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

Gang Jin, Houjun Qi, Zhanjie Li, Jianxin Han and Hua Li

Mathematical Problems in Engineering, 2017, vol. 2017, 1-8

Abstract:

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.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:9490142

DOI: 10.1155/2017/9490142

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