耐用度服从三参数Weibull分布的机床刀具在变加工条件下的可靠性评估

Reliability Assessment of Cutting-Tool for Machine Tools with Three-Parameter Weibull Distribution under Variable Machining Conditions

为了满足工件不同的粗、精加工和表面质量等加工工艺要求,同一把刀具除切削速度、进给量、切削深度等切削用量不断变化外,加工部位及零部件类型亦不断变化,即刀具的加工条件并非恒定不变。为了评估变加工条件下刀具的可靠性,在分析两参数Weibull分布等单一统计分布概率模型的基础上,综合考虑切削用量等物理因素对刀具使用寿命及可靠性的影响,并结合刀具寿命大于某一阈值的工程事实,应用Cox比例危险模型,建立了基于三参数Weibull分布的Cox比例危险模型。利用Nelson累积失效原理,给出了切削刀具在变加工条件下的各种加工时间在同一加工条件下的当量时间,解决了变加工条件下刀具加工时间的折合问题。结合贝叶斯仿真模型参数估计方法,揭示了刀具在变加工条件下的可靠度和故障率的变化规律,为更换不合格刀具提供了理论依据。实际案例分析结果显示,刀具可靠度及故障率函数均为分段函数,前者为分段连续单调递减,后者因受切削用量的影响,表现为分段不连续单调递增,且在不同加工条件时间分界点突变上跳或下跳。

To meet all kinds of processing requirements for such as rough/finish machining and workpiece surface quality,it is necessary to constantly change the cutting speed,feed rate and cutting depth of cuttingtools,and the types of machined parts and components are also changeable,so the processing conditions of cutting-tools are not constant.Based on the analysis of single probability model for two-parameter Weibull distribution and the comprehensive consideration of some physical factors,e.g.cutting parameters,which affect the life and reliability of cutting-tool,a Cox proportional risk model with three-parameter Weibull proportional hazard is constructed.The Nelson cumulative failure principle is utilized to give an equivalent time to different processing time,then the problem of how to transfer different processing time into an equivalent time is solved,which is regarded as the same machining condition.The change mechanism of reliability and failure rate for cutting-tool under variable processing condition is revealed with the Bayesian simulation model parameter estimation.A real example shows that both reliability and failure rate are piecewise functions,the former continuously and monotonically decreases,while the latter discontinuously but monotonically increases due to the effect of cutting parameters,and jumps up or goes down at different operating demarcation points.