毕业设计是对机械专业学生在毕业前的一次全面训练，目的在于巩固和扩大学生在校所学的基础知识和专业知识，训练学生综合运用所学知识分析和解决问题的能力。是培养、锻炼学生独立工作能力和创新精神之最佳手段。毕业设计要求每个学生在工作过程中，要独立思考，刻苦钻研，有所创新、解决相关技术问题。通过毕业设计，使学生掌握塔式起重机的总体设计、吊臂的设计、整体稳定性计算等内容，为今后步入社会、走上工作岗位打下良好的基础。

2、毕业设计（论文）任务内容和要求（包括原始数据、技术要求、工作要求等）：

（1）设计任务：

①总体参数的选择（QTZ500级别）

②结构形式

（2）总体设计

①主要技术参数性能

②设计原则

③平衡重的计算

④塔机的风力计算

⑤整机倾翻稳定性的计算

（3）吊臂的设计和计算

①吊臂的形式及尺寸（变截面）（双吊点）

②吊臂的强度、稳定性及刚度验算

（4）设计要求

①主要任务：学生应在指导教师指导下独立完成一项给定的设计任务，编写符合要求的设计说明书，并正确绘制机械与电气工程图纸，独立撰写一份毕业论文，并绘制有关图表。

②知识要求：学生在毕业设计工作中，应综合运用多学科的理论、知识与技能，分析与解决工程问题。通过学习、钻研与实践，深化理论认识、扩展知识领域、延伸专业技能。

③能力培养要求：学生应学会依据技术课题任务，完成资料的调研、收集、加工与整理，正确使用工具书；培养学生掌握有关工程设计的程序、方法与技术规范，提高工程设计计算、图纸绘制、编写技术文件的能力；培养学生掌握实验、测试等科学研究的基本方法；锻炼学生分析与解决工程实际问题的能力。

④综合素质要求：通过毕业设计，学生应掌握正确的设计思想；培养学生严肃认真的科学态度和严谨求实的工作作风；在工程设计中，应能树立正确的生产观、经济观与全局观。

⑤设计成果要求：

凡给定的设计内容，包括说明书、计算书、图纸等必须完整，不得有未完的部分，不应出现缺页、少图纸现象。

1）对设计的全部内容，包括设计计算、机械构造、工作原理、整机布置等，均有清晰的了解。对设计过程、计算步骤有明确的概念，能用图纸完整的表达机械结构与工艺要求，有比较熟练的认识图纸能力。对运输、安装、使用等也有一定了解。

2）说明书、计算书内容要精练，表述要清楚，取材合理，取值合适，设计计算步骤正确，数学计算准确，各项说明要有依据，插图、表格及字迹均应工整、清楚、不得随意涂改。制图要符合机械机械制图标准，且清洁整齐。

3）对国内外塔式起重机情况有一般的了解，对各种塔式起重机有一定的分析、比较能力。

其他各项应符合本资料有关部分提出的要求。

3、毕业设计（论文）成果要求（包括图表、实物等硬件要求）：

① 计算说明书一份

内容包括：设计任务要求的选型、设计计算内容、毕业实习报告等。作到内容完整，论证充分（包括经济性论证），字迹清楚，插图和表格正规（分别进行统一编号）、批准，字数要求不少于2万字；撰写中英文摘要；提倡学生应用计算机进行设计、计算与绘图。

② 图纸一套

1）总图一张（0号）

2）臂架装配图一张（0号）

3）臂架结构图五张（2号）

4）零件图若干张（4号）

4、主要参考文献：

[1] 哈尔滨建筑工程学院主编.工程起重机.北京：中国建筑工业出版社

[2] 董刚、李建功主编.机械设计.机械工业出版社

[3] 机械设计手册.化学工业出版社（5册）

[4] GB/T9462—1999 塔式起重机技术条件

[5] GB/T13752—1992 塔式起重机设计规范

[6] GB5144—1994 塔式起重机安全规程

5、本毕业设计（论文）课题工作进度计划：

起迄日期工作内容

2009.3.23-2009.3.28

2009.3.29-2009.4.13

2009.4.14-2009.4.20

2009.4.21-2009.5.15

2009.5.16-2009.6.5

2009.6.6-2009.6.19

2009.6.20-2009.6.26

熟悉整理资料

方案选择及总体设计

绘制总图

臂架设计

绘制臂架装配及结构图纸

绘制零件图纸

准备论文及答辩

摘要

本次设计在参照同类塔式起重机基础上，对QTZ500型塔式起重机进行总体设计及吊臂的设计。在吊臂设计工程中，采用了有限元法对其进行分析计算，采用了ANSYS10.0软件进行分析。

按照整机主要性能参数，确定各机构类型及钢结构型式，主要确定了吊臂的结构参数，并按照吊臂端部加载、跨中加载及根部加载三种工况分析。通过对吊臂作适当的简化，应用ANSYS10.0软件建立吊臂有限元模型，施加各工况载荷，进行求解，进而可得各工况下各节点受力情况及各单元所受轴向力、轴向应力大小及各工况下吊臂的变形挠度大小，并能演示吊臂加载过程的动画，清晰的展现了各工况下吊臂的受力性能。

通过修改模型参数，对不同模型进行分析比较。由比较不同模型在相同工况下的受力状况及刚度状况，综合分析强度和刚度条件，可得出受力最为合理的一组模型参数，通过对此组参数下模型进行强度及刚度校核，进而获得吊臂的最终参数结果。

关键词：QTZ500型塔式起重机吊臂有限元分析 ANSYS10.0

Abstract

Refers to the similar tower crane, this design is composed by the system design and the lazy arm design to the QTZ500 tower crane. In the lazy arm design progress, it has carried Finite Element method on the analysis computation, and used ANSYS10.0 software.

According to the entire machine main performance parameter, various organizations type and the steel structure pattern has been determined. The design parameter of operating modes which are composed of nose increase, the cross center increase and the root increase. Through the suitable simplification to the lazy arm, the lazy arm finite element model is establishment applied ANSYS10.0 software, and then exerted various operating modes load, carried on the solution. Then ANSYS10.0 software can calculate various pitch points stress situation, various units receive the axial stress size, and the lazy arm distortion size under various operating modes. Also it can demonstrate the animation in the process of the lazy arm increase. It has clearly displayed the lazy arm stress performance under various operating modes.

