装载机是一种用途非常广泛得工程机械，它广泛应用于铲装、搬运、卸载、平整散装物料，也可以对岩石硬土等进行轻度得铲掘工作。因此，它被广泛应用于建筑、公路、铁路、水电、港口、矿山及国防等工程中。装载机对加快工程建设速度、减轻劳动强度、提高工程质量、降低工程成本具有重要作用。所以装载机在国内外不论是品种还是产量，都有飞速发展，并且成为工程机械的主要品种之一。

我国的轮式装载机是从20世纪70年代初期发展起来的，与其他机种工程机械相比，轮式装载机的桥、箱、泵、阀及缸等零部件产品配套相对成熟，已经形成了比较完整的配套体系。而且自90年代以来，国内外工程机械进入了一个新的发展时期。工程机械产品以信息技术为先导，在发动机燃料燃烧与电控、液压控制系统、自动操纵、可视化驾驶、精确定位与作业、故障诊断与监控、节能与环保等方面，有了长足的进步。设计人员开发出了许多新结构和新产品。ZL50型装载机作为主导产品，经过多年的发展，质量水平得到不断提高，已经形成独立的产品系列和行业门类。近年来，国内外装载机的发展趋向于采用新结构新技术，并向机电一体化、电子化方向发展。

然而，我国装载机在设计上存在很多问题，主要集中在可靠性、结构设计强度等方面。而变速箱对于装载机来说又是重中之重，所以变速箱的设计好坏直接影响到装载机的使用寿命以及工作效率。虽然现在市场上的装载机已经日趋成熟，但对其进行改进设计，尤其是对装载机的变速箱进行改进设计，仍有非常重要的意义。

ZL50装载机所采用的是行星式动力换挡变速箱：

首先，星行变速箱的主要优点是，可通过在行星排中设计多个行星轮，使载荷由几对齿共同传递，减轻了每对齿上的载荷，以便选用较小的模数，从而减小齿轮体积，因此行星变速箱在径向方向尺寸较紧凑。但轴向尺寸则与所采用的行星排数目有关，当行星排数较多时，则轴向尺寸较大。另外还可实现输入与输出轴同心转动。

其中简单行星排是由太阳轮、齿圈、行星架和行星轮组成。由于行星轮轴向旋转与外界连接困难，故在行星排中只有太阳轮、齿圈和行星架三个元件能与外界相连，并称为基本元件。在行星排传递运动过程中，行星轮只起到传递运动的惰轮作用，与传动比无直接关系。其中三个基本元件的传递中仅有两个是独立参数，这表示行星排具有两个自由度。当以某种方式固定某一个元件后，行星排变成了一自由度系统，即可由转速方程式确定另外两元件的转速比。这样，通过将行星排三个基本元件分别作为固定件、主动件或从动件，则可组成六种方案。

由于zl50装载机采用双涡轮变矩器和机械自动变速装置相结合，可以得到较大的变矩系数，且高效率范围宽，其作用相当于变矩器加上一个二档自动变速箱（随外负荷变化，不需人操纵，自动换挡）。因此他后面的行星变速箱档位数可以减少，ZL50型装载机的行星变速箱，有两个行星排组成，只有两个前进挡和一个倒档。输入轴和输入齿轮做成一体，与二级涡轮输出齿轮常啮合，二档输入轴与二档制动器摩擦片连成一体。前后行星排的太阳轮、行星轮、齿圈的齿数相同。两行星排的太阳轮制成一体，通过花键与输入轴、二档输入轴相连。前行星排齿圈与后行星排星架、二档离合器受压盘三者通过花键连成一体。前行星排行星架和后行星排齿圈分别设有倒档、一档制动器摩擦片。

变速箱后部是一个分动箱，输出齿轮用螺栓和二档油缸、二档离合器受压盘连成一体，同变速箱输出齿轮组成常啮齿轮副，后者用花键和前桥输出轴连接。后桥输出轴前端用滑动轴承支撑在前桥输出轴后面中心孔内；后端则以滚动轴承支撑在壳体上。前、后桥离合套用花键和前、后桥输出轴相连，并可由拨叉波动，当离合套移向前面时，前后轮同时驱动；当离合套移向后面时，则只有前桥驱动。离合套通过拉杆、拨叉来操纵，并有锁定机构。

相比液力机械传动系统的装载机不能拖启动；当柴油机熄火后，便不能转向；不能利用柴油机进行排气制动。ZL50装载机的传动系统中设有“三合一”机构，可以解决这些问题。

此构件由以下零件组成，空转齿轮通过一个滚动轴承支撑在闭锁离合器被动鼓轴上，滑动啮合套与闭锁离合器被动鼓周通过花键连接。中间传动轴，其上固定着齿轮1，此齿轮与另一齿轮2啮合，齿轮3通过滚珠轴承和自由轮支撑在中间传动轴上。齿轮3与油泵齿轮相啮合，而油泵齿轮变矩器泵轮齿圈相啮合。

