Experimental Research on Tribological Behavior of Mechanical Seal Based on Face Vibration Measurement
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摘要:
针对接触式机械密封在运行过程中端面磨损引起性能退化缺乏有效的状态监测方法的问题，提出了用端面振动加速度测量机械密封摩擦学行为的方法. 搭建了机械密封试验台，开展了机械密封摩擦学行为测试试验，采集了密封端面振动信号，提取了端面振动特征参数，探究了端面振动敏感特征参数随机械密封摩擦学状态的演变规律，基于试验数据构建了机械密封性能退化评价准则. 结果表明：利用端面振动的监测方式可以实现机械密封的摩擦学状态监测；端面振动敏感特征参数模糊熵、均值和排列熵对摩擦学状态敏感；在密封介质压力一定的情况下，密封端面振动信号的模糊熵、均值和排列熵幅值随着机械密封转速的升高而升高，随着机械密封端面磨损程度的升高而升高；通过端面振动敏感特征参量可以表征机械密封的摩擦学状态.
Abstract:Mechanical seal is a key component in industrial production, and its safe and reliable operation are very important for the continuity of industrial production. There are many problems with the maintenance time of mechanical seals. Premature replacement of seals will increase production costs, and vice versa, it will cause security risks due to failure. Given the lack of an effective state monitoring method for the performance degradation caused by face wear of contact mechanical seals in the process of use, a method for measuring the tribological behavior of mechanical seals by face vibration acceleration was proposed. The test rig of the mechanical seal was built, the original waveform data of vibration acceleration of the stationary ring face was collected, and the tribological performance test of the mechanical seal was carried out. By replacing four rotating rings with different face surface roughness to simulate the operation to failure test of mechanical seal, the relationship between sensitive characteristic parameters of seal face acceleration and the increase of wear degree of the face was explored. By changing the rotational speed, the variation law of the sensitive characteristic parameters of the seal face acceleration with the rotational speed was explored, and then the evolution law of the sensitive characteristic parameters of the mechanical seal face vibration with the tribological regime was discussed. Based on the test data, the performance degradation evaluation method based on k-medoid clustering was attempted to establish, and the evaluation standard of mechanical seal performance degradation was established. The results showed that the face vibration acceleration monitoring method could be used to monitor the tribological regime of mechanical seals. Fuzzy entropy, mean entropy and permutation entropy were three face vibration-sensitive characteristic parameters that were sensitive to tribological regimes. With the increase of face wear degree, the face tribological regime gradually transiteds from the mixed friction state to the boundary tribological regime. The fuzzy entropy, mean value, and entropy of face vibration acceleration showed good sensitivity to the increase of face wear degree, among which the fuzzy entropy was more sensitive to the change of face wear degree than the mean value and entropy of arrangement. The fuzzy entropy, mean value, and permutation entropy of the face vibration of the stationary ring increased linearly with the increase of rotating speed under the mixed friction state of the mechanical seal. The fundamental frequency amplitude of the face vibration waveform increaseed with the increase of rotating speed, and the change of the fundamental frequency amplitude of the radial vibration waveform was more sensitive. The failure evaluation method of the mechanical seal was established. The three-dimensional vector coordinates of the original mean value of axial, radial, and tangential face vibration data were calculated in real-time. The Euclidean distance between the coordinates and the cluster center corresponding to the degenerate state was calculated. When the mechanical seal performance degradation level reached IV, it indicated that the mechanical seal might fail. The above conclusions could be used in engineering applications of seals. It was proved that the face vibration acceleration signal contained abundant information about the change of microstructure in the dynamic process and was sensitive to the change of microscopic motion in the elastic deformation. The face vibration acceleration measurement method monitoring of mechanical seals could help workers assess the status of seals and determine whether and what interventions were needed. This had great engineering value for the safe operation and life management of seals.
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机械密封失效是造成设备故障的主要原因之一，离心泵维修费大约有70%用于密封故障维修[1]. 过早更换密封件会增加生产成本，反之会因失效而造成安全隐患. 为了保证工业生产的连续性和安全性，同时降低生产成本，需要对机械密封端面进行实时监测，了解密封的运行状态[2-4].
机械密封正常工作时，由于密封介质、内部结构及工作条件(转速、介质、压力等)的不同，机械密封可能会经历边界润滑、混合润滑和流体动力润滑这3种不同的摩擦学状态. 对于机械密封摩擦学行为，常见的测试方法有端面温度[5]、端面膜厚[6-7]、端面膜压[8]、端面摩擦扭矩[9-10]以及声发射[11]等测量方法. 受机械密封空间结构的限制，以上摩擦学行为测试方法很难应用到工程实践中.
机械密封在运行过程中，端面振动信号蕴含着大量的摩擦学状态信息，端面液膜厚度、液膜压力、接触力和泄漏量等的变化与密封环的振动直接相关，剧烈振动还可能导致端面磨损加剧影响使用寿命[12-13]. 有学者研究了机械密封的壳体振动加速度测量方法[14]，但采集信号更多的受到转速、轴承和转子系统的影响而不是摩擦学行为影响.
本文中旨在提出1种基于端面振动加速度测量机械密封摩擦学行为的方法，提取端面摩擦学行为敏感振动特征参数，研究振动敏感特征参数随机械密封摩擦学状态演变的规律，建立机械密封性能退化评价准则，为机械密封预测性维修提供技术支撑.
1. 试验部分
1.1 试验设备
如图1(a)所示，设计并搭建了机械密封摩擦学行为测试试验台，包括机械密封组件、变频调速系统、润滑系统、冷却系统以及传感器和数据采集系统. 机械密封组件作为整个试验台的核心试验部件，主要由机械密封(主)、机械密封(辅)和密封试验腔体组成. 为了确保试验台的工程应用性，使用了ZLM IP 530/06型输油泵的工业机械密封，而不仅仅是1对盘式密封摩擦副；密封副材料为SIC-SIC，密封介质采用涡轮发动机航空润滑油.
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图 1 机械密封摩擦学行为测试试验台：(a)机械密封摩擦学性能试验台概览，(b)带传感器的工业机械密封，(c)传感器在静环上的安装位置图Figure 1. Tribological behavior test rig of mechanical seal: (a) general view of the mechanical seal tribological behavior test rig; (b) industrial mechanical seal with sensors; (c) installation position diagram of the sensor on the stationary ring如图1(b)所示，机械密封(主)为单端面接触式机械密封，其由动环、静环、推环和腔体等组成. 机械密封(辅)与机械密封(主)结构相同，其主要作用是防止密封介质泄漏到电机侧；主、辅密封背靠背布置，可以起到平衡轴向力的作用. 如图1(c)所示，4支热电偶传感器埋设于机械密封(主)静环背部直径为2 mm的盲孔内，2支三轴加速度传感器镶嵌于机械密封(主)静环背部的槽内.
