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For rotary machines, the measured vibration signals contain multiple frequency modulation components with much machine health information. Decomposing vibration signals of rotary machines into a series of sub-signal components with physical meaning is of great significance for a deep understanding of the machine properties in solving fault diagnosis problems. However, accurately detecting and decomposing frequency modulation components is a challenging problem. This article proposed a multiple frequency modulation components detection and decomposition approach for rotary machine fault diagnosis. Specifically, the amplitude and concentration at the orders (defined as multiple of the rotating frequency) of each signal to be analyzed are calculated, and thresholds are set to distinguish noise and non-noise signal components. Then the cross correlation between the non-noise signal components and an order ruler (constructed with normalized amplitude only on the orders of characteristic components of the faulty signal) is calculated to obtain the instantaneous frequencies (IFs) of these signal components. Finally, a variational algorithm framework defined only by the characteristic components of the faulty signal is used to achieve signal decomposition. The proposed method fully uses the inherent geometric relationship of the frequency modulation signal in the angular domain and is robust to strong environmental noise. Both the simulation example and the actual application cases demonstrated the effectiveness of the proposed method, which shows the potential in solving real industrial problems. [ABSTRACT FROM AUTHOR]

• Gearbox fault diagnosis using BFNCC is proposed for nonstationary condition. • The method can remove the effect of the structure transfer paths. • The proposed method is robust to the location of measuring points. • Method shows potential for a machinery with complicated structure transfer paths. The main challenges in gearbox condition monitoring and fault diagnosis are the heavy noises caused by harsh operating environments and the complicated nonstationary condition during the runtime. It is extremely difficult and even impossible to obtain sensitive fault characteristics through direct measurements. Thus, it is of great significance of fault characteristic inversion based on the structure vibration transfer paths for complicated mechanical systems fault diagnosis. This paper proposes a gearbox fault diagnosis method under nonstationary condition through using nonlinear chirp components extracted from bearing force (BFNCC). In the proposed method, the bearing dynamic forces are first identified based on the vibration transfer function matrix, and the intrinsic signal components are then decomposed through a nonlinear chirp mode decomposition method. The proposed method improved the quality of vibration signals by removing the effect of the structure vibration transfer paths. In comparison with order tracking, the BFNCC is capable of clearly reflecting the magnitude increase phenomenon under gear fault condition. Numerical simulation and experimental studies show that the proposed method is effective for gear fault diagnosis under nonstationary condition. The proposed method is demonstrated to be superior to the existing approaches and robust to the location of measuring points, and thus shows potential in machinery fault diagnosis under the interference of complicated structure transfer paths. [ABSTRACT FROM AUTHOR]