当发动机启动后，发动机由被动变为主动，它要反过来通过这条传动路线来驱动车轮。由于自由轮只能单向传动，反向传动时，它自动把动力切断，这样，防止有可能发动机通过两条传动路线来驱动车轮，发生干涉，使“三合一”机构受损。三合一机构存有一个缺点，当发动机突然熄火时，要想利用发动机制动和保持动力转向，需将啮合套迅速连接上，但往往难于结合上。

基于上述内容，此设计主要是改进变速箱，设计过程：变速箱行星机构进行运动学和动力学分析，行星变速箱传动方案简图设计，齿轮传动部分设计，换挡制动器和闭锁离合器设计，行星变速箱结构分析。跟紧装载机行业向高档、高技术含量和智能化方向发展的趋势，开发和生产具有自主知识产权、适合我国国情的重型车用变速器。

二、本课题的目的（重点及拟解决的关键问题）

轮式装载机总体设计，是机械设计制造及其自动化专业学习的一个重要的环节。通过设计提高我们对机构的分析能力，机械构造设计的能力，机电一体化系统设计能力，掌握实践生产过程自动化的设计方法，并锻炼机械类学生的综合素质。通过设计，我们将有关课程（如机械原理，机械设计，理论力学，材料力学，液压与气压传动，工程材料，材料成型，自动控制理论，电气控制，测试技术，数控技术，微型计算机原理及应用等）中所获得的理论知识在实际中综合地加以运用，并使这些知识得到巩固和发展，并使理论知识和生产密切的结合起来。

关键问题：了解装载机的发展状况和结构类型，确定装载机总体参数、总体布置；分析行星机构的运动学和动力学，其中包括运动分析、力矩分析、功率分析；分析行星齿轮变速箱，其包括行星变速箱组成、自由度和档位数分析，行星变速箱转速分析，行星变速箱力矩分析；设计行星变速箱传动方案简图；设计齿轮传动部分，包括基本参数的确定、配齿计算、齿轮的几何计算；分析行星变速箱结构，包括行星变速箱中不转动部分的支撑和定位、旋转零件的支撑和定位。编写符合要求的设计说明书，并正确绘制机械与液压工程图纸，独立撰写一分毕业论文，并绘制有关图表。

三、主要内容、研究方法、研究思路

（1）设计任务：

①装载机的发展状况和结构类别

②装载机总体参数的确定

③装载机的总体布置

④装载机变速箱传动特性分析

（2）装载机变速箱的设计和计算

①变速箱结构形式的选择

②变速箱行星排运动和受力分析

③行星变速箱传动方案简图设计

通过对资料的调查、收集、加工与整理，综合运用多学科的理论、知识与技能，分析解决变速箱设计中的问题。并且经过实习，了解变速箱的实际工作状况，在对变速箱设计过程中有所帮助外，还能使自己的设计更加接近实际。

四、总体安排和进度（包括阶段性工作内容及完成日期）

2013.3.29-2013.4.11 熟悉整理资料

2013.4.12-2013.4.25 方案选择及总体设计

2013.4.26-2013.5.9 绘制总图

2013.5.10-2013.5.23 变速箱传统系统分析

2013.5.24-2013.6.13 行星排设计及受力分析计算

2013.6.14-2013.6.22 绘制零件图纸

2013.6.23-2013.6.27 准备论文及答辩

五、主要参考文献

[1]吴永平等.工程机械设计机北京化学工业出版社 2007.

[2]杨占敏轮式装载机北京化学工业出版社,2007.

[3]吴庆鸣何小新工程机械设计武汉武汉大学出版社 2006.

[4]杨国平现代工程机械技术北京机械工业出版社 2006.

[5]杨晋升轮式装载机设计北京机械工业出版社 1986

[6]张光裕工程机械底盘构造与设计 1986

[7]同济大学主编铲土运输机械北京中国建筑工业出版社，1987.

[8]吉林工业大学编. 轮式装载机设计北京中国建筑工业出版社，1989.

[9]同济大学主编. 工程机械底盘构造与设计北京中国建筑工业出版社，1987.

[10]诸文农编. 底盘设计（上、下）北京机械工业出版社.

[11]许镇宇、邱宣怀主编. 机械零件北京人民教育出版社.

[12]机械零件课程设计.贵州：贵州人民出版社.

[13]吉林工业大学主编. 工程机械液压与液力传动北京机械工业出版社.

[14]东北工学院编.机械零件设计手册. 北京：冶金工业出版社.

[15]成大先主编机械设计手册北京化学工业出版社，2004.

[16]《机械工程标准手册》编委会编机械工程标准手册北京中国标准出版社，2002.

[17]黄宗益、薛瑞祺、阎以诵编著工程机械CAD 上海同济大学出版设，1990.

[18] 闻邦椿.机械设计手册（第五版）北京机械工业出版社，2010.

