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中国地质大学长城学院毕业设计任务书学生姓名商殿尊学号05208332班 级08机制3班指导教师杨义勇职称教 授单 位中国地质大学毕业设计题目湖南地区高压电线除冰机器人机构设计毕业设计主要内容和要求：该机器人采用机械除冰方式，利用冲击头沿轴线高速敲击高压线上的附冰，使附冰以块状的形式脱落。同时该机器人可通过更换打击头以适应不同直径规格的高压输电线。机器人的行走采用三个带槽轮子，紧夹高压线缆，以确保机器人在除冰过程平稳前行。该机器采用电磁感应耦合电源装置，自带可充电蓄电池，续航能力强。本文还介绍避免因发动机的震动引起高压输电线共振舞动的方法。同时，机器人可以携带检测和通信设备，对输电线路进行巡查作业。主要参考资料：1张屹，邵威，高虹亮，罗成. 高压输电线路除冰机器人的机构设计J.三学大学学报，2008.12，Vol.30 No.6：P69-72.2高虹亮，孟遂民，罗成，马小强.架空输电线路除冰机器人的结构设计J.电力建设，2009.3，Vol.30 No.3：P93-96.3甘辰予，陈劲生.LEGO 智能除冰机器人的设计J.大众科技，2009.10，No.10.4蒋正龙，陆佳政，雷红才，黄福勇. 湖南2008年冰灾引起的倒塔原因分析J.高电压技术，2008.11，Vol.34 No.11：P2468-2474.5 吴功平，肖晓晖，肖华，戴锦春，鲍务均，胡杰. 架空高压输电线路巡线机器人样机研制J.电力系统自动化，2006.7.10，Vol.30 No.13：P90-107.6 张运楚，梁自泽，谭民. 架空电力线路巡线机器人的研究综述J.机器人，2004.9，Vol.26 No.5:P467-473.7 许源 刘人玮 李军. 湖南电网防冻融冰体系改革之探讨J.2003,Vol.23 No.5:P24-27.毕业设计应完成的主要工作：1.毕业设计任务书2.毕业设计开题报告3.毕业设计文献综述4. 毕业设计的翻译文章及外文原文5.毕业论文6.相关图纸毕业设计进度安排：序号毕业设计各阶段内容时间安排备注1查阅资料并撰写毕业设计开题报告2011.12.10-2011.12.202指导教师审核开题报告,学生根据指导老师意见做进一步修改2011.12.21-2011.12.223系里组织开开题报告会2011.12.21-2011.12.224由指导老师指导查阅资料，并翻译外文资料2012.12.23-2011.12.315撰写文献综述，经指导老师审阅后着手毕业论文的写作2012.01.01-2012.01.206开始编写毕业设计工作计划，进入毕业设计的撰写2012.01.21-2012.03.067整改设计论文2012.04.29-2012.04.308毕业设计答辩2012.05.05-2012.05.19课题信息：课题性质： 设计 论文 课题来源： 教学 科研 生产 其它发出任务书日期： 2011.12.6 指导教师签名： 年 月 日教研室意见：教研室主任签名：年 月 日 学生签名：中国地质大学长城学院本科毕业设计外文资料翻译系 别： 工程技术系 专 业：机械设计制造及其自动化姓 名： 商殿尊 学 号： 05208332 2011 年12 月 30 日外文资料翻译译文1.1转子动态特性的轴承在每种类型的旋转机械中，转子振动的因素是很重要的设计。在最常见的应用中，主要的重点是适当的平衡，尽量减少转子剩余不平衡振动水平。在更先进的设计转速中，功率密度和性能受到实际的限制，那么将大大增加对转子动力学设计的水平和复杂程度的考虑。高性能涡轮机械技术要求最苛刻的地方分别在旋转机械方面的转子动力学以及其他许多重要的工程材料学方面。 先进的涡轮机械需要用广泛的计算研究和预测的转子动力学特性的成分进行设计，i.e., (i) 关键（共振）的速度，(ii) 响应和灵敏度转子质量不平衡分布，(iii)不稳定（自激）阈值的速度。标准治疗这种分析涉及到数学建模的转子和支持系统的范围内假定非线性动力学模型 1,2 。在专门的情况下（如刀片损失的事件）切合实际的预测不能没有包括占主导地位非线性 3 。然而，这是假设的动态线性，还有大多数转子动力学设计分析的工作要做。 在数学表述中的线性模型横向转子振动很简单，并体现在标准线性振动模型的任何多自由度系统，表现在以下紧凑型矩阵形式： M(q) + Cq + Kq = F(t) (1.1)在模式M, C, K =质量，阻尼和刚度的速度取决于系数矩阵q, q, q= 位移，速度和加速度矢量广义坐标（函数f （吨） ） =广义力载体 转子动力系统一个有趣的特点是，运动方程通常有非对称矩阵，尤其是刚度 K 和阻尼C矩阵。在 K 矩阵通常是非对称由于动态特性的轴承，密封和其他转子定子流体动力学相互作用力量。非对称的C矩阵源自转子陀螺效应和流体的惯性影响密封和程度较轻的轴承。一些研究提出了数学模型，使群众矩阵， M 档，也将非对称类似的原因， K 和C矩阵的非对称。然而，令人信服的理由，如在 2 中所描述，已说服了转子动力学说放弃这一想法，取而代之的是对称的质量矩阵。 虽然理论上正式声明的线性转子动力学分析模型是明确的，即均衡器。 （ 1.1 ） ，虽然计算算法，充分利用这一分析模型现在很标准，但事实仍然是想要可靠和准确的转子振动的预测仍然是一个相当大的挑战。为什么？众所周知的，是由于一些重要的“投入”不够好。因此，虽然存在许多有效的计算机代码，使转子振动分析， “产出”这种代码是唯一，好“投入” 。但最不确定的投入转子动态系数为轴承转子定子，密封件和其他转子定子流体动力学的相互作用。 液体膜动力轴承，是最常用的模型，为小扰动的杂质静态平衡立场，就是所谓的8 -系数刚度和阻尼模型，并具有下列形式：在这里，互动式的动态径向力组件（fx, fy）造成的径向位移（ X，Y ）的相对静态平衡态和径向速度（ X，Y ）这一位移。这个概念是画报图所示。1 。请注意，在该模型所描述的方程。 （ 1.2 ） ，该动力是一个功能只有位置和速度，而不是加速。这是符合古典雷诺润滑方程，其中忽略流体的惯性作用。此外，惰性少流，轴承刚度矩阵可非对称（即Kxy ！ = Kyx ） ，但同时阻尼矩阵应假定为对称（即Cxy = Cyx ） ，因为任何斜对称添加剂轴承阻尼矩阵必须有一个后果，流体的惯性作用 1 。在高雷诺数转子定子液环，如海豹和一些轴承（例如，水润滑轴承） ，这是不恰当的忽视流体的惯性的影响，因此，另外一组系数矩阵的需要，包括转子轨道振动加速度的影响后的总转子定子的互动动力。这导致一般各向异性模型显示如下：在这里，Dxy = Dyx时应实行。而有11个完全转子动态系数来确定上述各向异性线性模型。这些系数一般职能的轴转速和轨道频率。其中几个重要的独特功能CWRU转子动力学试验设施是它设定为允许提取的所有系数的各向异性模型与惯性，所描绘均衡器。 （ 1.3 ） 。目前大部分业务测试平台的基础之上更近似各向同性模型，这是严格只适用于旋转对称流场。对于各向同性的模式，均衡器。 （ 1.3 ）降低以下。原因减少版本的均衡器。 （ 1.4 ） （不包括惯性矩阵）不能用于流体轴承，是因为这种轴承，其基本功能，支持静态径向负荷，必须运行在相当大的静态偏心率，因此，是众所周知的转子动态相当各向异性。 静和混合（合并静水和动水）轴承，同时还有各向异性静态偏心，也受到频率特性的依赖惯性的影响，即使在其中的一部分，同时占主导地位的是粘性的影响。这是由于一些原因： （一）雄厚的财力（相比，薄膜厚度）的概念所固有的静/混合轴承， （二）流量的急剧区之间的过渡口袋，薄膜部分的轴承， （三）流体的惯性影响，流动供应线， （四）可能流体的惯性的影响，即使在薄膜部分。 考虑到所有上述考虑，很明显，转子动态上讲，混合轴承结合了最复杂的特点，既流体轴承和密封。也就是说，妥善处理混合轴承，需要考虑到双方的各向异性和惯性的影响，合并。 因此，线性模型体现在均衡器。 （ 1.3 ）是必要的。这并不排除潜在的有用的均衡器。 （ 1.2 ）或（ 1.4 ） ，甚至以下。