# Dynamic reliability analysis of bevel gear considering strength degradation

Due to the influence of random factors such as stress and environment, the strength degradation process is usually a continuous random process. The figure shows the stress strength interference theory considering strength degradation. It can be seen from the figure that under the continuous action of cyclic load, the strength distribution of the material shows a decreasing trend, and finally produces an interference area with the stress distribution, that is, there is a probability of failure.

In order to accurately evaluate the reliability change law of bevel gear in service, it is necessary to obtain the strength degradation law of bevel gear in service. The strength of bevel gear decreases with service time, and the strength at each time is called residual strength. The degradation of strength is determined by the amount of fatigue damage of materials, and the degradation form is related to the cumulative mode and amount of fatigue damage. At present, nonlinear fatigue damage theory is widely used in damage calculation, and its damage calculation formula is:

Where, n is the number of load cycles; NF is fatigue life; α Is the material parameter, which is related to load and material. According to the test of material fatigue damage curve, it is concluded that:

Where, σ M is the stress amplitude; σˉ Is the average stress; σ- 1 ( σˉ ) Is the fatigue limit of the material under symmetrical loading.

Thus, the residual strength model based on nonlinear cumulative damage can be obtained as follows:

Where, R (0) is the initial static fatigue strength (it is generally considered that the initial static fatigue strength follows the normal distribution); σ Max is the peak stress. The average value of initial static contact fatigue strength is 1500 MPa, and the average value of initial static bending fatigue strength is 500 MPa. The coefficient of variation of normal distribution is 0 1. It can be obtained that the initial contact fatigue strength and bending fatigue strength obey the normal distribution n (1, 500150) and n (500, 50).

Combined with the stress history of each bevel gear, the variation law of the residual strength of each bevel gear with the cycle ratio can be obtained. Where, the cycle ratio is the ratio of the number of current load cycles n to the fatigue life NF. The fatigue life NF is calculated according to the S-N curve equation of the material, that is:

Where, σ- 1 is the fatigue limit of the material; M is the material property index; N0 is the base number of stress cycle. For medium-sized steel parts, the cycle base N0 = 107, and M = 13 is taken in the preliminary calculation.

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