机械外文翻译转子轴承系统动态分析

1、机械外文翻译转子轴承系统动态分析 附件 英文文献翻译转子轴承系统动态分析机械工程硕士克利夫兰州立大学芬恩工程2009年高校科技本论文提出设计永磁交流发电机协会的有限元分析fea的方法协会管理公司被配置为一个由两个相同的悬臂空心滚动接触轴承协会管理公司的性能要求是16000最大工作速度小于0010的最大轴自由端位移一个悬臂梁的静态和动态结果进行了预测封闭形式解和有限元分析验证获得了从代码验证这些结果一个转子轴承系统的数学模型提出并分析了其动态不平衡响应时受到在自由端谐波激振力对于一个转子轴承几何建由设计为蓝本然后在使用二阶四面体实体单元最后六个转子轴承系统参数研究的有限元分析结果在这些参数研究参

2、数研究5转子轴承配置证明以满足协会管理公司第一个自然频率和位移要求第一个自然频率被确定为358171转这是22年的协会管理公司的最高运行速度倍此外最大稳态ux和位移235e - 06和106e - 05分别小于最大允许轴位移关键词转子轴承系统有限元分析 永磁发电机协会管理公司委员会顾问马吉德博士顾问 约翰弗特博士委员会成员保林博士委员会成员轴承系统分析做了基础kirk和grnter分析了碰摩转子弹性轴承阻尼支承的稳态和瞬态响应在调整运动方程时他们忽视转子弹性和圆盘的陀螺效应并提供设计图表在旋转体和非旋转体支承下的转子在一定速度范围内的最小振幅和力的改变smith研究弹性阻尼支承系统碰摩转子内部

3、阻尼的大量衰减lund和gunter表明弹性阻尼支承同样需要增加高速转子的稳定性另外lund和sternlichtdowrski和gunter表明可以通过设计轴承支撑系统显著降低传播力pilkey提供了一个两步程序法转子悬架优化系统从这些研究中发现系统动态特性受碰摩转子轴承支座系统的质量阻尼和刚度的影响gasch探讨了大型涡轮转轴的有限元分析他介绍了转子动力学分析基础通过方程获得了模态测试和模态分析vance给出了转子-轴承试验仪器转子-轴承系统模型的电脑分析和实验测量的比较结果包括基础得用阻抗效应传递矩阵法斯蒂芬森采和rouch采用有限元方法分析了转子-轴承系统他们提供了一个利用模态分析技术

4、的程序应用时可以测量频率响应包括动态基础结构许多有限元分析程序的发展都已经开发出来并且改善了转子-轴承系统的方程式例如布克公式在他们早期的调查研究中转动惯量回转力矩剪切变形轴向载荷和内部阻尼的影响都被忽视了nelson和 mcvaugh利用有限罗利梁来阐明转子-轴承系统包括上述额外特性zorzi和nelson在1977和1980年从事包括内部阻尼和轴向转矩的一般化相似模型此外nelson 和 greenhill利用timoshenko梁函数建立轴的公式 ozguven和ozkan另外提高了对轴的有限元模型的影响包括内部和粘性阻尼目前有许多软件包含动力响应分析固有频率和模态特征转子-轴承系统然而

5、这些软件可能有所限制如果涉及的基础太过于复杂在短暂的转子动力学历史前提下证明通过相互作用来实现理论与实践相结合最好的是旋转机械转子动力学并非独一无二的在这方面提供了一个不寻常的生动的数学例子最近分析和实验之间的平衡一直受现代计算工具的影响避免这些工具取代课程设计我们要注重学者的意见计算机代码的品质预言是基本模型的稳固和转子动力学家的物理角度利用特别算法得出的良好的工程师取得了满意的模型各式各样的算法和计算机代码影响工程师的判断优越的算法和计算机代码并不能改善坏模型或缺乏工程上的判断第三章 转子-轴承系统的数学建模与有限元分析根据rao在旋转机器中这样共振源的正弦曲线力是不平衡的例如转子-轴承系

