A second-order semi-discretization method for the efficient and accurate stability prediction of milling process

Jiang, Shanglei; Sun, Yuwen; Yuan, Xilin; Liu, Weirui

doi:10.1007/s00170-017-0171-y

Cited by 54 publications

(19 citation statements)

References 56 publications

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“…48 and Jiang et al. 49 that the local discretization errors of the UFDM and the 2nd SDM are O( h 3 ). Compared with the 2nd SDM and the UFDM, the proposed algorithm approximates the parameter matrix, the state term and the delay term by the second-order Lagrange interpolating polynomials as a whole unit.…”

Section: Algorithm Verification and Analysismentioning

confidence: 99%

“…Furthermore, the matrix multiplication is needed for the 2nd SDM during the construction of the transition matrix, while the construction of the transition matrix can be implemented with single matrix for the proposed method and the UFDM. Although exponential matrices in the 2nd SDM 49 are computed by an improved precise time-integration (PTI) algorithm, the numerical results of Jiang et al. 49 showed that its efficiency is still lower than the 2nd FDM.…”

Section: Algorithm Verification and Analysismentioning

confidence: 99%

“…Although exponential matrices in the 2nd SDM 49 are computed by an improved precise time-integration (PTI) algorithm, the numerical results of Jiang et al. 49 showed that its efficiency is still lower than the 2nd FDM. For these reasons, the proposed method and the UFDM are expected to achieve more efficient milling stability lobes prediction compared with the 2nd SDM.…”

Section: Algorithm Verification and Analysismentioning

confidence: 99%

“…Jiang et al. 49 developed an improved version of SDM (2nd SDM) for efficient and accurate stability prediction of milling operations.…”

Section: Introductionmentioning

confidence: 99%

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A novel stability prediction method for milling operations using the holistic-interpolation scheme

Qin

Tao

Liu

2019

Proceedings of the Institution of Mechanical Engineers, Part C:

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Currently, accurate and efficient determination of chatter-free cutting conditions is becoming increasingly important. This paper proposes a semi-analytical stability prediction method for milling processes using the holistic-interpolation scheme. The dynamics considering regeneration effect for milling operations is formulated as delay differential equations with time-periodic coefficients. The period of milling dynamic system is divided into two time periods according to the value of the coefficient matrix. On each small time interval for the forced vibration time period, the holistic-interpolation method is utilized by approximating the state term, the delay term, and the time-periodic parameter matrix as a whole unit with the second-order Lagrange interpolating polynomials. Then the Floquet transition matrix can be semi-analytically constructed for milling stability prediction according to Floquet theory. Finally, the benchmark examples of milling models are utilized to validate the effectiveness of the proposed method, which shows that the proposed algorithm achieves both high computational accuracy and efficiency.

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Section: Algorithm Verification and Analysismentioning

confidence: 99%

Section: Algorithm Verification and Analysismentioning

confidence: 99%

Section: Algorithm Verification and Analysismentioning

confidence: 99%

“…Jiang et al. 49 developed an improved version of SDM (2nd SDM) for efficient and accurate stability prediction of milling operations.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A novel stability prediction method for milling operations using the holistic-interpolation scheme

Qin

Tao

Liu

2019

Proceedings of the Institution of Mechanical Engineers, Part C:

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show abstract

“…Consequently, the SDMs are commonly utilized as benchmarks methods for other timedomain semianalytical methods. To obtain higher accuracy and efficiency, Jiang et al [23] presented a second-order semidiscretization method by utilizing Newton interpolation polynomials and improved precise time-integration algorithm. Different from the SDMs, Ding et al [24,25] developed the full-discretization methods (1st FDM and 2nd FDM) for milling stability prediction, in which the state term, the delay term, and the parameter matrix are approximated by linear interpolations, respectively.…”

Section: Introductionmentioning

confidence: 99%

Milling Stability Prediction with Multiple Delays via the Extended Adams‐Moulton‐Based Method

Tao

Qin

Liu

2017

Mathematical Problems in Engineering

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The occurrence of machining chatter may undermine the workpiece surface quality, accelerate the tool wear, and even result in serious damage to the machine tools. Consequently, it is of great importance to predict and eliminate the presence of such unstable and detrimental vibration. In this paper, we present an extended Adams-Moulton-based method for the stability prediction of milling processes with multiple delays. Taking the nonuniform pitch cutters or the tool runout into account, the regenerative chatter for milling operations can be formulated as delay differential equations with multiple delays. The dynamics model for milling regenerative chatter is rewritten in the state-space form. Dividing the spindle rotation period equally into small time intervals, the delay terms are approximated by Lagrange interpolation polynomials, and the Adams-Moulton method is adopted to construct the Floquet transition matrix. On this basis, the milling stability can be derived from the spectral radius of the transition matrix based on Floquet theory. The calculation efficiency and accuracy of the proposed algorithm are verified through making comparisons with the semidiscretization method (SDM) and the enhanced multistage homotopy perturbation method (EMHPM). The results show that the proposed method has both high computational efficiency and accuracy.

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Tensor-Based Automatic Arbitrary Order Computation of the Full-Discretization Method for Milling Stability Analysis

Ozoegwu

Eberhard

2019

Advanced Structured Materials

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A second-order semi-discretization method for the efficient and accurate stability prediction of milling process

Cited by 54 publications

References 56 publications

A novel stability prediction method for milling operations using the holistic-interpolation scheme

A novel stability prediction method for milling operations using the holistic-interpolation scheme

Milling Stability Prediction with Multiple Delays via the Extended Adams‐Moulton‐Based Method

Tensor-Based Automatic Arbitrary Order Computation of the Full-Discretization Method for Milling Stability Analysis

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