Diagnosis and classification of ball bearing faults in gyro motors by stator current signature analysis

DONG Lei, ZHOU Hao, PAN Long-fei, CHEN Wei, JIN Chen, LI Nan, LI Wei-min

(1. School of Mechanical Engineering, Hebei University of Technology, Tianjin 300130, China; 2. Tianjin Navigation Instruments Research Institute, Tianjin 300131, China)

Diagnosis and classification of ball bearing faults in gyro motors by stator current signature analysis

DONG Lei1,2, ZHOU Hao2, PAN Long-fei2, CHEN Wei2, JIN Chen2, LI Nan2, LI Wei-min1

(1. School of Mechanical Engineering, Hebei University of Technology, Tianjin 300130, China; 2. Tianjin Navigation Instruments Research Institute, Tianjin 300131, China)

Bearing faults are the most common failure mode in gyro motors. It is very difficult to distinguish the fault of each component in ball bearing, and it is a huge waste to replace a complete set of ball bearing without classifying replacement. To solve this problem, a new method, based on stator current signature analysis, is presented for classifying bearing faults in gyro motors. By collecting the stator current signal and using mathematical analysis tools, the features of the stator current are extracted, and the sequential backward selection (SBS) method is used to remove the superfluous and invalid features. And then, the best features are obtained and used to build the representation space. By using the hidden Markov model (HMM), the bearing typical faults, outer ring fault, inner ring fault, ball fault and cage fault can be classified accurately. The effectiveness of the proposed method is proved in a brushless DC gyro motor with different bearing faults, and the experimental results show that the accuracy of classification reaches 97.1%.

bearing faults; failure classification; hidden Markov models; gyro motor

The gyro-motor is a kind of important inertial sensors, used in mechanical gyroscopes widely. Bearings are critical mechanical components in gyro motors, and bearing failures account for a majority of failures, particularly in mechanical gyroscopes with rolling bearings. Many papers can be found to detect and classify bearing faults in induction machines[1-3], but it is a relatively new research area in gyro-motor. The faults classification of rolling bearings in gyro-motor will be an important investigated field for reliability and cost.

Vibration signals were previously applied to detect the bearing faults. In many situations, the methods based on vibration signals have proved their effectiveness too[4]. But in some specific cases, the acquisition of mechanical signal is very difficult and even impossible, and the motor current signal analysis (MCSA) would be preferable, which is a non-invasive method.

This paper presented a new method for bearing faults classification in gyromotor, which was based on stator current signature analysis. A set of features are extracted from the current in time domain. By the sequential backward selection (SBS) method, the best three features are selected to build the representation space, and then the HMMs are used to classify the failures of bearing. The experiment is tested in a brushless DC gyro motor with different bearing faults.

1 Basic concepts of current signal for bearing faults

Bearing faults are closely related with its structure, and radial ball bearings consist of a outer ring, a inner ring, balls and a cage, and the bearings structure and parameters is shown in Fig.1.

A rough classification identifies four classes: outer ring fault, inner ring fault, ball fault and cage fault.

When the faults of bearings occur in outer raceway, inner raceway, balls or cage, the unique frequency components in the vibration signals will be produced. In the paper [5], the bearing fault frequencies are given:

Where:of- the outer raceway fault frequency;if- the inner raceway fault frequency;bf- the ball fault frequency; fc- the cage fault frequency; fr- the rotor mechanical frequency; NB- the number of rolling elements; D- the pitch diameter; d- the ball diameter; φ- the ball contact angle.

The mechanical vibration would directly affect the magnetomotive force, and the special vibration frequency will generate special magnetomotive force. At the same time, the magnetomotive force would be related to the stator current. As a result, the mechanical faults, detected by measuring the current signal, can lead to the motor stator current distortion. Different kind of bearing faults can produce their own special characteristic frequencies, which relate to their operating conditions and configurations, so the special frequencies will reflect themselves in the current distortion. In short, a fault can build a kind of relation between special characteristic frequencies and current distortion, which presents itself.

Fig.1 Ball bearing structure and parameters

2 Architecture of proposed HMM approach

The HMM approach includes the following steps (shown in Fig.2).

The feature extraction step is that some features of bearing faults are extracted from the current signals, which apply some signal analysis techniques, such as the frequency domain, time domain, time-frequency domain analysis. Then the features can be processed to diagnose and track bearing degradation.

The feature selection step is that the extraction features are filtered by the sequential backward selection (SBS) or genetic algorithm approach (GA). By this way, irrelevant and redundant features can be removed, and some appropriate features can be acquired.

