Vibration acceleration time history obtained from a cutter holder was separated into three parts: chatter free state, transition one and chatter one. The reconstructed attractor and the probability density distribution for the vibration acceleration time series were studied in order to observe a system's behavior in geometric form. And Lyapunov exponent and Kolmogrov entropy were given for helping judgment of cutting state. Meanwhile, the relation curves of Lyapunov exponent and Kolmogrov entropy versus machining parameters were plotted and discussed. The studying showed that Lyapunov exponent and Kolmogrov entropy raise up when the amplitude of the vibration acceleration time history goes up from chatter free state, transition one and chatter one; in addition, the relation curves of Lyapunov exponent and Kolmogrov entropy versus machining parameters also raise up and look like stability lobes; the optimal machining parameters can be chosen to decrease the uncertainty of cutting vibration based on the corresponding experimental data.%取自刀架的振动加速度时间历程被分为三大部分:无颤振切削状态,过渡切削状态和颤振状态.这里分别从热力学角度和几何角度描述了切削系统的动力学行为,给出了与无颤振切削状态和颤振状态相对应的振动加速度时间序列的概率密度分布和三维重构吸引子.并计算了各阶段的Lyapunov指数和Kolmogrov熵.同时绘制并讨论了Lyapunov指数和Kolmogrov熵与切削加工参数的关系曲线.研究表明:Lyapunov指数和Kolmogrov熵与切削加工参数的关系曲线变化趋势相同,看起来象稳定阈图,这些曲线对切削加工参数的选择具有指导作用.并且,当切削状态从无颤振状态过渡到颤振状态时,Lyapunov指数和Kolmogrov熵将随振动幅值的增大而增大.
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