# S-N curve and P-S-N curve of low speed and heavy load gear

The number of fatigue cycles under four stress levels is counted in the order from small to large, and the order from the minimum life to the maximum life is 1 to 6.

Then the life reliability estimator P of the low-speed and heavy-duty gear is calculated according to the formula.

Where:

N – number of tests;

I-the ordinal number of each fatigue life.

Then the reliability estimates P corresponding to four different maximum stresses S1, S2, S3 and S4 are calculated by the formula.

Taking x = log n as abscissa and P as ordinate, the data are plotted on the normal probability coordinate paper created in origin and the fitting results are shown in Figure 1

It can be seen from Figure 1 that each data point is approximately on the fitting line, which indicates that each group of test data is subject to normal distribution. The higher the reliability is, the shorter the predicted fatigue life is, and the fatigue life with higher stress level is less than that with lower stress level; With the decrease of the stress level, the slope of the fitting line increases, that is, from “steep” to “flat”, which indicates that the higher the stress level is, the smaller the range of the predicted fatigue life is, and the result is more accurate, but the life is shorter; When the stress level is low, the predicted fatigue life is longer, but it is prone to mutation.

According to figure 1, the median logarithmic fatigue life estimator X50 can be obtained, and the reliability is 50%. At the same time, the logarithmic safety life estimator x99.9 can be obtained, and the reliability is 99.9%. According to the data, the maximum stress Smax takes log s as the ordinate and log NP as the abscissa. The median S-N curve with 50% reliability can be obtained by drawing and fitting the four data points of X50 in origin, and the P-S-N curve with 99.9% reliability can be obtained according to the data points of x99.9, as shown in Figure 2.

It can be seen from Figure 2 that with the decrease of stress level, the horizontal distance between the two curves becomes larger and larger, and the dispersion increases. That is to say, when the reliability is 50% and 99.9%, the range of predicted fatigue life increases. In this case, it is necessary to determine a value between 50% and 99.9% reliability when predicting the fatigue life of test gear, which can meet the requirements of high reliability and long fatigue life of test gear.

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