6、统旋转机械包括涡轮机电机风机发电机或转动轴不平衡是旋转机械振动的主要原因之一下图示31是机器的简化模型机器的总质量是m有两个偏心质量m2旋转方向相反角速度为常数w向心力 mew 2取决于导致激励m的每个质量两个相等的m2旋转方向相反两者的水平力相互抵消过主轴做一垂直平分的直线aa如图31所示质量块水平方向的角位置决定垂直分量所以运动方程为m是不平衡质量e是偏心量w是旋转角速度radst是时间s本章描述了转子-轴承系统的运动状态在有质量集中和恒定速度的自由旋转端转子是由两个相同的滚动轴承支承的空心转轴滚动轴承的作用是在运动中支承和定位转轴每个轴承之间有两个弹簧在弹簧之间有滚动体滚动体保证位置的准

7、确性另外还有保持架它的主要作用是保证滚动体的方向夹角左端点是转轴与齿轮紧密结合的驱动齿轮轴轴保证电机转子正常的终止31 转子轴承系统的数学建模动态建模需要确定转子轴承系统的动态特性和相关的振动问题早期的转子轴承系统动态建模也使用了系统分析或传递矩阵的方法传递矩阵法解决了动力学问题在频域分析中使其本身成为转子轴承系统的稳态响应prohl首次把该方法应用于转子轴承系统中同时被朗德和奥克特使用他们创立了转子在不间断系统中的传递矩阵研究了振动的失衡1970年有限元分析的功能被认可在这个领域中第一个研究的是booker基于各种理论许多研究者应用有限元分析延申了转子轴承系统的性能分析波尔克同样提出了一个瑞

8、利梁理论纳尔逊和mcvaugh改善了瑞利梁理论在转轴中的有限元分析包括平面因素转动惯量轴向载荷和旋转力矩gash提出了非稳态响应的线性阻尼公式zorzi和纳尔逊推广了这些发展纳尔逊增加了剪力使瑞利梁理论发展为铁摩辛柯系数在该模型中忽略了内应力剪切变形的影响后来kan扩展了研究考虑到转动惯量的影响轴向载荷传递力矩剪切变形内部滞后和粘性力的影响下图32所示举例说明了外力作用下旋转机械不平衡的数学建模由轴轴承和基础组成从图32在x和y轴中的运动方程分别为com微分得com由于外力导致的不平衡有恒定的转速32 转子系统的有限元模型回顾转子轴承系统的研究历程得出了转子系统的运动微分方程和一个典型的非平衡

9、旋转机械提出构建三维实体转子系统模型一个三维体模型是研究有限元分析的起点提出当受到偏心力作用保持恒定转速的自由端研究转子系统的动态特性图33描述了所提出的转子系统的结构图34给出了滚动轴承的尺寸外直径为3188inch内直径为2000inch和直径为0444凹槽的轴承坐离中心线1297inch图35所示为轴承套尺寸外径为3114inch内径为2047inch厚度0112inch图36所示轴承滚球的尺寸直径为0446inch球心到中心线的距离为1297inch图37所示轴承组件尺寸图38所示转子轴承系统的剖视图径向间隙为0000到-00003inch转轴的物理参数如表31轴承1和轴承2的参数如表

10、32转轴采用合金钢轴承1和轴承2采用不锈钢有限元模型由动力学分析和载荷限荷开始在模型结构的左端有一个固定载荷 只有自由度平面旋转时限制的自由度仍然无约束如图39一个约束限制轴承座平面自由度和转动自由度无约束如图310滚动体 滚珠 不受约束可以任意转动最后谐波载荷随时间的变化律相同如图311曲线的分析表明转子受力不平衡随时间的变化谐波加载类型为随时间变化的曲线正弦和余弦曲线的参数解出com电机转子的不平衡等效于距离中心距36e-7质量为227kg的质量块旋转角速度为167552rads所以力的大小fo mew2在轴端代com大小在x轴和y轴中的时间函数为在动态分析中时间关系曲线图从0开始05s结

