基于回归分析的准双曲面齿轮齿面误差修正
Flank error correction of hypoid gears based on regression analyses

针对准双曲面齿轮齿面加工误差的机床加工参数调整修正问题，建立了基于刀倾半展成法（HFT）的齿面方程，给出了齿面离散化方法和齿面加工误差的表达式。基于机床加工参数对齿面误差的灵敏度系数进行推导，给出了现有齿面误差修正方法的数学模型，并指出其不足。在此基础上提出了基于回归分析的齿面误差修正方法，通过加工参数的灵敏度系数向量与实测齿面误差向量的线性相关性分析来选择变量，在选取较少的加工参数作为调整变量的同时，减少了各参数所需的调整量。实际齿轮的误差修正试验证明了该方法的上述优点以及误差修正的有效性，可为其他齿面误差修正问题提供了一定的借鉴。
Abstract：Tooth surface equations are derived based on the hypoid-format-tilt (HFT) method to calculate the machine parameter correction for the flank machining error of hypoid gears. The tooth surface discretization method is given for the flank machining error. The sensitivity coefficient for the flank error machine parameters is used to develop a mathematical model for the flank error correction method to identify its disadvantages based on a regression analysis. The linear dependence of the sensitivity coefficient vector of the machine parameters is compared with the real flank error vector to identify the variables for the regression analysis, which reduces the number of machine parameters to be adjusted. Tests of the flank error correction of a real gear show the above advantages and the effectiveness of this method. Guidelines are given for other flank error correction problems.