（1.5 ） ，在某些特殊情况下，在特意的实验，并分析将证明这种简化。各向异性模型的惯性。 （ 1.3 ） ，当然是最好的办法，提供了一个已提供了足够的试验装置通用允许提取的所有系数的方程模型。 （ 1.3 ） 。 最近，动态特性，静水和混合轴承已引起特别注意，因为它们在高速涡轮机械中增加应用负载的支持要素。结合静水行动的动力效应许可证的混合轴承纳入转子设计在外部提供的润滑是不切实际或不可能的。在地方汽轮机油或其他外部润滑油，工作液中的转子可作为一种润滑剂。叶轮轴承指导中发现的核冷却剂泵和火箭发动机轴承液态氢或氧气泵是两个例子这种类型的应用程序。大承载能力的可能性，很长的寿命和更多的支持阻尼的反摩擦轴承使混合轴承更具吸引力。正是由于这些原因，美国宇航局目前正在大力推行混合轴承用于航天飞机和其他先进的发射系统。 静压轴承可以设计各种各样的配置如上 图2和 图3 说明更详细的几种不同的设计，有可能为实验，主旨，并结合实验和推力轴承。1.2 综 述 影响流体轴承性能的转子轴承系统已经被认识到了许多年。最早的一个尝试模型实验由斯托多拉 4 报道于1925年，他调查了油膜刚度对临界转速的骨干支持轴承的影响。进一步开展工作的建模与线性轴承因为它们影响到转子的动态特性，由哈格和桑基 5 斯塔雷特 6 报道。 早期对于静压轴承的兴趣出现在1940年年底，并且重点是他们的高负荷和刚度的能力是在没有滑动速度的要求和几乎为零脱离摩擦的条件下。早期出版物的静态负荷计算方法和设计曲线也提供了基本的静态刚度的信息，因为负荷计算可以作为一个功能的位移（即薄膜厚度） 。在20世纪60年代末，需要拥有一个全面的会计转子动态性能造成更完整的处理静水和混合轴承动态特性的东西。 戴维斯 7,8 利用贫瘠的土地，集中参数近似类型的研究动态行为的静压轴承。这种类型的分析可以公开表达形式来写的润滑油流量的轴承;这些问题都可以用来计算近似压力分布和力量。送达后，以确定性能特点层流静压轴承的优点和局限性的各种方法，包括薄土地的方法，这种方法也适用于由伦纳德和罗 9 罗 10 ，已由奥多诺霍等人获得。 11 。 1969年，亚当斯和夏皮罗 12 利用计算机分析，以确定挤压油膜垫性能的各种赔偿类型。也包含在参考是有见地的说明阻尼效应的内在轴承和静压之间的关系阻尼垫一个单位到一个普通平板具有相同的比例。 罗德和伊扎特 13 计算表明，效果明显的润滑油压缩在凹槽和补给线，动态行为特点是“打破频率”上面刚度急剧增加和阻尼急剧下降以及。这些结果也得到了韦斯纳斯 14 和高斯 15 和戈什 16 等人的分析，使用一阶摄动法，确定刚度和阻尼性能的同时旋转是受到飞机谐波的激发。影响可压缩流体在休会量被忽视。结果表明，改善动态特性有可能通过适当的选择压力和偏心率和供应的压力。罗 10 罗和郑 17 本理论刚度和阻尼的结果混合轴承，包括非对称部分的刚度矩阵抓住了其中的潜力自激转子振动。戈什 18 研究了流体惯性的影片土地层流，毛细管补偿混合轴承。他表明，流体的惯性的影响减少动刚度系数。 最近的理论治疗争取获得更多的流体力学，特别是动荡和流体的惯性作用，逐步成为更重要的高转速杂志正在成为至关重要的各种航空航天应用。罗德里夫和沃尔 19 分析了轴承设计的低温火箭涡轮泵使用液体气体作为润滑剂。有限差分格式包括动荡的影响，惯性和可压缩流体中的发展。几何包括一些凹降息的影响，但不包括轴向沟槽。流量，压力分布，和刚度进行了计算，但是，没有阻尼。实验计划是发达国家比较结果与理论模型。协定被认为是良好的比较特点。有限差分方法也采用海 20 的混合轴承有关的涡轮泵。该分析模型包括动荡和入口惯性的影响，但不可液体流动的同时，摩擦损失，承载能力和动态系数计算。实验验证了六个容器里，水润滑轴承杂交表明，流体的惯性在凹严重影响流量的预测相比，不包括此类惯性的影响。其他性能因素，并不是有很多影响。 阿瑞帝雷丝 ，瓦伦怀特，和夏皮罗 21 提出了一个数学模型预测的静态和动态性能特点湍流混合轴承。矩阵柱法 22 适用于可变规模有限差分网格是用来解决执政润滑方程在内部外地点。迭代计划之间的雷诺方程和流动连续性方程被启用。惯性效应在休会边缘，但被列入可压缩流体作用忽视。轴承审议了直径和审批相类似的可能是部署在火箭涡轮泵。液态氦和氧被用作润滑剂。 有限元技术已被布赛义德和曹莫利费尔 23 用来分析湍流混合轴承 。分析结果相比，得到了曹莫利费尔和尼古拉 24 的认可 。一般来说，协议被认为是良好的预测与实验的特点。 最近由圣安德烈斯 25,26 发表的一本出版物完整记载了惯性和高效率的数值分析准确预测的动态性能湍流混合轴承。散流的势头方程来描述湍流惯性流动轴承，特别考虑到下游的压力，发展的孔板补给线和隐窝边缘入口处的影响。这些分析都带进观点的重要性，流体力学和液体可压缩性的影响动态特性的混合轴承和生产标准，以确保稳定运行。数值结果预测的性能特点湍流混合轴承运行在任意中心。 格利尼克桥 27 ， （ 66年至1967年）发布了有关测量工作和鉴定轴承转子动力学系数的工作，从频域方程中得出轴承部分的120毫米模型同时或两个相互正交方向同时测量振幅和相位之间的相对运动轴承的刚度和阻尼计算系数。莫顿 28 通过这一技术更全面的计算了308毫米工业轴承的刚度和阻尼系数，并随后开发出一种技术，让一个步骤改变生效，适用于旋转轴。据估计由散射实验产生的刚度和阻尼会表现出相当的系数。跨阻尼条件特别差界定和莫顿将此归因于条件不足的矩阵，但他并不追求这一点。 帕金斯 30,31 采用了刚性转子与两个外部的独立的正弦负载。他调整了相对幅值和相位，使轴承的动议最早是纯粹的横向，然后是纯粹的纵向。因此，他能够简化运动方程。他评价系数为平原轴承的360 环状沟。当他相比，预测和衡量系数，他常常发现超过百分之百的分歧。 在1977年伯罗斯和斯坦韦 32 提出了利用伪随机二进制序列（ PRBS ）的时域方法进行数据分析。阿多元回归估计是在离散域或从时域性差别转子轴承模型。然而，这一估计可能会产生偏见 33 ，这项工作产生了明显的成果。与其优势相比，这种技术与其他方法的测试转子轴承系统已经经过了讨论 34 。使用多频测试 35,36,37 可以克服一些缺点与时域算法 32 。这种方法具有若干优点，其中包括所有的系统模式内订明的频率范围，高噪声抑制。该方法涉及迫使该系统在x和y方向，在所有频率范围内的频息，同时进行。然而，随着使用PRBS迫使类型的信号，有一种危险的饱和的系统，以便一些振幅频率是如此之大，非遇到非线性和测试变得无效。在 37 ， 38 布罗斯等人利用施罗德相谐波信号（ SPHS ） 克服了这一问题，他们希望在一个特定的频率范围内 39 激发由平等的振幅正弦信号的频率。 安田等人 40 同时转子系统由两个独立的统计学随机输入信号的测量频率响应函数水泵水封。 12动态系数分别提取采用最小二乘技术。该方法在较短的时间内获得的数据比席卷正弦的方法更激动人心。此外，数据的X方向和Y方向也同时获得。 诺德曼和斯克里 41 适用于冲击力的投入转子轴承系统，并采用了曲线拟合技术的频率响应函数获得的实验研究。该试验台的对称配置是刚性转子运行的两个“相同的”轴承。瞬态振动转子而引起的运用武力冲动转子（由转子突出一个“校准锤” ） 。输入信号（动力）和输出信号（位移转子）转化为频域和复杂的频率响应函数从而计算。分析频率响应函数，这取决于轴承系数，被安装在测量功能。刚度和阻尼系数结果拟合过程迭代最小二乘错误作为一个标准。同样的技术也适用于测定动态系数的环形湍流密封涡轮泵 42 。 神吉和川 43 构建了一个试验台的水密封对称配置和流动的支持下套管空气波纹管和液压传动。双方向前和向后圆形武力激发适用。解决后的未知阻抗的职能， 8刚度和阻尼系数的各向异性模型，得到了曲线拟合在广泛的频率范围。 潜在的航空航天应用了一些新的实验旨在测试水压和混合轴承转子动力学特点，包括在本论文和 44墨菲和瓦格纳 45 最近提出的刚度和阻尼系数提取同步轨道偏心杂志与制冷剂- 113的工作液。他们限制于无法从同步轨道提取惯性系数以及其他数据，来确定频率和所有的系数。 