Through the revision for model parameter, the analysis comparison is carried on the different model. Because the stress condition and rigidity condition of different model is compared under the same operating mode, and the generalized analysis intensity and the rigidity condition is carried on, a most reasonable model parameter can be obtained, though the intensity and the rigidity examination regarding this model, then the final parameter result of the lazy arm can be obtained.

Key words: QTZ500 tower crane Lazy arm Finite element analysis ANSYS10.0

第1章前言1

1.1 概述1

1.2 发展趋势1

第2章总体设计2

2.1 概述2

2.2 确定总体设计方案2

2.3 总体设计原则29

2.4 平衡臂与平衡重的计算31

2.5 起重特性曲线32

2.6 塔机风力计算34

2.7 整机的抗倾覆稳定性计算43

2.8 固定基础稳定性计算49

第3章吊臂的设计计算51

3.1 分析单吊点与双吊点的优缺点51

3.2 吊臂吊点位置选择51

3.3 吊臂结构参数参数53

3.4 有限元模型建立过程的几点简化53

3.5 吊臂结构的有限元分析计算54

3.6 计算结果分析70

3.7吊臂强度校核75

3.8 吊臂稳定性校核75

毕业设计小结84

致谢85

参考文献86

第1章前言

1.1 概述

塔式起重机是我们建筑机械的关键设备，在建筑施工中起着重要作用，我们只用了五十年时间走完了国外发达国家上百年塔机发展的路程，如今已达到发达国家九十年代末期水平并跻身于当代国际市场。

QTZ500型塔式起重机简称QTZ500型塔机，是一种结构合理，性能比较优异的产品，比较国内同规格同类型的塔机具有更多的优点，能够满足高层建筑施工的需要，可用于建筑材料和预制构件的吊运和安装，并能在市内狭窄地区和丘陵地带建筑施工。高层建筑施工中，它的幅度利用率比其他类型起重机高，其幅度利用率可达全幅度的80%。

QTZ500型塔式起重机是500kN·m上回转自升式塔机。上回转自升塔式起重机是我国目前建筑工程中使用最广泛的塔机，几乎是万能塔机。它的最大特点是可以架得很高，所以所有的高层和超高层建筑、桥梁工程、电力工程，都可以用它去完成。这种塔式起重机适应性很强，所以市场需求很大。

1.2 发展趋势

塔式起重机是在第二次世界大战后才真正获得发展的。在六十年代，由于高层、超高层建筑的发展，广泛使用了内部爬升式和外部附着式塔式起重机。并在工作机构中采用了比较先进的技术，如可控硅调速、涡流制动器等。进入七十年代后，它的服务对象更为广泛。因此，幅度、起重量和起升高度均有了显著的提高。

就工程起重机而言，今后的发展主要表现在如下几个方面：①整机性能：由于先进技术和材料的应用，同种型号的产品，整机重量要轻20%左右；②高性能、高可靠性的配套件，选择余地大、适应性好,性能得到充分发挥；③电液比例控制系统和智能控制显示系统的推广应用；④操作更方便、舒适、安全，保护装置更加完善；⑤向吊重量大、起升高度、幅度更大的大吨位方向发展。

第2章总体设计

2.1 概述

总体设计是毕业设计中至关重要的一个环节，它是后续设计的基础和框架。只有在做好总体设计的前提下，才能更好的完成设计。它是对满足塔机技术参数及形式的总的构想，总体设计的成败关系到塔机的经济技术指标，直接决定了塔机设计的成败。

总体设计指导各个部件和各个机构的设计进行，一般由总工程师负责设计。在接受设计任务以后，应进行深入细致的调查研究，收集国内外的同类机械的有关资料，了解当前的国内外塔机的使用、生产、设计和科研的情况，并进行分析比较，制定总的设计原则。设计原则应当保证所设计的机型达到国家有关标准的同时，力求结构合理，技术先进，经济性好，工艺简单，工作可靠。

2.2 确定总体设计方案

QTZ500塔式起重机是上回转液压自升式起重机。尽管其设计型号有各种各样，但其基本结构大体相同。整台的上回转塔机主要由金属结构，工作机构，液压顶升系统，电器控制系统及安全保护装置等五大部分组成。

2.2.1 金属结构

塔式起重机金属结构部分由塔顶，吊臂，平衡臂，上、下支座，塔身，转台等主要部件组成。对于特殊的塔式起重机，由于构造上的差异，个别部件也会有所增减。金属结构是塔式起重机的骨架，承受塔机的自重载荷及工作时的各种外载荷，是塔式起重机的重要组成部分，其重量通常约占整机重量的一半以上，因此金属结构设计合理与否对减轻起重机自重，提高起重性能，节约钢材以及提高起重机的可靠性等都有重要意义。

1. 塔顶

自升塔式起重机塔身向上延伸的顶端是塔顶，又称塔帽或塔尖。其功能是承受臂架拉绳及平衡臂拉绳传来的上部载荷，并通过回转塔架、转台、承座等的结构部件或直接通过转台传递给塔身结构。

自升式塔机的塔顶有直立截锥柱式、前倾或后倾截锥柱式、人字架式及斜撑式等形式。截锥柱式塔尖实质上是一个转柱，由于构造上的一些原因，低部断面尺寸要比塔身断面尺寸为小，其主弦杆可视需要选用实心圆钢，厚壁无缝钢管或不等边角钢拼焊的矩形钢管。人字架式塔尖部件由一个平面型钢焊接桁架和两根定位系杆组成。而斜撑式塔尖则由一个平面型钢焊接桁架和两根定位系杆组成。这两种型式塔尖的共同特点是构造简单自重轻，加工容易，存放方便，拆卸运输便利。

塔顶高度与起重臂架承载能力有密切关系，一般取为臂架长度的1/7-1/10，长臂架应配用较高的塔尖。但是塔尖高度超过一定极限时，弦杆应力下降效果便不显著，过分加高塔尖高度不仅导致塔尖自重加大，而且会增加安装困难需要换用起重能力更大的辅助吊机。因此，设计时，应权衡各方面的条件选择适当的塔顶高度。

