| 裘春航,李伟东,吕和祥.旋转机械系统多自由度非线性动力学数值分析[J].计算力学学报,2005,22(4):392~398 |
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| 旋转机械系统多自由度非线性动力学数值分析 |
| Numerical analysis of multi-degree of freedom problems in nonlinear dynamics for rotating machine systems |
| 修订日期：2003-10-13 |
| DOI：10.7511/jslx20054078 |
| 中文关键词: 转子系统 非线性油膜力 数值稳定性 非线性动力学特性 |
| 英文关键词:rotor-bearing system,nonlinear oil-film force,numerical stability,nonlinear dynamics characteristics |
| 基金项目:国家自然科学基金(19990510)资助项目. |
| 裘春航 李伟东 吕和祥 |
| 大连理工大学工程力学系,辽宁大连116023 |
| 摘要点击次数: 1496 |
| 全文下载次数: 18 |
| 中文摘要: |
| 首先将转子系统的动力响应问题归结为2n维未知向量v的一阶非线性动力学方程dv／dt=Hv＋f（v，t），并给出了求解这一方程的一次近似式法和三次多项式迫近法。在非稳态、非线性油膜力等作用下，以刚性Jeffcott转子与112个自由度的汽轮发电机组低压转子系统为例，用上述求解方法分析了它们的动力响应及非线性动力学特性；其问，还将计算结果与Runge—Kutta法、Newmark法的相应结果进行了比较，并深入讨论了数值稳定性问题。汽轮发电机组的算例表明对一些具有较复杂的非线性右端项，、同时规模又较大的问题，如果采用四阶Runge—Kutta法，才算几步就因数值骤然增大而失控；但若用同样步长的一次近似式，由于它是一种显式的无条件稳定算式，则计算过程迅速且结果合理可靠。 |
| 英文摘要: |
| Rotors mounted on fluid film bearings of turbines carry one or more disks. The total number of unknowns to be determined for their computational model may range up to several hundreds. This paper focuses on numerical analyzing for nonlinear dynamics system with multi-d.o.f. First two numerical methods to solve nonlinear dynamic response are formulated, and are successfully used in the analysis of an example with 112 d.o.f. of 200 MW rotor subjected to unsteady and nonlinear oil-film force, in which the disk unbalance and gravity effects have been taken into account. To examine the efficiency and reliability of the methods formulated in this paper, the examples are also used to study nonlinear dynamics phenomena, such as periodic doubling, quasi-periodic, and chaotic motion etc. The computational results have shown that the numerical stability of the method plays a very significant role. It must be pointed out that Runge-Kutta method is out of control for the 200 MW example. |
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