11、束增量为00005s如图312所示结果表明端点被选定为节点定位为反应时间在坐标uxuyuz轴中如图313所示1和1600分别为起始点和终止点增量为20在这微小量中阻尼的作用是微小的因而设为零转子轴承系统模型为下一步网格划分做好基础有限元网格为实体网格划分在正确划分下滑板设为变量配合横梁的啮合如图314全局单元大小为0225inch网格精度为0011inch 这两个值是根据两者的体积表面积和的悬臂梁模型其他几何特征为基础决定的全局元素单元尺寸的大小就是网格特征元素的大小而元素的尺寸偏差在网格元素实际的偏差大小允许内根据网格选项选择高质量的网格作为研究对象优质的网格促使自动生成四面体实体单元四的节

12、点六节点六边一般情况下元素产生更好的结果因为1们更准确地代表曲边2们更好的数学该网格类型设置为标准这个网格比网格器更快因此研究中使用在网格生成器的选项自动循环3设定为循环数目大小和08自动循环指示网格器自动重试网格模型中使用更小的全局元素的大小是由设计师依据全局元素和的大小此外在4个高斯点检查雅可比雅可比检查是基于对每个元素的位置点的数量将在检查高阶四面体单元失真滚动体之间的轴承套圈和轴承的表面进行模拟接口与一个全球性的接触状态设置为无渗透面接触接触条件和本地设置为面对面接触的转子轴承系统模型的网格参数定义和网格图312显示了系统的模型齿轮网格的建立使转子轴承系统的动力学分析迅速发展在下一章在

13、自由端受到谐波中六种不同参数的研究将测试它的动态特性第四章轴承转子参数法在定义的物理参数和特性的转子轴承系统的有限元分析的功能转子-轴承系统的不同构造可以用来执行一个参数模型的研究提供可接受的配置满足了永磁机性能要求的运动特性合理的配置参数研究也就有了ux轴和uy轴上最大的位移不大于0010 inch和固有频率接近20次的最大运行速度的永磁机构的运动特性转子与定子如果发生碰撞可能会导致的磨损恶化甚至是一个灾难性的故障而位移和固有频率是避免转子与定子碰撞的两种非常重要的设计要求转子-轴承系统几个尺寸变化提出了一种将用于执行参数研究的方法轴承与轴之间的距离a和传动轴的内部直径b c和d如图41是用

14、于几何尺寸参数的研究六个研究参数的结果通过生成有限元分析动力学研究结果都和32概述中是一样的在参数研究法一内直径是分别为0070inch 15inch176inch轴向距离为177inch如图42所示动力学研究中参数研究法提出了附件gh和i附件g表示为随时间变化量h为时间函数的uxuyuz的位移量i为振动频率总结转子系统的有限元分com表41总结了uxuyuz轴的最大位移量表42概括了前四个模型的振动频率参数研究法二内径是不变的但是轴向comch如图43所示动力学研究的参数法二结果在附件jklj为时间函数k为时间函数是uxuyuz的位移变化量l为模型的形状和相关的频率总结有限元分析的结com表

15、43概括了uxuyuz轴的最大位移变化量表44总结了前四个模型的振动频率参数研究法三内直径是固定值轴向comch如图44动力学研究的参数法三结果在附件mnpm为时间函数n为时间函数是uxuyuz的位移变化量p为模型的形状和相关的频率总结有限元分析的结com表45概括了uxuyuz轴的最大位移变化量表46总结了前四个模型的振动频率参数研究法四轴向尺寸与法一相同为177inch内comchcomchcomch如图45所示动力学研究的参数法四结果在附件qrsq为时间函数r为时间函数是uxuyuz的位移变化量s为模型的形状和相关的频率总结有限元分析的结com表47概括了uxuyuz轴的最大位移变化量表

16、48总结了前四个模型的振动频率参数研究法五轴向尺寸跟法二相同内comchcomchcomch如图46所示动力学研究的参数法五结果在附件tuvt为时间函数u为时间函数是uxuyuz的位移变化量v为模型的形状和相关的频率总结有限元分析的结com表49概括了uxuyuz轴的最大位移变化量表410总结了前四个模型的振动频率参数研究法六轴向尺寸跟法三相同内comchcomchcomch如图47所示动力学研究的参数法六结果在附件wxyw为时间函数x为时间函数是uxuyuz的位移变化量y为模型的形状和相关的频率总结有限元分析的结com表411概括了uxuyuz轴的最大位移变化量表412总结了前四个模型的振动

