灯泡贯流式水轮发电机组主轴的静动态有限元分析
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摘要
水轮发电机组是水力发电的关键设备。灯泡贯流式水轮机是开发低水头水力资源的优良机型。随着我国国民经济的发展，在经济发达的沿海地区和平原地区可开发的水力资源中，中高水头电站已逐步开发完毕。为适应经济飞速发展对电力的需求，开发低水头水力资源已提到了议事日程。由于我国开发贯流式机组较晚，机型以引进为主，多采用传统设计方法。应用有限单元法理论和优化设计思想并结合大型工程分析软件进行贯流式水轮发电机组的设计与开发，对于提高其设计水平和生产效率将是大有裨益的。
本论文运用有限单元法和模态分析理论，结合大型商业化工程分析软件UG和MSC.PATRAN/NASTRAN对灯泡贯流式水轮发电机组的关键部件之一——主轴进行了静力强度分析和振动模态分析。
首先，根据机组主轴的实际结构，应用大型三维实体几何建模软件UG建造其三维实体几何模型，省略相对细小的结构，简化模型。又因有限元分析的需要，将主轴模型分成三个部分，并省略法兰盘上的孔型结构。将几何模型导入到并行框架式有限元前后处理及分析系统MSC.PATRAN做有限元分析的前处理，构建了以十节点四面体单元为基本单元的有限元计算模型。同时，应用RBE3刚性单元以及MPC多点约束来模拟法兰盘上螺栓传递的分布载荷，使主轴的加载更符合实际情况。
其次，使用大型有限元软件MSC.NASTRAN对主轴的物理模型进行了静力强度分析计算，得出了主轴的应力分布和变形状态。分析结果表明：在由法兰盘向轴身过渡的轴段应力较大，而且比较复杂，通过对比材料的屈服应力极限，还有较大的强度储备；主轴在各种静载荷作用下，满足强度要求。
第三，在总结主轴发生振动的原因的基础上，应用大型有限元软件MSC.NASTRAN对主轴的振动模态进行分析。在计算频段0—300Hz范围内，得到了六阶振动模态，对应有六个固有频率和六个固有振型。经分析可知，在计算频段内，未发生整个主轴各部分同时振动的情况，多是局部的振动，而且多是弯曲振型。在机组运行的正常工作范围内，主轴发生共振的可能性是很小的。
通过对主轴的研究分析，为以后该型水轮发电机组的整机及其它零部件的有限元分析与优化设计以及动力响应计算奠定了一定的基础。
Turbine-Generator machine set is the crucial equipment of waterpower. Bulb Tubular Turbine-Generator is the eximious type that develops the hydraulic resources of low headwater. With the development of the national economy of our country, among the hydraulic resources that can be developed in economic developed coastal area and plain area, power stations of high and middle headwater have been developed completely step by step. To meet the demand of power with fast economic development, the development of the hydraulic resources of low headwater have mentioned agenda. It is benefit to improve the level of designing this type and production efficiency if the thought of Finite Elements Method and Optimization Design combined with engineering analysis software is applied into development and design of Bulb Tubular Turbine-Generator.
In this paper, main shaft, one of the key parts of Bulb Tubular Turbine-Generator, is analyzed with Finite Elements Method and the Theory of Modal Analysis combined with UG and MSC.PATRAN/NASTRAN, mainly static strength analysis and modal analysis.
Firstly, according to the actual structure of main shaft, three dimensions substance geometry model is built with UG, and the relative small structures are left out to predigest the model. Because of need of Finite Element Analysis, the model is divided into three parts, and left out the holes on flanges. Then the solid geometry model is entered into MSC.PATRAN to do the pre-treatment of FEA. It is disassembled by ten-noded tetrahedron elements. At the same time RBE3, a type of rigid element, and MFC (Multi-point Constraint) is applied to imitate the distribution load on flange plate that transmitted by bolts so as to make the loaded condition of main shaft accorded with actual condition more.