本设计采用前倾截锥柱式塔顶，断面尺寸为1.36m×1.36m。腹杆采用圆钢管。塔顶高5.945米。塔冒用无缝钢管焊接而成，顶部设有连接平衡臂拉杆和吊臂拉杆的铰销吊耳，以及穿绕起升钢丝绳的定滑轮，顶部应装有安全灯和避雷针。其结构如图2-1所示：

图2-1 塔顶结构图

2. 起重臂

1）构造型式

塔式起重机的起重臂简称臂架或吊臂，按构造型式可分为：小车变幅水平臂架；俯仰变幅臂架，简称动臂；伸缩式小车变幅臂架；折曲式臂架。

小车变幅水平臂架，简称小车臂架，是一种承受压弯作用的水平臂架，是各式塔机广泛采用的一种吊臂。其优点是：吊臂可借助变幅小车沿臂架全长进行水平位移，并能平稳准确地进行安装就位。因此此次设计采用小车变幅水平臂架。

小车臂架可概分为三种不同型式：单吊点小车臂架，双吊点小车臂架和起重机与平衡臂架连成一体的锤头式小车臂架。单吊点小车变幅臂架是静定结构，而双吊点小车变幅臂架则是超静定结构。幅度在40m以下的小车臂架大都采用单吊点式构造；双吊点小车变幅臂架结构一般幅度都大于50m。双吊点小车变幅臂架结构自重轻，据分析与同等起重性能的单吊点小车变幅臂架相比，自重均可减轻5%-10%。小车变幅臂架拉索吊点可以设在下弦处，也可设在上弦处，现今通用小车变幅臂架多是上弦吊点，正三角形截面臂架。这种臂架的下弦杆上平面均用作小车运行轨道。

2）分节问题

臂架型式的选定及构造细部处理取决于塔机作业特点，使用范围以及承载能力等因素，设计时，应通盘考虑作出最佳选择，首先要解决好分节问题。

小车臂架常用的标准节间长度有6、7、8、10、12m五种。为便于组合成若干不同长度的臂架，除标准节间外，一般都配设1~2个3~5m长的延接节，一个根部节，一个首部节和端头节。端头节构造应当简单轻巧，配有小车牵引绳换向滑轮、起升绳端头固定装置。此端头节长度不计入臂架总长，但可与任一标准节间配装，形成一个完整的起重臂。本次设计选用标准节长度为6m，另加上2m长的延接节。其示意图见图2-2：

图2-2臂架分节

3）截面形式及截面尺度

塔机臂架的截面形式有三种：正三角形截面、倒三角形截面和矩形截面。小车变幅水平臂架大都采用正三角形截面，本次设计的QTZ500采用正三角形截面。选用这种方式的优点是：节省钢材，减轻重量，从而节约成本。其尺寸截面形式如图2-3所示：

图2-3 臂架截面及其腹杆布置

1-水平腹杆2-侧腹杆3-上弦杆4-下弦杆

臂架一-五节：B=1020mm H=800mm

臂架六-九节：B=1017mm H=800mm

臂架截面尺寸与臂架承载能力、臂架构造、塔顶高度及拉杆结构等因素有关。截面高度主要受最大起重量和拉杆吊点外悬臂长度影响最大。截面宽度主要与臂架全长有关。设计臂架长度为50m，共分九节。

4）腹杆布置和杆件材料选用

矩形截面臂架的腹杆体系宜采用人字式布置方式，而三角形截面起重臂的腹杆体系既可采用人字式布置方式，也可采用顺斜置式。此两种布置方式各有特点。

当采用顺斜置式式，焊缝长度较短、质量不易保证。焊接变形不均匀，节点刚度较差，且不便于布置小车变幅机构。因此本设计选用人字式布置方式。其优点在于，这种布置方式应用区段不受限制，焊缝长度较长，强度易于保证，焊接变形较均匀，节点刚度较好，便于布置小车变幅机构。

臂架杆件材料有多种选择可能性。一般情况下，上吊点小车变幅臂架的上弦以选用16Mn实心钢为宜，但造价要高。因此本设计选用20号无缝圆钢管。其特点是：惯性矩、长细比要小，抗失稳能力高。下弦采用等边角钢对焊的箱型截面杆件，经济实用，具有良好的抗压性能。因此上弦杆选用89×8、89×7，下弦选用的角钢型号为：75×8、75×5，臂间由销轴连接。

5）吊点的选择与构造

吊点可分为单吊点和双吊点。其设计原则是：臂架长度小于50m，对最大起吊量并无特大要求，一般采用单吊点结构。若臂架总长在50m以上，或对跨中附近最大起吊量有特大要求应采用双吊点。采用单吊点结构时，吊点可以设在上弦或下弦。吊点以左可看作简支梁，以右可看作悬臂梁。在设计中采用双吊点。

3. 平衡臂与平衡重

QTZ500塔式起重机是上回转塔机。上回转塔机均需配设平衡臂，其功能是支撑平衡重（或称配重），用以构成设计上所需要的作用方向与起重力矩方向相反的平衡力矩，在小车变幅水平臂架自升式塔机中，平衡臂也是延伸了的转台，除平衡重外，还常在其尾端装设起升机构。起升机构之所以同平衡重一起安放在平衡臂尾端，一则可发挥部分配重作用，二则增大钢丝绳卷筒与塔尖导轮间的距离，以利钢丝绳的排绕并避免发生乱绳现象。

1）平衡臂的结构型式

平衡臂的构造设计必须保证所要求的平衡力矩得到满足。短平衡臂的优点是：便于保证塔机在狭窄的空间里进行安装架设和拆卸，适合在城市建筑密集地区承担施工任务的塔机使用，不易受邻近建筑物的干扰，结构自重较轻。长平衡臂的主要优点是：可以适当减少平衡重的用量，相应减少塔身上部的垂直载荷。平衡重与平衡臂的长度成反比关系，而平衡臂长度与起重臂之间又存在一定关系，因此，平衡臂的合理设计可节约材料，降低整机造价。