克鲁蒂蔡等人 46 最近建立了一个高速试验台研究水润滑轴承，并用它来测试静态孔口补偿混合轴承速度可达25000转。在他们的平台，测试轴承是自由暂停高速轴在中间立场的支持轴承。对照静态负荷适用于通过轮换耐钢丝绳。虽然只有静态负荷结果 46 ，动态测试指出了目前的进展情况。 墨菲斯科尔等 47 描述了多功能测试仪器来衡量转子动力学系数的轴承和密封件。径向磁轴承将用于静态和动态负载轴。径向磁轴承将用于静态和动态负载轴。迅速正弦波扫描是作为动力激发瞬态投入测试。测试环境密切关系到真正的火箭发动机涡轮泵的运行条件。1.3 问 题 的 声 明 这项研究在本论文集中的实验和理论确定转子动力学系数为石油喂静压口补偿轴承，其中包括混合效应轮换。当前利益和缺乏实验数据和充分的分析工具，强调需要这种类型的研究。在凯斯西储大学使用试验设施实验研究已完成。计算机代码的基础上有限差分模型被用来进行理论预测，同样的配置和经营状况的测试矩阵。代码确定静态和动态性能的动力，在制度层状没有流体的惯性，静水或混合轴承是不可使用润滑剂的。动态性能受到了扰动的位置和速度，解决了静态特性。改变力向量（综合压力）可以判断刚度和阻尼矩阵系数的混合轴承。 这一论断的安排如下：第二章中，测试平台和仪器仪表的描述。此外，实验过程中已列入第二章。第三章，位置所用的方法在衡量和确定转子动力学系数的轴承和密封件。特别是发达国家的方法是此工作的重点。发展功能混合/静压轴承静态和动态分析（ HBSADA ）计算机代码显示在第四章。之前，讨论方法的数值解，简要概述了一个典型的混合轴承的运作。实验和计算结果公布在第五章，误差分析也载于附录第五章。有关工作列入年底。外文原文1.1 ROTORDYNAMIC PROPERTIES OF BEARINGSRotor vibration considerations are important to the design of nearly every type of rotating machinery. In the least demanding applications, the primary focus is on adequate balancing of the rotor to minimize residual unbalance vibration levels. In more advanced designs, as rotational speed, power density and performance are pushed to practical limits, invariably the level and sophistication of required attention to rotor dynamical design considerations increase considerably. High performance turbo machinery is technologically the most demanding branch of rotating machinery in regards to rotor dynamics as well as many other critical engineering ingredients.Among the several required ingredients in the design of advanced turbo machinery are extensive computational studies and predictions of rotor dynamical characteristics, i.e., (i) critical (resonance) speeds, (ii) response and sensitivity to rotor mass unbalance distribution, and (iii) instability (self-excited) threshold speeds. Standard treatments of such analyses involve the mathematical modeling of the rotor and support system within the context of an assumed linear dynamics model 1,2. In specialized situations (e.g., blade loss events) realistic predictions can not be made without including dominant nonlinearities 3. However, it is with the assumption of dynamic linearity that most rotor dynamic design analyses are done.The mathematical formulation of the linear model for lateral rotor vibrations is quite straightforward, and is embodied within the standard linear vibration model for any multi-degree-of-freedom system, as shown in the following compact matrix form:M(q) + Cq + Kq = F(t) (1.1)whereM, C, K = mass, damping, and stiffness speed dependent coefficient matricesq, q, q= a displacement, velocity, and acceleration vectors of the generalized coordinatesF（t）=generalized force vectorAn interesting characteristic of rotor dynamical systems is that the equations of motion typically have non-symmetric matrices, especially the stiffness K and damping C matrices. The K matrix is typically non-symmetric because of dynamic characteristics of bearings, seals and other rotor-stator fluid dynamical interaction forces. Non-symmetry of the C matrix arises from the rotors gyroscopic effects and fluid inertia effects in seals and to a lesser degree in bearings. Some researches have proposed mathematical models which allow the mass matrix, M, also to be non-symmetric for similar reasons that the K and C matrices are non-symmetric. However, compelling arguments, such as made in 2, have convinced serious rotordynamicists to drop this idea in favor of a symmetric mass matrix.Although the mathematically formal