Abstract: To confirm the probability that met accuracy requirements of gear systems under the random factors effects,a practical method for kinematic accuracy reliability analysis of involute cylindrical gear system based on the gear accuracy theory and the saddlepoint approximation technology was presented.The influences of gear manufacturing error,axis run-out and assembly eccentric on gear system kinematic error were analyzed.The function expressions of mean,variance,third and fourth central moments of gear system transmission error were obtained.The probability density function and cumulative distribution function of gear system kinematic error was fitted by saddlepoint approximation technique.Based on national standards,the model for reliability analysis of gear system was established.Numerical example results proved the high accuracy and efficiency of proposed method.

Key words: gear system, kinematic accuracy, mechanical reliability , saddlepoint approximation

摘要： 为确定齿轮系统在随机因素影响下满足精度要求的概率,基于齿轮运动精度理论与鞍点逼近技术,提出一种渐开线圆柱齿轮系统运动精度可靠性分析方法,用以确定齿轮系统在随机因素影响下满足精度要求的概率。分析了齿轮加工误差、轴的径向跳动以及装配偏心对齿轮系统运动误差的影响,推导了齿轮系统运动误差的均值、方差、三阶和四阶原点矩的函数表达式,利用鞍点逼近方法拟合了齿轮系统运动误差的概率密度函数与概率分布函数。结合国家标准建立了齿轮系统运动精度可靠性分析模型。数值算例表明,该方法具有较高的求解精度和效率。

关键词: 齿轮系统, 运动精度, 机械可靠性, 鞍点逼近