指导教师意见：

摘要

Zl50装载机是我国轮式装载机系列中的中型产品，该机是一种较大型的以装卸散状物料为主的工程机械，广泛应用于矿山、基建、道路修筑、港口、货场、煤场等地进行装载、推土、铲挖、起重、牵引等作业。

本设计的步骤简单如下：1.对装载机的总体进行分析，确定总体参数；2.牵引计算，确定出各档及各档传动比；3.对装载机进行整体布置，并绘出总体布置图；4.变速箱的设计，这是本设计中最主要的部分，确定传动比，设计传动简图，配齿计算，得出齿圈、行星轮、太阳轮的齿数，并验算其合理性。然后进行齿轮设计；5.对离合器，轴、轴承的设计及选择。

此设计中，主要任务是设计变速箱及第二行星排，设计中采用了行星式动力换挡变速箱，它具有3个离合器和3根轴，且轴安装在壳体内，使变速箱结构简单、便于维修。变速箱具有两个前进挡和一个后退档，可以产生三个速度。

关键词：装载机液力机械传动系统行星式动力换挡变速箱

ABSTRACT

The loader ZL50 iswheel type and it is more bigger among the series made in our country.It is suitable for loading discharging materials and it applies for mine、capital contuction、road builing 、port、field、coalfield and carries loading 、pushing dust 、diging rising weight

The design of the simple steps are as follows: 1.the overall loader analysis , to determine the overall parameters; 2. traction calculation, determine the gear and the gear ratio; 3 .to loader for the overall layout, and draw the overall layout; 4.design of gearbox ,and it is the design of the main parts determination of design, transmission ratio, transmission diagram, gear tooth number calculation, the ring gear, a planet wheel, sun wheel, and check the rationality. Then the design of the clutch gear; 5. design and selection of shaft, bearing.

In my design, I adopt counter shaft power shift transmission’s construction is simple and maincenance is easy .the transmission has two forward and one reverse gear ,it can provide three speeds

KEY WORDS: lorder liquid engine driving system

Hydraulic torque conventer power shift gearbox

第1章前言1

第2章总体设计2

2.1 概述2

2.2 选择确定总体参数2

2.3 装载机底盘部件型式设计11

第3章牵引计算22

3.1 柴油机与变矩器联合工作的输入与输出特性曲线22

3.2 确定档位及各档传动比 28

3.3 运输工况牵引特性曲线 31

3.4 求出各档最高车速并分析牵引特性 33

第4章总体布置35

4.1 总体布置草图的基准 35

4.2 各组成部件的位置 35

4.3 计算平衡重 39

4.4 桥荷的分配 40

4.5 验算轮胎载荷 42

4.6 总体布置图 43

第5章行星式动力换挡变速箱设计 43

5.1 传动比的确定 44

5.2 传动简图设计 45

5.3 配齿计算 47

5.4 离合器设计53

5.5 齿轮设计56

5.6 轴的设计 59

5.7 轴承的选择计算 64

第6章毕业设计小节 66

参考文献68

毕业实习报告 69

第1章前言

ZL50轮式装载机是一种较大型的以装卸散状物料为主的工程机械，因其具有作业速度快、效率高、机动性好、操作轻便等优点，所以对于加快工程建设速度，减轻劳动强度，提高工程质量，降低工程成本都发挥着重要的作用，是现代机械化施工中不可缺少的装备之一。

ZL50轮式装载机是高效率、用途广泛的工程机械，广泛应用于建筑、矿山、道路、水电和国防建设等国民经济各个部门，不仅对松散的堆积物料可以进行装、运、卸等作业，还可以对岩石、硬土进行轻度挖掘工作。

ZL50轮式装载机属于ZL系列，采用轮式行走系，液力机械传动系，铰接式车架工作装置采用液压操纵。此类装载机具有机动性好、转向灵活、生产率高、操纵轻便等特点，一般后桥布置为摆动桥，增加了整机的稳定性，所以该机的安全性好。

ZL50轮式装载机为四轮驱动装载机，作业时以全轮驱动，空车运输时，为防止寄生功率，仅用前轮驱动，因此后桥的传动可以用啮合套脱开。ZL50装载机采用液压与液力机械传动，具有变速平稳、传动比大、作业效率高和无级变速等特点，应用十分广泛。其变速器采用行星齿轮变速器，换档操纵为液压式。ZL50装载机的主要特点：采用双涡轮变矩器、具有两个前进档一个倒退档的双行星传动动力换档变速器，以及能实现脱起动，内燃机熄火转向，排气制动的“三合一”机构。

第2章总体设计

2.1 概述

总体设计是极为关键的环节，是对所设计的机械的总设想。总体设计的成败关系到整部机械的经济技术指标，直接决定了机械设计的成败。

总体设计指导机构设计和部件设计的进行，在接受设计任务以后，应进行深入细致的调查研究。收集国内外同类机械的有关资料。了解当前国内外装载机的使用、生产、设计和科研情况，并进行分析比较，制定总的设计原则。设计原则应当保证保证所设计机型符合的方针、政策。在满足使用要求的基础上，力求结构合理，技术先进，经济性好，寿命长。制定总则之后，便可以编制设计任务书，在调研的基础上，运用所学知识，从优选择总体方案，以确保设计的成功。