statement of the linear-analysis rotor dynamics model is well defined, i.e., Eq. (1.1), and although computational algorithms to fully utilize this analysis model are now quite standard, the fact remains that performing reliable and accurate rotor vibration predictions is still a considerable challenge. Why? Because some of the important inputs are not well enough known. Thus, while numerous valid computer codes exist to make rotor vibration analyses, the outputs of such codes are only as good as the inputs. The most uncertain inputs are the rotor dynamic coefficients for the rotor-stator forces at bearings, seals and other rotor-stator fluid-dynamical interactions.For fluid-film hydrodynamic journal bearings, the most commonly used model, for small perturbations of the journal from the static equilibrium position, is the so-called 8-coefficient stiffness and damping model, and has the following form:Here, the dynamic interactive radial force components (fx, fy) are caused by the radial displacement (x, y) relative to the static equilibrium state and by the radial velocity (x, y) of this displacement. The concept is pictorially shown in Fig. 1. Note that in the model described by Eq. (1.2), the force is a function only position and velocity, but not acceleration. This is consistent with the classical Reynolds lubrication equation, which neglects fluid inertia effects. Also, for inertia less flow, the bearing stiffness matrix can be non-symmetric (i.e., Kxy!= Kyx ),but the bearing damping matrix should be postulated as symmetric (i.e., Cxy = Cyx ), since any skew-symmetric additive to the bearing damping matrix must be a consequence of fluid inertia effects 1. In the case of higher Reynolds number rotor-stator fluid annuli, such as seals and some bearings (e.g., water lubricated bearings), it is not appropriate to neglect fluid inertia effects and, thus, an additional set of matrix coefficients are needed to include rotor orbital-vibration acceleration influences upon the total rotor-stator interaction dynamic force. This leads to the general anisotropic model shown as follows:Where, Dxy=Dyx shoud be imposed.And,There are totally 11 rotor dynamic coefficients to be determined in the above anisotropic linear model. These coefficients are generally functions of shaft spin speed and orbit frequency. One of the several important unique features of the CWRU rotor dynamics test facility is that it is configured to permit extractions of all the coefficients of the anisotropic model with inertia, as depicted in Eq. (1.3). Most currently operational test rigs are based upon the more approximate isotropic model, which is strictly valid only for rotationally symmetric flow fields. For the isotropic model, Eq. (1.3) reduces to the following.The reason a reduced version of Eq. (1.4) (without the inertia matrix)is not used for hydrodynamic journal bearings is because such journal bearings, by their basic function to support static radial loads, must run at considerable static eccentricity and, thus, are well known to be rotor dynamically quite anisotropic.Hydrostatic and hybrid (combined hydrostatic and hydrodynamic) journal bearings, while also anisotropic under static eccentricity, can also exhibit frequency dependence characteristic of inertia effects, even when the film part of the bearing is dominated by the viscous effects. This is so for a number of reasons: (i) the