Calculation of parameters of the modernized Weibull equation

Abstract

The results of fatigue resistance tests are described by various equations, the most common of which are the power law equation, the exponential equation, and the Weibull equation. The choice of each of them depends on the specific task at hand. Most often, two-parameter equations are preferred - the power and exponential equations ‒ as they are the simplest and most versatile. To select a particular equation, it is necessary to establish a criterion, or a group of criteria, which could be used to justify the decision. One such obvious criterion is the correlation coefficient. The results of numerous experiments indicate that it is practically the same for the power law and exponential models of the fatigue curve, and for the Weibull equation, in its canonical form, it is usually slightly lower. The paper solves the problem of increasing the correlation coefficient of the Weibull equation by replacing one of the parameters (endurance limit) with a variable value. The required result was achieved by varying the three values of this equation when constructing a fatigue curve using the least squares method. Calculations were performed in Excel and the Maxima computer mathematics system