齿轮传动的节圆偏差及其概率分布参数分析

Analysis of Pitch Deviation and Probability Distribution Parameters of Gear Transmission

齿轮传动中的节圆偏差反映了其运动误差传递的本质,从齿轮传动原理及齿轮实际啮合的几何位置关系出发,对节圆偏差的主要来源及不同因素影响下的节圆偏差计算方法分别进行了研究,建立了在各种因素综合作用下的节圆偏差计算方法。由概率分布组合的大数定律及中心极限定理判定节圆偏差近似服从正态分布,进而结合"3σ"原则建立了节圆偏差概率分布均值和方差的定量计算方法,为分析齿轮传动运动精度及运动可靠性奠定了基础。

The pitch deviation reflects the nature of its kinematic error propagation in pinion unit. According to the theory of pinion unit and the geometric positional relationship of the actual gear meshing, this paper studies the main source of the pitch deviation and the calculation methods of the pitch deviation under the in- fluence of different factors. The pitch deviation calculation method was constructed under the integrated effects of the various factors. The pitch deviation was determined as approximate normal distribution by the law of large numbers combined by the probability distribution and the central limit theorem. Futher more, combining the Alpha principle, the quantitative calculation method of the mean and variance of probability distribution of the pitch deviation were established, which laid foundation for the analysis of kinematic accu- racy and kinematic reliability analysis of pinion transmission .