Fig.2 HMM-based fault classification approach

The classification step is that a set of historical data will be divided into the M different classes (M-classes), which are collected from normal and abnormal bearings with the same operating conditions. The M-classes stand for the M degradation states, and the data are used to train HMMs. When new data are gained, the type of faults can be classified by the HMM.

2.1Feature extraction

To increase the effectiveness of the fault bearings classification, the extraction of health indicators is necessary. In the paper [6], the time domain features are used as health indicators for bearing faults, and these features are shown in Tab.1.

Tab.1 The features of time domain

The features can be easily extracted from the current signature, and it has been reported that the kurtosis can indicate early stages of bearing failures[7]. With the state of degradation reaching an advanced state, the effectiveness of kurtosis value will be decrease. As the two representative features of the energy, the average power and the standard deviation can been applied to localize defects with limited success. The crest factor can be a good indicator to early stages of bearing failures too, because it is the ratio of the peak to the standard deviation. The skewness and the mean value can also reflect the bearing defects with limited success, as they increase, the bearing appears to deteriorate.

2.2Feature selection

In order to obtain a good classification result, the main condition is to select a set of efficient parameters among the initial candidates. The parameters subset can make the criterion maximize, which have separately took account of the various operating modes or classes.

The sequential backward selection method is a kind of efficient method in feature selection. This method is following the process:

At step k, we can gain the relationship the subsets

The subspacekV minimizes the selective function: Vk,iand the subspace Vk-1by the criterion.

Fig.3 illustrates this method with d = 5 and d' = 2, and the paper [9] can supply more detailed reference.

Fig.3 General diagram of sequential backward selection method

The genetic approach, inspired by the concept of natural selection, is a nondetermistic optimization method and can be used effectively in feature selection. But the method applies to deal with random numbers, and more reference can been supplied in the paper [8].

2.3Classification

The hidden Markov model, introduced by Rabiner, can be applied to model and analyze complicated stochastic processes[9]. In the paper [10], HMMs are used for bearing fault diagnosis and prognostics. A set of features, extracted from vibration signal, are converted into observation sequences to estimate the HMM parameters. In order to obtain the parameters, the observation sequences are grouped into different classes and processed by HMMs, which represent the health status of the bearing. Then new data, grouped into observation sequences, are processed by each of the HMMs, and the health status of the bearing is classified in accordance with the maximum of the likelihoods acquired from each HMM.

Each HMM is characterized by five elements:

N:The number of states in the model S=｛S1,S2,…,SN｝.

M:The number of possible observation symbols at each state V=｛v1,v2,…,vM｝.

A:A state-transition matrixA={aij}, Where: aij=P[qt+1= Sj|qt=Si] 1≤i,j≤N. The aijis the probability of being in state Sjat time t+1, given that it is in state Siat time t, and the qtrepresents the current state.

B:A state-dependent observation density matrix , B={bj(k)}, where: bj(k)=P[ot=vk|qt=Sj], 1≤j≤N, 1≤k≤M, The bj(k) denotes the probability of the observation otin the state Sjat time t.

π:A initial probability value π={πi}, where: πi= P［q1=Si］, 1≤i≤N.

In order to gain a HMM, The probabilities A, B, and π are necessary. For convenience, the compact notation λ=(A,B ,π) is used to denote a HMM.

The HMM can solve three basic problems: the evaluation, decoding and learning. Usually the evaluation and learning are used to solve the classification problem, which includes two steps: training and classifying.

1) Training: In order to maximize the probability P(O|λ), we have to estimate the model parameters λ=(A,B ,π), with a finite observation sequence O=(o1,o2,…,oT) extracting a set of measurements from each class. Given a model parameters λ and a observation sequence O, the Baum–Welch algorithm can adjust the parameters of A, B, and π to maximize the likelihood of the observation sequence O. By using this algorithm, we can obtain the re-estimation formulas to renew the HMM parameters (A,B,π): where αt(i ) and βt(i) are called the forward and backward variables separately. αt(i) is defined as:

Where: α1(i)=πibi(o1), 1≤i≤N .

The βt(i) is defined as:

Where: βT(i)=1, 1≤i≤N .

2) Classifying: By training, we have obtained a HMM with complete parameters. Given an observation sequence O=(o1,o2,…,oT) extracted from a gyromotor measure, the probability P(O|λ) is given by: The HMM, for which the probability is maximum, denotes the fault condition of gyro-motor bearing. A gyro-motor bearing fault can be classified by the steps shown in Fig.4.

