弧齿锥齿轮弯曲应力计算

Accurate Calculation of Bending Stress on Spiral Bevel Gears

提出了一种计算弧齿锥齿轮弯曲应力过程的应力影响矩阵方法。此方法应用应力叠加原理,将二次插值得到的接触迹线应力影响矩阵与载荷分布矩阵相乘,建立齿根弯曲应力影响矩阵,从而得到随载荷过程而变化的齿根过渡曲面上的弯曲应力过程。只需一次有限元计算,便可获得整个啮合周期的齿根过渡曲面上弯曲应力分布变化过程。该方法计算精确且极大地简化了计算过程。

A method of the stress influencing matrix is proposed for calculating bending stress courses on teeth root of spiral bevel gears is proposed by using stress superposition principle. The stress influencing matrix of mesh nodes on the surface of the gear teeth and on nodes of its contact lines is established by using 2-D interpolation and then is multiplied by the load distributing matrix on the nodes. Therefore,the bending stress courses on the gear teeth root are obtained. By means of generating the flexibility matrix on the gear teeth root the finite element calculation of this method is only needed once to obtain the distributing conditions of loads on the working surface of the gear teeth and distributing conditions of the bending stresses on root surface of the gear teeth for whole meshing period. The method of the stress influencing matrix is as accurate as the finite element method,but can save computer memory and calculating time to a great extent.