deep pockets (compared to film thickness) concept inherent in hydrostatic/hybrid bearings, (ii) the sharp flow-area transition between pockets and thin-film portions of bearing, (iii) fluid inertia effects in the flow-supply line, and (iv) possible fluid inertia effects even within the thin film portions.Taking all of the above into account, it is apparent that rotor dynamically speaking, hybrid journal bearings combine the most complicated features of both hydrodynamic journal bearings and seals. That is, proper treatment of hybrid bearings requires taking account of both anisotropic and inertia effects, combined. Thus, the linear model embodied in Eq. (1.3) is required. This does not preclude potential usefulness of Eq. (1.2) or (1.4) or even the following, Eq. (1.5), in certain special situations, after bona fide experiments, and analyses would justify such simplifications.The anisotropic model with inertia, Eq. (1.3), is certainly the best approach, provided one has available a test apparatus sufficiently versatile to permit extraction of all the coefficients of the model in Eq. (1.3).Recently, dynamic characteristics of hydrostatic and hybrid journal bearings have attracted particular attention because of their increased application as load support elements in high speed turbo machinery. The combination of hydrostatic action with the hydrodynamic effects permits the hybrid bearing to be incorporated into rotor designs where externally supplied lubrication is impractical or just impossible. In place of turbine oil or other external lubricants, the working fluid in the rotor can be used as a lubricant. Impeller guide bearings found in nuclear coolant pumps and rocket motor bearings in liquid hydrogen or oxygen pumps are two examples of this type of application. Large load capacity, the possibility of very long life and increased support damping over anti-friction bearings make hybrid bearings attractive. It is for these reasons that NASA is now vigorously pursuing hybrid bearings for the Space Shuttle and other advanced launching systems.Hydrostatic bearings can be designed in a wide variety of configurations as indicated in Fig. 2. Fig. 3 illustrates in more detail the several different designs that are possible for journal, thrust, and combined journal and thrust bearings.1.2 LITERATURE REVIEWThe influence of fluid bearings on the performance of rotor-bearing systems has been recognized for many years. One of the earliest attempts to model a journal bearing was reported in 1925 by Stodola 4, who investigated the effect of oil-film stiffness on the critical speed of a shaft supported in journal bearings. Further work on the modeling and linearization of bearings as they affect the rotors dynamic behavior was reported by Hagg and Sankey 5 and Starlight 6.Early interest in hydrostatic journal bearings emerged in the late 1940s and was focused on their high load and stiffness capability without a sliding velocity requirement and with virtually zero break-away friction. Early publications of static load calculation methods and design curves also provided the basic static stiffness information since load could be computed as a function of displacement (i.e., film thickness). In the late 1960s, the need for a fuller accounting of rotor dynamic performance resulted in more complete handling of hydrostatic and hybrid journal bearings dynamic properties.Davies 7,8 