涡轮泵转子的临界转速研究(Ⅳ)分布质量轴的传递矩阵法

Critical rotational speed of turbo pump rotor (Ⅳ)transfer matrix method for the distributed mass shaft

根据旋转的 Timoskenko梁的运动微分方程式 ,导出分布质量轴段的 4× 4阶精确传递矩阵 ,计入轴分布质量的平动惯量、转动惯量、陀螺力矩和剪切变形的影响 ,并计算了三个转子的临界转速。算例的计算结果表明 ,轴模型是否按分布质量考虑、是否计入平动惯量、转动惯量、陀螺力矩和剪切变形 ,对临界转速有明显的差别 ;同时在等截面轴不分段情况下 ,传递矩阵的计算结果和精确解一致性很好 ,表明计算实际转轴临界转速时 ,只需按截面不同划分轴段 ,即所取的轴分段数量少 。

According to the moving partial differential equations of the rotating Timoskenko beam,the 4×4 exact transfer matrix of the involved translational inertia,rotational inertia,gyroscopic moments and shear deformation of the distributed shaft mass were deduced.This matrix was also applied to three numerical examples of the critical rotation speeds calculations.The results of calculation show that the critical rotation speeds are different significantly when taking into account translational inertia,rotational inertia,gyroscopic moments and shear deformation of the distributed shaft mass or not.Meanwhile,the results of the transfer matrix method considering shaft mass etc.are consistent with the exact solutions on the condition which the equal cross section shaft do not need divide section.This shows that it just divides section of the shaft according to different cross section when calculating the practical critical rotation speeds.Therefore,the precision of transfer matrix is very high even if the number of divided section is very few.