常用平衡臂有以下三种结构型式：

（1）平面框架式平衡臂，由两根槽钢纵梁或由槽钢焊成的箱形断面组合梁河系杆构成。在框架的上平面铺有走道板，走到板两旁设有防护栏杆。其特点是结构简单，加工容易。

（2）三角形断面桁架式平臂，又分为正三角形断面和倒三角形断面两种形式。此类平衡臂的构造与平面框架式平衡臂结构构造相似，但较为轻巧，适用于长度较大的平衡臂。从实用上来看，正三角形断面桁架式平衡臂似不如倒三角形断面桁架式平衡臂。

（3）矩形断面格桁结构平衡臂，其特点是根部与座在转台上的回转塔架联接成一体，适用于小车变幅水平臂架特长的超重型自升式塔机。

参考文献

【1】刘佩衡．塔式起重机使用手册．北京：机械工业出版社.2002．

【2】张质文，虞和谦等．起重机设计手册．北京：中国铁道出版社．1997．

【3】顾迪民．工程起重机．北京：中国建筑工业出版社．1988．

【4】王金诺，于兰峰．起重运输机金属结构．北京：中国铁道出版社.2002．

【5】张凤山，董红光．塔式起重机构造与维修.北京：人民邮电出版社．2007．

【6】张青．工程起重机结构与设计．化学工业出版社．2008．

【7】董刚、李建功主编．机械设计. 机械工业出版社．

【8】成大先．机械设计手册．化学工业出版社（5册）．

【9】机械设计手册编委会．机械设计手册．机械工业出版社（6册）．

【10】 GB/T9462—1999 塔式起重机设计条件．

【11】 GB/T13752—1992 塔式起重机设计规范．

【12】 GB/T5144—1994 塔式起重机安全规程．

【13】刘鸿文．材料力学．北京：高等教育出版社．2002．

【14】邢静忠．ANSYS应用实例与分析．科学出版社．2006．

【15】刘坤．ANSYS有限元方法精解．国防工业出版社．2005．

【16】李柱，徐振高．互换性与测量技术．北京：高等教育出版社．2002．

【17】张东升．机械零件及建筑机械．重庆：重庆大学出版社.2003．

【18】现行建筑机械规范大全．北京：中国建筑工业出版社.1995．

【19】吴庆鸣，何小新．工程机械设计．武昌：武汉大学出版社.2006．

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内容简介：: MR imaging at high magnetic fieldsMasaya Takahashia,*, Hidemasa Uematsub, Hiroto HatabuaaDepartment of Radiology, Beth Israel Deaconess Medical Center, Boston, MA 02115, USAbDepartment of Radiology, University of Pennsylvania Medical Center, Philadelphia, PA, USAReceived 12 November 2002; received in revised form 13 November 2002; accepted 14 November 2002AbstractRecently, more investigators have been applying higher magnetic field strengths (3?/4 Tesla) in research and clinical settings.Higher magnetic field strength is expected to afford higher spatial resolution and/or a decrease in the length of total scan time due toits higher signal intensity. Besides MR signal intensity, however, there are several factors which are magnetic field dependent, thusthe same set of imaging parameters at lower magnetic field strengths would provide differences in signal or contrast to noise ratios at3 T or higher. Therefore, an outcome of the combined effect of all these factors should be considered to estimate the change inusefulness at different magnetic fields. The objective of this article is to illustrate the practical scientific applications, focusing on MRimaging, of higher magnetic field strength. First, we will discuss previous literature and our experiments to demonstrate severalchanges that lead to a number of practical applications in MR imaging, e.g. in relaxation times, effects of contrast agent, design ofRF coils, maintaining a safety profile and in switching magnetic field strength. Second, we discuss what will be required to gain themaximum benefit of high magnetic field when the current magnetic field (5/1.5 T) is switched to 3 or 4 T. In addition, we discussMR microscopy, which is one of the anticipated applications of high magnetic field strength to understand the quantitativeestimation of the gain benefit and other considerations to help establish a practically available imaging protocol.# 2002 Elsevier Science Ireland Ltd. All rights reserved.Keywords: Magnetic resonance imaging; Higher magnetic field strength; Contrast agent1. IntroductionThanks to recent technological development, whole-body magnetic resonance (MR) scanners at highermagnetic field strengths (/3 T) have been introducedinto research and clinical settings. In the beginning, oneof the main reasons to install higher fields was its highersensitivity to the blood oxygenation level-dependenteffect for functional MR imaging of the brain 1.Recently, more investigators applied these higher mag-netic field strengths to both research and conventionalclinical settings. The expectation for higher magneticfields in MRI is the improvement in signal-to-noise ratio(SNR) due to higher signal intensity (SI), where themost significant benefit is to decrease the length of timerequired to obtain images. Then, higher spatial resolu-tion may be achievable. One question is how it improvesor practically how beneficial it is when we switch thecurrent magnetic field (5/1.5 T) to 3 or 4 T.Several studies have reported and discussed theadvantages of higher magnetic field in, for example,delineation of various brain lesions 1 or cardiacstructures 2,3. Dougherty et al. 2 reported that theSNR of the anterior myocardium at 4 T was 2.9 timeshigher than that of the same region at 1.5 T. Bernstein etal. demonstrated contrast enhanced imaging at 3 T andconcluded that higher spatial resolution at 3 T couldimprove diagnostic accuracy 4. In addition, if highermagnetic field can provide better image quality, it maybe reasonable to expect a reduction in total injection ofcontrast agent, for example, in MR angiography whichneeds to cover a larger area of the peripheral artery 5or the lung 6,7. However, such speculation would bedifficult to prove as higher magnetic fields change otherimaging aspects besides SNR.Many theoretical and experimental studies have beenemployed to demonstrate the magnetic field dependen-cies. Besides SNR, the magnetic field-dependence is* Corresponding author. Tel.: ?/1-617-667-0198; fax: ?/1-617-667-7021.E-mail address: mtakahas (M. Takahashi).European Journal of Radiology 46 (2003) 45?/52/locate/ejrad0720-048X/02/$ - see front matter # 2002 Elsevier Science Ireland Ltd. All rights reserved.PII: S0720-048X(02)00331-5well-documented in tissue relaxation times 8?/10, aswell as in MR contrast agent effects (e.g. R1, R2 or R2*relaxivities) 11,12. SNR depends upon imaging para-meters, RF coil sensitivity and machine adjustments,such as magnetic field homogeneity, accuracy in excita-tion/refocusing pulse settings, etc. These theoretical andexperimentally proven properties suggest that imagingparameters must be reconfigured for different magneticfields. Unlike relaxation time and MR contrast agenteffects, the benefit to signal intensity at higher magneticfield should be compared under nearly identical experi-mental conditions. Therefore, it is imperative to quan-tify the practical differences in terms of SNR andcontrast-to-noise ratios (CNR) between higher andlower (B/1.5 T) magnetic fields. However, the studiesof direct comparisons between SNRs and CNRs as anoutcome of the combined effect of several magneticfield-dependent parameters at different fields comparedwith the theoretical values are substantially sparse.Hence, it is still unclear how much benefit we can gainin SNR or what we can/should do in switching a currentmagnetic field strength (5/1.5 T in most cases) to ahigher magnetic field. In this article, we consider themagnetic field dependent alterations, e.g. MR signal onthe image, relaxation times, effects of contrast agent,design of RF coil and safety profile. Then, we evaluatethe scientific expectations for MR imaging on a highermagnetic field to quantify the scientific and technicalissues relative to safe human experimentation. Further,the feasibility of MR microscopy, which is one of theexpectations of higher fields, is discussed.2. SI, SNR and CNRThe question of optimum field strength has been asubject of intense controversy for over a decade. Theinterest in higher fields stems from the fact that SNRsincrease with field strength (v), where SI and noise havedifferent magnetic field-dependencies.SI8(number of spins)?