employed the thin lands-lumped parameter typeofapproximation to study dynamic behavior of hydrostatic journalbearings. This type of analysis enables closed form expression to be written for lubricant flow rates over the bearing lands; these can be used to calculate the approximate pressure distribution and forces. Such a method, applied also by Leonard and Rowe 9 and Rowe 10, served to determine the performance characteristics of laminar flow hydrostatic bearings. The advantages and limitations of various methods including thin-land methods have been given by ODonoghue et al. 11.In 1969 Adams and Shapiro 12 used computer analysis to determine squeeze film pad performance with the various compensation types. Also contained in that reference is an insightful description of the damping effect inherent in hydrostatic bearings and the relationship between the damping of a flat pad to that of a plain flat plate having the same proportions.Rohde and Ezzat 13 computationally demonstrated the pronounced effects of lubricant compressibility in recesses andsupply line, with dynamic behavior characterized by a breakfrequency above which stiffness increases sharply and dampingdecreases sharply as well. These results also were supported by the analysis of Ghosh and Viswanath 14 and Ghosh et al. 15. Ghosh 16, using a first order perturbation method, determined stiffness and damping properties for bearing with nonrotating journal subjected to plane harmonic excitation. The effect of fluid compressibility in the recess volume was neglected. The results show that an improvement of dynamic characteristics is possible by proper choice of pressure and eccentricity ratios and supply pressure. Rowe 10 and Rowe and Chong 17 present theoretical stiffness and damping results for hybrid bearings, including the non-symmetric portion of the stiffness matrix which captures the potential for self-excited rotor vibration. Ghosh 18 investigated the fluid inertia on the film lands of laminar flow, capillary compensated hybrid journal bearing. He showed that fluid inertia effects reduce the dynamic stiffness coefficients.Recent theoretical treatments have sought to capture more of the fluid mechanics, specifically turbulence and fluid inertia effects which become progressively more important as high journal rotational speeds are becoming critical to various aerospace applications. Redecliff and Vohr 19 analyzed bearing designs for the cryogenic rocket turbopump using liquid gases as the lubricant. A finite difference scheme including the effects of turbulence, inertia, and compressibility in the fluid film was developed. The geometry included a number of recesses cut in the bearing, but did not include axial grooves. Flow rates, pressure distribution, and stiffness were calculated, however, damping was not. An experimental program was developed to compare results with the theoretical model. Agreement was found to be good for the compared characteristics.Finite difference approach was also employed by Heller 20 for hybrid bearings related to turbopumps. The analytical model included turbulence and entrance inertia effects, but for incompressible fluid. The bearing flow, friction loss, load capacity, and dynamic coefficients were calculated. Experimental verification for a six pocket, water lubricated hybrid bearing, showed that fluid inertia at recesses grossly affected flow rates in comparison to