装载机总体参数的选择就是对装载机主要性能提出总体的要求，作为整机和总体设计的依据。

总的设计原则：

1．遵守“三化”：零件标准化、产品系列化、部件

2．采用“四新”：新技术、新结构、新材料、新工艺。

3．满足“三好”：好制造、好使用、好维修。

装载机总体参数主要包括：发动机功率，载重量，装载机自重，车速，牵引力，铲起力，轴距，轮距，最大卸载高度，最小转向半径，轮胎尺寸，整机外形尺寸。

2.2选择确定总体参数

目前，装载机的总体设计中有计算法、类比法及综合运用计算等三种设计方法，限于我们的条件，我们的设计采用计算法和类比法综合运用的方法，比较法就是参考国内外已有的同类型机种的参考尺寸，结合我们要设计的机型的具体要求，参照确定其参数尺寸。

总体参数的确定包括以下内容：

2.2.1确定轴距和轮距

1．轴距是装载机总体设计中的主要尺寸，一般是用比较法初步选取，然后通过绘制总布置，才能准确地选定轴距。轴距L的主要影响以下三个方面的性能：

（1）轴距增大，有利于提高整车的纵向稳定性。轴距增加还可以减少装载机在行驶中之前后颠覆，提高行驶平稳性，减少司机疲劳。

（2）轴距增长如其它条件不变时，最小转弯半径增加。

（3）轴距增长，相应的车架、传动轴等都要增长，所以装载机自重增加。

此外，轴距的改变，还会影响车架受力和整机的通过性。

2．大部分装载机前后轮距相同，且前后轮用相同的轮胎。

（1）轮距增加，可提高整机横向稳定性，但最小转弯半径将增加，影响机动性。

（2）轮距增加会造成铲斗斗宽的增加。因为在作业中要保护轮胎不被碰伤，一般铲斗要比轮胎宽50――100mm（单侧），所以轮距增加，铲斗宽度相应加宽，这样就降低单位斗刃长度上的插入力。

综上所述，参考同类产品初选：

轴距 3300mm 轮距 2200mm

2.2.2初选轮胎:

装载机多在松软、潮湿或干硬不平的地面上工作，为了降低接地比压，增加轮胎支承面积，改善附着性能和缓冲性能，多采用低压宽基轮胎。在国外，宽基轮胎多采用无内胎轮胎，它工作安全，散热性好，寿命较长。必要时其内部还可注入氯化钙溶液，以增加装载机作业时的稳定性和附着性能。轮式装载机的轮胎费用占整机费的10%—15%，占装载机使用费用的25%—50%，因此，正确的选择轮胎，延长轮胎的使用寿命，对降低生产成本，具有重要的意义。

装载机的轮胎应根据轮胎所受负荷，作业场地情况和运输距离来选择。它除了满足一定的承载能力外，还需要有很好的耐磨、抗穿刺性、牵引性、散热性和缓冲性能。对于常在松软地面上作业的装载机，为了发挥其牵引力，要求轮胎有较好附着性能，应采用牵引型轮胎，其特点是轮胎表面沟槽宽度大于凸起花纹的宽度（二倍以上），能使花纹压入软土中，产生比较大的抓土能力。花纹呈“八”字形或“人”字型，具有较好的自动排除沟槽中泥土的能力，它的橡胶层薄，散热快，因此可在较高的速度下运转。

轮式装载机在矿山、碎石厂作业时，轮胎外侧最易受损伤，为了保护轮胎，或将外部胎肩部分加厚，或将外侧半个胎面作成光胎面，采用耐切割的胶料，以提高抗切割性能。对于用在矿山碎石硬路面作业的装载机，要求轮胎具有耐磨和抗穿刺的能力，应采用岩石型轮胎，其特点是凸起花纹的宽度大于槽宽，橡胶层厚，花纹深，不易被尖刀刺穿或切割，使其在岩石等硬地面作业时使用寿命长。但其散热差，不宜作长距离或高速行使。

参考文献

[Ⅰ]吴永平等.工程机械设计机北京化学工业出版社 2007.

[Ⅱ]杨占敏轮式装载机北京化学工业出版社,2007.

[Ⅲ]吴庆鸣何小新工程机械设计武汉武汉大学出版社 2006.

[Ⅳ]杨国平现代工程机械技术北京机械工业出版社 2006.

[Ⅴ]杨晋升轮式装载机设计北京机械工业出版社 1986

[Ⅵ]张光裕工程机械底盘构造与设计 1986

[Ⅶ]同济大学主编铲土运输机械北京中国建筑工业出版社，1987.

[Ⅷ]吉林工业大学编. 轮式装载机设计北京中国建筑工业出版社，1989.

[Ⅸ]同济大学主编. 工程机械底盘构造与设计北京中国建筑工业出版社，1987.

[Ⅹ]诸文农编. 底盘设计（上、下）北京机械工业出版社.

[ⅱ]许镇宇、邱宣怀主编. 机械零件北京人民教育出版社.

[ⅲ]机械零件课程设计.贵州：贵州人民出版社.

[ⅳ]吉林工业大学主编. 工程机械液压与液力传动北京机械工业出版社.