润滑系统包括循环油泵、油箱、调节阀及附属管线，循环油泵将航空润滑油从油箱中输送到密封腔体，使用调节阀对密封腔体压力进行调节并维持设定压力，润滑油将摩擦副产生的热量带走并返回到油箱. 冷却系统包括风冷式冷水机、油箱冷却盘管、阀门及管线等，循环冷却水用于冷却润滑油及变频电机壳体.
数据采集系统由NI 9234数据采集卡、NI 9213数据采集卡、热电偶温度传感器、压电式三轴加速度传感器和LabVIEW虚拟仪器等组成. 数据采集卡的采样时间设定为为1 s，采样频率设定为为25.6 Hz，每个数据文件包含25 600个加速度和温度采样点，每隔10 s记录1组数据文件以利用LabVIEW虚拟仪器完成加速度时域分析和频域分析.
变频调速系统主要包括变频调速三相异步电动机、变频器及控制台. 变频调速三相异步电动机额定频率为100 Hz，功率为40 kW，电压为380 V. 通过控制台对变频器进行调节，可以实现三相异步电动机转速在0~6 000 r/min的连续变化.
1.2 机械密封端面磨损变化时端面振动加速度数据采集试验
一般情况下机械密封失效时间最短为6个月[15]，完成机械密封“运转到泄漏”退化周期的摩擦学行为试验需要时间较长. 在摩擦副运行工况稳定且润滑条件较好的情况下，短时间内完成机械密封性能退化摩擦学行为试验存在困难. 为了在较短时间内完成机械密封“运转到泄漏”退化试验，采用1个崭新的动环和3个在输油泵站长期应用且磨损程度不同的动环来代替机械密封性能退化的4个阶段.
按照行业标准《机械密封 第1部分：技术条件》 (JB/T4127.1-2013)规定，机械密封主要零件的使用技术要求为硬质材料密封端面表面粗糙度Ra应不大于0.2 μm. 测量范围Ra为0.05~15.00 μm的便携式表面粗糙度仪TR 100滑动测量4个动环的表面粗糙度值列于表1中，4个动环的外貌照片如图2所示. 用光学影像测量仪测得4个动环的表面形貌照片如图3所示，按端面磨损程度升序命名为1#、2#、3#和4#动环，代表端面性能退化的第I、II、III和IV阶段；4#动环端面粗糙度0.32 μm，按照JB/T 4127.1-2013行业标准，应该判定为失效状态密封环.
表 1 动环表面粗糙度测量值Table 1. Surface roughness measurement value of rotating ringRing number Surface roughness, Ra/μm 1# 0.07 2# 0.09 3# 0.20 4# 0.32 ![]()
图 2 动环外貌照片：(a) 1#，(b) 2#，(c) 3#，(d) 4#Figure 2. Rotation ring exterior diagram: (a) 1#, (b) 2#, (c) 3# and (d) 4#![]()
图 3 动环表面形貌的影像照片：(a) 1#，(b) 2#，(c) 3#，(d) 4#Figure 3. Rotation ring surface micrographs: (a) 1#, (b) 2#, (c) 3# and (d) 4#机械密封端面磨损的振动加速度数据采集试验工况为转速均3 000 r/min，试验腔体压力恒定为0.2 MPa，4个性能退化阶段运行时间均为3.5 h. 机械密封端面磨损变化时端面振动加速度数据采集试验采集的数据信息列于表2中. 每个阶段采集静环端面轴向(Z)、径向(Y)和切向(X)3个方向的振动加速度数据，4个性能退化阶段共采集12组数据.
表 2 定转速试验样本信息Table 2. Constant speed test sample informationRing File size (time unit: 10 s) Sample file 1# 1 200 X1、Y1、Z1 2# 1 200 X2、Y2、Z2 3# 1 200 X3、Y3、Z3 4# 1 200 X4、Y4、Z4 1.3 机械密封转速变化时端面振动加速度数据采集试验
机械密封转速变化的端面振动加速度数据采集试验设计为5个阶段，转速分别为1 000、1 150、1 350、1 650和2 100 r/min，每个阶段持续时间为2 h，试验腔体压力恒定0.4 MPa，采用1对崭新的动环和静环进行试验，每个阶段采集密封环轴向(Z)、径向(Y)和切向(X) 3个方向的数振动数据，5个转速阶段共采集15组数据. 机械密封转速变化的摩擦学行为试验采集的数据列于表3中.
表 3 变转速试验样本信息Table 3. Variable speed test sample informationSpeed/(r/min) File size (time unit: 10 s) Sample file 1 000 700 X5、Y5、Z5 1 150 700 X6、Y6、Z6 1 350 700 X7、Y7、Z7 1 650 700 X8、Y8、Z8 2 100 700 X9、Y9、Z9 2. 端面性能退化振动加速度敏感特征指标构建
2.1 端面振动特征参数提取
基于表2采集的机械密封端面磨损变化时的端面振动加速度数据，提取端面振动信号的统计量特征和熵特征. 各特征值的计算方法列于表4中[16].