predictions not including such inertia effects. Other performance factors were not nearly as much affected.Artiles, Walowit, and Shapiro 21 presented a numerical model for prediction of the static and dynamic performance characteristics of turbulent hybrid bearings. The matrix column method 22 applied to a variable-size finite difference grid was used to solve the governing lubrication equations at interior field points. An iterative scheme between the Reynolds equation and a flow continuity equation was employed. Inertia effects at the recess edges were included but the fluid compressibility effect at the recess volumes was neglected. The bearings considered had diameters and clearances similar to those that could possibly be deployed in rocket turbopumps. Liquid helium and oxygen were used as the lubricants.A finite element technique has been used to analyze turbulent hybrid bearings by Bou-Said and Chaomleffel 23. The analytical results were compared to those obtained by Chaomleffel and Nicolas 24. In general, agreement was found to be good for the predicted and experimental characteristics.The recent publications by San Andres 25,26 present full inertial and efficient numerical analysis for accurate prediction of the dynamic performance of turbulent flow hybrid journal bearings. Bulk-flow momentum equations are employed to describe the turbulent-inertial flow within the bearing film lands with special considerations to pressure developments downstream of the orifice supply line and recess edge entrance effects. These analyses have brought into perspective the importance of hydrodynamic and liquid compressibility effects in the dynamic characteristics of hybrid bearings and produced criteria to insure stable operation. Numerical results presented predict the performance characteristics of turbulent flow hybrid journal bearings operating at arbitrary journal center eccentricities.Published work related to the measurement and identification of the bearing rotordynamic coefficients date from Glienicke 27, (1966-67), who harmonically excited the bearing segment of a 120 mm model bearing in two mutually orthogonal directions while measuring the amplitude and phase of the relative motion between the bearing and journal. The stiffness and damping coefficients were calculated from the frequency domain equations. Morton 28 adopted this technique on a full-scale 308 mm industrial bearing to calculate stiffness and damping coefficients, and subsequently 29 developed a technique which allows a step change in force to be applied to a rotating shaft. The resulting estimated stiffness and damping coefficients exhibited considerable experimental scatter. The cross-damping terms were particularly poorly defined and Morton attributed this to ill-conditioning of the receptance matrix but he did not pursue the point.Parkins 30,31 used a rigid rotor with two external, independent sinusoidal loads. He adjusted the relative amplitudes and phases so that the bearing motion was first purely horizontal and then purely vertical. As a result, he was able to simplify the equations of motion. He evaluated the coefficients for a plain journal bearing with a 360 circumferential groove. When he compared predicted and measured coefficients, he often found over 100 percent differences.In 1977 Burrows and Stanway 32 proposed the use of a pseudo-random-binary sequence (PRBS) with a time-domain