考虑主轴扭转变形的轴系振动模型
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摘要
针对大型水力发电机组传统上忽略轴系扭转变形的假设可能导致轴系振动分析出现较大偏差的问题,采用Lagrange方法建立轴系振动方程和含轴系扭转效应的转子运动方程,通过定义广义动量,将这2个方程构建为统一形式的一阶微分方程组.以发电机转子上的阻力矩和水轮机转轮上的动力矩为纽带,构建包括水力系统、发电机、励磁、调速系统在内的完整水力机组模拟运行系统,并采用二阶Runge-Kutta法进行仿真计算.计算结果表明,在机组故障扰动条件下,计入轴系的弹性对轴系横向振动的影响不大,主轴扭转刚度对稳定工况下轴的扭转变形影响较大;故障扰动下,发电机转子和水轮机转轮之间的扭转角变化趋势与有功变化趋势基本一致.仿真表明,所建立的轴系扭振模型能反映轴系振动的基本特征,模型是合理的.
The traditional assumption ignoring torsion deformation in shaft of hydro-turbine generator units( HTGU) may lead to a large deviation from the actual situation in analyses of shafting vibration.Thus,two equations,i. e.,shafting vibration equation and rotor motion equation with torsion effect were established based on the Lagrange method. Further,a unified first-order differential equation was configured with them by defining a generalized momentum. Taking the resistance torque on the generator rotor and the driving torque on the turbine runner as the link,a complete HTGU operating simulation system,including the hydraulic system,generator,excitation controller and governor,was established and solved by making use of the second-order Runge-Kutta method. The calculated results show that the considered torsion effect has a little influence on the lateral vibration of the shaft under unit fault disturbance conditions,but has a great impact on the torsion deformation in the shaft under stable operating conditions. Under unit fault disturbance conditions,the variation trend of torsional angle between the generator rotor and the turbine runner is basically consistent with that of active power.These simulations show that the torsion vibration model can represent essential features of the shafting vibration,and hence it is reasonable.
The traditional assumption ignoring torsion deformation in shaft of hydro-turbine generator units( HTGU) may lead to a large deviation from the actual situation in analyses of shafting vibration.Thus,two equations,i. e.,shafting vibration equation and rotor motion equation with torsion effect were established based on the Lagrange method. Further,a unified first-order differential equation was configured with them by defining a generalized momentum. Taking the resistance torque on the generator rotor and the driving torque on the turbine runner as the link,a complete HTGU operating simulation system,including the hydraulic system,generator,excitation controller and governor,was established and solved by making use of the second-order Runge-Kutta method. The calculated results show that the considered torsion effect has a little influence on the lateral vibration of the shaft under unit fault disturbance conditions,but has a great impact on the torsion deformation in the shaft under stable operating conditions. Under unit fault disturbance conditions,the variation trend of torsional angle between the generator rotor and the turbine runner is basically consistent with that of active power.These simulations show that the torsion vibration model can represent essential features of the shafting vibration,and hence it is reasonable.
引文
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[14]李耀辉，朱双良．基于无水启动试验数据计算水泵轴系特征参数[J]．排灌机械工程学报，2017,35(8):659-665.LI Yaohui,ZHU Shuangliang. Calculating characteristic parameters of water pump shafting based on data under no-water start test[J]. Journal of drainage and irrigation machinery engineering,2017,35(8):659-665.(in Chinese)
[15]殷洪权．大型多级离心泵机组轴系的扭转振动分析[J]．化工设备与管道，2014,51(5):57-61.YIN Hongquan. Torsional vibration analysis of shafts in large multi-stage centrifugal pump set[J]. Process equipment and piping,2014,51(5):57-61.(in Chinese)
[16]倪以信，陈寿孙，张宝霖．动态电力系统的理论和分析[M]．北京:清华大学出版社，2002.
[2] KUNDER P．电力系统稳定与控制[M]．本书翻译组，译．北京:中国电力出版社，2001.
[3]徐自力，窦柏通，范小平，等．基于分层模态综合法的大型汽轮发电机组转子-末级叶片耦合系统扭转振动分析[J]．动力工程学报，2014,34(12):938-944.XU Zili,DOU Baitong,FAN Xiaoping,et al. Coupled torsional vibration analysis of shaft-last stage blade system in large turbo-generator units using CMS method with nested substructures[J]. Journal of Chinese Society of Power Engineering,2014,34(12):938-944.(in Chinese)
[4] ROUFFAUD R,HLADKY-HENNION A C,LEVASSORT F. A combined genetic algorithm and finite element method for the determination of a practical elasto-electric set for 1-3 piezocomposite phases[J].Ultrasonics,2017,77:214-223.