表 4 时域、频域和熵计算方法Table 4. Time domain, frequency domain and entropy calculation methodParamaters Formula Paramaters Formula Mean $ {F_1} = \dfrac{1}{N}\displaystyle\sum\limits_{i = 1}^N {{x_i}} $ Waveform index $ {F_{13}} = \dfrac{{{F_2}}}{{\left| {{x_i}} \right|}} $ Root contact-mean-square $ {F_2} = \sqrt {\dfrac{1}{N}\displaystyle\sum\limits_{i = 1}^N {x_i^2} } $ Peak indicator $ {F_{14}} = \dfrac{{{F_{12}}}}{{{F_2}}} $ Root amplitude $ {F_3} = {\left(\dfrac{1}{N}\displaystyle\sum\limits_{i = 1}^N {\sqrt {\left| {{x_i}} \right|} } \right)^2} $ Pulse indicator $ {F_{15}} = \dfrac{{{F_{12}}}}{{\left| {{x_i}} \right|}} $ Absolute value $ {F_4} = \dfrac{1}{N}\displaystyle\sum\limits_{i = 1}^N {\left| {{x_i}} \right|} $ Margin factor $ {F_{16}} = \dfrac{{{F_{12}}}}{{{F_3}}} $ Skewness $ {F_5} = \dfrac{1}{N}\displaystyle\sum\limits_{i = 1}^N \left(\dfrac{{{x_i} - \bar x}}{\sigma } \right)^3 $ Skewness factor $ {F_{17}} = \dfrac{{{F_5}}}{{F_8^3}} $ Kurtosis $ {F_6} = \dfrac{1}{N}\displaystyle\sum\limits_{i = 1}^N \left(\dfrac{{{x_i} - \bar x}}{\sigma } \right)^4 $ Kurtosis factor $ {F_{18}} = \dfrac{{{F_6}}}{{F_8^4}} $ Variance $ {F_7} = \sqrt {\dfrac{1}{N}\displaystyle\sum\limits_{i = 1}^N {({x_i} - \bar x} )} $ Average frequency $ {F_{19}} = \dfrac{{\displaystyle\sum\nolimits_{k = 1}^K {\left( {{f_k}X(k)} \right)} }}{{\displaystyle\sum\nolimits_{k = 1}^K {X(k)} }} $ Standard deviation $ {F_8} = \sqrt {\dfrac{1}{N}\displaystyle\sum\limits_{i = 1}^N {({x_i} - \bar x} {)^2}} $ Gravity frequency $ {F_{20}} = \sqrt {\dfrac{{\displaystyle\sum\nolimits_{k = 1}^K {\left( {f_k^4X(k)} \right)} }}{{\displaystyle\sum\nolimits_{k = 1}^K {\left( {f_k^2X(k)} \right)} }}} $ Maximum $ F_9=\mathrm{max}(x_i) $ Root mean square frequency $ {F_{21}} = \sqrt {\dfrac{{\displaystyle\sum\nolimits_{k = 1}^K {\left( {f_k^2X(k)} \right)} }}{{\displaystyle\sum\nolimits_{k = 1}^K {X(k)} }}} $ Minimum $ F_{10}=\mathrm{min}(x_i) $ Frequency standard deviation $ {F_{22}} = \sqrt {\dfrac{{\displaystyle\sum\nolimits_{k = 1}^K {\left[ {{{\left( {{f_k} - {f_{19}}} \right)}^2}X(k)} \right]} }}{K}} $ Peak $ F_{11}=\mathrm{max}(\left|x_i\right|) $ Entropy $ F_x=-\displaystyle\sum\limits_{j=1}^{2^i}p_j\mathrm{log_2}p_j $ Peak-to-peak $ {F_{12}} = {F_{10}} - {F_9} $ ‒ ‒ Note: $ {F_x} $represented the characteristic value of vibration acceleration, N denoted the number of data file groups, $ {x_i} $denoted the time domain sequence of the signal, $ i $was the serial number of the time domain sequence of the signal, $ \bar x $ represented the mean value of vibration acceleration data in time series, $ X(k) $was the spectral amplitude, K was the number of spectral lines, $ {f_k} $was the frequency of the signal, k was the serial number of discrete values in time domain, and $ {p_j} $was the jth variable probability. (1) 时域特征可以直接表征信号随着时间的变化，单一特征无法准确表征密封端面的摩擦学状态，本文中采用F1~F18共18种时域特征信号对密封端面摩擦学状态进行表征，其中有量纲指标F1~F12共12个，无量纲指标F13~F18共6个.
频域分析是设备状态分析领域中最常用也是最重要的手段之一，本文中对F19~F22共4个频域特征进行分析.
(2) “熵”泛指设备运行状态的1种量度，以及某些设备运行状态可能出现的程度[17]. 经验模态分解、小波包分解和变分模态分解方法[18]已经广泛应用于工业设备状态评估中；熵可以反映出振动信号的信息量和复杂度，熵越大，不确定性越大，复杂性越大.
基于小波包分解方法，对分解信号进行熵特征提取. 通过提取F23小波包能量熵以表征信号在不同尺度上的能量分布，提取F24小波奇异熵以表征原始信号的复杂程度. 首先，应用变分模态分解(VMD)方法提取分解信号的熵特征，变模态分解的模态个数K设置为3；然后，计算各分量的样本熵、信息熵、排列熵、模糊熵和散布熵. 采用上述方法提取的密封端面振动信号的熵特征列于表5中.
表 5 熵特征Table 5. Entropy characteristicsSymbols Specifications F23 Wavelet energy entropy F24 Wavelet singular entropy F25-27 Sample entropy F28-30 Information entropy F31-33 Permutation entropy F34-36 Fuzzy entropy F37-39 Dispersion entropy 建立1个高维特征集来表征机械密封端面摩擦学状态，在特征值筛选和去除冗余不敏感特征的基础上，构建1个多维敏感特征子集，探索从不同维度表征机械密封摩擦学状态信息.
2.2 端面振动敏感特征参数筛选
用合适的端面振动特征参数表征密封端面的摩擦学特性，可以掌握其摩擦磨损过程中的变化规律[19]. 特征选择的目的是在不牺牲摩擦学状态表征精度的前提下去除冗余和无用特征. 信号中包含着有效信号与干扰信号，从信号中提取有效信号必须要用到各种有效的信号处理方法[20]. 当机械密封运行过程中摩擦学状态发生变化时，密封端面振动信号与正常工作振动信号会产生一定差异，时域特征通常反映振动信号的能量信息，频域特征通常反映信号的周期信息. 因此，对机械密封性能进行摩擦学状态表征的充要条件是选取和构建合适的特征指标. 摩擦学状态表征的第一步是构建敏感特征指标集，理想特征指标应具有单调性、相关性和鲁棒性3个关键性质[21-22].
(1) 单调性
单调性常作为设备健康指数与摩擦学状态一致性的评价标准[23]，取值范围为[0, 1]. 在机械密封摩擦学行为变化过程中，若指标与时间呈正比或反比，其单调性为1；若指标变化趋势不明显，其单调性为0. 单调性计算公式如式(1)所示[21].
$$ \mathrm{m}\mathrm{o}\mathrm{n}\left(X\right)=\frac{\left|{\displaystyle \sum }_{i=1}^{n}\varepsilon \left({x}_{i}-{x}_{i-1}\right)-{\displaystyle \sum }_{i=1}^{n}\varepsilon \left({x}_{i-1}-{x}_{i}\right)\right|}{n-1} $$ (1) 式中， $ \mathrm{m}\mathrm{o}\mathrm{n} $表示单调性指数， $X = \left( {{x_1},{x_2}, \cdot \cdot \cdot ,{x_n}} \right)$是健康指数时间序列， $ \varepsilon \left( x \right) = \left\{ {\begin{array}{*{20}{c}} 1&{x \geqslant 0} \\ 0&{x < 0} \end{array}} \right. $为单位阶跃函数， $n$为健康指数总样本数.