(voltage induced by each spin)(1)As shown in Eq. (1), theoretically, the signal intensityfrom a MR experiment is proportional to the square ofthe static magnetic field (v2) since both number ofspins that can be observed and voltage induced by eachspin increase linearly as magnetic field (v) increases.Noise is proportional to the static magnetic field (v),when all noise comes from a sample, resulting in anSNR that is proportional to v in the case. On the otherhand, noise is proportional to one-quarter of v (v1/4)when all noise comes from the RF coil, resulting in anSNR that is proportional to v7/4. Therefore, SNR canbe expected to increase more than 2.7 (?/4/1.5) times at4 than at 1.5 T. If this is true, since the SNR scales as thesquare root of the number of image averages, the timeneeded to obtain the same SNR is reduced by a factor of8.To confirm this theory, we imaged the brain in asubject at both fields. To make our comparison betweenthe magnetic fields as direct as possible, the same sets ofexperiments in the same subjects were conducted at both4 and 1.5 T on the commercially supplied whole-bodyMR scanners (SignaTM, General Electric Systems, Mil-waukee, WI) with the equipped head coils. Fig. 1 showsthe T1-weighted images (top) and T2-weighted images(bottom) obtained in the same level of the brain of thesame subject. Each image was obtained with a conven-tional spin echo sequence with the same imagingparameters at 1.5 and 4 T, respectively. These imagesshowed different tissue contrast between the magneticfields even though the images were acquired with thesame set of imaging parameters. In the quantitativemeasurements of SI, we found that 4 T increased the SIin both white and gray matter (Fig. 1). In addition, thoseenhancement ratios were also different between theimaging parameters (T1-WI and T2-WI). Thus, 4 Tprovides a different tissue contrast compared with 1.5 Tusing the same set of imaging parameters, which mightbe inconsistent with theoretical values.3. Relaxation timesAs discussed above, SNR in biological tissue wasfound to be in approximate proportion to field strength.However, the practically achievable SNR gain may besomewhat less since the above theory assumes that allparameters except the magnetic field are consistent. Onereason for the discrepancy is the increase in T1 relaxa-tion time with increasing field strength. SI is a functionof relaxation time that is, in turn, magnetic field-dependent 3. In theory, T1 value increases in amagnetic field-dependent manner in most biologicaltissues of which the correlation time (tc) of tissue wateris :/10?8s 13, whereas T2 value does not change (Fig.2). Comparisons of relaxation times in humans havebeen published in the literature. Jezzard et al. andDuewell et al. presented a comparison of T1 and T2relaxation times in human subjects between 1.5 and 4 Tin the brain and several peripheral regions 9,10 (Table1). In any tissue, T1 relaxation times are prolonged at ahigher magnetic field, while T2 relaxation times aresomewhat shortening. Those results are consistent withprevious reports (Fig. 2). To confirm this phenomenon,we conducted the same set of phantom experiments atboth 4 and 1.5 T on the same whole-body MR scannerswith head coils 14. Phantoms included different con-centrations of Gd-complex aqueous solution with eachphantom representing tissue with a different T1 relaxa-M. Takahashi et al. / European Journal of Radiology 46 (2003) 45?/5246tion time. In this study, the trains of spin echo imageswith varied TRs or TEs were obtained with the samecommercial clinical scanners with the head coils de-scribed above. The relaxation times (T1, T2) for allphantoms were determined at both 1.5 and 4 T from thefitting curves. The results in this confirmatory studydemonstrated that any T1 relaxation times were pro-longed (1.10?/1.47 times) at 4 T compared with those at1.5 T, while T2 values were identical or slightlyshortened (Table 2).Further, a standard contrast-enhanced MR angio-graphic sequence (3D spoiled gradient recalled acquisi-tionorSPGR)sequencewiththesameimagingparameters was utilized to confirm changes in SI. PeakSNRs at 4 T increased at least 2.21 times highercompared with those at 1.5 T. Moreover, peak CNRsat 4 T increased at least 1.59 times higher compared withthose at 1.5 T in the range of Gd concentrationsexpected during clinical use. In addition, those enhance-ments of SNR and CNR were a function of a flip anglethat we used. Based on those results, using higherFig. 1. T1- and T2-weighted images of a human subject obtained at 1.5 and 4 Tesla. Each image was acquired with the same set of imagingparameters (TR/TE is indicated in the parentheses), respectively. Note that different magnetic fields provided different image contrast.Fig. 3. Cross-sectional T1-weighted image of a fixed excised spinalcord of the larval sea lamprey. Image was obtained at 9.4 Texperimental machine; resolution was 9?/9 mm resolution. See Ref.27.Fig. 2. Magnetic field dependency in T1 and T2 relaxation times,modified from Ref. 13.M. Takahashi et al. / European Journal of Radiology 46 (2003) 45?