基于非线性最小二乘法的数控转台可靠性评估及优化

Reliability evaluation using nonlinear least squares method and optimization of CNC rotary tables

  • 摘要: 数控转台作为机床核心功能部件,其可靠性保障对数控机床的发展至关重要。为此提出一种基于非线性最小二乘优化法的参数估计方法,通过对数控转台的故障数据进行统计处理、模型假定,利用该方法估计未知参数,并采用Kolmogorov-Smirnov(K-S)检验验证该系列数控转台故障数据分布符合三参数威布尔分布模型。基于该模型,计算得出此系列数控转台的平均故障间隔时间(mean time between failures, MTBF)、平均修复时间(mean time to repair, MTTR)和可用度(availability, A)等关键可靠性指标。通过对比极大似然法、相关系数法所建立模型的拟合效果,证明非线性最小二乘优化法的有效性。最后基于Ansys Workbench平台对该型数控转台的薄弱部位进行优化和六西格玛可靠性分析。为数控机床及其功能部件的可靠性评估及优化提供有效方法参考。

     

    Abstract: The reliability of CNC rotary tables, as core functional components of machine tools, is crucial for CNC machine tool development. A parameter estimation method based on the nonlinear least squares optimization algorithm is proposed in this study. Fault data from CNC rotary tables were statistically processed and subjected to model assumptions. Unknown parameters were subsequently estimated using the proposed method. The Kolmogorov-Smirnov (K-S) test was employed to verify that the failure data conforms to a three-parameter Weibull distribution model. Based on this validated model, key reliability metrics—including mean time between failures (MTBF), mean time to repair (MTTR), and availability (A)—were calculated for the series of rotary tables. Comparative analysis of the fitting performance between models established using the maximum likelihood method and the correlation coefficient method confirmed the effectiveness of the nonlinear least squares optimization approach. Finally, structural optimization and six Sigma reliability analysis were conducted on identified vulnerable components of the rotary table using the Ansys Workbench platform. This research provides an effective methodological reference for the reliability evaluation and optimization of CNC machine tools and their functional components.

     

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