways. For these cases, it is pointed out that the concept of stability is understood on the scale of the principal period of the system—that is, the speed modulation period for variable spindle speed machining and the tooth passing period for constant spindle speed machining

Fast generation of stability charts for time-delay systems using continuation of characteristic roots

Many dynamic processes involve time delays, thus their dynamics are governed by delay differential equations (DDEs). Studying the stability of dynamic systems is critical, but analyzing the stability of time-delay systems is challenging because DDEs are infinite-dimensional. We propose a new approach to quickly generate stability charts for DDEs using continuation of characteristic roots (CCR). In our CCR method, the roots of the characteristic equation of a DDE are written as implicit functions of the parameters of interest, and the continuation equations are derived in the form of ordinary differential equations (ODEs). Numerical continuation is then employed to determine the characteristic roots at all points in a parametric space; the stability of the original DDE can then be easily determined. A key advantage of the proposed method is that a system of linearly independent ODEs is solved rather than the typical strategy of solving a large eigenvalue problem at each grid point in the domain. Thus, the CCR method significantly reduces the computational effort required to determine the stability of DDEs. As we demonstrate with several examples, the CCR method generates highly accurate stability charts, and does so up to 10 times faster than the Galerkin approximation method.Comment: 12 pages, 6 figure

Chatter in interrupted turning with geometrical defects: an industrial case study

In this paper, machine tool chatter arising in an interrupted turning process is investigated in a strong industrial context with a complex flexible part. A detailed analysis of the real cutting process is performed with special respect to the geometrical defects of the part in order to highlight the source of machine tool vibrations. The analysis is completed by simple models to estimate the forced vibrations in interrupted turning, the gyroscopic effect, and the mode coupling using a new simplified formulation. Then, a new dynamical model with interrupted cutting and geometrical inaccuracies—runout and orientation of eccentricity—is presented. Stability analysis of this model is performed by the semi-discretization method, an improved technique for analyzing delay-differential equations. The use of all these models on a given machining configuration allows comparing several vibration mechanisms. Thus, behavior’s specificities are highlighted, especially the influence of eccentricity runout on stability. A sensitivity analysis shows the effect of the value and the orientation of the geometrical defects for low speed conditions. Then this result are extrapolated to high-speed conditions to look for possible new stable cutting conditions and shows a period doubling flip instability, never described before in turning operations. The main focus of this paper is developing and exploring a stability model for interrupted cutting in turning with geometrical defects. The complexity of the industrial context led to methodically compare different chatter and vibration mechanisms; this approach can be generalized to other industrial contexts

A comparison of analytical cutting force models

The modeling of dynamic processes in milling and the determination of stable cutting conditions have become increasingly important for the optimization of manufacturing processes. Analytic approaches and time domain simulations based on simplified dynamic systems are used to identify chatter-free machining conditions. Stresses applied to the system are generally estimated by cutting force models. The goal of this paper is to compare the influence of the cutting force models on the stability limits. Numerical simulations of a simplified, generic milling machine model are therefore performed, while varying the cutting force approach. In order to distinguish stable from unstable cutting conditions a numerical stability criterion is used. The resulting stability charts are then investigated and analyzed to show the effect of the different cutting force models

Uncharted Stable Peninsula for Multivariable Milling Tools by High-Order Homotopy Perturbation Method

In this work, a new method for solving a delay differential equation (DDE) with multiple delays is presented by using second- and third-order polynomials to approximate the delayed terms using the enhanced homotopy perturbation method (EMHPM). 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 the cutting milling operation process was used. To further assess the accuracy of the proposed method, a milling process with a multivariable cutter is examined in order 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.This research was funded by Tecnológico de Monterrey through the Research Group of Nanotechnology for Devices Design, and by the Consejo Nacional de Ciencia y Tecnología de México (Conacyt), Project Numbers 242269, 255837, 296176, and National Lab in Additive Manufacturing, 3D Digitizing and Computed Tomography (MADiT) LN299129