# Study on propagation law of heavy-duty gear under different initial crack angles

The equivalent stress at the crack tip under different crack inclination angles is extracted and plotted, and the equivalent stress under three different torques as shown in Figure 1 is studied.

As shown in Figure 1, it is the variation curve of the equivalent stress at the crack tip with the crack Inclination under three different torques. It is found that the trend of the curve is basically the same under different torques. At the same inclination angle, if the torque decreases, the variation trend of equivalent stress also decreases.

The crack dip angle is in the range of 5 ° to 45 °. It can be seen from the curve that the value of equivalent stress decreases gradually along the positive direction of X axis; In the range of 45 ° to 60 °, the value of equivalent stress increases. In the range of 60 ° to 75 °, the value of equivalent stress begins to decrease with the gradual increase of degree. To sum up, when the inclination angle is 60 °, the curve of equivalent stress at the crack tip reaches the peak, that is, the crack propagation will be easier at this time.

The curve of crack tip displacement under different crack inclination is shown in Figure 2. It can be seen from Figure 2 that under the same crack inclination, the displacement of crack tip also shows an increasing trend with the increase of torque. The crack dip angle is in the range of 5 ° – 60 °. It can be seen from the curve that the displacement of crack tip increases along the positive direction of X axis; When the crack dip angle is in the range of 60 ° – 75 °, the displacement tends to decrease due to the gradual increase of the dip angle. To sum up, when the crack angle is 5 °, the crack propagation is the slowest and the displacement value at the crack tip is the smallest. When the angle increases to 60 °, the displacement value reaches the peak, and the crack propagation is also the most intense.

The initial crack inclination was measured α Study the crack propagation law in the range of 5-75 °, set the initial crack position H0 = 68mm and the initial crack length A0 = 6mm.

As shown in Fig. 2, curve 1 is the propagation trajectory curve when the crack inclination is 5 °. At first, the crack propagation is relatively smooth, then the propagation direction is towards the rim, and finally the crack propagation is towards the tooth root; Curves 2, 3, 4 and 6 correspond to the propagation trajectory curves when the crack inclination is 15 °, 30 °, 45 ° and 75 °, respectively. The propagation laws of the four cases are relatively similar. In these four cases, the crack propagation direction initially faces the rim, and the crack propagation finally faces the tooth root; Curve 5 is the propagation trajectory curve when the crack inclination is 60 °. The initial propagation direction of the crack points to the rim, and then the crack propagation becomes smooth. In the later stage, the propagation direction points to the rim again and deviates from the top of the gear tooth. In short, the crack propagation trajectory of gear is basically the same under different crack angles, and is less affected by the initial crack angle.

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