(2) 相关性
相关性能够反应该特征指标对于同类设备的普适性[23]，取值范围为[0, 1]. 相关程度越高，取值越靠近1，表征效果越明显；反之越低. 相关性用式(2)来表示[21].
$$ \mathrm{C}\mathrm{o}\mathrm{r}\mathrm{r}\left(\mathit{X}\right)=\frac{\left|n\displaystyle\sum_{ }^{ }x_it_i-\displaystyle\sum_{ }^{ }x_it_i\right|}{\sqrt{\left[n\displaystyle\sum_{ }^{ }x_i^2-\left(\sum_{ }^{ }x_i\right)^2\right]-\left[n\displaystyle\sum_{ }^{ }t_i^2-\left(\displaystyle\sum_{ }^{ }t_i\right)^2\right]}} $$ (2) 式中， $ \mathrm{C}\mathrm{o}\mathrm{o}\mathrm{r} $表示相关性指数， $X{\text{ = (}}{x_1},{x_2},\cdots,{x_n}{\text{)}}$为某种性能退化指标序列， $ T{\text{ = (}}{t_1},{t_2},\cdots,{t_n}{\text{)}} $为相应的监测指标时间序列.
(3) 鲁棒性
鲁棒性反映摩擦学状态表征指标对干扰的鲁棒性[23]，取值范围为[0, 1]，取值越大,其鲁棒性越好. 鲁棒性可用式(3)来表示[21].
$$ \mathrm{R}\mathrm{o}\mathrm{b}\left(X\right)=\frac{1}{n}\sum_{ }^{ }\mathrm{\mathit{\mathrm{exp}}}\left(-\frac{x_i-\tilde{x_i}}{x_i}\right) $$ (3) 式中， $ \mathrm{R}\mathrm{o}\mathrm{b} $表示鲁棒性指数， $\tilde {x}_i $为对应的摩擦学状态表征指标的趋势序列，采用五点三次平滑法得出.
(4) 敏感度
基于机械密封摩擦学状态表征指标的单调性、相关性和鲁棒性特性构建敏感度指标，作为摩擦学状态表征指标优化的目标函数. 对敏感度指标进行排序即可筛选敏感特征指标. 敏感度可用式(4)来表示[24].
$$ \mathrm{S}\mathrm{e}\mathrm{n}\mathrm{s}={w}_{1}\mathrm{M}\mathrm{o}\mathrm{n}\left(X\right)+{w}_{2}\mathrm{C}\mathrm{o}\mathrm{r}\mathrm{r}\left(X\right)+{w}_{3}\mathrm{R}\mathrm{o}\mathrm{b}\left(X\right) $$ (4) 式中，Sens为敏感度指标，wi为单个摩擦学状态表征指标的属性权重，因其本身特性不同，赋予不同的属性权重. 为消除人为因素的影响，本文中选用熵权法分配属性权重.
熵权法首先计算摩擦学状态表征指标的变化程度，依据变化程度大小确定客观权重[25]. 某个摩擦学状态指标的信息熵Ei越小，表明指标值的变化程度越大，信息越多，在监测中越重要，权重越大；反之，则表明该指标在综合评价中重要性略差，其权重越小. 假设有m个评价指标、n个评价对象的实际数据，将其归一化后转变为标准化数据 $\left\{ {{d_{ij}}} \right\}$，定义其第 $i$个指标的熵为
$$ {E_i} = - \frac{1}{{\ln n}}\sum\limits_{j = 1}^n {{f_{ij}}\ln {f_{ij}},i = 1,2, \cdot } \cdot \cdot ,m $$ (5) 式中， ${f_{ij}} = \left( {1 + {d_{ij}}} \right)/\displaystyle \sum\limits_{j = 1}^n {\left( {1 + {d_{ij}}} \right)} $，由熵确定第 $i$个指标的熵权重为
$$ {w_i} = \left( {1 - {E_i}} \right)/\left( {n - \sum\limits_{i = 1}^m {{E_i}} } \right) $$ (6) 将式(6)代入式(4)中得到基于熵权的敏感度模型，敏感度值与单调性、相关性和鲁棒性等指标取值呈正相关. 敏感度值越高时，说明该指标对机械密封摩擦学行为越敏感.
2.3 端面振动敏感特征指标构建
机械密封端面磨损的振动加速度数据采集试验分别采集了端面X、Y和Z方向4个性能退化阶段的振动加速度原始波形数据. X1234代表了静环端面X方向性能退化周期的振动加速度原始波形数据，Y1234代表了静环端面Y方向性能退化周期的振动加速度原始波形数据，Z1234代表了静环端面Z方向性能退化周期的振动加速度原始波形数据，每组数据包含4 800组数据文件. 首先，分别提取X1234、Y1234和Z12343组振动波形信号的统计学特征、频域特征、变模态分解和小波包分解后的熵特征，共得到39个特征构成原始特征向量集，并计算出特征向量值；然后，将39个特征向量值采用式(7)反正切归一化 处理，消除各特征值大小差异，利用基于熵权的敏感度特征筛选方法计算各特征参数的敏感度值.
$$ x^*=\frac{\mathrm{arc}\tan x\times2}{\mathrm{\text{π}}} $$ (7) 式中， $ {x^*} $表示反正切归一化后的特征向量的敏感度值， $ \mathrm{arc}\tan $表示函数返回此数值表达式的反正切值.
39个特征参数的敏感度值计算结果如图4所示，根据敏感度值大小筛选出敏感度最高的3个敏感度指标. 敏感度最高的3个端面振动特征指标列于表6中，其中模糊熵最敏感，代表随密封端面退化程度的增大，振动信息的不确定程度升高；其次是均值，作为有量纲时域特征指标，均值是对振动信号波动状况的直观体现，可以反映机械密封的摩擦学状态；最后是排列熵，可反映机械密封摩擦学状态时间序列随机性、复杂度以及振动信号的突变特征.