17、频率总结参数研究法得出uxuy轴最大位移和固有频率如表413所示一阶固有频率是最低的共振频率正如表413所示 在181e-06英寸时管子的稳态ux位移的最大值符合参数化研究中的法二而最大稳态uy位移在106e-05英寸时符合参数化研究的法五参数化研究的法二使用最靠近轴承与轴承的轴向距离 102英寸 和以最小的转子轴内部直径 070150176 参数化研究的法五使用最靠近轴承与轴承之间的轴向距离 102英寸 就像参数化研究法二不同的是最大的转子轴内部直径为 100170180 上述结果表明一个有最短轴承与轴承间距轴向距离的转子-轴承系统会导致最大的ux和uy位移这是由于悬臂式系统总体结构此外最高

18、的转子系统固有频率在11747953时符合参数化研究中取得的法六而最低的转子系统固有频率在3750763方根秒时符合参数化研究的法五参数化研究的法六使用轴承间的最长轴向距离227英寸 和最大的转子轴内部直径 100170180 参数化研究最短的法五使用轴承间的最短轴向距离 102英寸 和最大的转子轴内部直径 100170180 上述结果和所期望的轴承间的最短轴向距离的最低固有频率一样而轴承间的最长轴向距离的固有频率是系统最高第五章 总结和展望作为假设悬臂梁的挠度自然固有频率和振型均用封闭分析解的方法闭合形式的准确性预测相比验证了有限元模拟得到结果基本一致一种基于转子-轴承系统的数学模型被提出了

19、并且使用cosmosworks分析自激振荡的动态不平衡响应一个6转子-轴承配置12 有限元模型的分布参数turborotcom紧密联系起来1972年asme工业工程学刊第94卷pp126-13213 转子-轴承系统的动力学利用有限元素comjm mcvaugh 1976年asme行业工程学刊第27卷第3期pp593-60014 转子-轴承系统的有限元模拟与内部阻尼 e - s zorzi 1977年纳尔逊asme电力工程学刊第99pp71-7615 转子-轴承系统的动力学轴向扭矩有限元的方法 e - zorzi 1980年6月纳尔逊asme电力工程学刊第102pp158-16116 一个有限的

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22、ry rayleigh-schmidt方法应用静态和自由振动问题叶文裕伯特1984年工业数学2004pp65-6727 变截面梁抑制自由振动有中度的肿块whcom1987年噪音及振动vol117pp555 - 57028 振动的携带集中质量梁杨健国高尔1973年杂志pp821-822 apllied数学vol4029 动力学响应悬臂梁的肿块kounadis 29岁 an1975年工程力学师asme101 emspp695-70630 机械振动译s s 饶 联经出版事业公司1986年31 在旋转的与振动的轴心 1894年dunkerley philosiphical交易伦敦皇家学会第一轮的手第一

23、部分pp279-36032 公式求解振动频率降到最低的弹性系统batzori1974年噪音及振动学会会刊pp563-564 编辑写信时dunkerley 33 横向振动的时期承载轴偏差的经验dunkerley合理确定规则旋转速度亨亨jefcott 33条1919年英国皇家学会学报的伦敦vol95没有 a666pp106-115 34 瑞利的原理和应用工程多佛纽约g 殿和bickly wg1956年35h holzer模具berechnung drehschwin恺撒gungen拱德国柏林192136hefettis f航空科学1949年10月pp625-634愿1954年pp359-360 h

24、olzer修改方法首先comuting扭转37 冲击和振动手册 piersol哈里斯和科尔哈里斯麦克格劳-希尔公司第五版2002年38答muszynskarotordynamics泰勒与弗朗西斯集团2005年39 一般计算方法的临界转速柔性转子1945年硕士prohl asme应用力学杂志李强等译 北京pp14240comcom1967年美制工业工程学刊第1 - 11页vol89 785-796计算与试验研究了柔性转子系统的不平衡41com1974年mse工程报告亚利桑那州立大学有限元模型解决刚性圆盘系统柔性转子系统固有频率和关键的旋转速度42 理论的声音瑞利1945年多佛出版物纽约43 振动

