A novel scheme with high accuracy and high efficiency for surface location error prediction

Dai, Yuebang; Li, Hongkun; Peng, Defeng; Fan, Zhenfang; Yang, Guowei

doi:10.1007/s00170-021-07153-9

Cited by 5 publications

(4 citation statements)

References 30 publications

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“…Put the matrixs G and V into the transition matrix of the dynamical model Ψ using Equations. ( 36)- (39) Calculate the characteristic value of the transition matrix of the dynamical model Ψ using Equation. (40) Paint the SLDs according to Floquet theory using Equation.…”

Section: Mathematical Algorithm Of the Proposed Hfdmmentioning

confidence: 99%

“…Step 6: Put the matrices G and V into the transition matrix of the dynamical model Ψ using Equations ( 36)- (39).…”

Section: Mathematical Algorithm Of the Proposed Hfdmmentioning

confidence: 99%

“…Due to the Runge phenomenon, convergence and accuracy were not always better with the increasing approximate order of the interpolation algorithm. Dai and his co-workers [38,39] suggested a new predictive scheme based on the Newton polynomial-Chebyshev nodes. Later, some scholars expanded on this idea in their FDM methods to further reduce the computing time of the matrix exponentials.…”

Section: Introductionmentioning

confidence: 99%

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A Hybrid Full-Discretization Method of Multiple Interpolation Polynomials and Precise Integration for Milling Stability Prediction

Yang

You

2023

Mathematics

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As milling chatter can lead to poor machining quality and limit the efficiency of productivity, it is of great significance to learn about milling chatter stability and research the effective and fast prediction of milling stability. In this study, a hybrid full-discretization method of multiple interpolation polynomials and precise integration (HFDM) is proposed for milling stability prediction. Firstly, the third-order Newton interpolation polynomial, third-order Hermite interpolation polynomial and linear interpolation are applied to approximate the state term, delay term and periodic coefficient matrix, respectively. Meanwhile, the matrix exponentials can be calculated based on the precise integration algorithm, which can improve computational accuracy and efficiency. The numerical simulation results indicate that the proposed method can not only effectively generate a stability lobe diagram (SLD) but also obtain better prediction accuracy and computation efficiency. A milling experiment is offered to demonstrate the feasibility of the method.

show abstract

Section: Mathematical Algorithm Of the Proposed Hfdmmentioning

confidence: 99%

“…Step 6: Put the matrices G and V into the transition matrix of the dynamical model Ψ using Equations ( 36)- (39).…”

Section: Mathematical Algorithm Of the Proposed Hfdmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Hybrid Full-Discretization Method of Multiple Interpolation Polynomials and Precise Integration for Milling Stability Prediction

Yang

You

2023

Mathematics

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show abstract

“…Huang et al [24] proposed a third-order full-discretization approach that approximates the state term using third-order Newton interpolation and the time-delay term using thirdorder Hermite interpolation. Dai et al [25,26] introduced a unique prediction approach that replaces the original uniform time nodes with Newton polynomial-Chebyshev nodes to address the Runge phenomena.…”

Section: Introductionmentioning

confidence: 99%

A precise and efficient updated third-order full-discretization approach for chatter stability analysis of the milling process

Yang,

Zhou,

Yang

et al. 2024

Preprint

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Stability prediction of milling is of great significance as the regenerative chatter can reduce the machining quality and limit the efficiency of productivity. The stability lobe diagrams (SLDs) are the most popular used prediction approach, which is determined by solving the delay-differential equations (DDEs) describing the milling dynamic system. In this study, a precise and efficient updated third-order full-discretization approach (PE3rdFDM) considering the analytical solution of the free vibration is proposed to determine the SLDs. In each time interval discretized, the state term is defined approximately by the third-order Hermite interpolation polynomial and the derivative values needed to conduct the Hermite interpolation are provided by the original DDEs. To handle the time-delay term, the original integral of the equation obtained by directly integrating the DDE is divided into two parts. For the part with the time delay term, the updated numerical integration formula derived in the past literature is used for approximation. Moreover, the precise integration (PI) algorithm is utilized to calculate the matrix exponentials efficiently and accurately. At last, the transition matrix is established to determine SLDs. To comprehensively appraise the performance of the proposed approach, comparisons between the proposed approach and other prediction approaches are carried out. It includes the analysis of the convergence rate, SLDs obtained by various prediction approaches in different milling conditions, analysis of time cost, the sum of absolute error (SAE), and the arithmetic mean of relative error (AMRE). The above indicators are introduced in the study to estimate the prediction accuracy of the various approaches quantitatively. The results show that the proposed approach not only has high calculation efficiency but also has high prediction accuracy. It is very suitable to carry out the stability prediction in all kinds of milling conditions.

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Calculation boundary vulnerability of numerical algorithm in milling stability prediction

Dai

Lundbäck

et al. 2022

Int J Adv Manuf Technol

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A novel scheme with high accuracy and high efficiency for surface location error prediction

Cited by 5 publications

References 30 publications

A Hybrid Full-Discretization Method of Multiple Interpolation Polynomials and Precise Integration for Milling Stability Prediction

A Hybrid Full-Discretization Method of Multiple Interpolation Polynomials and Precise Integration for Milling Stability Prediction

A precise and efficient updated third-order full-discretization approach for chatter stability analysis of the milling process

Calculation boundary vulnerability of numerical algorithm in milling stability prediction

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