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图 4 39维原始特征参数敏感度分布Figure 4. Sensitivity distribution of 39-dimensional original characteristic parameters表 6 敏感特征Table 6. Sensitive featuresSpecifications Symbols Sensitivities Fuzzy entropy F34 0.341 642 Mean F1 0.335 528 Permutation entropy F32 0.332 426 3. 端面振动加速度敏感特征参数随摩擦学状态变化规律
3.1 端面振动加速度敏感特征参数随端面磨损程度变化的规律
密封端面形状各异的微凸体对机械密封的摩擦学状态有着显著影响. 正常情况下，机械密封处在混合摩擦学状态；端面磨损会改变微凸体曲率半径，端面摩擦学状态随着微凸体曲率半径的变化而变化. 本试验中研究试图揭示端面振动加速度特征参数随磨损程度增加的变化规律.
采用均值、模糊熵和排列熵作为敏感特征参数，研究其在轴向、径向和切向3个维度随机械密封退化周期的摩擦学状态变化趋势. 图5所示为轴向、径向和切向敏感特征退化曲线，样本编号1~1 200为1#动环的摩擦学特性，1 201~2 400为2#动环的摩擦学特性，2 401~3 600为3#动环的摩擦学特性，3 601~4 800为4#动环的摩擦学特性.
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图 5 轴向、径向和切向敏感特征退化曲线：(a) 模糊熵，(b) 均值，(c) 排列熵Figure 5. Degradation curves of axial，radial and tangential sensitive features: (a) fuzzy entropy, (b) mean value and (c) permutation entropy由图5(a)、(b)和(c)可以看出，随着动环端面磨损程度的加剧，均值、模糊熵以及排列熵均呈现上升趋势. 摩擦副的摩擦学状态从性能退化周期的I阶段的混合摩擦学状态逐步过渡到性能退化周期的II~IV阶段的边界摩擦学状态；在边界摩擦学状态下，随着磨损程度增加，端面微凸体的数量增多，端面轴向、径向和切向3个方向的摩擦力均会增大，进而引起端面振动加速度增加. 如图5(a)所示，随着端面磨损程度的增大，端面轴向、径向和切向3个方向上的模糊熵变化趋势基本一致并呈现上升趋势，其中切向模糊熵对磨损程度变化较敏感；在性能退化周期的III阶段前期，3个方向的模糊熵呈现了宽幅振荡，随后稳定上升. 如图5(b)所示，在性能退化周期的I~II阶段，端面磨损程度变化较小，均值变化趋势不明显；端面性能退化程度到III和IV阶段时，均值比I和II阶段有了显著的增大，但均值在III阶段呈现宽幅振荡状态. 如图5(c)所示，随着端面磨损程度的增大，端面轴向、径向和切向3个方向上的排列熵变化趋势基本一致并呈现上升趋势，但端面径向排列熵比轴向和切向排列熵更敏感；在性能退化程度的II和III阶段，轴向、径向和切向3个方向的模糊熵均呈现一定程度的宽幅振荡现象.
综上所述，随着端面磨损程度的增加，端面摩擦学状态从混合摩擦状态逐步过渡到边界摩擦学状态，端面振动加速度模糊熵、均值和排列熵对于端面磨损程度的增加均表现出了较好的敏感性，其中模糊熵相比较均值和排列熵对于端面磨损程度的变化更敏感.
3.2 端面振动加速度敏感特征参数随转速变化的规律
基于1.3节中机械密封转速变化时的端面振动加速度数据，分别计算X56789、Y56789和Z56789对应的轴向、径向和切向模糊熵、均值和排列熵. X56789代表了静环端面X方向5个转速下的振动加速度原始波形数据，Y56789代表了静环端面Y方向5个转速下的振动加速度原始波形数据，Z56789代表了静环端面Z方向5个转速下的振动加速度原始波形数据，每组数据包含3 500组数据文件.
混合摩擦状态下的机械密封摩擦副周向摩擦力(极坐标系)随着转速的升高而增加，静环端面振动加速度也会随着转速的升高而增加. 图6所示为机械密封端面振动敏感特征参数随着机械密封转速变化的曲线. 如图6(a~c)所示，随着转速的增大，模糊熵值由0.1增大至0.7左右，均值由0.1 m/s2增大至0.8m/s2左右，排列熵由0.7增大至6左右；模糊熵、均值和排列熵随着转速的升高呈现线性增加趋势，并且在轴向、径向和切向3个方向上的变化趋势基本一致.
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图 6 端面敏感特征参数随转速变化曲线：(a)模糊熵，(b)均值，(c)排列熵Figure 6. Change curve of face sensitive characteristic parameters with rotational speed: (a) fuzzy entropy, (b) mean value and (c) permutation entropy图7所示为端面振动波形基频幅值随转速变化的曲线. 机械密封转速从1 000增大至1 150、1 350、1 650和2 100 r/min时，对应的计算振动加速度波形基频为20、23、27、33和42 Hz的幅值，绘制成端面振动波形基频幅值-转速曲线. 如图7所示，端面振动波形基频幅值随着转速的升高而增加，其中径向振动波形基频幅值相对切向和轴向振动波形基频幅值变化更敏感.
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图 7 端面振动波形基频幅值随转速变化曲线Figure 7. Variation curve of fundamental frequency amplitude of face vibration waveform changing with rotational speed综上所述，机械密封混合摩擦状态下，静环端面振动模糊熵、均值和排列熵随着转速的升高呈现线性增加；端面振动波形基频幅值随着转速的升高而增加，且径向振动波形基频幅值变化更敏感.
3.3 机械密封失效评价方法
采用某输油站预防性维修更换的密封环作为试验器材，按照磨损程度定义为2#动环、3#动环和4#动环，其测量的粗糙度分别为0.09、0.20和0.32 μm. 众所周知，密封环在运行中无法测量端面粗糙度并进行健康状态评价.
基于前述端面模糊熵、均值和排列熵3类敏感特征参数摩擦学状态变化规律研究成果，将密封环性能退化周期I、II、III和IV阶段的轴向、径向及切向的敏感特征值进行K中心聚类分析[26]，计算出每个性能退化阶段的三维坐标聚类中心，分别作为机械密封失效模糊熵评价准则、均值评价准则和均值评价准则，如图8、图9和图10所示；实时计算轴向、径向和切向的三维敏感特征值，计算该矢量坐标与退化状态对应的聚类簇心的欧氏距离，采用最近邻原则匹配确定当前退化等级，实现机械密封性能退化状态评价.
