Milling stability analysis using the spectral method

Ding, Yong; Zhu, Limin; Zhang, XiaoJian; Ding, Han

doi:10.1007/s11431-011-4611-x

Cited by 33 publications

(13 citation statements)

References 52 publications

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“…On this basis, the spectral method with exponential convergence rate [68] and the variable-step integration method suitable for the multiple time delay systems [69] are proposed.…”

Section: Integral Equation Based Methodsmentioning

confidence: 99%

On time-domain methods for milling stability analysis

Ding

Zhu

2012

Chin. Sci. Bull.

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As a basic and advanced machining technique, the high-speed milling process plays an important role in realizing the goal of high performance manufacturing. From the viewpoint of machining dynamics, obtaining chatter-free machining parameters is a prerequisite to guaranteeing machining accuracy and improving machining efficiency. This paper gives an overview on recent progress in time domain semi-analytical methods for chatter stability analysis of milling processes. The state of art methods of milling stability prediction in milling processes and their applications are introduced in detail. The bottlenecks involved are analyzed, and potential solutions are discussed. Finally, a brief prospect on future works is presented. High speed milling is widely utilized in manufacturing of complex surfaces for the fields of aerospace, ship, automotive, dies and molds etc., due to its advantage of obtaining high machining accuracy and high material removal rate with keeping low-amplitude cutting forces. Regarding to modeling of machining processes, the research topics on high speed milling can be categorized as: tool path planning, machining dynamics and machining physical modeling. Tool path planning is to plan the tool path according to the workpiece model, machining strategy and required machined error [1][2][3][4][5]. From the viewpoint of machining dynamics, the relative vibration between the workpiece and cutter in the milling process is the main reason of reducing product surface quality and limiting the production efficiency. To suppress the vibration impact by optimizing the machining parameters, the following two questions need to be addressed.(1) Stability analysis based on the dynamics of milling processes. As far as chatter vibrations are concerned, there are four different mechanisms: regeneration [6], mode coupling [7], friction [8] and thermo-mechanics of chip formation [9]. In milling processes, regenerative chatter is the most common form of self-excited vibration to reduce surface quality and machining efficiency [10,11]. The works on analysis of the stability of milling processes focus on calculating the stability boundary of the machining parameters based on the dynamic models characterizing the milling processes.(2) Machining accuracy analysis on the basis of stability analysis. Due to forced vibrations in milling processes, chatter-free machining parameters cannot ensure high performance machining. Vibration-induced surface errors can be classified as surface location error (SLE) [12] and surface roughness [13]. It is essential to take the stability and dynamical errors into account in machining optimization models to achieve high performance milling.

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“…On this basis, the spectral method with exponential convergence rate [68] and the variable-step integration method suitable for the multiple time delay systems [69] are proposed.…”

Section: Integral Equation Based Methodsmentioning

confidence: 99%

On time-domain methods for milling stability analysis

Ding

Zhu

2012

Chin. Sci. Bull.

Self Cite

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“…Therefore, the accuracy of the proposed method has a peak, and the best rate of convergence for the NDM is O(τ 13 ). When higher computational precision is required, the DQM [41] or spectral method [29] is avialable because the Chebyshev-Gauss-Lobatto sampling grid points are used in these methods to avoid Runge's phenomenon in equidistant interpolation, and the exponential convergence can be achieved, as shown in Fig. 4a.…”

Section: Rate Of Convergence Analysismentioning

confidence: 99%

“…To further enhance the computational accuracy, the spectral method [29] is proposed which can achieve high rate of convergence and high computational efficiency. Khasawneh et al [30] also developed a spectral element approach for the stability of delay systems which has exponential rates of convergence.…”

Section: Introductionmentioning

confidence: 99%

Prediction of chatter stability in high speed milling using the numerical differentiation method

Zhang

Chen

Ding

et al. 2016

Int J Adv Manuf Technol

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A numerical differentiation method is presented to predict the high speed milling stability of a two degrees of freedom (DOF) system based on the finite difference method and extrapolation method. The milling dynamics taking the regenerative effect into account are represented as linear periodic delayed differential equations (DDE) in the state space form. Then, each component of the first derivative of the state function versus time at the discretized sampling grids is approximated as a weighted linear sums of the state function values at its neighboring grid points, where the weight coefficients are calculated based on the extrapolation method. As such, the DDE on the forced vibration duration is approximately discretized as a series of algebraic equations. Thereafter, the Floquet transition matrix can be constructed on one tooth passing period by combining the analytical solution of the free vibration and the algebraic equations of the forced vibration. Finally, the milling stability is determined according to Floquet theory. The stability diagrams and convergence of critical eigenvalues in comparison with the benchmark algorithms (the semi-discretization method and numerical integration method) via experimentally verified examples are utilized to demonstrate the effectiveness and efficiency of the proposed method.

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“…Based on the direct integration scheme Ding et al presented the firstorder full-discretization method [12] and second-order full-discretization method [13], Quo et al [14] proposed the third-order full-discretization method. Then, Ding et al proposed the spectral method [15], numerical integration method [16], differential quadrature method [17] and Legendre polynomial-based method [18] for stability prediction in milling. Li et al [19] proposed the complete dicretization method for milling stability prediction, in this method the Euler's method is used to replace the direct integration scheme.…”

Section: Introductionmentioning

confidence: 99%

Stability prediction of thin-walled workpiece made of Al7075 in milling based on shifted Chebyshev polynomials

Yan

Liu

Wang

et al. 2016

Int J Adv Manuf Technol

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With the rapid development of aerospace technology, Al7075 has been widely used for structural components. High-speed milling is one of the most effective ways to improve machining efficiency of Al7075. During the milling process, regenerative chatter which restricts the milling quality and productivity often occurs. With the aim of avoiding regenerative chatter, stability lobe diagram (SLD) is widely used to obtain chatter-free parameters. This work presents a stability prediction method by using shifted Chebyshev polynomials. The milling dynamics with consideration of the regenerative effect is described by time periodic delaydifferential equations (DDEs). The transition matrix of the milling system is constructed with the help of ChebyshevGauss-Lobatto (CGL) points. In order to demonstrate the accuracy of the proposed method, the rate of convergence of the proposed method is compared with that of the classical benchmark methods. On the other hand, in the process of thinwalled workpiece milling, the dynamic behavior of the workpiece depends on the tool position. To study the influence of the tool position dependent dynamics on the chatter stability of the thin-walled workpiece, a three-dimensional SLD is obtained. The verification experiments are conducted to verify the reliability of the proposed method. The results show that the experimental results are consistent with the predicted results.

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Milling stability analysis using the spectral method

Cited by 33 publications

References 52 publications

On time-domain methods for milling stability analysis

On time-domain methods for milling stability analysis

Prediction of chatter stability in high speed milling using the numerical differentiation method

Stability prediction of thin-walled workpiece made of Al7075 in milling based on shifted Chebyshev polynomials

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