基于混沌相空间重构的数控机床运动精度演化分析

数控机床运动精度状态的变化是一个复杂非线性动力系统的时空演化过程,难以通过数学建模方法分析其演化规律。提出基于混沌相空间重构理论的数控机床运动精度演化分析方法。根据混沌系统内在的规律性和有序性,分析基于相空间重构的数控机床精度演化原理,对数控机床运动精度的一维时间序列进行相空间重构,从而得到与原系统拓扑同构的高维相空间。提出用相点轨迹描述运动精度在相空间中的演化规律,构造一个非线性演化模型,用相点的多维分量构成输入向量,对其精度趋势进行演化。实验结果表明,基于混沌相空间重构的演化模型,可以很好地追踪数控机床运动精度的演变趋势和规律,且具有较高的演化精度。

Evolution analysis of CNC machine tool motion precision based on chaotic phase space reconstruction

The change of CNC machine tool motion precision is a temporal spatial evolution process of complex nonlinear dynamical system, and it is difficult to analyze its evolution law with mathematical modeling. The CNC machine tool motion precision evolution analysis method based on chaotic phase space reconstruction theory is proposed. Firstly, according to the chaotic system inner orderliness and regularity, the CNC machine tool motion precision evolution principle based on phase space reconstruction is analyzed. The phase space reconstruction of the one dimensional time series of NC machine tool motion precision is proposed, the high dimensional phase space with the same topological isomorphism is obtained. Secondly, it is proposed that the phase point trajectory is employed to describe the motion precision evolution law in phase space, the nonlinear prediction model is constructed. The phase point multi dimensional component is used to construct the input vector, and the precision evolution trend can be predicted. The experiment results indicate that the prediction model based on chaotic phase space reconstruction can trace the evolution trend and regularity of the CNC machine tool motion precision properly and can achieve high prediction precision.