Stability prediction of milling process with variable pitch and variable helix cutters

Jin, Gang; Zhang, Qichang; Hao, Shuying; Xie, Qizhi

doi:10.1177/0954406213486381

Cited by 25 publications

(44 citation statements)

References 26 publications

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“…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

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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.

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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

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“…Altintas et al [8] and Budak [9,10] presented a model for predicting the milling stability with VPC. Sims et al [11], and Jin et al [12,13] investigated the effect of VPC or VHC (variable helix cutter) about the stability with semi-discrete method. And then, Stepan et al [14] improved the milling stability with VPC.…”

Section: Introductionmentioning

confidence: 99%

Dynamic milling stability prediction of thin-walled components based on VPC and VSS combined method

Zhang

Hao

et al. 2020

J Braz. Soc. Mech. Sci. Eng.

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In the milling process, the coupling deflection and the dynamic characteristics of the cutter-workpiece system are time variant as the material removal and the change of cutter position. The milling stability of the system is dynamic because of the time-varying stiffness. In this study, the model of time-varying system has been developed. Variable pitch cutter (VPC) and variable spindle speed (VSS) are, respectively, typical method of passive control and active control to suppress the chatter, and two methods are compatible. The arithmetic of VPC and VSS combined method has been developed and verified effectively. Dynamic milling stability prediction of stiffness time-varying system for thin-walled components based on VPC and VSS combined method has been developed. And then, the dynamic milling stability of stiffness time-varying system for thin-walled components has been predicted. Keywords Thin-walled components • Dynamic milling stability • Stiffness time-varying system • VPC & VSS • SLD k Modal stiffness (N/mm) ξ Damping ratio ω n Natural frequency (Hz)

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“…The so-called spectral element approach was introduced by Khasawneh and Mann [50] for stability analysis of timeperiodic delay equations with multiple delays. Jin et al [51][52][53] presented an improved SDM to investigate the effect of the tool geometries on the stability trends for variable pitch or variable helix milling. Sims [54] introduced an efficient approach to variable helix tool stability based upon the Laplace transform.…”

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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Stability prediction of milling process with variable pitch and variable helix cutters

Cited by 25 publications

References 26 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

Dynamic milling stability prediction of thin-walled components based on VPC and VSS combined method

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

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