25、的turbo-rotors流动电影轴承弹性基础r的裂缝学报2004年噪音及振动vol120pp175-182 原文dynamic analysis of a rotor-bearing systemsandi elhibirbachelor of science in mechanical engineeringcleveland state universityaugust 1997submitted in partial fulfillment of requirements for the degreemaster of science in mechanical engineering

26、at thecleveland state universitymay 2009dynamic analysis of a rotor-bearing systemsandi elhibirabstractthis thesis presents the results of the finite element analysis fea approach for designing a permanent magnet alternator pma the pma is configured as a cantilever hollow shaft supported by two iden

27、tical rolling contact bearings the performance requirements of the pma are a imum operating speed of 16000 rpm with a imum shaft displacement of less than 0010 in at its free endthe static and dynamic results of a cantilever beam was predicted by closed form solutions and verified to those results o

28、btained from fea for code validation a mathematical model of a rotor-bearing system was proposed and analyzed for its dynamic unbalance response when subjected to a harmonic excitation force at the free end the proposed design for a rotor-bearing geometry was modeled by solidworks and then analyzed

29、in cosmosworks using second order tetrahedral solid elementslastly the fea results of six parametric studies of a rotor-bearing system are presented in these parametric studies the rotor-bearing configuration from parametric study no5 proved to satisfy the pma first natural frequency and displacemen

30、t requirements the first natural frequency was determined to be 358171 rpm which is 22 times of the imum operating speed of the pma additionally the imum steadystate ux and uy displacements were obtained at 235e-06 in and 106e-05 in respectively which is less than the imum allowable shaft displaceme

31、ntchapter iintroduction11 historical backgroundvarious studies have incorporated foundation effects in rotor-bearing system analyses kirk and gunter 1 analyzed the steady state and transient responses of the jeffcott rotor for elastic bearings mounted on damped and flexible supports they disregarded

32、 the rotor flexibility and the disk gyroscopic effects in the formulation of the governing equations of motion and provided design charts for both turned and off-turn support conditions to minimize the foundation characteristics of the rotor amplitude and force transmitted over a given speed range s

33、mith 2 investigated the jeffcott rotor with internal damping to include a mass less damped and flexible support system lund 3 and gunter 4 showed that damped and flexible support might also improve the stability of high-speed rotors in addition lund and sternlicht 5 dowrski 6 and gunter 7 demonstrat

34、ed that a significant reduction in transmitted force could be achieved through proper design of a bearing support system pilkey 8 presented an efficient two-stage procedure for optimizing suspension systems of rotors from these studies the dynamic performance problems in association with the foundat

35、ion effects on mass damping and stiffness of the jeffcott rotor incorporating the bearing support systems could be found gasch 9 explored rotating shafts of large turbo-rotors by way of finite element analysis he introduced foundation dynamics into the rotor equations via reacceptance analysis which

36、 was obtained from modal testing and modal analysis vance 10 provided comparison results for computer predictions and experimental measurements on a rotor-bearing test apparatus modeling the rotor-bearing system to include foundation impedance effects by using the transfer matrix method stephenson a

37、nd rouch 11 have utilized the finite element method to analyze rotor-bearing foundation systems they provided a procedure using modal analysis techniques which when applied could measure the frequency response functions to include the dynamic effects of the foundation structuremany finite element pr

38、ocedures developed have been implemented and geared toward generalizing and improving the formulation of the rotor-bearing system such as by ruhl and booker 12 in their early investigation the effects of rotary inertia gyroscopic moments shear deformation axial load and internal damping have been ne

39、glected nelson and mcvaugh 13 have utilized the raleigh beam finite to formulate the rotor-bearing systems by including the additional effects mentioned above zorzi and nelson 14 in 1977 and 1980 15 worked on the generalization of a similar model by including internal damping and axial torque respec

40、tively further nelson 16 and greenhill 17 utilized the timoshenko beam shape functions to establish the shaft element formulation ozguven and ozkan 18 additionally improved the shaft finite element model by including the effect of internal hysteric and viscous dampingthere are many software packages

41、 available today for analyzing dynamic responses natural frequencies and modal characteristics of rotor-bearing systems 19 20 however the software may be limited if the involved foundation is very complexthese brief histories of rotordynamics help justify the premise that behavior of rotating machin

