基于混沌吸引子的数控机床运动误差表征与溯因

doi:10.3901/JME.260303

摘要/Abstract

摘要： 数控机床运动误差的变化是一个具有混沌特性的非线性演化过程，其内在结构状态决定了运动精度的非线性动力学演化轨迹即混沌吸引子，这为机床运动误差表征与溯因开辟了全新思路。为此，从数控机床精度演化的非线性动力学行为角度，提出基于混沌吸引子研究运动误差演化的本质特征及其表征方法。首先，利用数控机床的圆运动轨迹建立运动误差模型，对机床运动误差的各时序特征进行混沌验证，以证明数控机床运动误差的演化具有混沌特性。然后，在相空间重构不同误差因素引起的运动误差混沌吸引子，建立混沌吸引子和数控机床运动误差的映射模型，提出基于混沌吸引子的数控机床运动误差表征方法。进一步，引入基于麻雀搜索算法的离散小波变换对时间序列进行降噪处理，解决运动误差受到噪声干扰难以恢复混沌吸引子相图的问题。最后，从运动误差混沌序列中提取和恢复出动力系统原有的规律和本质特征，在高维相空间重构机床运动精度演化轨迹，根据混沌吸引子特征追溯数控机床精度变化因素。实验表明，所提出方法重构出的混沌吸引子几何结构较为清晰，能特征鲜明地识别出数控机床多源运动误差因素，并具有较强的适应性。

关键词: 运动误差, 相空间重构, 混沌吸引子, 麻雀搜索, 离散小波变换

Abstract: The variation of motion error in CNC machine tools is a nonlinear evolution process with chaotic characteristics. The intrinsic structural state of CNC machine tools determines the nonlinear dynamical evolution trajectory of motion accuracy, namely the chaotic attractor, which opens up a new approach for characterizing and tracing the causes of motion error in CNC machine tools. Therefore, from the perspective of the nonlinear dynamic behavior of the precision evolution of CNC machine tools, a method for essential characteristics and further characterization of motion error evolution based on chaotic attractors is proposed. Firstly, a motion error model is established using the circular motion trajectory of CNC machine tools. The time-series characteristics of motion error are verified through chaotic theory, demonstrating that the evolution of motion error exhibits chaotic characteristics. Then, chaotic attractors of motion error caused by different error factors are reconstructed in phase space, and a mapping model between these chaotic attractors and motion error of CNC machine tools is established. A method for characterizing the motion error of CNC machine tools based on chaotic attractors is proposed. Furthermore, the discrete wavelet transform based on sparrow search algorithm is introduced for time series denoising, addressing the problem that noise interference obscures the phase diagram of chaotic attractors. Finally, the original laws and essential characteristics of the dynamic system are extracted and recovered from the chaotic sequence of motion error. The evolution trajectory of motion accuracy is reconstructed in high-dimensional phase space, and the factors affecting the accuracy variation of CNC machine tools are traced based on the characteristics of chaotic attractors. Experimental results show that the geometric structure of the reconstructed chaotic attractor is relatively clear, and multi-source motion error factors of CNC machine tools can be identified with distinct features and strong adaptability.

Key words: motion error, phase space reconstruction, chaotic attractor, sparrow search, discrete wavelet transform

中图分类号:

TH161

杜柳青, 崔楷华, 余永维. 基于混沌吸引子的数控机床运动误差表征与溯因[J]. 机械工程学报, 2026, 62(13): 309-321.

DU Liuqing, CUI Kaihua, YU Yongwei. Characterizing and Tracing of Motion Error in CNC Machine Tools Based on Chaotic Attractors[J]. Journal of Mechanical Engineering, 2026, 62(13): 309-321.

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链接本文: http://www.cjmenet.com.cn/CN/10.3901/JME.260303

http://www.cjmenet.com.cn/CN/Y2026/V62/I13/309

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