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This paper investigates the performance of the conventional bispectrum (CB) method and its new variant, the modulation signal bispectrum (MSB) method, in analysing the electrical current signals of induction machines for the condition monitoring of rotor systems driven by electrical motors. Current signal models which include the phases of the various electrical and magnetic quantities are explained first to show the theoretical relationships of spectral sidebands and their associated phases due to rotor faults. It then discusses the inefficiency of CB and the proficiency of MSB in characterising the sidebands based on simulated signals. Finally, these two methods are applied to analyse current signals measured from different rotor faults, including broken rotor bar (BRB), downstream gearbox wear progressions and various compressor faults, and the diagnostic results show that the MSB outperforms the CB method significantly in that it provides more accurate and sparse diagnostics, thanks to its unique capability of nonlinear modulation detection and random noise suppression.

Rolling element bearing is a vital component in rotating machinery, such as a wind turbine (WT) system. By accurately monitoring its health condition, the faults can be detected at an early stage, providing sufficient lead time to perform maintenance and hence reducing accidents and economic losses. Bearing usually suffers from various wears and tears, which result in a gradual increase in clearance through its lifetime. Insufficient understanding of vibration characteristics under different clearances brings difficulties for bearing condition monitoring. Thus, this paper presents a nonlinear bearing vibration model with six degrees of freedom (DOF) to investigate the vibration characteristics under different radial clearances and load conditions. Then, a dedicated bearing test is established to verify the reasonability and effectiveness of the vibration model. Furthermore, a comprehensive simulation analysis is conducted to study the vibration characteristics over an extended range of the internal radial clearance and external load. Results show that the dynamic force on each ball presents an impulse whose magnitudes increases whereas the pulse width reduces with clearance increases. Ball pass frequency of outer race (BPFO) is the dominant modulation component and the frequency is in accordance with the number of dynamic force impulses. Two indicators, i.e., root mean square (RMS) value and spectral centroid, are proposed to indicate clearance changes. In general, they show an uptrend with the increase in clearance, which is in line with the dynamic force increasing with clearance, especially the spectral centroid of the low frequency band. However, it should be noted that the RMS value and spectral centroid exhibit a fluctuating behavior due to nonlinear vibration responses. For the first time, this study shows the details of vibration characteristics with clearance variations and provides a foundation for monitoring the bearing conditions before any obvious local defects on raceways.

In the motor current signal, the characteristic frequency of broken rotor bar (BRB) fault is modulated by the supply frequency and it decreases with the decrease of the load, resulting it to be easily buried under light load conditions. Teager-Kaiser energy operator (TKEO) has shown better performance to detect BRB faults than classical methods, such as envelope and spectral analysis. However, the original definition of TKEO leads to its result lack of physical meanings and the causal processing in TKEO can lead to phase distortion and non-ideal filter characteristics. Therefore, this paper proposes a normalized frequency domain energy operator (FDEO) for the BRB fault diagnosis, which does not require causal processing and calculates multiple differentiations in the frequency domain with equal accuracy in one operation. Furthermore, normalized FDEO removes the influence of the supply frequency followed by spectral analysis to extract fault features. The mathematical model of induction motor under healthy and faulty condition are studied in this article. Then, the proposed approach is experimentally validated with seeded one and two BRB faults operating under various load conditions. To verify the effectiveness, the results are compared with TKEO, envelope and spectral analysis. It was found that the proposed method provides slightly obvious fault features with respect to TKEO, especially when the IMs run under light load conditions with two BRB faults. Index Terms-Broken rotor bar, Induction motor, Motor current signature analysis, Frequency domain energy operator， Fault diagnosis. NOMENCLATURE () instantaneous amplitude the amplitude of the fault frequency for fault case the amplitude of the fault frequency for normal case the modulation index Envsq[ ()] the squared envelope of () ℱ Fourier transform ℱ −1 inverse Fourier transform BRB fault characteristic frequency supply frequency rotating frequency the amplitude of the supply current

Envelope analysis is an effective method for characterizing impulsive vibrations in wired condition monitoring (CM) systems. This paper depicts the implementation of envelope analysis on a wireless sensor node for obtaining a more convenient and reliable CM system. To maintain CM performances under the constraints of resources available in the cost effective Zigbee based wireless sensor network (WSN), a low cost cortex-M4F microcontroller is employed as the core processor to implement the envelope analysis algorithm on the sensor node. The on-chip 12 bit analog-to-digital converter (ADC) working at 10 kHz sampling rate is adopted to acquire vibration signals measured by a wide frequency band piezoelectric accelerometer. The data processing flow inside the processor is optimized to satisfy the large memory usage in implementing fast Fourier transform (FFT) and Hilbert transform (HT). Thus, the envelope spectrum can be computed from a data frame of 2048 points to achieve a frequency resolution acceptable for identifying the characteristic frequencies of different bearing faults. Experimental evaluation results show that the embedded envelope analysis algorithm can successfully diagnose the simulated bearing faults and the data transmission throughput can be reduced by at least 95% per frame compared with that of the raw data, allowing a large number of sensor nodes to be deployed in the network for real time monitoring.