# Blade Crack Diagnosis Based on Blade Tip Timing and Convolution Neural Networks
## 2 Method
### Testing Device  
In this study, the blade vibration testing system based on BTT is devised to obtain vibration signal data from real cracked blades. The system components are shown in Figure 5. The test platform mainly consists of a rigid support cast iron platform, a servo motor, and bearing support.  
Figure 4: Convolutional neural network structure.  
Figure 5: BTT test system structure.  
The height dimension is much larger than the width and thickness dimensions for free blades with long and thin geometries, such as compressor first-stage blades, fan blades, and turbine final-stage blades. In this study, to improve signal collectability and reduce the influence of noise, a simplified trapezoidal flat blade with a long and thin geometry is designed. In addition, the method can be extended to applications with characteristics similar to the blade design in this research, such as the compressor's first-stage blade. The test blade is loaded in two ways: first, by centrifugal force in the rotating state, and second, by an airflow excitation force applied to the top position of the blade to cause vibration, which is also similar to the real blade loading conditions. The blade damage form in this research only includes crack failure, which has two characteristics: location and depth.  
Straight blades are used for the test. The thickness of the blades is 1.2 mm, and the length is 120 mm. Cracks in this test are designed at three locations, including the top, middle, and root of the blade. The maximum machining depth of the blade crack is 30% of the depth of the section where the crack is located. The test speed is 1500 rpm.  
The test object of this study is a full-circle model blade with a blade thickness of 1.2 mm and a blade length of 120 mm. The specific blade material and geometric parameters are shown in Table 1.  
Figure 6 shows the installation position of the blade, the shape parameters of the blade, and the cracks in the root position.  
\begin{table}
\begin{tabular}{c c} \hline
**Project** & **Parameter** \\ \hline Material & ASTM 1045 \\ \hline Number of blades & 12 \\ \hline Disc diameter/mm & 120 \\ \hline Height of blade/mm & 138 \\ \hline Height of the bottom of the blade/mm & 62 \\ \hline Top length/mm & 34.4 \\ \hline Bottom length/mm & 20 \\ \hline Thickness of blade/mm & 1.2 \\ \hline \end{tabular}
\end{table}
Table 1: Material and geometric parameters of the blade.  
Figure 6: Test blades and crack locations.  
The objective of this test is to detect the crack location and crack depth of the blade based on the BTT signal obtained from the cracked blade test. The vibration signal acquisition is affected by random errors such as sampling frequency, system device installation deviation, and noise.  
The number of BTT data with random crack depths obtained for each crack location in the testing is set to 30, while one set of crack-free conditions is added for comparison. The test duration of each group is 90 s, and the data volume of the fault diagnosis input signal is increased 10 times by further averaging each group of test data into 10 segments of data samples.