摘要
为拟合疲劳寿命服从威布尔分布的小样本P-S-N(失效概率-应力-循环次数)曲线,提出了小样本疲劳寿命试验数据统计分析与P-S-N曲线拟合方法。根据疲劳寿命均值和标准差与应力水平的线性关系,基于已知的最高级应力水平的疲劳寿命分布参数,使用疲劳寿命算术平均值替代其他级应力水平均值(期望),获得疲劳寿命均值与应力水平的线性关系。根据此关系,将不同级应力水平的疲劳寿命等效到最高级应力水平,检验等效寿命与最高级应力水平疲劳寿命的均值相对误差,反推各级应力水平疲劳寿命的统计参数,从而实现了P-S-N曲线的拟合。算例结果表明:使用全部疲劳寿命数据时,所提方法拟合结果与传统方法拟合结果相对误差小于1%;对于拟合设计的2组方案(8-5-5和8-3-3),所提方法与传统方法拟合结果相对误差小于10%;所提方法能够得到较为合理的参数,获得较好的P-S-N曲线拟合结果。
To fit the P-S-N curves of small sample, whose fatigue lives obeying Weibull distribution, a statistical analysis method of fatigue lives of small sample and a fitting scheme of P-S-N curves are proposed. According to the linear relationship between the mean or standard deviation of fatigue lives and the stress level under the logarithmic coordinates, the distribution parameters of the highest stress level are considered, the arithmetic means of fatigue lives are chosen instead of the means at other stress levels to obtain the linear relationship between the means of fatigue lives and the stress levels under the logarithmic coordinates. Following this relationship, the fatigue lives at different stress levels can be equivalently transformed to the highest stress level, and the relative errors between the means of fatigue lives and the equivalent fatigue lives are checked at the highest stress level. Then the distribution parameters of each stress level are achieved to fit the P-S-N curves. When all fatigue lives in a reference are used, the relative error of fitting results between the proposed method and the traditional method is less than 1%. By virtue of two groups of fitting schemes of small samples(8-5-5 and 8-3-3), the relative errors between the proposed method and the traditional method are less than 10%. The proposed method is also able to obtain more reasonable parameters and fit more accurate P-S-N curves.