Secondly, static strength of main shaft is analyzed and calculated with MSC.NASTRAN to gain the stress distribution and deformed state of main shaft. Analysis result shows: the stress on the part of transition from flange to shaft body is greater and more complex; by contrast with material submitted stress limit, strength reserve of main shaft is still greater. In a word, main shaft meets the requirement under various static loads.
Finally, on the basis of the reasons of vibration of main shaft, its modes are analyzed with MSC. NASTRAN. There are 6 modes in 0-300 Hz scope, corresponding 6 natural frequencies and 6 normal mode of vibration. By analysis, it is known that there is not the condition that each part of main shaft at the same time vibrates in calculating frequency scope, but mainly local vibration and curved modal shape. In the normal working conditions the possibility that main shaft occurs resonance is very small.
The research for main shaft has laid certain foundation for analysis with FEM and optimization design of overall machinery and others parts and calculation of vibration responds.
本论文运用有限单元法和模态分析理论，结合大型商业化工程分析软件UG和MSC.PATRAN/NASTRAN对灯泡贯流式水轮发电机组的关键部件之一——主轴进行了静力强度分析和振动模态分析。
首先，根据机组主轴的实际结构，应用大型三维实体几何建模软件UG建造其三维实体几何模型，省略相对细小的结构，简化模型。又因有限元分析的需要，将主轴模型分成三个部分，并省略法兰盘上的孔型结构。将几何模型导入到并行框架式有限元前后处理及分析系统MSC.PATRAN做有限元分析的前处理，构建了以十节点四面体单元为基本单元的有限元计算模型。同时，应用RBE3刚性单元以及MPC多点约束来模拟法兰盘上螺栓传递的分布载荷，使主轴的加载更符合实际情况。
其次，使用大型有限元软件MSC.NASTRAN对主轴的物理模型进行了静力强度分析计算，得出了主轴的应力分布和变形状态。分析结果表明：在由法兰盘向轴身过渡的轴段应力较大，而且比较复杂，通过对比材料的屈服应力极限，还有较大的强度储备；主轴在各种静载荷作用下，满足强度要求。
第三，在总结主轴发生振动的原因的基础上，应用大型有限元软件MSC.NASTRAN对主轴的振动模态进行分析。在计算频段0—300Hz范围内，得到了六阶振动模态，对应有六个固有频率和六个固有振型。经分析可知，在计算频段内，未发生整个主轴各部分同时振动的情况，多是局部的振动，而且多是弯曲振型。在机组运行的正常工作范围内，主轴发生共振的可能性是很小的。
通过对主轴的研究分析，为以后该型水轮发电机组的整机及其它零部件的有限元分析与优化设计以及动力响应计算奠定了一定的基础。
Turbine-Generator machine set is the crucial equipment of waterpower. Bulb Tubular Turbine-Generator is the eximious type that develops the hydraulic resources of low headwater. With the development of the national economy of our country, among the hydraulic resources that can be developed in economic developed coastal area and plain area, power stations of high and middle headwater have been developed completely step by step. To meet the demand of power with fast economic development, the development of the hydraulic resources of low headwater have mentioned agenda. It is benefit to improve the level of designing this type and production efficiency if the thought of Finite Elements Method and Optimization Design combined with engineering analysis software is applied into development and design of Bulb Tubular Turbine-Generator.
In this paper, main shaft, one of the key parts of Bulb Tubular Turbine-Generator, is analyzed with Finite Elements Method and the Theory of Modal Analysis combined with UG and MSC.PATRAN/NASTRAN, mainly static strength analysis and modal analysis.
Firstly, according to the actual structure of main shaft, three dimensions substance geometry model is built with UG, and the relative small structures are left out to predigest the model. Because of need of Finite Element Analysis, the model is divided into three parts, and left out the holes on flanges. Then the solid geometry model is entered into MSC.PATRAN to do the pre-treatment of FEA. It is disassembled by ten-noded tetrahedron elements. At the same time RBE3, a type of rigid element, and MFC (Multi-point Constraint) is applied to imitate the distribution load on flange plate that transmitted by bolts so as to make the loaded condition of main shaft accorded with actual condition more.
