灰色系统建模理论在机床主轴疲劳寿命设计中的应用研究

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数级，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，并求解灰色系统的微分方程 。通过残差模型的修正，提高模型精度，再运用灰色系统模型的还原模型，可计算出任一应力水平下的安全寿命值。为机床主轴的安全寿命计算提供了新的途径，具有较大的推广应用价值。

Research of Grey System Modelling Theory in Machine Tool Axles''Fatigue Span Design

With the ways and theories of gray system and regarding the relationship between fatigue strength and span as a gray system,a corresponding certain number of the safe span was gotten,when the level of fatigue strength was averagely divided into several degrees.And a smooth dispersed function was gotten by adding the number of safe span.with it,a model of gray system was built and the equation in the gray system was worke out.By correcting the model,raising the exactness of the model and returning the model in the system,the safe span in any level strength could be computed.The method provided a new way for the calculation of safe span of machine tool axles and had a promising future.