二维随机载荷作用下疲劳寿命的研究

基于Goodman公式和Miner损伤定则，提出了一种考虑载荷均值影响的二维随机载荷作用下疲劳寿命的计算方法。在此基础上以幅值和均值均符合正态分布的随机载荷为研究对象，推导出了其当量载荷的概率密度函数和等效载荷的数学模型，采用Gauss-Legendre求积公式进行积分运算，对该载荷作用下的疲劳寿命进行了研究。分析了等效载荷随载荷均值和幅值不同分布参数变化而变化的规律，并与不考虑载荷均值的一维随机载荷作用下的等效载荷进行了对比。研究结果表明：载荷均值μm的正负变化对等效载荷产生明显的影响，负的μm导致等效载荷降低，甚至低于一维随机载荷作用下的等效载荷；而正的μm会导致等效载荷迅速增大以至到远大于一维随机载荷作用的等效载荷；当μm=0时，二维随机载荷则略高于一维随机载荷作用的等效载荷。

Research on Fatigue Life under Two Demension Random Stresses

Based on Goodman formula and Miner damage rule, a calculation method of fatigue life was presented under two dimension random stresses considering influences of mean stress. The mathematical  models of the probability density function of equivalent stress and the equivalent stress of two dimension random stress were deduced whose mean stress and stress amplitude followed Gaussian distribution. By integrating with Gauss-Legendre integration formula, the fatigue life was studied under the stress. The change regulations of the equivalent stress with the change of the distribution parameters of mean stress and stress amplitude were analyzed. The equivalent stress was compared with that under one dimension random stress not considering influences of mean stress. The results show: with positive and negative direction changing of the mean values of mean stress“μm”, the equivalent stress will be influenced obviously. Negative μm will result in equivalent stress reduction, even less than it under one dimension conditions. Positive μm will result in rapidly increase of equivalent stress, even greater than it under one dimension conditions. When μm=0, the equivalent stress under two dimension is a little more than it under one dimension conditions.