approach to data analysis. A multiple regression estimator was developed in the discrete domain from the state representation of the differential rotor-bearing model. However, this estimator may produce biased estimates 33, and this was apparent in the results presented in this work. The advantages of this technique compared with other methods of testing rotor-bearing systems have been discussed in 34. Some of the disadvantages associated with the time-domain algorithm 32 can be overcome by the use of multifrequency testing 35,36,37. This method offers several advantages which include certainty of exciting all system modes within the prescribed frequency range, and high noise rejection. The method involves forcing the system in both x and y directions, at all frequencies within the range of interest, simultaneously. However, with using PRBS forcing type signal, there is a danger of saturating the system so that amplitudes at some frequencies are so large that non-linearities are encountered and the test becomes invalid. In 37, 38 Burrows et al. overcame this problem by using Schroeder-phased harmonic signal (SPHS), which is made up of equal-amplitude sinusoidal signals whose frequencies are those which one wishes to excite within a particular frequency range 39.Yasuda et al. 40 simultaneously excited the rotor system by two statistically independent random input signals to measure frequency response functions of pump water seal. The 12 dynamic coefficients were extracted by applying the least-square technique. The method required shorter time to acquire data than a swept sine exciting method. Also, data of the X-direction and Y-direction are obtained simultaneously.Nordmann and Schollhorn 41 applied impact force as input to rotor-bearing system and used a curve-fitting technique to the frequency response functions obtained experimentally. The test rig had a symmetric configuration with a rigid rotor running in two identical journal bearings. Transient .ibrations of the rotor were caused by applying a force impulse to the rotor (by striking the rotor with a calibrated hammer). Input signals (forces) and output signals (displacements of the rotor) were transformed into the frequency domain and the complex frequency response functions thus calculated. Analytical frequency response functions, which depend on the bearing coefficients, were fitted to the measured functions. Stiffness and damping coefficients were results of iterative fitting process with least squares error as a criterion. The same technique was also applied to the determination of dynamic coefficients of annular turbulent seals in turbopumps 42.Kanki and Kawakami 43 constructed a test rig for water seals with symmetric configuration and floating casing supported by air bellows and hydraulic actuators. Both forward and backward circular force excitation were applied. After solving for the unknown impedance functions, the 8 stiffness and damping coefficients of anisotropic model were obtained by curve fitting in a wide frequency range.The potential aerospace applications are spawning a number of new experimental efforts aimed at measuring hydrostatic and hybrid bearing rotordynamic characteristics, including the work presented in this dissertation and 441. Murphy and Wagner 45 have recently presented stiffness and damping coefficients extracted from a synchronously orbiting eccentric journal with Refrig