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W.Traupel所著《热力透平机》一书,引证齐备,立论精当,在汽机专业同行中享有盛誉。最近见到该书第二卷1982年新版,抢先读了其中的第20章《叶片与叶轮的振动》,感到科技进步确实很快,但有待解决的问题仍然不少。因此摘录部分论述和其计算方法,供读者参考。直杆的扭转振动系按扭振偏微分方程求解,同时采用系数ψ_t来考虑截面的弯曲。ψ_t=I_p/J_t,其中J_p和J_t分别为截面的极惯性矩和有效的扭转惯性矩。ψ_t的计算步骤如下:将叶片型线改成对称的但厚度分布不变的新型线,其主惯性矩为J_1和J_2;相同的惯性矩将有一个主轴为a和b的椭圆形型线,且
The book “Heat Turbine” by W. Traupel, with a complete set of citations and excellent arguments, enjoys a good reputation among steam turbine professionals. I recently saw the 1982 edition of Volume II, the new edition of 1982, where I first read Chapter 20, “Vibration of Leaves and Impellers,” and I feel that technological progress is indeed fast but there are still many outstanding problems to be solved. Therefore excerpt part of the discussion and calculation methods for readers reference. The torsional vibration of the straight rod is solved by partial differential equation of torsional vibration and the coefficient ψ_t is used to consider the bending of the cross section. ψ_t = I_p / J_t, where J_p and J_t are the polar moment of inertia of the cross section and the effective torsional moment of inertia, respectively. The calculation procedure of ψ_t is as follows: change the blade profile to a new type of line whose symmetry but the same thickness distribution, whose main moments of inertia are J_1 and J_2; the same moment of inertia will have an elliptical profile with major axes a and b, And