Abstract
The prediction of regenerative chatter stability has long been recognized as an important issue of concern in the field of machining community because it limits metal removal rate below the machine’s capacity and hence reduces the productivity of the machine. Various full-discretization methods have been designed for predicting regenerative chatter stability. The main problem of such methods is that they can predict the regenerative chatter stability but do not efficiently determine stability lobe diagrams (SLDs). Using third-order Newton interpolation and third-order Hermite interpolation techniques, this study proposes a straightforward and effective third-order full-discretization method (called NI-HI-3rdFDM) to predict the regenerative chatter stability in milling operations. Experimental results using simulation show that the proposed NI-HI-3rdFDM can not only efficiently predict the regenerative chatter stability but also accurately identify the SLD. The comparison results also indicate that the proposed NI-HI-3rdFDM is very much more accurate than that of other existing methods for predicting the regenerative chatter stability in milling operations. A demonstrative experimental verification is provided to illustrate the usage of the proposed NI-HI-3rdFDM to regenerative chatter stability prediction. The feature of accurate computing makes the proposed NI-HI-3rdFDM more adaptable to a dynamic milling scenario, in which a computationally efficient and accurate chatter stability method is required.
Highlights
It was proved that the ZOA can perform well in regenerative chatter stability prediction tasks, not readily applicable to low radial immersion milling is a common problem for ZOAs in regenerative chatter stability prediction. e MF method extended the study of ZOA to consider the harmonics of the tooth-passing frequencies for low radial immersion machining processes
In the present research, based on third-order Newton interpolation polynomial and third-order Hermite interpolation polynomial techniques, this study proposes a straightforward and effective third-order full-discretization Method to predict the regenerative chatter stability in milling operations
When the third-order Newton interpolation algorithm approximated the state item, the proposed NI-HI-3rdFDM increased the efficiency by 84.8% (1-37/243) compared with the 3rdH-NAM and by 17.8% (1-37/45) compared with the 3rdUFDM under the similar accuracy condition. erefore, it can be concluded that a third-order Newton interpolation of state item and a third-order Hermite interpolation of time-delay item were a good compromise between the performance and the execution time of the proposed NI-HI-3rdFDM
Summary
It is generally accepted that the behavior characteristic of a milling operation is just as much the product of DDE as the morphology. us, by considering regenerative effects, the behavior which can be adequately explained by the classical mathematical theory of milling dynamics is described in state-space form by the equation as follows: x_ (t) A0x(t) + B(t)[x(t) − x(t − T)],. The periodic-coefficient term is achieved by linear interpolation at the time span [kτ, (k + 1)τ], resulting in. 3. The Proposed Method for Milling Stability Analysis e motion of a single DOF milling system with single discrete time delay can be expressed as a functional differential equation as follows: q€(t). In order to evaluate the convergence rate of different time-domain methods such as the NIM, 3rdHAM, 3rdFDM, and the proposed NI-HI-3rdFDM, the local error ||u| − |u0|| is expressed as the function of the discrete number. The SLD of the proposed NI-HI-3rdFDM was relatively identical to that of the 1stFDM and the 1stSDM, but the computation time of the proposed NI-HI-3rdFDM was much less than that of the 1stFDM and the 1stSDM under the same milling parameters. For a/D 0.05, the runtime of the proposed NI-HI-3rdFDM decreased from 200 s to 160 s when compared with the 1stFDM and from 1197 s to 160 s when compared with the 1stSDM
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