/5247magnetic fields seems to be beneficial in CNRs as well asin SNRs even without optimization of imaging para-meters at each magnetic field.A relationship between the SI of a gradient echosequence, the relaxation time and the optimal flip angle(ao: Ernst angle), can be expressed as follows:SI?b?1 ? exp(?TR=T1) ? exp(?TE=T2?) ? sin a1 ? exp(?TR=T1) ? cos a(2)andcos ao?exp(TR=T1)(3)where b is the scaling factor and a is the flip angle. SI isdetermined by its relaxation times (T1 and T2*) inindividual tissue conditions in any imaging sequence.This implies that the same intensity will not be obtainedwith the same set of imaging parameters due to thealternation of relaxation times at different magneticfield. Since T1 values at higher magnetic field are longerthan those at lower magnetic field, the TR, presumablyas well as the flip angle, should be longer (smaller forflip angle) to optimize the SNR of the same sample atthe higher field. Using longer TR, the advantage in SI ata higher field would be less in unit time. In other words,since the primary limitation imposed by long T1relaxation time at higher magnetic field strength isreflected in the TR, the SNR per unit time is optimizedwith an Ernst angle pulse and the shortest achievablevalue of TR/T1. The necessity of optimization ofimaging parameters was presented in a previous work.Keiper et al. 15 compared the usefulness in thediagnosis of white matter abnormalities in multiplesclerosis patients following the optimization of imagingparameters between 1.5 and 4 T. Their results demon-strated that MR imaging at 4 T (512?/256 matrix) coulddepict smaller lesions that could not be detected at 1.5 T(256?/192 matrix), implying that the higher resolutionat 4 T provides higher accuracy of diagnosis in the samepatients with almost identical total scan time.Although T2 values were substituted for T2* in thephantom study because T2 and T2* values should betheoretically identical in phantoms in each magneticfield 16, it is considered to be different from theconditions in some tissues where the T2* value ismuch shorter than the T2 value in some tissues. Amagnitude of susceptibility (g) is proportional to themagnetic field as shown in the following equation 17:g?Dx2?B0RGz?(4)where Dx is the difference in magnetic susceptibility ofadjoining substances, B0(?/v) is the static magneticfield, R is the cross section radius and Gzis the read-outgradient. However, this effect on T2* depends on T2 intissue since 1/T2* is a function of T2 and T2? (R2*?/R2?/R2?) 18. The shorter T2 and T2* values at ahigher magnetic field may cause a larger decrease in theSNR and CNR than would be expected in some tissue,such as the lung. Previously, we found that the CNRincreased in the central arteries of the lung, but did notincrease in the pulmonary peripheral arteries at 4 T asthe dose of contrast agent increased, ranging from 0.05to 0.2 mmol/kg body weight 19. Therefore, the optimalimaging parameters for the clinical application shouldbe carefully considered, particular when an undesirableT2* effect may be involved.4. Relaxivities of Gd-complexThe R1 relaxivity of MR contrast agent is dependentupon various parameters, such as the type of contrastagent 20, temperature and tissue environment as wellas magnetic field strength 11,12. R1 relaxivity of aparamagnetic contrast agent is higher at lower fieldstrength 11. R2 and R2* values should be theoreticallyidentical in phantoms in each magnetic field 16.In the phantom study described above, the authorsattempted to compare the effects of contrast agent. Foran accurate determination of the efficacy of Gd-complex(R1, R2 and R2*), only some of the relaxation timesTable 1Comparison of T1 and T2 relaxation times in human subject 9,10TissueT1 (s)T2 (ms)1.5 T4 T1.5 T4 TBrainaGray matter0.9?/1.3*1.7277?/9063White matter0.7?/1.1*1.0462 ?/8050Muscleb0.981.833126Fatb0.310.394738Bone marrowb0.290.424742aLezzard et al. 9.bDuewell et al. 10.* From previous literature.Table 2Comparison of T1 and T2 relaxation time in gadolinium doped watersolution at room temperature, modified Ref. 14Gd concentration (mmol/l)T1 (ms)T2 (ms)1.5 T4 T1.5 T4 T025563636164315040.125106715669118620.54195623483511.251912531601602.51231428483567814342At room temperature.M. Takahashi et al. / European Journal of Radiology 46 (2003) 45?/5248(T1, T2) that could be excellently fitted to the curve (r ?/0.995) were reciprocally plotted against the concentra-tions of Gd at both 4 and 1.5 T. As a result, R1 and R2relaxivity values were determined to be 2.95 and 4.82 (l?/s?1?/mmol?1) at 4 T and 3.89 and 4.67 (l?/s?1?/mmol?1)at 1.5 T, respectively. R1 at 4 T was lower (:/25%) thanR1 at 1.5 T, while the R2 at 4 T was almost that at 1.5 T(Table 3). Hence, we found that R1 relaxivity decreasesas the magnetic field strength increases, while R2relaxivity does not change as much, which is consistentwith previous reports 16.Unlike Gd-complex, R2 and R2* might be consider-ably changed depending upon the type of contrast agent(e.g. super paramagnetic iron oxide: SPIO), applicationroot and/or tissues. This suggested that we should alsoconsider the use of the MR contrast agent, though it isnot clear whether this change is substantially effective incurrent clinical usage at higher magnetic field.5. RF coilThe application of higher magnetic field strengths toMR imaging (particular in whole body imaging) is moredemanding because of the difficulty in building RF coilssince the penetration of radio frequency into the tissuebecomes harder 3,21. It is necessary to understand therelationship between SNR and RF coil, since anincomplete RF coil may sacrifice the advantage inSNR at increased magnetic field strength. RF coilcharacteristics, especially a receive coil, significantlyimpactSNR.SNRincreaseswithdecreasingcoildiameter. Thus, the coil sensitivity of the head coil is:/3-fold higher than that of the body coil. The surfacecoilwithsmallerdiametergainsmoresensitivity,whereas the SNR drops off very rapidly with increasingdepth from the surface. To cover these difficulties, anarray of surface coils must be developed. Reported byWright et al. 22, another idea to increase coil sensitivityand further improve SNR is to reduce coil temperature,thus lowering its resistance and thermal noise voltagesand increasing its Q, while keeping the sample at roomtemperature. The cryogenic SNR gain would be greatestfor coil and sample configurations having QL/QUcloseto 1.6. Safety considerationTheoretical calculations of the interaction of highmagnetic fields with human subjects have been reviewed.To date, no hazardous physical