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图 8 机械密封性能退化模糊熵评价标准Figure 8. Mechanical seal performance degradation fuzzy entropy evaluation criteria![]()
图 9 机械密封性能退化均值评价标准Figure 9. Mechanical seal performance degradation mean value evaluation criteria![]()
图 10 机械密封性能退化排列熵评价标准Figure 10. Mechanical seal performance degradation permutation entropy evaluation criteria采用聚类方法建立机械密封性能退化评价准则应该满足所有聚类簇心应尽量分布在对角线方向上，理想情况下应该成1条直线[27]. 从图8~10对比分析看出，机械密封性能退化排列熵和模糊熵评价准则难以区分机械密封性能退化的第I~III阶段，且聚类簇心不满足分布在1条对角线上的要求；机械密封性能退化均值评价准则可以明确区分第II~IV阶段，且聚类簇心分布在对角线上，满足性能退化评价准则要求，本文中选择均值评价准则实现机械密封性能退化评价.
综上所述，机械密封的失效评价方法为实时计算轴向、径向和切向的端面振动原始数据均值的三维矢量坐标，计算该坐标与退化状态对应簇心的欧氏距离，采用最近邻匹配原则匹配机械密封的退化状态；当机械密封性能退化等级达到IV级预示着机械密封可能失效.
4. 结论
a. 利用端面振动加速度的测量方法，在机械密封补偿环镶嵌加速度传感器，采集到的振动加速度敏感特征参数随摩擦学状态变化而变化，可以实现机械密封的摩擦学行为监测.
b. 随着端面磨损程度的增加，端面摩擦学状态从混合摩擦状态逐步过渡到边界摩擦学状态，端面振动加速度模糊熵、均值和排列熵对于端面磨损程度的增加均表现出了较好的敏感性，其中模糊熵相比较均值和排列熵对于端面磨损程度的变化更敏感.
c. 机械密封混合摩擦状态下，静环端面振动模糊熵、均值和排列熵随着转速的升高呈现线性增加；端面振动波形基频幅值随着转速的升高而增加，且径向振动波形基频幅值变化更敏感.
d. 尝试建立了机械密封性能退化均值评价准则，计算静环端面振动均值的轴向、径向和切向三维矢量坐标与评价准则对应4个簇心的欧氏距离，采用最近邻匹配原则匹配机械密封的退化状态，可实现机械密封性能退化状态评价.
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图 1 机械密封摩擦学行为测试试验台：(a)机械密封摩擦学性能试验台概览，(b)带传感器的工业机械密封，(c)传感器在静环上的安装位置图
Figure 1. Tribological behavior test rig of mechanical seal: (a) general view of the mechanical seal tribological behavior test rig; (b) industrial mechanical seal with sensors; (c) installation position diagram of the sensor on the stationary ring
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图 2 动环外貌照片：(a) 1#，(b) 2#，(c) 3#，(d) 4#
Figure 2. Rotation ring exterior diagram: (a) 1#, (b) 2#, (c) 3# and (d) 4#
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图 3 动环表面形貌的影像照片：(a) 1#，(b) 2#，(c) 3#，(d) 4#
Figure 3. Rotation ring surface micrographs: (a) 1#, (b) 2#, (c) 3# and (d) 4#
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图 4 39维原始特征参数敏感度分布
Figure 4. Sensitivity distribution of 39-dimensional original characteristic parameters
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图 5 轴向、径向和切向敏感特征退化曲线：(a) 模糊熵，(b) 均值，(c) 排列熵
Figure 5. Degradation curves of axial，radial and tangential sensitive features: (a) fuzzy entropy, (b) mean value and (c) permutation entropy
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图 6 端面敏感特征参数随转速变化曲线：(a)模糊熵，(b)均值，(c)排列熵
Figure 6. Change curve of face sensitive characteristic parameters with rotational speed: (a) fuzzy entropy, (b) mean value and (c) permutation entropy
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图 7 端面振动波形基频幅值随转速变化曲线
Figure 7. Variation curve of fundamental frequency amplitude of face vibration waveform changing with rotational speed
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图 8 机械密封性能退化模糊熵评价标准
Figure 8. Mechanical seal performance degradation fuzzy entropy evaluation criteria
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图 9 机械密封性能退化均值评价标准
Figure 9. Mechanical seal performance degradation mean value evaluation criteria
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图 10 机械密封性能退化排列熵评价标准
Figure 10. Mechanical seal performance degradation permutation entropy evaluation criteria
表 1 动环表面粗糙度测量值
Table 1 Surface roughness measurement value of rotating ring
Ring number Surface roughness, Ra/μm 1# 0.07 2# 0.09 3# 0.20 4# 0.32 
下载: 导出CSV
表 2 定转速试验样本信息
Table 2 Constant speed test sample information
Ring File size (time unit: 10 s) Sample file 1# 1 200 X1、Y1、Z1 2# 1 200 X2、Y2、Z2 3# 1 200 X3、Y3、Z3 4# 1 200 X4、Y4、Z4
下载: 导出CSV
表 3 变转速试验样本信息
Table 3 Variable speed test sample information
Speed/(r/min) File size (time unit: 10 s) Sample file 1 000 700 X5、Y5、Z5 1 150 700 X6、Y6、Z6 1 350 700 X7、Y7、Z7 1 650 700 X8、Y8、Z8 2 100 700 X9、Y9、Z9
下载: 导出CSV
表 4 时域、频域和熵计算方法
Table 4 Time domain, frequency domain and entropy calculation method
Paramaters Formula Paramaters Formula Mean $ {F_1} = \dfrac{1}{N}\displaystyle\sum\limits_{i = 1}^N {{x_i}} $ Waveform index $ {F_{13}} = \dfrac{{{F_2}}}{{\left| {{x_i}} \right|}} $ Root contact-mean-square $ {F_2} = \sqrt {\dfrac{1}{N}\displaystyle\sum\limits_{i = 1}^N {x_i^2} } $ Peak indicator $ {F_{14}} = \dfrac{{{F_{12}}}}{{{F_2}}} $ Root amplitude $ {F_3} = {\left(\dfrac{1}{N}\displaystyle\sum\limits_{i = 1}^N {\sqrt {\left| {{x_i}} \right|} } \right)^2} $ Pulse indicator $ {F_{15}} = \dfrac{{{F_{12}}}}{{\left| {{x_i}} \right|}} $ Absolute value $ {F_4} = \dfrac{1}{N}\displaystyle\sum\limits_{i = 1}^N {\left| {{x_i}} \right|} $ Margin factor $ {F_{16}} = \dfrac{{{F_{12}}}}{{{F_3}}} $ Skewness $ {F_5} = \dfrac{1}{N}\displaystyle\sum\limits_{i = 1}^N \left(\dfrac{{{x_i} - \bar x}}{\sigma } \right)^3 $ Skewness factor $ {F_{17}} = \dfrac{{{F_5}}}{{F_8^3}} $ Kurtosis $ {F_6} = \dfrac{1}{N}\displaystyle\sum\limits_{i = 1}^N \left(\dfrac{{{x_i} - \bar x}}{\sigma } \right)^4 $ Kurtosis factor $ {F_{18}} = \dfrac{{{F_6}}}{{F_8^4}} $ Variance $ {F_7} = \sqrt {\dfrac{1}{N}\displaystyle\sum\limits_{i = 1}^N {({x_i} - \bar x} )} $ Average frequency $ {F_{19}} = \dfrac{{\displaystyle\sum\nolimits_{k = 1}^K {\left( {{f_k}X(k)} \right)} }}{{\displaystyle\sum\nolimits_{k = 1}^K {X(k)} }} $ Standard deviation $ {F_8} = \sqrt {\dfrac{1}{N}\displaystyle\sum\limits_{i = 1}^N {({x_i} - \bar x} {)^2}} $ Gravity frequency $ {F_{20}} = \sqrt {\dfrac{{\displaystyle\sum\nolimits_{k = 1}^K {\left( {f_k^4X(k)} \right)} }}{{\displaystyle\sum\nolimits_{k = 1}^K {\left( {f_k^2X(k)} \right)} }}} $ Maximum $ F_9=\mathrm{max}(x_i) $ Root mean square frequency $ {F_{21}} = \sqrt {\dfrac{{\displaystyle\sum\nolimits_{k = 1}^K {\left( {f_k^2X(k)} \right)} }}{{\displaystyle\sum\nolimits_{k = 1}^K {X(k)} }}} $ Minimum $ F_{10}=\mathrm{min}(x_i) $ Frequency standard deviation $ {F_{22}} = \sqrt {\dfrac{{\displaystyle\sum\nolimits_{k = 1}^K {\left[ {{{\left( {{f_k} - {f_{19}}} \right)}^2}X(k)} \right]} }}{K}} $ Peak $ F_{11}=\mathrm{max}(\left|x_i\right|) $ Entropy $ F_x=-\displaystyle\sum\limits_{j=1}^{2^i}p_j\mathrm{log_2}p_j $ Peak-to-peak $ {F_{12}} = {F_{10}} - {F_9} $ ‒ ‒ Note: $ {F_x} $represented the characteristic value of vibration acceleration, N denoted the number of data file groups, $ {x_i} $denoted the time domain sequence of the signal, $ i $was the serial number of the time domain sequence of the signal, $ \bar x $ represented the mean value of vibration acceleration data in time series, $ X(k) $was the spectral amplitude, K was the number of spectral lines, $ {f_k} $was the frequency of the signal, k was the serial number of discrete values in time domain, and $ {p_j} $was the jth variable probability.
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表 5 熵特征
Table 5 Entropy characteristics
Symbols Specifications F23 Wavelet energy entropy F24 Wavelet singular entropy F25-27 Sample entropy F28-30 Information entropy F31-33 Permutation entropy F34-36 Fuzzy entropy F37-39 Dispersion entropy
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表 6 敏感特征
Table 6 Sensitive features
Specifications Symbols Sensitivities Fuzzy entropy F34 0.341 642 Mean F1 0.335 528 Permutation entropy F32 0.332 426
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[1] 金良, 孙见君, 冯飞, 等. 机械密封试验装置研究进展[J]. 液压气动与密封, 2021, 41(7): 90–96 Jin Liang, Sun Jianjun, Feng Fei, et al. Research progress of mechanical seal testing device[J]. Hydraulics Pneumatics & Seals, 2021, 41(7): 90–96
[2] 张尔卿, 傅攀, 陈侃, 等. 机械密封端面接触状态的声发射监测方法[J]. 润滑与密封, 2014, 39(8): 8–13,34 doi: 10.3969/j.issn.0254-0150.2014.08.002 Zhang Erqing, Fu Pan, Chen Kan, et al. Mechanical fluid seal end face contact state monitoring based on acoustic emission[J]. Lubrication Engineering, 2014, 39(8): 8–13,34 doi: 10.3969/j.issn.0254-0150.2014.08.002
[3] 赵文静, 金杰, 孟祥铠, 等. 涉海装备用机械密封技术研究现状及发展趋势研究[J]. 摩擦学学报, 2019, 39(6): 792–802 doi: 10.16078/j.tribology.2018172 Zhao Wenjing, Jin Jie, Meng Xiangkai, et al. State of the art and development trend of mechanical seal for marine equipment[J]. Tribology, 2019, 39(6): 792–802 doi: 10.16078/j.tribology.2018172
[4] 李克斯, 张尔卿, 傅攀, 等. 不完备先验知识下的机械密封端面磨损状态评估研究[J]. 摩擦学学报, 2016, 36(6): 717–725 doi: 10.16078/j.tribology.2016.06.008 Li Kesi, Zhang Erqing, Fu Pan, et al. Condition assessment on mechanical seal face wear based on incomplete prior knowledge[J]. Tribology, 2016, 36(6): 717–725 doi: 10.16078/j.tribology.2016.06.008
[5] 彭旭东, 金杰, 李定, 等. 高速涡轮泵机械密封端面温度变化规律研究[J]. 摩擦学学报, 2019, 39(3): 313–318 doi: 10.16078/j.tribology.2018095 Peng Xudong, Jin Jie, Li Ding, et al. Analysis of face temperature in mechanical seal applied in the high speed turbo pump[J]. Tribology, 2019, 39(3): 313–318 doi: 10.16078/j.tribology.2018095
[6] Reddyhoff T, Dwyer-Joyce R, Harper P. Ultrasonic measurement of film thickness in mechanical seals[J]. Sealing Technology, 2006, 2006(7): 7–11. doi: 10.1016/s1350-4789(06)71260-0
[7] 彭旭东, 金杰, 孟祥铠, 等. 汽液两相流机械密封的研究进展[J]. 摩擦学学报, 2019, 39(5): 643–655 doi: 10.16078/j.tribology.2018093 Peng Xudong, Jin Jie, Meng Xiangkai, et al. Research progress on the liquid face seal of vapor-liquid two-phase flow[J]. Tribology, 2019, 39(5): 643–655 doi: 10.16078/j.tribology.2018093
[8] 孟祥铠, 江莹莹, 赵文静, 等. 考虑空化效应的螺旋槽机械密封液膜动力学特性研究[J]. 摩擦学学报, 2019, 39(2): 171–180 doi: 10.16078/j.tribology.2018091 Meng Xiangkai, Jiang Yingying, Zhao Wenjing, et al. Fluid film dynamic characteristics of spiral-grooved mechanical seals with cavitation effect[J]. Tribology, 2019, 39(2): 171–180 doi: 10.16078/j.tribology.2018091
[9] Ayadi K, Brunetière N, Tournerie B, et al. Experimental and numerical study of the lubrication regimes of a liquid mechanical seal[J]. Tribology International, 2015, 92: 96–108. doi: 10.1016/j.triboint.2015.05.022
[10] 王小燕, 孟祥铠, 刘鑫, 等. 核主泵用流体动压型机械密封耦合模型与性能分析[J]. 摩擦学学报, 2013, 33(02): 169–176 doi: 10.16078/j.tribology.2013.02.011 Wang Xiaoyan, Meng Xiangkai, Liu Xin, et al. Coupling model and performance analysis of hydrodynamic mechanical seal for reactor coolant pump[J]. Tribology, 2013, 33(02): 169–176 doi: 10.16078/j.tribology.2013.02.011
[11] Towsyfyan H. Investigation of the nonlinear tribological behaviour of mechanical seals for online condition monitoring[D]. West Yorkshire: University of Huddersfield, 2017.