[ⅴ]东北工学院编.机械零件设计手册. 北京：冶金工业出版社.

[ⅵ]成大先主编机械设计手册北京化学工业出版社，2004.

[ⅶ]《机械工程标准手册》编委会编机械工程标准手册北京中国标准出版社，2002.

[ⅷ]黄宗益、薛瑞祺、阎以诵编著工程机械CAD 上海同济大学出版设，1990.

[ⅸ] 闻邦椿.机械设计手册（第五版）北京机械工业出版社，2010.

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内容简介：: Science China Press and Springer-Verlag Berlin Heidelberg 2010 Review Mechanical Engineering SPECIAL TOPIC: Huazhong University of Science and Technology October 2010 Vol.55 No.30: 34083418 doi: 10.1007/s11434-010-3247-7 Tool path generation and simulation of dynamic cutting process for five-axis NC machining DING Han1*, BI QingZhen2, ZHU LiMin2 & XIONG YouLun1 1 State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China; 2 State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai 200240, China Received October 9, 2009; accepted December 29, 2009 Five-axis NC machining provides a valid and efficient way to manufacture the mechanical parts with complex shapes, which are widely used in aerospace, energy and national defense industries. Its technology innovations have attracted much attention in re-cent years. In this paper, the state-of-the-art techniques for five-axis machining process planning are summarized and the chal-lenging problems are analyzed from the perspectives of tool path generation, integrated geometric/mechanistic simulation and machining stability analysis. The recent progresses in accessibility-based tool orientation optimization, cutter location (CL) plan-ning for line contact and three-order point contact machining, shape control of cutter envelope surface and milling stability pre-diction are introduced in detail. Finally, the emerging trends and future challenges are briefly discussed. five-axis machining, tool path generation, integrated geometric/mechanistic simulation, dynamics simulation Citation: Ding H, Bi Q Z, Zhu L M, et al. Tool path generation and simulation of dynamic cutting process for five-axis NC machining. Chinese Sci Bull, 2010, 55: 34083418, doi: 10.1007/s11434-010-3247-7 In conventional three-axis NC machining only the transla-tion motions of the cutter are permitted while the cutter ori-entation is allowed to change in a five-axis machine tool because of the two additional rotational axes. The advan-tages of five-axis NC machining mainly depend on the con-trol of tool orientations: (1) The collision between the part and the cutter can be avoided by selecting the accessible tool orientation, which provides the ability to machine the complicated shapes such as aerospace impeller, turbo blade and marine propeller. (2) A large machining strip width can be obtained if the tool orientation is properly planed so that the tool tip geometry matches the part geometry well. Also, the highly efficient flank milling can be applied to machine aerospace impeller by using a five-axis machine tool. (3) The cutting conditions can be improved in five-axis ma-chining. For example, it is possible to shorten the tool overhang length if the tool orientation is optimized. Deter-mining the safe and shortest tool length is very helpful when *Corresponding author (email: dinghan) the surface is machined in a confined space, in which only the small-diameter cutters can be used. The cutting area of a cutter, which affects the cutting force, cutter wear and ma-chined surface quality can also be controlled by changing the cutter orientation. Besides the above advantages, there exist several chal-lenging problems in five-axis machining. Since the tool orientation is adjustable, it is hard to image the complicated spatial motion of the tool. Thus, it is much more difficult to generate the collision-free and high efficient tool paths, which limits its wide application. Furthermore, the cutting force prediction and dynamics simulation are more complex because the involved cutting parameters are time-varying during the machining process. Current works about five- axis machining fall into three categories 1: tool path gen-eration, integrated geometric/mechanistic simulation and dynamics simulation, as shown in Figure 1. Tool path gen-eration is the process to plan the cutter trajectory relative to the part based on the part model, machining method and tolerance requirement. The cutter trajectory affects greatly DING Han, et al. Chinese Sci Bull October (2010) Vol.55 No.30 3409 the cutting efficiency and quality. It is also the foundation of integrated geometric/mechanistic simulation, which de-pends on the cutting geometry and cutting force modeling techniques. The cutting geometry reflects the meshing state between the cutter and the workpiece during the material removing process. By integrating the cutting geometry and cutting force models, the transient cutting force can be pre-dicted. The cutting force then can be applied to dynamics simulation, feedrate scheduling, and prediction and com-pensation of deformation. The goal of dynamics simulation is to predict the cutting stability and the machined surface profile based on the cutting force and the dynamics charac-teristics of the machine tool-cutter-fixture system. Dynam-ics simulation is helpful to optimize the cutting parameters and the tool path. The literatures on five-axis NC machining are enormous. A lot of related commercial systems have been developed, such as the general-purpose CAM softwares UG and CATIA, the special CAM software Max-AB for machining impeller and Turbosoft for machining blade, and the dy-namics simulation software CutterPro. European Commis-sion supported a project about flank milling optimization that is called “Flamingo”. Because of the obvious advan-tages of flank milling in cutting efficiency and surface qual-ity, a number of famous companies (SNECMA, Rolls Royce, Dassault Systmes) and a university (Hannover) participated in this project. The researches on five-axis high-efficiency and high-precision machining have also been carried out in some famous companies, such as United Technologies, Pratt & Whitney and Concepts NREC. Do-mestic researchers have developed some CAM systems such as KM, 5BDM and Dynacut, but the fundamental re-searches and industrial applications of