On the stability of high-speed milling with spindle speed variation

Seguy, Sébastien; Insperger, Tamás; Arnaud, Lionel; Dessein, Gilles; Peigné, Grégoire

doi:10.1007/s00170-009-2336-9

Cited by 117 publications

(46 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…However, most of them were developed with the aim of constructing stability charts for milling processes, such as the analysis of the milling system with runout [25], with variable pitch/helix cutter [26][27][28][29][30], with variable-spindle speed [31][32][33], or with serrated cutter [34,35]. In order to verify the proposed method, two typical milling operations are chosen and considered.…”

Section: Verification Of Methodsmentioning

confidence: 99%

A Method for Stability Analysis of Periodic Delay Differential Equations with Multiple Time-Periodic Delays

Jin

et al. 2017

Mathematical Problems in Engineering

View full text Add to dashboard Cite

Delay differential equations (DDEs) are widely utilized as the mathematical models in engineering fields. In this paper, a method is proposed to analyze the stability characteristics of periodic DDEs with multiple time-periodic delays. Stability charts are produced for two typical examples of time-periodic DDEs about milling chatter, including the variable-spindle speed milling system with one-time-periodic delay and variable pitch cutter milling system with multiple delays. The simulations show that the results gained by the proposed method are in close agreement with those existing in the past literature. This indicates the effectiveness of our method in terms of time-periodic DDEs with multiple time-periodic delays. Moreover, for milling processes, the proposed method further provides a generalized algorithm, which possesses a good capability to predict the stability lobes for milling operations with variable pitch cutter or variable-spindle speed.

show abstract

Section: Verification Of Methodsmentioning

confidence: 99%

A Method for Stability Analysis of Periodic Delay Differential Equations with Multiple Time-Periodic Delays

Jin

et al. 2017

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

“…Bayly and his colleagues developed the temporal finite element analysis (TFEA) method [19], which can be generalized to the non-linear TFEA formulation [20] and prediction of the surface location error in milling [21,22]. Insperger and Stépán explored the semi-discretization method (SDM) [23,24], and the first-order SDM [25], which are widely used in many cases, such as stability analysis for up-milling and down-milling [26,27], stability prediction for milling processes with variable time delays [28], in consideration of the loss-of-contact and feed-rate effects [29], milling with variable pitch and variable helix milling tools [30], milling with spindle speed variation [31], etc. Wan et al [32] recently proposed an improved semi-discretization method for predicting the chatter stability of milling processes considering multiple delays, i.e., the effects of runout and variable pitch of tools.…”

Section: Introductionmentioning

confidence: 99%

Milling stability analysis using the spectral method

Ding

Zhu

Zhang

et al. 2011

Sci. China Technol. Sci.

View full text Add to dashboard Cite

This paper focuses on the development of an efficient semi-analytical solution of chatter stability in milling based on the spectral method for integral equations. The time-periodic dynamics of the milling process taking the regenerative effect into account is formulated as a delayed differential equation with time-periodic coefficients, and then reformulated as a form of integral equation. On the basis of one tooth period being divided into a series of subintervals, the barycentric Lagrange interpolation polynomials are employed to approximate the state term and the delay term in the integral equation, respectively, while the Gaussian quadrature method is utilized to approximate the integral term. Thereafter, the Floquet transition matrix within the tooth period is constructed to predict the chatter stability according to Floquet theory. Experimental-validated one-degree-of-freedom and two-degree-of-freedom milling examples are used to verify the proposed algorithm, and compared with existing algorithms, it has the advantages of high rate of convergence and high computational efficiency. milling stability, delayed differential equation, integral equation, spectral method, Floquet theory Citation:Ding Y, Zhu L M, Zhang X J, et al. Milling stability analysis using the spectral method.

show abstract

“…Ahmadi and Ismail [14] explored the stability lobes in milling including process damping by utilizing multi-frequency and semi-discretization methods. Seguy et al [15] studied the stability of high-speed milling with spindle speed variation in the semi-discrete domain. Alternatively, Ding et al [16] developed a full-discretization method, and Guo et al [17] extended this method to a third-order format.…”

Section: Introductionmentioning

confidence: 99%

Study on the construction mechanism of stability lobes in milling process with multiple modes

Wan

Zhang

et al. 2015

Int J Adv Manuf Technol

View full text Add to dashboard Cite

The stability of milling process dominated by multiple modes was traditionally predicted in the time domain by only selecting the most flexible mode. This paper theoretically studies the construction mechanism of stability lobes by simultaneously considering all dominant modes and provides an efficient method to predict stability lobes of milling systems with multiple modes in the time domain. It is theoretically proved that the effective stability lobes of milling system with multiple modes is made up of the lowest envelop of the stability lobes achieved with each single mode; hence, lowest envelop method (LEM) is established to predict the ultimate stability lobe by taking the lowest envelop of a group of stability lobes, which are calculated by separately considering different dominant modes composing the overall dynamic compliance. Typical advantage of LEM lies in that the computation time and the memory usage required in stability prediction can be greatly reduced for time domain solution. Moreover, the accuracy of prediction can be increased, when the effects of multiple modes are taken into account instead of considering only the most flexible mode. Formulation of the dynamic milling process with multiple modes is derived in semi-discrete time domain by including the effects of multiple delays. A series of simulations and experiments demonstrate the high efficiency and validity of LEM.

show abstract

On the stability of high-speed milling with spindle speed variation

Cited by 117 publications

References 37 publications

A Method for Stability Analysis of Periodic Delay Differential Equations with Multiple Time-Periodic Delays

A Method for Stability Analysis of Periodic Delay Differential Equations with Multiple Time-Periodic Delays

Milling stability analysis using the spectral method

Study on the construction mechanism of stability lobes in milling process with multiple modes

Contact Info

Product

Resources

About