Fig.4 Scheme of HMM-based fault classification

3 Experimental results

A brushless DC gyro motor (24 V, 6000 r/min, 1.5 W) is used to verify the proposed approach. Five identical bearings are prepared for the gyro motor, and the five bearings are created artificially different conditions: the outer ring fault, the inner ring fault, the ball fault, the cage fault and the health condition. Then the bearings are used in the gyro motor separately, and the bus current signals are extracted. The aim is to prove the classification method.

The number of samples per signature is 10 000, with the same sampling rate of 20 Hz. Every condition is sampled 10 examples and 50 acquisitions have been obtained totally. In the 50 examples, the 15 acquisitions, with 3 examples from each class, are used to select the best features, and the remaining 35 are used to prove the proposed method efficiency. The Tab.2 shows composition of the training and testing samples.

Tab.2 Composition of the training and testing samples

The Fig.5 (a), (b), (c), (d), (e) and (f) show 6 extracted statistical features from the current signature, whichhave been shown in Tab.1. Each datumxican be defined by a set of relevant features xi=[θ1,θ2,θ3,θ4,θ5,θ6], and used to track the degradation of bearings. But not all features are effective, and invalid features will reduce the efficiency of the fault classification.

Fig.5 Current features of bearings

The Fig.5 shows none can respectively classify the 5 conditions, and the skewness is not good indicator in Fig.5(c) obviously. The remaining features can not be selected directly. By the sequential backward selection (SBS) method, the best 3 features are selected to build features space (Fo=[θ4,θ6,θ2]), which is shown in Fig.6. The features are:

- The standard deviation of currentσ(2θ);

- Kurtosis K(4θ);

- The average power of current P(6θ).

Fig.6 Feature space by the best feature

We use 3 observation sequences (Oi=｛oi1,oi2,…,oiT｝, for i=1,2,3,4,5 and T=4) to train each HMM, and the initial parameters are defined as:

By training, the best HMMs parameters (Ai,πi), which maximize probability P(Oi|λi), are given as follow:

Tab.3 The best HMMs parameters

The 35 remaining classification results are shown in Tab.4. Except one, the rest 34 are all correct, and the right rate is equal to 97.1%. These results present that the new method can classify the typical bearing faults of gyro motors.

Tab.4 Classification results

4 Conclusion

This paper has introduced a novel classification method for bearing faults in gyro motors using stator current signals in time domain. Five different bearing conditions have been considered: outer ring fault, inner ring fault, ball fault, cage fault and health condition. From the acquired current signals, the best features are extracted by the sequential backward selection (SBS) method, and used to build the representation space. Then the classification process is carried out by HMM. The fault classification system has been trained with 5 different operation conditions, with 3 examples from each class, and the remaining 35 are used to certify the method effectiveness. The experimental data, from a brushless DC gyro motor with different bearing fault conditions, prove that the method is effective.

Reference:

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由定子電流信號分析陀螺電機滾珠軸承故障診斷與分類

董 磊1,2，周 灝2，潘龍飛2，陳 偉2，金 琛2，李 楠2，李為民1
（1. 河北工業(yè)大學 機械工程學院，天津 300130；2. 天津航海儀器研究所 天津 300131）

在陀螺電機中，軸承故障是最普遍的失效形式。針對陀螺電機球軸承中各組成部分出現(xiàn)故障難以區(qū)分，而更換整套軸承又造成巨大浪費的問題，提出了一種基于電流信號分析的陀螺電機軸承故障分類方法。該方法通過采集定子電流信號，并應用數(shù)學分析工具，提取出定子電流的特征信號。通過使用順序遞推法排除了冗余和無效特征，然后用最佳的特征信號建立特征空間。通過使用隱馬爾科夫模型，對軸承的典型故障（外環(huán)故障、內(nèi)環(huán)故障、球故障和保持架故障）進行了準確的分類。該方法的有效性在一臺具有不同軸承故障的直流無刷陀螺電機上得到驗證，實驗結(jié)果顯示分類的正確率達到97.1%。

軸承故障；故障分類；隱Markov模型；陀螺電機

U666.1

A

1005-6734(2015)03-0415-06

2015-01-15；

2015-05-08

裝備預研支撐技術項目（62101050802）；國防預先研究重點項目（513090501）

董磊（1979—），男，博士研究生，高級工程師，主要從事慣性元件及可靠性的研究。E-mail：dongleihit@126.com

聯(lián) 系 人：李為民（1964—），男，教授，博士生導師。E-mail：vmin@hebut.edu.cn

10.13695/j.cnki.12-1222/o3.2015.03.025