five-axis machining are still in the primary level. Current commercial CAM systems provide a lot of strategies for tool path generation and simulation of dy-namic cutting process. However, the performances in intel-ligence, usability and computation efficiency still need to be improved. For instance, the selection of the strategy for cut-ter orientation optimization depends on the skill of the pro-grammer; it is difficult to automatically generate the opti-mum tool orientations that consider simultaneously all the Figure 1 Three challenging problems in five-axis NC machining. objectives required by the practical cutting process, such as collision avoidance, large effective cutting width, globally cutter orientation smoothness and shorter tool length. Also, most of the existing works about dynamics simulation aim to three-axis machining. Models and algorithms applicable to five-axis machining need to be explored. 1 Tool path generation Tool path generation is the most important technology in NC programming. The critical problem in five-axis ma-chining is to plan cutter orientations. Theoretically, the tool orientation can be any point on the Gauss Sphere. In fact, the feasible tool orientations are only a limited area on the Gauss Sphere because of the constraints of global collision avoidance and machine joint angle limits. To improve ma-chining efficiency and quality, the tool orientation of each cutter location (CL) data should be optimized by consider-ing the important factors related to a practical cutting proc-ess. The factors consist of geometrical constraints, kine-matic constraints, dynamic characteristics and physical fac-tors. How to take into account these factors is the most challenging issue in the research of tool path generation. 1.1 Collision avoidance Collision avoidance must be first considered in the process of tool path generation. There are mainly two kinds of ideas to avoid interference: (1) First generating and then adjusting cutter orientation to avoid collision. (2) Access-based tool path generation. With the former idea, cutter orientations are first planned according to some strategies. A collision detection method is then used to detect the collision be-tween the tool and the parts. If collision occurs, the tool orientations must be changed as shown in Figure 2. With the latter idea, the cutter orientations are generated directly in the accessibility cones as shown in Figure 3. The research about the first idea focuses on the algo-rithms to improve the collision detection efficiency and ad-just cutter orientations to avoid collision. In practical appli-cations, tool paths are usually composed of thousands to hundred thousands of tool positions. The collision detection often requires large computation time and resource. There-fore lots of algorithms have been proposed to improve the computation efficiency of collision detection 2,3. When machining a complex shape, the detection and adjustment processes usually repeat several times. Collision avoidance is of first concern. It is difficult to consider other factors affect-ing the cutting process when adjusting cutter orientations. The access-based tool path generation method consists of two steps. Collision-free cutter orientations at every cutter contact (CC) point are first computed. The set of colli-sion-free cutter orientations is called accessibility cone. The cutter orientations are then generated in the accessibility 3410 DING Han, et al. Chinese Sci Bull October (2010) Vol.55 No.30 Figure 2 Detecting and adjusting cutter orientation to avoid collision 2. (a) Collision detection; (b) adjust cutter orientation. Figure 3 Access-based collision-free tool path generation. (a) Accessi-bility cone; (b) collision-free tool path. cones. The most obvious merit of this method is that the iterative process of adjusting cutter orientations can almost be avoided. Based on the accessibility cone, the manufac-turability can be directly determined. Furthermore, the cut-ter orientation optimization can be carried out in the colli-sion-free space. Other objectives such as cutting forces and velocity smoothness may also be considered. The problem with this idea is the difficulty in efficiently computing ac-cessibility cones. Usually computing accessibilities will cost large computation time because complex shape may consist of hundreds of thousands of polygonal meshes. Some algo-rithms were proposed to improve computation efficiency such as the C-space (Configuration Space) methods 4,5 and visibility-based methods 610. Though C-space is an elegant concept to deal with collision avoidance, the free C-space cannot be explicitly and efficiently computed. Wang et al. 5 showed that the elapsed time to compute an accessibility cone for a part composed of only 10000 trian-gles would be 1190.33 min. Furthermore, the algorithm did not consider the collision of the tool holder. A cutter can be abstracted as a light ray that emits from the CL point if its radius is ignored. Then the problem of collision avoidance is transformed into that of visibility. We 68 described cutters visibility cone using the concept of C-space and proposed three strategies to accelerate the computation speed using the hidden-surface removal techniques in com-puter graphics. The manufacturability of a complex surface was also analyzed based on the visibility cone. However, the conventional visibility is only the necessary condition of accessibility because a milling tool usually consists of sev-eral cylindrical shapes with finite radii. The real accessible directions cannot be directly obtained from the visibility cone, and secondary collision checking and avoidance strat-egies are still needed 9. The accessibility will be equal to the visibility if both the machined surface and the interfer-ence checking surface are replaced by their offset surfaces 10. However, the offset surface is usually not easy to ob-tain and the collision avoidance of the tool holder cannot be guaranteed. Furthermore, the method only applies to ball- end cutters and cannot be extended to other types of