Robust stability of milling operations based on pseudospectral approach

Hajdu, Dávid; Borgioli, Francesco; Michiels, Wim; Insperger, Tamás; Stépàn, Gábor

doi:10.1016/j.ijmachtools.2019.103516

Cited by 25 publications

(5 citation statements)

References 24 publications

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“…It is worth noting that the chatter stability must be determined using the Floquet theory. If the modulus of any eigenvalue in Φ 1 exceeds 1, the system is unstable; if the moduli of all eigenvalues in Φ 1 are less than 1, the system is stable [ 21 , 22 ]. Therefore, the boundary curve between the unstable and stable regions in the lobe diagram can be used as the criterion for judging whether chatter occurs.…”

Section: Composite Cotes-based Methodsmentioning

confidence: 99%

Predicting Milling Stability Based on Composite Cotes-Based and Simpson’s 3/8-Based Methods

Ren

Zheng

2022

Micromachines

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Avoiding chatter in milling processes is critical for obtaining machined parts with high surface quality. In this paper, we propose two methods for predicting the milling stability based on the composite Cotes and Simpson’s 3/8 formulas. First, a time-delay differential equation is established, wherein the regenerative effects are considered. Subsequently, it is discretized into a series of integral equations. Based on these integral equations, a transition matrix is determined using the composite Cotes formula. Finally, the system stability is analyzed according to the Floquet theory to obtain the milling stability lobe diagrams. The simulation results demonstrate that for the single degree of freedom (single-DOF) model, the convergence speed of the composite Cotes-based method is higher than that of the semi-discrete method and the Simpson’s equation method. In addition, the composite Cotes-based method demonstrates high computational efficiency. Moreover, to further improve the convergence speed, a second method based on the Simpson’s 3/8 formula is proposed. The simulation results show that the Simpson’s 3/8-based method has the fastest convergence speed when the radial immersion ratio is large; for the two degrees of freedom (two-DOF) model, it performs better in terms of calculation accuracy and efficiency.

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Section: Composite Cotes-based Methodsmentioning

confidence: 99%

Predicting Milling Stability Based on Composite Cotes-Based and Simpson’s 3/8-Based Methods

Ren

Zheng

2022

Micromachines

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“…According to the Floquet theory, if any module of the eigenvalues of the state transition matrix exceeds one, the system motion is unstable; otherwise, if all modules of the eigenvalues of the state transition matrix are less than one, the system motion is stable [ 32 ]. Therefore, the boundary curve for the stable and unstable regions in the lobe diagram can be used as a criterion to judge whether chatter occurs.…”

Section: Mathematical Modelmentioning

confidence: 99%

Milling Stability Prediction: A New Approach Based on a Composited Newton–Cotes Formula

et al. 2023

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Based on a composited Newton–Cotes formula, this paper proposes a numerical method to predict milling stability considering regenerative chatter and focusing on rate and prediction accuracy. First, the dynamic model of milling motion is expressed as state-space equations considering regenerative chatter, with the tooth passing period divided into a set of time intervals. Second, a composited Newton–Cotes formula is introduced to calculate the transition function map for each time interval. Third, the state transition matrix is constructed based on the above-mentioned transition function, and the prediction stability boundary is determined by the Floquet theory. Finally, simulation analysis and experimental verification are conducted to verify the effectiveness of the proposed method. The simulation results demonstrate that, for the milling model with a single degree of freedom (DOF), the convergence rate and prediction accuracy of the proposed method are higher than those of the comparison method. The experimental results demonstrate that, for the milling model with two DOFs, the machining parameters below the prediction stability boundary can avoid the chatter as much as possible, ensuring the machined surface quality.

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“…To avoid the corresponding small-amplitude oscillations consistently, theoretical and/or extensive experimental stability analysis needs to be carried out with respect to the underlying milling operation (see Beri et al (2020); Eynian (2019); Hajdu et al (2020); Stepan et al (2014)). The boundaries of the linearly stable domains indicate the birth of chatter.…”

Section: Motivationmentioning

confidence: 99%

“…The exploitation of these kinds of islands may open new ways in practice to increase the efficiency of material removal processes. Nevertheless, chatter-free cutting is not assured within these formations (see Dombovari and Stepan (2012); Shi and Tobias (1984)) due to various internal or external dynamical uncertainties of the machine tool such as the cutting tool fitting to the holder, temperature or lubrication (see Abele et al (2010); Altintas (2012); Budak et al (2006); Hajdu et al (2020); Stepan et al (2019)). To check the possible use of the stability islands in an industrial environment, bifurcation analysis needs to be accomplished near the stability boundaries (see Dombovari and Stepan (2015); Dombovari et al (2019); Kalmar-Nagy et al (2001)), which provides information about the robustness of stable cutting subjected to perturbations.…”

Section: Stability Chartsmentioning

confidence: 99%

Effect of axial force on the stability of milling: Local bifurcations around stable islands

Béri

Stépàn

2021

Journal of Vibration and Control

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In this paper, the stability properties of milling processes are presented when the axial component of the cutting force is also taken into account as a compressive force acting on the cutting tool. The mechanism of the material removal operation is described by a one degree-of-freedom oscillator subjected to the so-called surface regeneration effect. This can be represented mathematically by a nonlinear, time-periodic, delay differential equation. The regenerative compression affects the natural frequency of the system, which is modelled through the lateral stiffness variation of the bearing support of the main spindle. This extension of the general milling model leads to the birth of stable islands within the originally unstable parameter domain. Since the exploitation of these regions may open new ways in practice for increasing the efficiency of machining, the domain of attraction is investigated qualitatively near the stability boundaries of the stable island by means of a semi-analytical method.

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Robust stability of milling operations based on pseudospectral approach

Cited by 25 publications

References 24 publications

Predicting Milling Stability Based on Composite Cotes-Based and Simpson’s 3/8-Based Methods

Predicting Milling Stability Based on Composite Cotes-Based and Simpson’s 3/8-Based Methods

Milling Stability Prediction: A New Approach Based on a Composited Newton–Cotes Formula

Effect of axial force on the stability of milling: Local bifurcations around stable islands

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