42、ery is best achieved through interplay between theory and practice rotor dynamics is not unique in this regard but does offer an unusual number of vividexamples lately the balance between analysis and experience has been affected by the emergence of modern computational tools lest a fascination with

43、 these tools replace the lessons of practice we would be wise to heed the words of dara childs 21 the quality of predictions from a computer code has more to do with the soundness of the basic model and the skill and physical insight of the rotor dynamicist than the particular algorithm used good en

44、gineers get good results from good models leading to sound engineering judgments with a variety of algorithms or computer codes superior algorithms or computer codes will not cure bad models or a lack of engineering judgmentchapter mathematical modeling and finite elementanalysis of a rotor-bearing

45、systemaccording to rao 30 a common source of such a sinusoidal force is unbalancein a rotating machine or as in our case the rotor-bearing system rotating machines include turbines electric motors fans generators or rotating shafts unbalance ain rotating machinery is one of the main causes of vibrat

46、ion a simplified model of such a machine is shown in figure 31 belowthe total mass of the machine is m and there are two eccentric masses m2rotating in opposite directions with a constant angular speed of rotation w the centrifugal force mew2 2 due to each mass will cause excitation of the mass m we

47、 consider two equal masses m2 rotating in opposite directions in order to have the horizontal components of excitation of the two masses cancels each other out howeverthe vertical components of excitation add together and act along the axis of symmetry aa in figure 31 if the angular position of the

48、masses is measured from a horizontal position the total vertical component of the excitation is always given by 30therefore the equation of motion is derived as 30where m is the unbalanced mass e is the eccentricity w is the angular speed of the rotating shaft in radians per second and t is time is

49、secondsthis chapter describes a proposed design of a rotor-bearing system for analyzing its own behavior when subjected to a concentrated mass with a constant speed of rotation at its free end this concentrated mass represents the mass of the rotating unbalanced pm rotor the rotor shaft is hollow an

50、d supported by two identical ball bearings the rolling element bearings are mechanical parts whose role is to support and locate the rotor shaft during operation each bearing contains two rings and between the rings rolling elements as bearing balls the rolling elements allow the relative motion bet

51、ween the rings as well the correct positioning of themadditionally there exists a cage whose main function is to keep the adequate angular separation of the rolling elements the left end of the system is the drive end that incorporates gear teeth which mates with a pinion for driving the shaft the s

52、haft supports a pm rotor at the right end free end of the shaft31 mathematical model of a rotor-bearing systemthe dynamic modeling of the rotor-bearing system is required to understand its dynamic behavior and the associated vibration problems early dynamic models of the rotor-bearing system were fo

53、rmulated either analytically or using the transfer matrix approach the transfer matrix method solves dynamic problems in the frequency domain which makes itself reasonable to analyze the steady-state responses of the rotorbearing system this method was first applied to the rotor-bearing system by pr

54、ohl 39 and was employed by lund and orcutt 40 they constructed the transfer matrix of the rotor in sense of a continuous system and investigated the unbalance vibrations experimentally and analytically in the 1970s the potential of finite element method was recognized the first studies in this area

55、were by ruhl and booker 12 based on various beam theories many researchers have extended the capability of the rotor-bearing system analysis using the finite element method polk 41 presented a rayleigh beam rayleigh 42 finite element in his work nelson and mcvaugh 13 improved the rayleigh beam theor

56、y in a finite rotating shaft element which included the effects of translational and rotary inertia axial load and gyroscopic moments gash 43 refined the formulation by considering the destabilizing effect due to linear internal viscous damping these developments were subsequently generalized by zor

57、zi and nelson 14 nelson 16 added shear deformation to the rayleigh beam theory to develop a timoshenko beam element in this model shear deformation effects was included but internal damping was neglected laterkan 18 extended these works by considering the effects of rotary inertia axial load gyrosco

58、pic moments shear deformations and internal hysteric and viscous damping in the same model figure 32 shown below illustrates a mathematical model of the external forces acting on a typical configuration of an unbalanced rotating machine which consists of the components of a shaft bearings and foundationfrom figure 32 the equations of motion in the x and y directions aresolving for equations 33 and 34 the differential equation becomesrearranging equations