行星轮系混合故障振动调频调幅机理和诊断方法研究

The special engagement of planetary gear train, the time-varying vibration response and the multiple modulation sideband with same frequencies limit the existing vibration model to explain the frequency and amplitude modulation mechanism. Additionally, the difference between vibration signals of fault mode and normal mode is quite small, making it difficult to recognize the fault, which leads to a relatively high misdiagnosing rate. Kinetic models of planetary gear train are built, which considers the frequency modulation caused by rotation speed fluctuation, then the mapping relation between the frequency/amplitude modulation features and the fault mode as well as its damaging level is studied to acquire the high-precision mathematical model of faulty vibration response. Based on the periodicity and correlation of faulty feature signal in time and frequency domain under speed-varying condition, three types of dictionary are constructed, namely the harmonic modulation dictionary with analytic expression, the analytic modulation dictionary based on the edited cepstrum method and the learning dictionary based on the sliding window de-noising K-SVD. The fast block sparse algorithm based on nuclear norm and convex relaxation optimization is designed, which is employed to obtain the sparse coefficients for amplitude and frequency modulation features. The square amplitude demodulation, the first kind of Bessel function demodulation and the least-squares optimization method are used to successively separate the amplitude modulation component and the frequency modulation component. A novel diagnosis strategy is researched based on the characteristic variation rule of amplitude modulation, frequency modulation or amplitude and frequency modulation. A complete set of theoretical achievement and engineering application technology of gear train about ‘mechanism research-extraction of fault feature-diagnosis method’ is finally formed.

行星轮系具有特殊的啮合运动，其振动响应具有时变性和多组同频率调制边带特征，现有振动模型解析其调频调幅机理局限性明显，而故障模式与正常模式差异性小，辨识难度大，导致传统诊断方法误诊率高。通过建立考虑转速波动调频因素的行星轮系动力学模型，解析调频调幅特征与故障模式及其损伤程度的映射关系，获得故障振动响应信号的高精度数学模型。利用变速工况下轮系故障特征信号在时域或角域的周期性和相关性，构造谐波调幅调频解析式字典、基于倒频谱编辑法的解析式冲击调制字典和基于滑窗降噪K-SVD法的学习式冲击调制字典，设计基于核范数凸松弛优化的分块稀疏快速算法，提取故障调幅调频信号。利用平方幅值解调、第一类贝塞尔函数频率解调和最小二乘优化法先后分离调幅成分和调频成分，研究基于调幅或调频或调幅调频特征变化规律的轮系故障诊断新策略，形成一套完善的齿轮系统“机理研究-故障特征提取-诊断方法”的理论成果和工程应用技术。

项目以行星轮系为对象，研究了行星轮系振动调幅调频机理，提出了变工况下轮系故障特征的提取方法和调制信号分离方法，对齿轮故障诊断具有重要意义和工程实用价值。.(1) 研究了行星轮系齿轮故障产生的周期性转速波动对啮合刚度、时变传递路径函数和啮合力方向投影函数的影响，建立了太阳轮、单个行星轮和齿圈分别出现平稳型或冲击型故障时的振动响应现象学模型，分析齿轮故障时调制边带的产生机理和分布特征。利用刚柔耦合模型求解太阳轮和齿圈故障时振动调幅调频响应，对比分析了行星轮系故障时振动调幅调频响应和调制边带的分布特征。.(2) 基于齿轮系统故障调制机理和稀疏分解理论，提出一种变工况下齿轮混合故障特征提取的方法。提出了一种基于啮合谐波极值搜索的无转速计阶次跟踪分析新方法，将变工况下时域的非平稳信号高精度地转换为角域的准平稳信号。随后，基于稀疏分解方法对齿轮混合故障信号进行特征分离与提取。提出了表征平稳型故障时变特征的子字典构造方法。基于倒频谱编辑法解卷积识别系统模态参数，精确构造表征冲击响应特征的解析子字典。同时研究基于原始振动信号的滑窗降噪 K-SVD 学习子字典的构造方法。最后，推导了正交匹配追踪和快速迭代阈值收缩两种稀疏系数快速求解算法，显著地提高了算法求解效率。.(3) 基于齿轮故障振动调幅调频信号数学模型，提出了一种将啮合频率谐波附近的调幅调频信号准确分离的方法。该方法结合平方幅值解调和第一类贝塞尔函数与调频函数的关系，建立关于调幅调频参数的非线性方程组，并利用信赖域反射最小二乘优化算法求解参数，从而将啮合调制边带中的调幅和调频边带有效分离提取故障特征。.(4) 额外增加了永磁同步电机的扭转振动控制方法研究。揭示了电压谐波在电机驱动系统中的闭环传递机理，提出了用于抑制电流谐波和电机的输出转速波动的谐波注入法，包括电流谐波抑制方法和转速谐波抑制方法,解决了谐波注入法在部分工况下失效的问题。

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