数控机床马尔可夫过程下的超单元可靠性建模技术

Reliability Modeling Technology of Superelements for CNC Machine Tools with Markov Process

将数控机床按其功能层次划分为主系统与辅助系统。研究了主系统与辅助系统之间的关系,提出超单元可靠性建模技术概念,将辅助系统以超单元的形式嵌入到关联主系统的可靠性模型中,并建立了基于马尔可夫过程的数控机床主系统动态可靠性分析数学模型,降低了系统的状态空间。在此基础上,假设各主系统为相互独立的模块,采用克罗内克方法对数控机床的整机稳态可靠性指标进行计算。最后,以某型号数控外圆磨床为例,通过实际数据求解其可靠性指标,分析其可靠性状况,验证了模型的正确性和适用性。

The CNC machine tool was divided into main systems and auxiliary systems according to its functional hierarchy. The relationship between main systems and auxiliary systems was researched, the reliability modeling technology of superelement was proposed, the auxiliary systems were embedded into the reliability mathematic model of main systems in the form of superelement, and a dynamic reliability analysis model of CNC machine subsystems based on Markov process was established, which reduced the state space of the system. Based on these, assuming that each main system is the independent model, the steady reliability index of the CNC machine was calculated with Kronecker method. Finally, a case of CNC cylindrical grinding machine was given, with its reliability analyzed by solving the reliability index of the actual data; therefore, the result demonstrated the correctness and applicability of the model.