or physiological phe-nomena have been shown. The mechanism consideredincluded orientation of macromolecules and mem-branes, effects on nerve conduction, electrocardiogramsand electroencephalograms, and blood flow.The most current clinical MR imagers at lowermagnetic field (5/1.5 T) equip up to 25 mT/m. If highermagnetic fields are to be used to archive higher spatialresolution, the gradient strength must increase. In thecombination of higher statistic magnetic field andgradients, strength may be an issue in some applicationsdue to limitations in the current FDA guidelines forspecific absorption rate (SAR). SAR is defined asfollow:SAR?sjEj22r?tTR?NPNS(5)where s is conductivity, E is the electric field, r is tissuedensity, t is pulse duration and NPand NSare numberof pulses and image slices, respectively. Since E isproportional to static magnetic field, SAR greatlyincreases at higher magnetic field, which may limit theapplication in number of slices, selection of flip angle,etc. Additionally, RF energy is absorbed more effec-tively at higher frequencies; RF absorption, as expressedby SAR, must be carefully monitored. This could be amajor concern in any application at high field strengthas Bottomley et al. previously suggested 21.7. MR microscopyIn using a higher magnetic field, the investigatorsexpect images with higher spatial resolution to be morebeneficial in research and clinical settings. Recently,transgenic and genetically engineered mouse modelshave been used increasingly and have led to importantadvances in many scientific communities. Thus, therehas been an increased demand to image mice in vivowith a microscopic method. Whereas micro-computedtomography (m-CT) can potentially generate higher-resolution images 23, MR is unique in that it is alsoable to provide detailed information on anatomy andfunction of soft tissues. Many excellent works have beenreported in transgenic mice model genotype to pheno-type 24,25, in which most of the cases were conductedwith an experimental image scanner at a high magneticfield.Besidestransgenicimaging,measurementofapparent diffusion coefficients of water molecules wasTable 3Comparison of relaxivities of gadolinium (Gd)-complex in aqueoussolution, modified Ref. 14Relaxivities1.5 T4 TR13.892.95R24.674.82R2*4.554.67* mmol?1s?1at room temperature.M. Takahashi et al. / European Journal of Radiology 46 (2003) 45?/5249performed in a single neuron 26. More recently, asingle axon in an excised lamprey spinal cord (Fig. 3)27 was demonstrated and an apparent diffusioncoefficient of the single axon was measured 28.The techniques of very high resolution MR imaginghave been developed largely in the past decade 26. MRmicroscopy has been developed in trabecular boneimaging at the clinical magnetic field strength B/1.5 T.There are at least two reasons for applying MRmicroscopy to bone imaging. First, high signal contrastis raised between bones and surrounding tissue (bonemarrow). Second, a smaller RF coil can be designed forthe wrist or ankle. It is amenable to micromorphometryex vivo and in vivo in laboratory animals and even inhumans 29?/32. The authors have provided new andinteresting information on the use of quantitative in vivoMR microscopy and spectroscopy in conjunction withdigital image processing to evaluate the epiphyseal andmetaphyseal tissues of rabbits treated with dexametha-sone at a 1.5 T clinical scanner 33.One of the difficulties of imaging microarchitecture invivo is achievement of sufficient resolution and SNR toresolve individual structures. The capability for directvisualization will have implications for acquiring suffi-cient image quality in vivo. As we discuss below, thehigher the SNR, the longer the total scan time. How-ever, we need to consider the interface between thedesire for reasonable data acquisition times and ade-quate SNR, in particular in vivo imaging. Here, wediscuss the imaging factors regulating spatial resolutionin considering the protocol for a high resolution imageat high magnetic field.SNR is the most limiting factor to increased spatialresolution in MR imaging, since scan time for a givenSNR scales as the inverse sixth power of the linear voxeldimension 34. SNR is primarily a function of voxelsize, which is determined by the number of samples inthe phase encoding and frequency encoding directions(in-plane resolution), the slice thickness (d) and the fieldof view in both directions, frequency (FOVf) and phase(FOVp) encodings. Hence, decreasing voxel size eitherby decreasing field of view or slice thickness or byincreasing the matrix size, decreases SNR 35. There-fore, any parameter determining voxel volume will alsoaffect SNR, where SNR depends upon FOV quadrati-cally in the same matrix size. The noise averagingprocess of repeated sampling has important implicationson SNR. In theory 35, SNR increases as the squareroot of the number of samples collected. This holds truefor the number of phase encodings (Np), the number offrequency encodings (Nf) as well as the number of signalacquisitionsornumberofexcitations(NEX).The combining factors above can be summarized asfollows:SNR?FOVf? FOVp?ffiffiffiffiffiffiffiffiffiffiffiNEXp? dffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiNf? Npp(6)Thus, it is true that changing the number of frequencyand phase encodings affects both voxel size and signalaveraging. The net effect is an inverse square rootrelationship between SNR and the product of phaseand frequency encoding. By contrast, SNR scales as thesquare root of the number of excitations. Hence,doubling SNR requires quadrupling of NEX, whichexacts a scan time penalty. Spatial resolution is typicallyexpressed in terms of pixel size that is determined as theratio of FOV divided by the number of phase orfrequency encodings. Hence, we can decide spatialresolution in either of two ways: by manipulating theFOV or the matrix size. Changing slice thickness alsoaffects resolution, albeit in a different way. Increasingslice thickness causes increased partial volume blurring.The effect of pixel size on image is demonstrated in Fig.4. Fig. 4(A) shows a 3D projection image of the distalfemoral epiphysis of a live rabbit obtained at a 1.5 Tclinical scanner with 98?/98?