Effective and fast prediction of milling stability using a precise integration-based third-order full-discretization method

Yang, Wen-An; Huang, Chao; Cai, XuLin; You, Youpeng

doi:10.1007/s00170-019-04790-z

Cited by 24 publications

(18 citation statements)

References 42 publications

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“…Ref. [14][15][16][17][18][19][20][21][22][23][24][25][26]. The first step is to equally discretize the time period T into m small intervals, that is, T = mτ, where the division [kτ, (k+1)τ] represents one small time interval of T with k = 0, 1, 2, … m.…”

Section: Mathematical Model and Calculation Methodsmentioning

confidence: 99%

“…The discretization method has been widely investigated and applied as an interesting and efficient time domain method [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. By equally discretizing the time period and approximating the delayed term with different polynomials, the zeroth-order and first-order semi-discretization methods ( ZSDM and FSDM ) were proposed by Insperger and Stepan, respectively [12,13].…”

Section: Introductionmentioning

confidence: 99%

“…Subsequently, third-order [19][20][21][22] and higher-order [23][24][25] FDMs were proposed to increase the precision of the stability prediction. In the referenced literature, the thirdorder Newton polynomial [19,20] and third-order Hermite polynomial [21,22] were used, respectively, to estimate the sate term, while the delayed term was interpolated by the Lagrange, Newton, or Hermite polynomials with different orders. Ozoegwu et al [23,24] proposed the least squares method to predict the SLD, where the accuracy of the method could reach to fourth order.…”

Section: Introductionmentioning

confidence: 99%

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Milling stability prediction based on the hybrid interpolation scheme of the Newton and Lagrange polynomials

Xia

Wan

Luo

et al. 2021

Int J Adv Manuf Technol

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The stability lobe diagram (SLD) is commonly used to determine the suitable cutting parameters of the machining system in order to achieve a chatter-free machining process. An improved full discretization method (FDM) is proposed to predict the SLD based on the hybrid interpolation scheme of the Newton and Lagrange polynomials. In order to solve the SLD, a thirdorder Newton polynomial is employed to interpolate the state term of the physical space equation of the system. Meanwhile, to investigate the influence of the interpolation order on predicting the SLD, the delayed term is estimated using the Lagrange polynomials of orders one to four successively. Subsequently, after constructing the transition matrix, a series of calculation for the stability prediction are carried out by applying Floquet theory. The calculated results from these proposed methods demonstrate that the FDM with a second-order Lagrange polynomial is optimal, and further has better computational performance compared with some existing discretization methods. Lastly, the influences of the dynamic parameters on chatter stability are analyzed according to the proposed FDM. When the stiffness and damping ratio increase, the limit cutting depth will be enhanced. The increasing natural frequency not only causes an obvious shift of the lobes to the right, but also raises the limit cutting depth to some extent. These theoretical analyses can guide the prediction and improvement of the chatter stability of a machining system.

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Section: Mathematical Model and Calculation Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Milling stability prediction based on the hybrid interpolation scheme of the Newton and Lagrange polynomials

Xia

Wan

Luo

et al. 2021

Int J Adv Manuf Technol

View full text Add to dashboard Cite

show abstract

“…The comparative study shows that the prediction accuracy reaches the highest when the order of the full-discretization method is four. In the framework of FDM, extensive methods [16][17][18][19][20][21][22][23][24][25][26][27][28] have been proposed to explore the method with both high prediction accuracy and high computational efficiency. In recent years, Jiang et al [29] developed a second-order SDM (2nd SDM), in which the delayed term is approximated by second-order Newton interpolation polynomial.…”

Section: Introductionmentioning

confidence: 99%

An updated Simpson-Based Method for Chatter Stability Prediction in Milling

Yan¹,

Zhang²,

Jia³

et al. 2021

Preprint

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An updated Simpson-based method (USBM) is presented for milling stability analysis. Firstly, the delay differential equation (DDE) is employed to describe the milling process mathematically. Then, the tooth passing period is divided into two subintervals, i.e., the free and forced vibration intervals. Only the forced vibration interval is divided into many equal small-time intervals. Subsequently, the DDE in the state space is solved based on direct integration. By combining the two-step Simpson method and the semi-discretization method, the state transition matrix of the milling system is constructed. The comparison of convergence rate is conducted to validate the accuracy of the proposed method. The results show that the proposed method converges faster than the benchmark methods. The stability lobe diagrams for the one degree of freedom (one-DOF) and two degrees of freedom (two-DOF) milling systems are also obtained by different methods for further evaluation. Meanwhile, the computation time analysis is also carried out. It is revealed that the proposed USBM has advantages in both accuracy and efficiency. Besides, the proposed method can accurately and efficiently predict the stability of milling with both large and low immersion conditions.

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“…Milling is one of the major machining processes that can obtain finished products with desired geometry, dimensions, and surface roughness by material removal. During milling operations, the most common self-induced vibration defined as regenerative chatter is a significant obstacle limiting improvements of the production efficiency and processing quality [1][2][3]. e regenerative chatter is caused by the forces generated during the dynamic cutting process and is not dependent on the external periodic forces.…”

Section: Introductionmentioning

confidence: 99%

Robust Chatter Stability Prediction of the Milling Process considering Uncertain Machining Positions

Deng

Zhou

Yang

et al. 2020

Mathematical Problems in Engineering

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Milling stability is a function of the tool point frequency response functions (FRFs), which vary with the movements of the moving parts within the whole machine tool work volume. The position-dependent tool point FRFs result in uncertain prediction of the stability lobe diagram (SLD) for chatter-free machining parameter selection. Taking the variations of modal parameters to represent the variations of tool point FRFs, this paper introduces the edge theorem to predict the robust milling chatter stability. The application of the edge theorem requires the minimum and maximum modal parameters within the machining space defined by the machining position and machining allowance information. Then, radial basis function artificial neural networks (RBFANNs) are used to predict the position-dependent modal parameters in X and Y directions based on the sample information of machining positions and related modal parameters at the tool point. Moreover, sample machining spaces are determined based on the aforementioned sample positions, and the trained RBFANNs are used to obtain corresponding sample extreme modal parameters. On this basis, RBFANNs for predicting the position and machining allowance-dependent extreme modal parameters can also be trained, and they are combined with the edge theorem and zero exclusion condition to calculate robust pairs of the spindle speed (n) and limiting axial cutting depth (aplim) and then plot the robust SLD (RSLD). A case study was performed on a real three-axial vertical machining center, and the plotted RSLD considering position variations was compared with the traditional SLD. Results of the chatter tests show that the RSLD can provide more reliable (ap, n) pairs to guarantee the milling stability, validating the feasibility of the proposed robust milling chatter stability prediction method.

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Effective and fast prediction of milling stability using a precise integration-based third-order full-discretization method

Cited by 24 publications

References 42 publications

Milling stability prediction based on the hybrid interpolation scheme of the Newton and Lagrange polynomials

Milling stability prediction based on the hybrid interpolation scheme of the Newton and Lagrange polynomials

An updated Simpson-Based Method for Chatter Stability Prediction in Milling

Robust Chatter Stability Prediction of the Milling Process considering Uncertain Machining Positions

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