基于Copula函数的数控车床可靠性综合分配方法

A Comprehensive Reliability Allocation Method for Numerical-controlled Lathes Based on Copula Function

针对串联系统可靠性分配问题,以基于潜在失效模式与后果分析(FMEA)评价指标非线性修正函数的综合分配方法为基础,提出一种考虑故障相关性的综合分配方法。考虑可靠性分配问题中的多因素影响,建立一种考虑因素重要程度的可靠性分配矩阵。针对FMEA评价指标的局限性,分别建立了严重度和失效频率的非线性转换关系,即FMEA修正函数。基于Gumbel Copula函数及Kendall相关系数,建立失效相关系数矩阵,并计算各子系统的相关失效严重度。推导基于Copula函数的串联系统可靠性计算公式,并以此为依据对各子系统的可靠性进行分配。以数控车床主轴系统为例,利用该方法对其进行子系统可靠性分配,阐述了该方法的特点及适用性。对是否考虑故障相关性的分配结果进行比较,认为考虑故障相关性能够为各子系统分配更低的可靠度,从而减小加工及维护成本。

An allocation method which considers fault correlation is proposed for the reliability allocation of series systems based on the non-linear transform functions of failure mode and effects analysis （ FMEA）. In consideration of the multiple factors that affect the reliability allocation, an reliability allo- cation matrix is established by employing the significance factors. The non-linear transform laws of failure severity and failure frequency are established to address the limitation of FMEA. A coefficient matrix of fault correlation is established based on Gumbel Copula function and Kendall correlation coefficients, and the correlated failure severities of subsystems are calculated. The equation of calculating the reliability of series system is derived based on Copula function. This equation is employed to guide the reliability allo- cation. Finally, the characteristics of the method are analyzed by taking a spindle system of a computer- ized numerical controlled （CNC） lathe for example. The allocation results are compared, which consideres dependent and independentfauhs of subsystems. The result shows that the the allocation method with fault correlation can be used to provide the lower reliability allocation of subsystems, thus reducing processing and maintenance costs.