疲劳寿命的灰色建模研究

STUDY ON GREY MODELLING OF FATIGUE LIFE-SPAN

运用灰色系统的理论及方法 ,将疲劳应力与寿命的相互制约关系看成一个灰色系统 ,将疲劳试验的应力水平均匀分成 5级 ,并找出与之对应的安全寿命的白化值。通过对安全寿命值数列的一次累加 ,生成一个光滑离散函数。据此建立灰色系统模型GM(1,1) ,并求解灰色系统的微分方程。通过残差模型GM (1,1)的修正 ,提高模型精度 ,再运用灰色系统模型GM(1,1)的还原模型 。

The mutual influences between fatigue stress and life span are regarded as a grey system. Stress levels of fatigue experiment are divided into five levels here and the corresponding white data of safe life are found. On the basis of accumulated generating operation of life span data, a smooth discrete function is generated. The generated discrete function follows exponential law, reduces the randomness of data, hence strengthens regularity. Its Grey System Model GM(1,1) is constructed, and differential equation of grey system is sloved. Precision of model has been further improved by the residual correction. Using recovery (regenerating) treatment of Grey System Model GM(1,1), safe life data under any stress level are calculated. Thus a reliable method is provided for finite life span design of machine elements.