# Analysis of calculation results of stress intensity factor at leading edge of root crack of heavy-duty gear

Under the set parameters, the gear model is simulated. As shown in the figure, the trend distribution of stress intensity factor at the front end of semi elliptical crack at the tooth root is shown. The value of the ordinate axis in the figure is: stress intensity factor; The ratio of the length of the front crack point to the initial point and the total length of the model is the value of x-axis.

It can be seen from figure (a) that the maximum and minimum values of and are 607.9mpa · MML / 2 and 403.9mpa · MM1 / 2 respectively. By observing the figure, it can be seen that it is a U-shaped regular distribution, and the figure trend is high low high, and both ends are symmetrical. According to the formula, the increase of displacement has the same growth trend as the tensile displacement at the crack front, with a magic growth. The tensile stress at the end of the elliptical crack is greater than that in the middle, which is the reason for the U-shaped distribution of K I at the crack front. According to figure (b), the minimum value and minimum value of K Ⅱ are – 5.4mpa · MM1 / 2 and 8.3mpa · MM1 / 2 respectively. By observing the figure, it can be seen that it is an inverted U-shaped distribution, and the figure trend is low high low, and both ends are symmetrical. Compared with the above figure, the trend of K I is just the opposite. According to the formula, it can be concluded that the increase of displacement has the same growth trend as the tension displacement at the crack front, with the increase of K Ⅱ. Because the stress in the middle of the crack includes the shear force in the horizontal direction of the crack surface and the shear force in the normal direction of the crack tip, which are all acting together and greater than the end point, the distribution trend of K Ⅱ is parabola. The shear force parallel to the crack surface and perpendicular to the crack tip in the middle of the elliptical crack is greater than that at the end, which is the reason for the parabolic distribution of the crack front. The two maximum values of K Ⅲ are -7.9mpa · MM1 / 2 and 88mpa · MM1 / 2 respectively. According to the formula, the trend of K Ⅱ is synchronized with the tearing displacement at the front of the crack, the initial points change gently, and the trend is basically a straight-line growth law.

According to the above results, the overall curves of K Ⅱ and K Ⅲ are located below the K Ⅰ curve, and the maximum values of K Ⅱ and K Ⅲ account for 1.3% and 1.4% compared with the maximum values of K Ⅰ. Therefore, the stress intensity factor of type I is the dominant influencing factor, and its value is much greater than that of type II and type III in the process of tooth root crack propagation, indicating that the open crack is the main manifestation of the whole propagation process of tooth root crack of heavy-duty pinion.

The main influencing factor of material fracture is stress intensity factor, and the judgment parameters are also related to stress crack shape, load, intensity factor and crack size. Therefore, it is very important to further study the influence of crack shape, load and crack size on the open crack.

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