Second-order full-discretization method for milling stability prediction

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

doi:10.1016/j.ijmachtools.2010.05.005

Cited by 167 publications

(88 citation statements)

References 19 publications

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“…Considering the convergence of existing methods has been compared in the literatures [37], so here the comparisons of convergence between the proposed method and second-order full discretization method are given. The parameters of the dynamic milling process are the same as those in Insperger's work [4].…”

Section: Convergence Estimatesmentioning

confidence: 99%

“…In addition, literatures [33,34] also developed numerical methods to predict the stability lobes. Recently, Ding et.al [35] introduced a numerical integration scheme to obtain the stablity lobes, and then they [36,37] developed first-order and second-order full-discretization methods (FDM). Subsequently, Zhang et al [38] presented a variablestep integration FDM method for milling chatter stability prediction with multiple delays.…”

Section: Introductionmentioning

confidence: 99%

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Prediction of stability limit for multi-regenerative chatter in high performance milling

Guo

Sun

Jiang

et al. 2014

Int. J. Dynam. Control

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Chatter is one of the most important factors that inhibit the improvement of productivity and deteriorate the machined surface quality in milling process. In order to obtain good surface quality, classical machining process usually has to take conservative milling parameters. Based on the authors' previous work, this paper presented a new thirdorder discretization method to compute the stability lobes considering multi-regenerative chatter effect. A mathematical model, which is suitable for the dynamic system with non-uniform pitch cutter or cutter run-out, is first established for multi-regenerative chatter. Then, three examples are performed to test the validity of the proposed method. The first example is for the case that the system takes a non-uniform pitch cutter. In the second example, after the modal parameters, run-out parameters and cutting force parameters are gained from experiments, the stability lobes are predicted using the proposed method and subsequently testified by a series of experiments. The third example is for the case of existing cutter run-out. The final computation and experiment results indicate the effectiveness and validity of the proposed method. It is applicable in high performance machining for achieving a good parameter combination.

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Section: Convergence Estimatesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Prediction of stability limit for multi-regenerative chatter in high performance milling

Guo

Sun

Jiang

et al. 2014

Int. J. Dynam. Control

View full text Add to dashboard Cite

show abstract

“…Ding et al [1] subsequently extended the discretization scheme to the periodic coefficient matrices and the associated state terms to develop the so-called full-discretization method. The full-discretization method turned out to be slightly less accurate than semi-discretization method of same order [9,10] but it is as incisive in revealing various stability features of milling. The breakthrough with the advent of full-discretization method is that considerable amount of CT has been saved.…”

Section: Introductionmentioning

confidence: 99%

“…An ingenious application of the Hermite interpolation theory by Liu et al [12] has led to a full-discretization method with further improvements in accuracy and CT. Least squares approximated first and second order full-discretization methods have been introduced in [18] to save considerable amount of CT of the original full-discretization methods in the works [1,10]. The basic interest in this work is to introduce a simplification called Partial Averaging (PA) that further reduces computational cost from the perspectives of amount of analysis involved and CT without loss of accuracy.…”

Section: Introductionmentioning

confidence: 99%

Reducing computational requirement of stability analysis of milling by partial averaging

Ozoegwu

Sam

2014

Manufacturing Rev.

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-The trapezoidal rule and Taylor theorem are used to establish a novel reformulation technique called Partial Averaging (PA). PA is seen to reduce computational time (CT) of computer central processing unit (CPU) without lose of accuracy. Two types of PA are proposed, one involves use of trapezoidal rule to give a map called Full Trapezoidal Rule Map with Partial Averaging (FTRMPA) while the other is achieved through exact analysis to give a map called Partial Trapezoidal Rule Map with Partial Averaging (PTRMPA). The latter is demonstrated to be more accurate and more time conserving in stability analysis of milling process (both one and two degree of freedom systems were considered) and delayed damped Mathieu equation. With all other things being equal the results of stability analysis of fully-immersed milling process using FTRMPA and PTRMPA are seen to be identical with those of full-discretization by Ding et al. [1] further validating the presented reformulation. PA is applied on the Second Order Least Squares Approximated Full-discretization method of [18] to illustrate its usefulness for reducing the cumbersome analysis and CT of the full-discretization method when analysis gets more complicated by higher order interpolation/ approximation theory.

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“…They proposed a predefined nonequidistant discretization scheme to reduce computational cost and increase accuracy of the method. Recently, Ding et al [9,14,15] improved the discretization method and get more higher computing efficiency, and their method can be used for simultaneous prediction of stability and surface location error in low radial immersion milling. The discretization method tests every group set of spindle speed and cutting depth whether to deter the milling system is stable or not.…”

Section: Introductionmentioning

confidence: 99%

An Efficient Approach for Identifying Stable Lobes with Discretization Method

Luo

Zhang

2013

Advances in Mechanical Engineering

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This paper presents a new approach for quick identification of chatter stability lobes with discretization method. Firstly, three different kinds of stability regions are defined: absolute stable region, valid region, and invalid region. Secondly, while identifying the chatter stability lobes, three different regions within the chatter stability lobes are identified with relatively large time intervals. Thirdly, stability boundary within the valid regions is finely calculated to get exact chatter stability lobes. The proposed method only needs to test a small portion of spindle speed and cutting depth set; about 89% computation time is saved compared with full discretization method. It spends only about 10 minutes to get exact chatter stability lobes. Since, based on discretization method, the proposed method can be used for different immersion cutting including low immersion cutting process, the proposed method can be directly implemented in the workshop to promote machining parameters selection efficiency.

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Second-order full-discretization method for milling stability prediction

Cited by 167 publications

References 19 publications

Prediction of stability limit for multi-regenerative chatter in high performance milling

Prediction of stability limit for multi-regenerative chatter in high performance milling

Reducing computational requirement of stability analysis of milling by partial averaging

An Efficient Approach for Identifying Stable Lobes with Discretization Method

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