cutters. We 11,12 proposed a high-efficient algorithm to compute the accessibility cone using graphics hardware. The algo-rithm has almost linear time complexity and applies to both flat-end and torus-end cutters. Generally, the CL point can be specified by the CC point, outward normal direction of the machined surface and cutter orientation. If the viewing direction is opposite to the cutter orientation, the global ac-cessibility of the cutter is then equal to the complete visi-bilities of the involved cylinders and cones. This equiva-lence provides an efficient method for detecting the acces-sibility of the milling cutter by using the occlusion query function of the graphics hardware. The computation effi-ciencies of the three algorithms are compared in Table 1. It is found that the computation time of our algorithm is less than 2% of that in 9 even though both the number of tri-angles and the number of cutter orientations are greater than 10 times of those in 9. The average computation time for one cutter orientation at one contact point is less than 2 of that in 9. The average computation time is also much less than that in 3 even though the number of inputted triangles is much greater than that in 3. 1.2 Cutting efficiency Nowadays, ball-end cutters are widely employed for five-axis NC machining. The major advantages of ball-end milling are that it applies to almost any surface and it is Table 1 The comparison of computation time Inputted models Method Computation platform Triangle Cutter center point Cutter orientations Computation time Average computa-tion time Ref. 9 SGI work station, Dual CPU 250M 10665 1500 80 51.63 m 2.58102 s Ref. 3 CPU 2.4G, RAM 512M 12600 50000 1 61.61s 1.23103 s Our method 12 CPU 2.4G, RAM 512M 139754 2000 1026 60.53 s 2.95105 s DING Han, et al. Chinese Sci Bull October (2010) Vol.55 No.30 3411 relatively easy to generate the tool path. From the manufac-turers point of view, however, the main disadvantage of ball-end milling is that it is very time consuming. It may require more finish passes and each pass removes only a small amount of material. Compared with ball-end cutter, non-ball-end cutter possesses more complex geometry, and exhibits different “effective cutting profiles” at different locations. Thus, it is possible to position the cutter so that its “effective cutting profile” well matches the design surface, which results in a great improvement of the machining strip width. Hence, increasing attention has been drawn onto the problem of tool path optimization for milling complex sur-faces with non-ball-end cutters. In five-axis machining, the machined surface is formed by the swept envelope of the cutter surface. The true ma-chining errors are the deviations between the design surface and the cutter envelope surface. It is well known that the shape of the cutter envelope surface cannot be completely determined unless all the cutter positions are given 13,14. Due to the difficulty and complexity in locally modeling the cutter envelope surface, most works adopted the approxi-mate or simplified models, which formulate the problem of optimal cutter positioning as that of approximating the cut-ter surface to the design surface in the neighborhood of the current CC point 15. These optimization models do not characterize the real machining process. Also, they only apply to certain surfaces or cutters. Only a few works have addressed the cutter positioning problem from the perspective of local approximation of cutter envelope surface to design surface 1517. For a flat-end or disk cutter, Wang et al. 15 and Rao et al. 16 developed the third- and second-order approximate models of the cutter envelope surface, respectively. However, for such a cutter, its envelope surface is swept by the cutting circle, which is not a rotary surface. Therefore, the two me-thods cannot be applied to other types of rotary cutters. Re-cently, Gong et al. 17 developed a mathematical model that describes the second-order approximation of the enve-lope surface of a general rotary cutter in the neighborhood of the CC point, and then proposed a cutter positioning strategy that makes the cutter envelope surface have a con-tact of second-order with the design surface at the CC point. However, theoretically speaking, a third-order contact be-tween the cutter envelope surface and the design surface could be achieved by adjusting the cutter orientation. This means that the cutter location planning based on the sec-ond-order model does not take full advantage of the effi-ciency and power that the five-axis machining offers. The above models are not compatible with each other. Also, the optimal CL is determined by solving two equations derived from the second- and third-order contact conditions. Due to the constraints of machine joint angle limits, global colli-sion avoidance and tool path smoothness, maybe there is no feasible solution to this system of equations. In our recent works 18,19, the geometric properties of a pair of line contact surfaces were investigated. Then, based on the observation that the cutter envelope surface contacts with the cutter surface and the design surface along the characteristic curve and cutter contact (CC) path, respec-tively, a mathematical model describing the third-order ap-proximation of the cutter envelope surface according to just one given cutter location (CL) was developed. It was shown that at the CC point both the normal curvature of the normal section of the cutter envelope surface and its derivative with respect to the arc length of the normal section could be de-termined by those of the cutter surface and the design sur-face. This model characterizes the intrinsic relationship among the cutter surface, the cutter envelope surface and the design surface in the vicinity of the CC point. On this basis, a tool positioning strategy was proposed for effi-ciently machining free-form surfaces with non-ball-end cutters. The optimal CL was obtained by adjusting the in-clination and tilt angles of the cutter until its envelope sur-face and the design surface had the third-order