Abstract: With the decreasing of spindle failure rate in CNC machine tools,it is increasingly difficult to obtain a large number of failure data sample for normal working conditions of machine tools.Therefore,estimating the Mean Time between Failures (MTBF) of the spindle for small sample data is particularly crucial.There are many improvement methods for Bootstrap in existing research,but most sampling mode are concentrated within the data interval and without considering expanding beyond the grouping interval.The original samples were expanded in three directions using the improved Bootstrap method in this paper,which were used to estimate the scale and shape parameters of the Weibull distribution,and then the MTBF of the machine spindle was calculated.The value of MTBF was compared with the traditional Bootstrap method.The improved method could not only improve the efficiency of data expansion but also improve the accuracy of MTBF estimation.The correlation coefficient method not only expanded the range of initial values,but also simplified the process of estimating displacement parameters.Therefore,a three parameter Weibull distribution model was established to obtain more accurate reliability reference indicators for CNC machine tool spindles,which had high reference value for engineering practice.

Key words: mean time between failures, CNC machine tool spindle, small samples, Bootstrap method, 3-parameter Weibull

摘要： 随着数控机床主轴故障率的下降,针对正常工况的机床来说,想要获得大量的样本故障数据愈加困难,因此针对小样本数据的主轴平均故障间隔时间(MTBF)估计尤为关键。目前已有很多Bootstrap(自助法)的改进方法研究,但是多数抽样方式集中于数据区间内,没有考虑向分组区间外扩充。文中采用改进Bootstrap法在三个方向上扩充原始样本,利用扩充后的样本来估计威布尔分布的尺度参数和形状参数,进而计算机床主轴的MTBF,将其值与改进前的自助法进行比较,改进后的方法既能提升数据扩容效率,又能提高MTBF估计精度,结合相关系数法不仅拓展了初值范围,而且简化了位移参数估计过程,因此建立三参数威布尔分布模型,得到更加精确的数控机床主轴可靠性参考指标,对工程实践有较高的参考价值。

关键词: 平均故障间隔时间, 数控机床主轴, 小样本, Bootstrap法, 三参数威布尔