质量矩阵对水轮机组固有振动模态计算结果的影响

Influence of mass matrix on natural model of hydraulic turbine

针对如何采用有限元法选用适当的单元质量矩阵模式对大型水轮机过流部件进行高精度、高效率和低成本的模态分析问题,本文详细介绍了一致质量矩阵和集中质量矩阵,并以三峡混流式水轮机组为例,数值模拟水轮机转轮、导叶和叶片的前若干阶固有模态,对两种矩阵所得结果进行了比较分析。结果表明,两种质量矩阵模式对低阶固有模态（前30阶）影响不大,固有频率计算值相对误差不超过2%,对应阶数的固有振型相似,而对高阶固有模态（30-100阶）影响显著,固有频率计算值相对误差达到4.25%,且固有振型不同;质量矩阵模式对水轮机转轮、叶片和导叶固有模态的影响随着模态阶数增加而变大,集中质量矩阵计算效率较一致质量矩阵高。从计算精度、效率和成本综合考虑,建议低阶固有模态分析采用集中质量矩阵,高阶固有模态分析采用一致质量矩阵。该研究为水轮机过流部件的动力设计和数值计算提供科学依据,也为水轮机过流部件进一步的动力学分析奠定了基础。

To choose an appropriate mass matrix for performing accurate, effective and low cost model analysis of large-scale hydraulic turbine components, the consistent mass matrix and lumped mass matrix are analyzed in detail. Taking a large Francis turbine with X-blades in Three Gorges hydro-power station as an expample, the first several mode shapes and natural frequencies of the turbine runner, guide vanes and blades are investigated, and the results obtained by using two mass matrix models are analyzed. The results show that the influence of mass matrix on the simulation results of low order modes is low, the maximum relative error is less than 2 %, the mode shapes are similar; but on the high order modes are obvious, the maximum relative error is 4.25 %, the high order mode shapes have great differences. It is found that the influence of the mass matrix on natural characteristics increases with the modal orders, and computational efficiency of 1 mass matrix is higher than that of consistent mass matrix. For the reason of accuracy, efficiency and low cost simulation, the lumped mass matrix and consistent mass matrix should be used for low order modes and high order modes respectively. The results provide scientific references for hydraulic turbine design and numerical simulation, and the foundation is established for the further analysis of structural dynamics.