少齿数非对称斜齿轮根切与动态特性的研究

基于齿轮加工原理，建立了非对称齿条刀具法面方程，通过齐次坐标进行矩阵转换，推导了产形轮的齿廓方程.利用产形轮表面根切点的切向量为零，求解出不发生根切的径向变位系数取值范围，为少齿数非对称斜齿轮的参数取值提供依据.根据该齿轮啮合有限元模型，计算出轮齿在完整啮合周期下，齿根节点各向加速度和齿根VonMises应力随时间变化的规律，分析了不同速度和不同载荷对齿根冲击应力的影响.对啮合的齿轮副进行齿顶修形，得到不同修形量时的齿根冲击应力曲线.结果表明:x，y和z方向对非对称少齿数斜齿轮振动的影响都很大，转速比转矩对冲击的影响要大，适当的修形会减小冲击应力.

Study on Undercutting and Dynamic Performance for Asymmetric Helical Gear with Low-Number Teeth

The equation of asymmetric rack cutter in the normal plane was established based on gear machining principle. Through matrix transformation with the homogeneous coordinate， the profile equation of generating gear was derived. The tangent vector of undercutting point on the surface of generating gear tooth is zero. The range of addendum modification coefficient when undercutting doesn’t occur was obtained， providing the basis for parameter selection in gear design. Based on the finite element model of gear engagement， the change of the tooth root acceleration and Von Mises stress within a meshing cycle was analyzed. In addition， the influences of different torque and speed on tooth root impact stress were investigated. The relationship between the impact stress and gear top modification was achieved. The results showed that for asymmetric helical gear with low number teeth， three directions of x， y and z are all important to gear vibration. Rotating speed affects gear impact more significantly than torque， and appropriate modification will reduce the impact stress.