Stability Prediction on Mathieu Equation of Delayed Periodic Term Based on Full-Discretization Method

Liang Meng,Ming Zhen Li,Shan Jun Li,Yan Lin Zhang

Applied Mechanics and Materials（2013）

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Abstract

Delay Periodic Mathieu Equation (DPME), a kind of Delay differential equation (DDE), is used modeling machining operation. Stability analysis of DDE denotes the stable and unstable area between spindle speed and cutting depth of machining situation. This paper presents full-discretization method (FDM) to analyze stability for delayed periodic Mathieu Equation. Stability lobes are constructed for DPME with different time-period/time-delay ratios

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Key words

full-discretization method,machining stability,mathieu equation

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