谐波减速器柔性薄壁轴承振动信号分析和损伤特征提取

The inner and outer rings of flexible thin-wall bearing are ellipse, and the normal vibration signal of this bearing contains the periodic shocks that occur only when ordinary bearings are damaged. When flexible thin-wall bearing is damaged, the periodic shocks caused by the damage are mixed with the normal periodic shocks, and it is worth studying to extract the damage periodic shocks of flexible thin-wall bearing in the background of normal periodic shocks of flexible thin-wall bearing, and moreover, the damage shock frequency of flexible thin-wall bearing is time-varying, which makes it more difficult to extract the damage features. Singular value decomposition (SVD) and optimal wavelet analysis are used to extract the damage vibration feature of flexible thin-wall bearing. The distribution rule of non-zero singular values of vibration signal of flexible thin-wall bearing under normal and damaged conditions is studied, and the effects of matrix type and dimension on this distribution rule are studied so that the appropriate matrix type and dimension can be determined for the vibration signal of flexible thin-wall bearing. Using the distribution rule and according to the difference of distribution rule of non-singular values of normal and damaged vibration signal, the separation of damage periodic shocks of flexible thin-wall bearing from the normal periodic shocks is transformed to the selection of singular values, and the inherent relationship between the singular values and frequencies is studied, the damage shock feature can be separated by SVD reconstruction. The wavelet parameter equation being utilized, the optimal wavelet basis that is suitable for the damage feature extraction of flexible thin-wall bearing is obtained by the optimization algorithm, and the weak damage vibration feature is extracted by the optimal wavelet-SVD algorithm. The time variation characteristics of damage shock frequency of flexible thin-wall bearing is analyzed theoretically, and the real time variation of damage shock frequency is obtained by short time Fourier transform and continuous wavelet transform, so that the theoretical result of time variation of flexible thin-wall bearing can be verified. Through these modern signal processing methods, the feature extraction and damage identification of flexible thin-wall bearing are finally solved, which is a new development for bearing vibration monitoring.

柔性薄壁轴承的内、外圈是椭圆，其正常的振动信号含有普通轴承损伤时才会出现的周期性冲击，在周期性冲击背景下提取因轴承损伤引起的周期性冲击是一个难题，这种损伤冲击频率还具有时变性。采用奇异值分解(SVD)和最优小波分析实现对柔性薄壁轴承不同元件损伤的振动特征信息提取，研究柔性薄壁轴承正常和损伤时振动信号的非零奇异值分布规律及差异，并研究矩阵型式和维数对这种分布规律的影响，确定合适的矩阵及维数，将对柔性薄壁轴承正常和损伤时的周期性冲击分离转化为对奇异值的选择，研究奇异值和频率成分的内在联系，通过SVD重构分离出损伤冲击特征。利用小波参数方程，通过优化算法寻求适于柔性薄壁轴承损伤特征提取的最优小波基，并通过最优小波-SVD算法实现对微弱损伤特征信息的提取。从理论上分析柔性薄壁轴承损伤冲击频率的时变性，并用短时傅立叶变换和连续小波变换分析冲击频率的实际时变性，最终解决这种轴承的特征提取和损伤识别。

柔性薄壁轴承是一种特殊的新型轴承，其工作时内外圈是椭圆，故障特征和故障频率非常独特，与普通滚动轴承完全不同，目前对这种轴承故障分析和特征提取的研究非常少。本项目从理论上系统研究了柔性薄壁轴承的故障频率特性，推导得到了柔性薄壁轴承外圈损伤、内圈损伤和滚动体损伤时的特征频率公式，证明在转速恒定下这种轴承的故障特征频率不是一个定值，而是在一定范围内周期性波动，波动频率是转频的两倍，并通过实验进行验证。发现柔性薄壁轴承滚动体中心轨迹和节椭圆并不一致，从理论上分析了滚动体中心相对于节椭圆和保持架的运动轨迹，纠正了现有文献关于滚动体中心和保持架的相对运动轨迹是一个椭圆的错误论断。从理论上证明柔性薄壁轴承存在径向速度和径向加速度，且径向速度和加速度是时变的，其变化频率是轴承转频的两倍，普通滚动轴承并不存在径向速度和径向加速度。提出了柔性薄壁轴承一种新的速度分布模型，纠正了现有模型的缺陷和不足。研究了柔性薄壁轴承的背景周期性冲击的频率分布，证明背景周期性冲击的基频是转频的两倍。分析了背景周期性冲击的奇异值分布规律，发现了奇异值和背景冲击频率的内在关系，提出一种频率添加奇异值分解法，精确地分离出背景周期性冲击。提出一种改进谐波小波包来分离背景周期性冲击，改进谐波小波包的各子带中心频率和带宽针对背景周期性冲击的频率分布特点设计，有效克服了传统谐波小波包分解层数大、子带数量多且难于选择含故障冲击的子带的缺点。从理论上分析了Morlet小波的波形相似性特征提取原理，证明存在一个最优小波基和柔性薄壁轴承的故障冲击相似，故障冲击在此小波基获得最大投影，而背景周期性冲击则被极大抑制，从而准确提取到故障冲击特征。提出了一种基于Gini指数的时间重分配多同步压缩变换，极大提高了短时傅里叶变换的时频聚集性，准确提取到了柔性薄壁轴承的故障频率的波动特性。项目研究结果对于柔性薄壁轴承基础理论发展和故障诊断理论具有十分重要的意义。