Abstract
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.
Highlights
In machining operations, chatter vibration is still one of the main constraints to high productivity and part quality
We present an extended Adams-Moulton-based method for the stability prediction of milling processes with multiple delays
The computation time of the proposed method can be reduced by 67–70% and 45–52%, compared with those of the semidiscretization method (SDM) and the enhanced multistage homotopy perturbation method (EMHPM), respectively
Summary
Chatter vibration is still one of the main constraints to high productivity and part quality. Taking the nonuniform pitch cutters or the case tool runout into account, the regenerative chatter models for milling operations are described by delay differential equations with multiple delays. Based on the updated semidiscretization method from [21], Wan et al [46] developed a unified method to predict milling stability with multiple delays arising in variable pitch cutters or cutter runout. Zhang et al [47, 48] developed an improved FDM and a variable-step NIM for the stability prediction of milling operations with multiple delays. By combining threeorder FDM and variable interpolation technique, Guo et al [56] proposed a time-domain semianalytical method for prediction of milling stability lobes with nonuniform helix tools.
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