/300 mm3spatial resolu-tion. The total scan time was :/20 min. Fig. 4(B)demonstrates a 3D projection of the small trabecularbone specimen from the proximal tibiae in rats. Loca-tions have been matched to a cube highlighted in Fig.1(A). The imaging was performed on a 9.4 T experi-mental machine with a total scan time of :/55 min toafford 39 mm isotropic voxel. Comparing these twoimages, the reduction in voxel size from 98?/98?/300mm3in vivo conducted at 1.5 T (Fig. 4A) to 39 mm3exvivo at 9.4 T (Fig. 4B) presently entails an approximate50-fold SNR penalty. This could not be recovered fullyby the magnetic statistic field increase from 1.5 to 9.4 Twhen the RF coil insert was the same and had the samesensitivity. This obviously means that the RF power isdissipated beneficially by increasing Q in smaller RFcoils for SNR gain. Basically, RF coil sensitivity (Q-dumpling) is reciprocal in proportion to its diameter21.According to the discussion above, the achievablebenefit in SNR might be a factor of 4 after optimizationof imaging parameters when the magnetic field strengthis changed from 1.5 to 3 or 4 T in clinical situations,where the RF coils have almost the same sensitivitybetween the fields. This contributes to image resolutionincreasing at a factor of up to 4 in the same scan time,e.g. 128?/128 to 256?/256 matrix. In this case, the slicethickness should be kept constant. When we prefer tosave scan time, we can reduce the number of excitationsby half, since SNR is proportional to the square of thetotal scan time. If we want further advances, develop-ment of RF coil, image acquisition, restoration andprocessing techniques should be involved.We estimated the benefits for MR imaging when thecurrent MR scanner with magnetic field strength ofM. Takahashi et al. / European Journal of Radiology 46 (2003) 45?/5250B/1.5 T is replaced with a higher field up to 3 or 4 T. Anumber of practical implications in the imaging ofbiological tissues at higher field strength must beconsidered. The gain in SNR from the higher magneticfield strength may be substantially offset by prolongedT1 relaxation times, thus optimization of the imagingparameters is important. Although it was not discussedin this review, higher magnetic field must produce betterfrequency resolution of near degenerated resonancesthat are not resolvable at lower field in magneticresonance spectroscopy. Another motivation for highmagnetic field is the ability to use other nuclei (e.g.23Na,39K), rather than protons, for which sensitivities are notsufficient to be observed at lower magnetic field.Recently, whole-body MR scanners with much highermagnetic fields (8?/10 T) have been developed and somehave been applied in human studies.In conclusion, MR imaging at a higher magnetic fieldstrength (/3 Tesla) will be opening a new arena. Theappropriate optimizations, such as image acquisition,development in RF coil design and image processingalgorithms with adequate safety profiles, would expandthe applications.AcknowledgementsWe would like to thank Dr Shigeru Kiryu at BethIsraelDeaconessMedicalCenter/HarvardMedicalSchool for his assistance in article preparation.References1 Thulborn KR. Clinical rationale for very-high-field (3.0 Tesla)functional magnetic resonance imaging. Top Magn Reson Ima-ging 1999;10:37?/50.2 Dougherty L, Connick TJ, Mizsei G. Cardiac imaging at 4.0Tesla. Magn Reson Med 2001;45:176?/8.3 Noeske R, Seifert F, Rhein KH, Rinneberg H. Human cardiacimaging at 3 T using phased array coils. Magn Reson Med2000;44:978?/82.4 Bernstein MA, Huston J, III, Lin C, Gibbs GF, Felmlee JP. High-resolution intracranial and cervical MRA at 3.0 T: technicalconsiderationsandinitialexperience.MagnResonMed2001;46:955?/62.5 Boos M, Lentschig M, Scheffler K, Bongartz GM, Steinbrich W.Contrast-enhanced magnetic resonance angiography of peripheralvessels. Different contrast agent applications and sequencestrategies: a review. Invest Radiol 1998;33:538?/46.6 Hatabu H, Gaa J, Kim D, Li W, Prasad PV, Edelman RR.Pulmonary perfusion and angiography: evaluation with breath-hold enhanced three-dimensional fast imaging steady-state pre-cession MR imaging with short TR and TE. Am J Roentgenol1996;167:653?/5.7 Hany TF, Schmidt M, Hilfiker PR, Steiner P, Bachmann U,Debatin JF. Optimization of contrast dosage for gadolinium-enhanced 3D MRA of the pulmonary and renal arteries. MagnReson Imaging 1998;16:901?/6.8 Duewell SH, Wolff SD, Wen H, Balaban RS, Jezzard P. MRimaging contrast in human brain tissue: assessment and optimiza-tion at 4 T. Radiology 1996;199:780?/6.9 Jezzard P, Duewell S, Balaban RS. MR relaxation times in humanbrain: measurement at 4 T. Radiology 1996;199:773?/9.10 Duewell SH, Ceckler TL, Ong K, et al. Musculoskeletal MRimaging at 4 T and at 1.5 T: comparison of relaxation times andimage contrast. Radiology 1995;196:551?/5.11 Lauffer RB. Magnetic resonance contrast media: principles andprogress. Magn Reson Q 1990;6:65?/84.12 Vander Elst L, Laurent S, Muller RN. Multinuclear magneticresonance characterization of paramagnetic contrast agents. Themanifold effects of concentration and counterions. Invest Radiol1998;33:828?/34.13 Gadian DG. In: Gadian DG, editor. Nuclear magnetic resonanceand its applications to living systems. New York: OxfordUniversity Press, 1982.14 Uematsu H, Dougherty L, Takahashi M, et al. A directcomparison of signal behavior between 4.0 Tesla and 1.5 Tesla:a phantom study. Eur J Radiol 2002;45:154?/159.15 Keiper MD, Grossman RI, Hirsch JA, et al. MR identification ofwhite matter abnormalities in multiple sclerosis: a comparisonbetween 1.5 T and 4 T. Am J Neuroradiol 1998;19:1489?/93.16 Fernandez-Seara MA, Wehrli FW. Postprocessing technique tocorrect for background gradients in image-based R*(2) measure-ments. Magn Reson Med 2000;44:358?/66.Fig. 4. (A) Three dimensional (3D) projection image of the distal femoral epiphysis of a live rabbit covering the volume analyzed. Projectiondirection is inferior to superior at an angle of 308 relative to the femoral anatomic axis. (B) 3D projection image of the small trabecular bonespecimen from the proximal tibiae in rats. Locations have been matched to a cube highlighted in (A). (A) and (B) were obtained on 1.5 T clinical and9.4 T experimental machines in the total scan time of :/20 and 55 min, respectively.M. Ta

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