蒙特卡洛法在减速箱公差分析中的应用

Application of Monte Carlo Method in Tolerance Analysis of Gearboxes

【目的】减速箱零件的公差直接影响着齿轮箱的质量、性能及生产成本,选择适宜的方法进行尺寸链分析与计算有助于提高零配件装配精度。【方法】以蜗轮轴向密封精度要求为例,遵循尺寸链计算规范,推导了极值法、概率法、蒙特卡洛法在尺寸链公差分析中的计算公式,并进行了实例分析,对比了极值法、概率法和蒙特卡洛法三种方法求解封闭环尺寸公差的优劣。【结果】使用蒙特卡洛法的公差结果与概率法结果接近,分别为0.174 2 mm、0.289 6 mm,使用极值法求解得到的结果值最大,为0.515 mm,证明了使用蒙特卡洛法计算得到的公差带范围更加合理、精度更高。【结论】使用蒙特卡洛法进行尺寸链计算,可以放大组成环公差,适当降低零部件的加工精度,一定程度上可以减少加工成本,本研究可为同类线性尺寸链计算提供参考。

[Objective]The tolerance of gearbox parts directly affects the quality,performance and production cost of the gearbox.Choosing a suitable method for dimensional chain analysis and calculation can help improve the assembly accuracy of spare parts.[Method]Taking the accuracy requirements of worm gear axial sealing as an example,following the dimension chain calculation specifications,the calculation formulas of extreme value method,probability method and Monte Carlo method in dimension chain tolerance analysis were derived,and an example analysis was conducted to compare the advantages and disadvantages of extreme value method,probability method and Monte Carlo method in solving closed ring dimension tolerances.[Result]The tolerance results obtained by using Monte Carlo method are close to those obtained by probability method,with values of 0.1742 mm and 0.2896 mm,respectively.The maximum value obtained by using extreme value method is 0.515 mm,which proves that the tolerance band range calculated by using Monte Carlo method is more reasonable and has higher accuracy.[Conclusion]Using Monte Carlo method for dimension chain calculation can enlarge the tolerance of the composition ring,appropriately reduce the machining accuracy of the components,and to some extent reduce the machining cost.This study can provide reference for similar linear dimension chain calculations.