[5]闫涵，文俊，李蓉，等．HVDC换相失败引起汽轮机轴系扭振的机理分析[J]．智能电网，2017,5(3):231-238.YAN Han,WEN Jun,LI Rong,et al. Mechanism analysis of steam-turbine generator shafting torsional vibration caused by HVDC commutation failure[J].Smart grid,2017,5(3):231-238.(in Chinese)
[6]宋志强，马震岳．考虑水力和电磁激励的水电机组轴系统的扭转振动分析[J]．水力发电学报，2012,31(3):240-245.SONG Zhiqiang,MA Zhenyue. Analysis on torsional vibrations of hydro generator shaft system considering hydraulic and electromagnetic excitations[J]. Journal of hydroelectric engineering,2012,31(3):240-245.(in Chinese)
[7]唐健，赖喜德，彭悦蓉，等．考虑密封作用的混流式水轮机转轮动力特性分析[J]．大电机技术，2015(4):43-46,51.TANG Jian,LAI Xide,PENG Yuerong,et al. Dynamic analysis of francis turbine runner considering the effect of sealing[J]. Large electric machine and hydraulic turbine,2015(4):43-46,51.(in Chinese)
[8]孔繁余，王婷，张洪利．基于流场数值模拟的多级泵转子动力学分析[J]．江苏大学学报(自然科学版)，2011,32(5):516-521.KONG Fanyu,WANG Ting,ZHANG Hongli. Rotor dynamic analysis of multistage pump based on numerical simulation of flow field[J]. Journal of Jiangsu University(natural science edition),2011,32(5):516-521.(in Chinese)
[9]王正伟，喻疆，方源，等．大型水轮发电机组转子动力学特性分析[J]．水力发电学报，2005,24(4):62-66.WANG Zhengwei,YU Jiang,FANG Yuan,et al. The characteristic analysis of rotor dynamics of large hydraulic generatin unit[J]. Journal of hydroelectric engineering,2005,24(4):62-66.(in Chinese)
[10]安学利，周建中，刘力，等．水轮发电机组横向振动特性分析[J]．润滑与密封，2008,33(12):40-43.AN Xueli,ZHOU Jianzhong,LIU Li,et al. Lateral vibration characteristics analysis of the hydrogenerator set[J]. Lubrication engineering,2008,33(12):40-43.(in Chinese)
[11] WANG Ligang,CAO D Q,HUANG Wenhu. Nonlinear coupled dynamics of flexible blade-rotor-bearing systems[J]. Tribology international,2010,43(4):759-778.
[12] ZENG Yun,ZHANG Lixiang,GUO Yakun,et al. The generalized Hamiltonian model for the shafting transient analysis of the hydro turbine generating sets[J]. Nonlinear dynamics,2014,76(4):1921-1933.
[13]曾云，张立翔，张成立，等．水力机组紧急停机过程轴系振动仿真分析[J]．固体力学学报，2014,35(专辑):115-120.ZENG Yun,ZHANG Lixiang,ZHANG Chengli,et al.Shafting vibration simulation of hydro turbine generating sets on emerency shut down transient[J]. Chinese Journal of solid mechanics,2014,35(S1):115-120.(in Chinese)
[14]李耀辉，朱双良．基于无水启动试验数据计算水泵轴系特征参数[J]．排灌机械工程学报，2017,35(8):659-665.LI Yaohui,ZHU Shuangliang. Calculating characteristic parameters of water pump shafting based on data under no-water start test[J]. Journal of drainage and irrigation machinery engineering,2017,35(8):659-665.(in Chinese)
[15]殷洪权．大型多级离心泵机组轴系的扭转振动分析[J]．化工设备与管道，2014,51(5):57-61.YIN Hongquan. Torsional vibration analysis of shafts in large multi-stage centrifugal pump set[J]. Process equipment and piping,2014,51(5):57-61.(in Chinese)
[16]倪以信，陈寿孙，张宝霖．动态电力系统的理论和分析[M]．北京:清华大学出版社，2002.
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