Secondly, static strength of main shaft is analyzed and calculated with MSC.NASTRAN to gain the stress distribution and deformed state of main shaft. Analysis result shows: the stress on the part of transition from flange to shaft body is greater and more complex; by contrast with material submitted stress limit, strength reserve of main shaft is still greater. In a word, main shaft meets the requirement under various static loads.
Finally, on the basis of the reasons of vibration of main shaft, its modes are analyzed with MSC. NASTRAN. There are 6 modes in 0-300 Hz scope, corresponding 6 natural frequencies and 6 normal mode of vibration. By analysis, it is known that there is not the condition that each part of main shaft at the same time vibrates in calculating frequency scope, but mainly local vibration and curved modal shape. In the normal working conditions the possibility that main shaft occurs resonance is very small.
The research for main shaft has laid certain foundation for analysis with FEM and optimization design of overall machinery and others parts and calculation of vibration responds.
引文
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[3] Romcke, N.; Victory, J. J. Modern Small-Scale FRANCIS Turbines Development and Experience. Proceedings of the Society of Photo-Optical Instrumentation Engineers, 1980 (11): 15～22
[4] He, Guo Ren; Huang, Fu Wen. Research and Testing of the Hydraulic Performance of S-type Tubular Turbine. ASME, Fluids Engineering Division, 2001, 43: 11～17
[5] Borgwardt, Loren C.; Leonardson, Kenneth R.; Schuchard, Marvin E. CORNELL Hydro Station: Five Years Experience with Tubular-Type Turbine-Generating Units. Proceedings of the American Power Conference, 1983, 45:1078～1084
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[7] Zhou Bolin, Zhu Hongan. Construction of Hydropower Station with Bulb Tubular Type Units. Yangtze River, 1997, 28(7):22～24
[8] Feng, Yanxiang. Improvement on bulb tubular turbine unit at Majitang water power plant. Large Electric Machine and Hydraulic Turbine, 1998 (2):41～42
[9] 游赞培．从长洲水利枢纽机组的选择论国内大型灯泡贯流式机组的发展方向．珠江现代建设，1996(2)：2～8
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[17] 马秋成，肖良红，等．UG建模方法的探讨．机械设计与研究，2002，18(1)：40～41
[18] 马秋成，罗益宁，等．基于UG的齿轮三维建模和消除轮齿投影线的方法．机械设计与研究，2001，17(1)：27～28
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[21] 黄晋英．发动机结构的有限元建模与动态特性分析．太原：华北工学院硕士学位论文，2000
[22] Young S.; Santiago, Leonard D. Surface Ship Shock Modeling and Simulation: Two-dimensional Analysis Shin. Shock and Vibration, 1998, 5(2):129～137
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[24] 王勖成，邵敏．有限单元法基本原理和数值方法(第2版)．北京：清华大学出版社，1997
[25] 王守信．有限元法教程．哈尔滨：哈尔滨工业大学出版社，1994
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[29] Barker, D.K. Johnson, J.C. Johnson, E.H. et al. Design of Practical Composite Structure Using Enhancements to MSC.Nastran Structural Analysis and Optimization. Structural Dynamics and Materials Conference, AIAA, 2002: 1095～1105
