燃气轮机拉杆转子考虑接触效应的扭转振动模态分析

燃气轮机转子一般是由多个层叠的轮盘通过拉杆组合而成，各轮盘接触面由磨削加工形成。粗糙度测试结果表明磨削加工的实验拉杆转子轮盘面具有两个不同分形结构的区域。利用结构函数法计算了这种双重分形面的轮廓曲线的分形维数D1、D2和分形粗糙度参数G1、G2 。采用双重分形几何描述接触表面的拓扑结构，并根据赫兹接触理论导出接触微凸体的切向接触刚度。弹塑性双重分形面的切向接触刚度等于所有微观弹性接触点的切向接触刚度的总和。粗糙层是由相接触的微凸体所构成的，其抗扭刚度模化为接触转子轮盘间的一个抗扭弹簧。通过三维有限元模态分析和实验模态分析得到了拉杆转子在不同预紧力下的扭振模态频率。通过上述计算和实验结果识别了粗糙层的抗扭刚度，实验测试结果和理论计算结果相一致，这表明上述接触层抗扭刚度的双重分形模型实合理的，可以有效地考虑接触效应对拉杆转子扭转振动模态频率的影响。

Torsional vibration modal analysis for a rod-fastened gas turbine rotor considering contact effects

Gas turbine rotors are usually assembled with several laminated wheels and tie bolts,the contact surfaces of the wheels are grinded.Roughness measurements on grinded wheel surfaces of a tested rod-fastened rotor show that they have two different fractal structure regimes.Here,the fractal dimension D1,D2 and roughness parameter G1,G2 of each bifractal surface profile were calculated with the structure function method.The bifractal geometry was used to describe the surface topography and the tangential stiffness of contacting asperities was derived with Hertz contact theory.The tangential contact stiffness of an elastic-plastic bifractal surface was the sum of stiffnesses of all elastic micro-contacts.The torsional stiffness of a roughness layer formed with contacting asperities was modeled as a torsional spring between contact wheels.The torsional modal frequencies of the rod-fastened rotor under different preloads were obtained through both 3-D finite element modal analysis and experimental modal analysis.The torsional stiffness of the roughness layer was identified from the above results and its theoretical torsional stiffness was consistent with the test data.It was shown that the proposed bifractal model for the torsional stiffness of a roughness layer is reasonable and effective to consider influence of contact effects on torsional vibration modal frequencies.