[12] Pan Xiang, Liu Zhongdi, Xu Rong, et al. Early warning of damaged wind turbine blades using spatial-temporal spectral analysis of acoustic emission signals[J]. Journal of Sound and Vibration, 2022, 537: 117209. doi: 10.1016/j.jsv.2022.117209
[13] 贺立峰. 船用机械密封环振动问题的研究[D]. 武汉: 武汉理工大学, 2010 He Lifeng. Research on Vibration of Marine Mechanical Sealing Ring[D]. Wuhan: Wuhan University of Technology, 2010
[14] Luo Yin, Zhang Wenqi, Fan Yakun, et al. Analysis of vibration characteristics of centrifugal pump mechanical seal under wear and damage degree[J]. Shock and Vibration, 2021, 2021: 1–9. doi: 10.1155/2021/6670741
[15] 朱奥辉, 傅攀, 陈官林. 基于Elman神经网络与PSO算法的机械密封端面摩擦状态识别[J]. 润滑与密封, 2016, 41(9): 93–96,101 doi: 10.3969/j.issn.0254-0150.2016.09.017 Zhu Aohui, Fu Pan, Chen Guanlin. Recognition on friction state of mechanical seal face based on Elman neural network and PSO algorithm[J]. Lubrication Engineering, 2016, 41(9): 93–96,101 doi: 10.3969/j.issn.0254-0150.2016.09.017
[16] Wang Qingfeng, Wang Shuai, Wei Bingkun, et al. Weighted K-NN classification method of bearings fault diagnosis with multi-dimensional sensitive features[J]. IEEE Access, 2021, 9: 45428–45440. doi: 10.1109/ACCESS.2021.3066489
[17] Li Jingchao, Guo Jian. A new feature extraction algorithm based on entropy cloud characteristics of communication signals[J]. Mathematical Problems in Engineering, 2015, 2015: 1–8. doi: 10.1155/2015/891731
[18] Dragomiretskiy K, Zosso D. Variational mode decomposition[J]. IEEE Transactions on Signal Processing, 2014, 62(3): 531–544. doi: 10.1109/TSP.2013.2288675
[19] 於秋萍, 孙见君, 涂桥安, 等. 接触式机械密封基本性能研究进展[J]. 流体机械, 2015, 43(2): 41-47 Yu Qiuping, Sun Jianjun, Tu Qiaoan, et al. Research Progress in Basic Properties of Contacting Mechanical Seal[J], 2015, 43(2): 41-47
[20] 李舜酩, 郭海东, 李殿荣. 振动信号处理方法综述[J]. 仪器仪表学报, 2013, 34(08): 1907–1915 doi: 10.19650/j.cnki.cjsi.2013.08.031 Li Shunming, Guo Haidong, Li Dianying. Summary of vibration signal processing methods[J]. Journal of Instrumentation, 2013, 34(08): 1907–1915 doi: 10.19650/j.cnki.cjsi.2013.08.031
[21] 侯晓东, 杨江平, 邓斌, 等. 基于多指标相似性的T/R组件剩余寿命融合预测方法[J]. 国防科技大学学报, 2019, 41(4): 190–198 doi: 10.11887/j.cn.201904027 Hou Xiaodong, Yang Jiangping, Deng Bin, et al. Fusion prediction method of remaining useful life for T/R module based on multi-index similarity[J]. Journal of National University of Defense Technology, 2019, 41(4): 190–198 doi: 10.11887/j.cn.201904027
[22] Qiu Guangqi, Gu Yingkui, Chen Junjie. Selective health indicator for bearings ensemble remaining useful life prediction with genetic algorithm and Weibull proportional hazards model[J]. Measurement, 2020, 150: 107097. doi: 10.1016/j.measurement.2019.107097
[23] 张程. 数据驱动的离心泵健康评估方法和维修策略研究[D]. 北京: 北京化工大学, 2021 Zhang Cheng. Research on health assessment method and maintenance strategy of data-driven centrifugal pump[D]. Beijing: Beijing University of Chemical Technology, 2021
[24] Harrath S, Ben Ali J, Zouaghi T, et al. A new adaptive prognostic strategy based on online future evaluation and extended Kalman filtering[C]//2019 6th International Conference on Control, Decision and Information Technologies (CoDIT). IEEE, 2019: 2033–2038.
[25] 李耀华 王星州. 飞机液压系统故障诊断[J]. 计算机工程与应用, 2019, 55(05): 232–236,264 Li Yaohua, Wang Xingzhou. Fault diagnosis of aircraft hydraulic system[J]. Computer Engineering and Applications, 2019, 55(05): 232–236,264
[26] Park H S, Jun C H. A simple and fast algorithm for K-medoids clustering[J]. Expert Systems With Applications, 2009, 36(2): 3336–3341. doi: 10.1016/j.eswa.2008.01.039
[27] 程晓涵, 汪爱明, 花如祥, 等. 24种特征指标对轴承状态识别的性能研究[J]. 振动测试与诊断, 2016, 36(02): 351–358, 406 Cheng Xiaohan, Wang Aiming, Hua Ruxiang, et al. Studying on property of 24 characteristic indexes to bearing state recognition[J]. Journal of Vibration, Measurement & Diagnosis, 2016, 36(02): 351–358, 406
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