Complete discretization scheme for milling stability prediction

Li, Mingzhen; Zhang, Guojun; Huang, Yu

doi:10.1007/s11071-012-0651-4

Cited by 79 publications

(38 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where [a, b] is the domain of functions f and g. The solution of (13) always satisfies (22) however, if a solution satisfies (22), that does not imply that it also satisfies (13). System of equations (13) and (22) are equivalent if and only if (22) is true for all possible ψ test functions of the function space (i.e., if the left-hand side of (13) is orthogonal to all elements of the function space).…”

Section: Derivation Of the Methodsmentioning

confidence: 99%

“…This system of equations gives the finite dimensional approximation of weak form (22). Since (28) weights r k residual functions by ψ i test functions along the domain of solution, this method, used for the discretization of operator equations, was named weighted residuals by Crandall in [11].…”

Section: Derivation Of the Methodsmentioning

confidence: 99%

“…In the recent decades several numerical methods have been developed for the linear stability analysis of time-periodic delay-differential equations (DDEs). Examples for such methods are the multifrequency solution [1,5], semi-discretization [17], full discretization [12], complete discretization [22], Chebyshev continuous time approximation [10] and the recently presented spectral element method [18,19,20], which is the subject of this paper. The method was first published in [18] for autonomous DDEs with single delay, thereafter it was extended in [19] to autonomous DDEs with distributed delay and generalized to time-periodic DDEs with multiple point delays in [20].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Extension of the spectral element method for stability analysis of time-periodic delay-differential equations with multiple and distributed delays

Lehotzky

Insperger

Stépàn

2016

Communications in Nonlinear Science and Numerical Simulation

View full text Add to dashboard Cite

Section: Derivation Of the Methodsmentioning

confidence: 99%

Section: Derivation Of the Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Extension of the spectral element method for stability analysis of time-periodic delay-differential equations with multiple and distributed delays

Lehotzky

Insperger

Stépàn

2016

Communications in Nonlinear Science and Numerical Simulation

View full text Add to dashboard Cite

“…Besides, these methods do not lose any numerical precision and have higher computational efficiency than the SDM. Li et al [8] introduced a complete discretization scheme for milling stability analysis. In this method, all time-dependent items of the DDE were discretized.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional stability prediction and chatter analysis in milling of thin-walled plate

Zhao

Wang

2016

Int J Adv Manuf Technol

View full text Add to dashboard Cite

Stability lobe diagram can be used for selecting proper milling parameters to perform chatter-free operations and improve productivity during milling of thin-walled plates. This paper studies the machining stability in milling of thin-walled plates and develops a three-dimensional stability lobe diagram of the spindle speed, tool position, and axial depth of cut. The workpiece-holder system is modeled as a 2-degree-of-freedom system considering that the tool system is much more rigid than the thin-walled plate, and dynamic equations of motion described for the workpieceholder system are solved numerically in time domain to compute the dynamic displacements of the thin-walled plate. Statistical variances of the dynamic displacements are then employed as a chatter detection criterion to acquire the stability lobe diagram. The experimentally obtained stability limits correspond well with the predicted stability limits. In addition, influence of feed rate on stability limits is also investigated. By performing frequency analysis of the measured cutting forces to judge if chatter occurs, it is found that feed per tooth has little influence on the stability limits. However, feed per tooth impacts the machined surface quality. The results show that the surface quality drops by increasing feed per tooth.

show abstract

“…Al-Regib and Ni [13] developed a normalized chatter detection index based on the Wigner time-frequency distribution. Li et al [14] put forward a complete discretization scheme for milling stability prediction, where all time-dependent items of the DDE were discretized. Khasawneh and Mann [15] presented a spectral element approach for stability analysis of delay systems.…”

Section: Introductionmentioning

confidence: 99%

Analysis of the machining stability in milling thin-walled plate

Zhao

Wang

2015

2015 IEEE International Conference on Robotics and Biomimetics (ROBIO)

View full text Add to dashboard Cite

Abstract-The thin-walled plate parts are widely used in the aeronautical industry. Research on the machining stability in end milling of thin-walled plate is of great significance to improve the materials remove rates and optimize milling parameters. Analyzing the influence of milling parameters on the milling stability is conducive to choosing appropriate cutter and milling machine in actual milling. In this study, statistical variances of the dynamic displacements are employed as a chatter detection criterion to acquire the stability lobe diagram. The milling experiment results show that the obtained stability lobe diagram can predict the stability domain well. Based on this stability theory, the influences of modal parameters and tooth number on the machining stability are analyzed systematically by simulation, which is significant for choosing an appropriate cutting condition.

show abstract

Complete discretization scheme for milling stability prediction

Cited by 79 publications

References 17 publications

Extension of the spectral element method for stability analysis of time-periodic delay-differential equations with multiple and distributed delays

Extension of the spectral element method for stability analysis of time-periodic delay-differential equations with multiple and distributed delays

Three-dimensional stability prediction and chatter analysis in milling of thin-walled plate

Analysis of the machining stability in milling thin-walled plate

Contact Info

Product

Resources

About