[30] MSC公司．MSC．Nastran—世界公认的CAE工业标准．计算机辅助设计与制造，2002(5)：59～62
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[2] Wang, Jianhua; Yang, Xiaolin. Selection of tubular bulb type units for WP hydropower station. Yangtze River, 1997, 28 (11): 20～21
[3] Romcke, N.; Victory, J. J. Modern Small-Scale FRANCIS Turbines Development and Experience. Proceedings of the Society of Photo-Optical Instrumentation Engineers, 1980 (11): 15～22
[4] He, Guo Ren; Huang, Fu Wen. Research and Testing of the Hydraulic Performance of S-type Tubular Turbine. ASME, Fluids Engineering Division, 2001, 43: 11～17
[5] Borgwardt, Loren C.; Leonardson, Kenneth R.; Schuchard, Marvin E. CORNELL Hydro Station: Five Years Experience with Tubular-Type Turbine-Generating Units. Proceedings of the American Power Conference, 1983, 45:1078～1084
[6] 杨晓琳．浅析灯泡贯流式机组的选型设计．人民长江，1996，27(3)：24～26
[7] Zhou Bolin, Zhu Hongan. Construction of Hydropower Station with Bulb Tubular Type Units. Yangtze River, 1997, 28(7):22～24
[8] Feng, Yanxiang. Improvement on bulb tubular turbine unit at Majitang water power plant. Large Electric Machine and Hydraulic Turbine, 1998 (2):41～42
[9] 游赞培．从长洲水利枢纽机组的选择论国内大型灯泡贯流式机组的发展方向．珠江现代建设，1996(2)：2～8
[10] 刘满宏．灯泡贯流式水轮机设计制造水平综述．东方电机，1994(1)：74～78
[11] 尹国军，张国明．用ANSYS程序进行灯泡式水轮发电机组的静力分析．东方电机，1994(1)：128～135
[12] 金维明．结合UGⅡ与MSC／NASTRAN计算振动特性的方法．航空与航天，1997(4)：20～22
[13] 解跃青，雷雨成．商务用车车身有限元建模及分析．机械设计与制造，2002(2)：52～53
[14] 刘承宗，赵惠麟．复杂钢构件的非线性有限元分析．东南大学学报，1997，27(A11)：17～22
[15] 李霞，王强．UG软件在挖掘机三维仿真设计中的应用．矿山机械，1999，27(5)：19～20
[16] 王蕴华，周大勇．UG在天线结构设计中的应用．电子机械工程，2000(3)：42～44
[17] 马秋成，肖良红，等．UG建模方法的探讨．机械设计与研究，2002，18(1)：40～41
[18] 马秋成，罗益宁，等．基于UG的齿轮三维建模和消除轮齿投影线的方法．机械设计与研究，2001，17(1)：27～28
[19] Modeling User Manual, Version 15.0. Unigraphics Solutions Inc, 1998
[20] Unigraphics Essentials User Manual, Version 15.0. Unigraphics Solutions Inc, 1998
[21] 黄晋英．发动机结构的有限元建模与动态特性分析．太原：华北工学院硕士学位论文，2000
[22] Young S.; Santiago, Leonard D. Surface Ship Shock Modeling and Simulation: Two-dimensional Analysis Shin. Shock and Vibration, 1998, 5(2):129～137
[23] Young S.; Santiago, Leonard D. Surface ship shock modeling and simulation Shin. ASME, Pressure Vessels and Piping Division, 1997, 351 (7): 29～34
[24] 王勖成，邵敏．有限单元法基本原理和数值方法(第2版)．北京：清华大学出版社，1997
[25] 王守信．有限元法教程．哈尔滨：哈尔滨工业大学出版社，1994
[26] 张国瑞．有限元法．北京：机械工业出版社，1991
[27] 白忠喜．有限单元法基础教程．吉林：吉林科学技术出版社，1992
[28] 龙驭球．有限元法概论(第2版)．北京：高等教育出版社，1991
[29] Barker, D.K. Johnson, J.C. Johnson, E.H. et al. Design of Practical Composite Structure Using Enhancements to MSC.Nastran Structural Analysis and Optimization. Structural Dynamics and Materials Conference, AIAA, 2002: 1095～1105
[30] MSC公司．MSC．Nastran—世界公认的CAE工业标准．计算机辅助设计与制造，2002(5)：59～62
[31] MSC．PATRAN-基于并行工程的框架式前后处理及有限元集成分析系统．The MSC．Software Corporation
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