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The vibration signals analysis is a very effective and reliable method for detecting the gear failures. Because the vibration signals acquired from the gear in the variable speed condition often contain more useful fault information, the analysis of the gear vibration signals during the variable speed condition has been a hot research topic. In this paper, a method based on the multiscale chirplet path pursuit (MSCPP) and the linear canonical transform (LCT) has been applied to diagnose the gear fault in the variable speed condition for the first time. First, by using the MSCPP method to estimate the instantaneous meshing frequency, the suitable signal segment approximation to the acceleration or deceleration process can be selected. Then, because the LCT is a novel and efficient nonstationary signals analysis tool, the optimal LCT spectrum of the selected signal has been attainted to diagnose the gear faults based on the properties of the LCT. In addition, the simulations and the experimental evaluation are provided to verify the effectiveness of the proposed method.

The gear is an important device and has a wide range of applications in industry. However, owing to abrasion and other reasons, the gears may have many kinds of faults, such as pitting, chipping, and the serious crack [

A number of failure diagnosis methods have been used to diagnose the gear faults in variable speed condition, for example, the traditional time frequency analysis methods, self-adaptive signal processing methods, and data driven methods [

The linear canonical transform (LCT) is a generalization of the Fourier transform (FT) and the fractional Fourier transform (FRFT), which has four-parameter family of linear integral transform [

However, in variable speed condition, the gear vibration signals contain many different components, which are not approximated to the LFM signals. The vibration signals acquired from the acceleration or deceleration processes of the gears are often a short period of the gear vibration signals in variable speed condition. In order to apply the LCT method to diagnosis of the gear faults in variable speed condition, the vibration signals acquired from the acceleration or deceleration processes should be selected at first. In practice, it is difficult to only obtain the gear vibration signals during acceleration or deceleration processes directly. Nevertheless, the shaft rotational frequency (SRF) is time varying in the acceleration or deceleration processes, which can be seen as an indicator to select the acceleration or deceleration processes [

In this paper, the multiscale chirplet path pursuit (MSCPP) has been used in the estimation of the IF of the gear vibration signals, which is a widely used and efficient method for IF estimation [

In this paper, the MSCPP method and the LCT have been applied to analyze the vibration signals to diagnose the gear faults in variable speed condition for the first time. First, by using the MSCPP, the IF of the vibration signals obtained from the variable speed condition can be estimated. Then, based on the IF of the vibration signals, we can choose the suitable signal segment, which can be seen as the acceleration or deceleration processes. In addition, according to the gradient of the instantaneous frequency of the selected signal segment, the optimal LCT parameters can be obtained based on the properties of the LCT [

The block diagram of the proposed method.

The remaining parts of this article are organized as follows. In Section

The MSCPP method was first introduced in [

In each time interval, by computing the maximum projection coefficient

The LCT of a signal

When the gear causes a partial failure, the amplitude and phase of the vibration signal of the gear are modulated, which are periodic with the gear’s rotation frequency [

The SRF

The simulated gear vibration signal without noise.

The simulated gear vibration signal with noise.

The FT of the simulated gear vibration signal with noise.

Now, to obtain the fault features from the simulated gear vibration signal and diagnose the gear faults, the MSCPP and the LCT are applied. According to the above analysis, we first use the MSCPP method to estimate the instantaneous frequency of the simulated gear vibration signal. Because the sampling frequency is 2000 Hz, we let the search range and the search step lengths of the frequency slope be −100 to 100 Hz/s and 1 Hz/s, respectively. The search range and the search step lengths of offset coefficients are 0 to 100 Hz and 1 Hz, separately. The points of any dyadic time span is 32. Therefore, we can obtain that

Estimated instantaneous frequency of the simulated gear vibration signal.

The LCT of the simulated gear vibration signal with noise.

Moreover, since the results obtained in Figure

In Section

Platform of experiment.

Firstly, the vibration signal attained from a normal gear in variable speed condition is presented in Figure

The vibration signal obtained from the normal gear.

The FT of the vibration signal obtained from the normal gear.

Estimated instantaneous frequency of the signal presented in Figure

The LCT of the selected signal segment.

Then, Figure

The vibration signal obtained from the fault gear.

The FT of the vibration signal obtained from the fault gear.

Estimated instantaneous frequency of the signal presented in Figure

The LCT of the selected signal segment from the fault gear.

Another vibration signal obtained from the fault gear.

The FT of the vibration signal presented in Figure

In addition, in order to further verify the correctness of the proposed algorithm, Figure

Estimated instantaneous frequency of the signal presented in Figure

The LCT of the selected signal segment presented in Figure

Based on the normal case and two fault cases, it is shown that the method proposed in this can diagnose the gear faults in variable speed condition. However, the MSCPP and LCT method only can show that the gear faults happened, and our research directions will be the diagnosis of the types and the severity of the gear faults.

In this paper, a method based on the MSCPP and the LCT has been applied to diagnose the gear faults in the variable speed condition for the first time. Firstly, the preliminaries of the MSCPP and the LCT have been presented. Then, the proposed method of the simulated gear vibration signals have been showed. At last, in order to further verify the correctness of the proposed algorithm, the diagnosis of actual gear vibration signals also has been presented. It is indicated that the proposed method can diagnose the gear faults availably. In the future, the diagnosis of early gear faults, intermittent gear faults, and multiple gear faults also will be our future research directions.

The authors declare that they have no conflicts of interest.

This work was supported by the National Natural Science Foundation of China (61374135, 61633005, 61673076, and 51637004), the National Key Research and Development Plan: Important Scientific Instruments and Equipment Development (2016YFF0102200), and Central Military Equipment Development Department Pre-Research Project (41402040301).