contact at the CC point, which resulted in a wide machining strip. The strategy can handle the constraints of joint angle limits, global collision avoidance and tool path smoothness in a nature way, and applies to general rotary cutters and com-plex surfaces. Numerical examples demonstrated that the third-order point contact approach could improve the ma-chining strip width greatly as compared with the recently reported second-order one. A comparison of the machining strip widths using different CLs for the five-axis machining of a helical surface with a toroidal cutter is summarized in Table 2. The values of the tool parameters chosen for simu-lation are: radius of the torus R=10 mm, and radius of the corner r=2.5 mm. Compared with the point milling, the flank milling can increase the material removal rate, lower the cutting forces, eliminate necessary hand finish and ensure improved com-ponent accuracy. It offers a better choice for machining slender surfaces. Lartigue et al. 20 proposed an approach to globally optimize the tool path for flank milling. The basic idea is to deform the tool axis trajectory surface so that the tool envelope surface fits the design surface ac-cording to the least-squares criterion. To simplify the com-putation, an approximate distance measure was employed. For a cylindrical cutter, Gong et al. 21 presented the error propagation principle, and transformed the problem into that of least-squares (LS) approximation of the axis trajectory surface to the offset surface of the design surface. In these two works, not the local geometric error, but the geometric Table 2 Comparison of the machining strip widths for different CLs Tolerance (mm) Ball-end cutter (R = 5.5 mm) Toroidal cutter (Second order contact) Toroidal cutter (Third order contact) = 0.005 0.69 2.48 5.28 = 0.01 0.98 3.12 6.14 3412 DING Han, et al. Chinese Sci Bull October (2010) Vol.55 No.30 error between the envelope surface of the cutter and the design surface, was of the first concern. Thus it was called the global optimization method. Although the LS method was easy for implementation and efficient in computation, it could not incorporate readily the non-over- cut constraint required by semi-finish milling, and more importantly, it did not conform to the minimum zone crite- rion recommended by ANSI and ISO standards for toler- ance evaluation. Fur-thermore, the geometric deviation of the machined surface from the nominal one was not clearly defined and the influ-ence of the deformation of the tool axis trajectory surface on the change of this deviation was not quantitatively analyzed. In our studies 22,23, the maximum orthogonal distance from the point on the design surface to the tool envelope surface was introduced to characterize the geometric error of the machined surface. The first-order gradient and sec-ond-order Hessian matrix of the distance function about the control parameters governing the form of the axis trajectory surface were derived. On this basis, the complete principle, model and algorithm for global tool path optimization for five-axis flank milling using cylindrical cutters were devel-oped from the perspective of surface approximation follow-ing the minimum zone criterion, and applied to flank mill-ing of non-developable ruled surface. The geometrical pre-cision was improved about 30% compared with the existing algorithms. Another advantage is that our method can easily deal with the overcut-free constraints. The comparison re-sults are listed in Table 3. In our model, the envelope sur-face of the cutter was of no concern due to the fact that the envelope surface of a cylindrical cutter is the offset surface of the tool axis trajectory surface. Therefore, the approach was only applicable to cylindrical cutters, and could not be generalized to optimize the tool paths of other types of ro-tary cutters. Cylindrical cutters can satisfy most of the demands for flank milling. However, when an application requires flank milling within a confined space, a conical cutter may prove to be more suitable because it has a smaller tip and a stronger shank in comparison with a cylindrical cutter which has a small diameter. Recently, increasing attention has been drawn onto the problem of using a conical cutter for flank milling. In our recent works 24,25, based on the observation that conical surface can be treated as a canal surface, i.e. envelope surface of one-parameter family of spheres, the swept envelope of a conical cutter was repre-sented as a sphere-swept surface. Then, an approach was presented to efficiently compute the signed distance between Table 3 The comparison of flank milling tool path generation algorithm RRD 27 MBM 28 Gong et al. 21 Our method 22 Maximum undercut (mm) 0.220 0.264 0.093(0.228) 0.068(0.228) Maximum overcut (mm) 0.220 0.211 0.119(0.172) 0.067(0.172) a point in space and the swept surface without constructing the swept surface itself. The first order differential incre-ment of the signed point-to-surface distance with respect to the differential deformation of the tool axis trajectory sur-face was derived. By using the distance function, the tool path optimizations for semi-finished and finished millings with conical cutters are formulated as two constrained opti-mization problems in a unified framework. The sequential approximation algorithm along with a hierarchical algo-rithmic structure is developed to solve them. The proposed theories and methods apply to general rotary cutters. Here, an example of tool path optimization for flank milling of a blade of an impeller with a conical cutter is reported. The blade was defined by two directrices, which were both B-spline curves of Order 3. The cutter parameters were: the bottom radius was 6.25 mm, height 30 mm, and taper angle 10. And 50100 points were sampled from the design sur-face. A smooth axis trajectory surface was generated by using Chious method 26. The maximum undercut and overcut were 0.0896 mm and 0.0239 mm, respectively. Af-ter optimization of the axis trajectory surface, the maximum undercut and overcut reduced to 0.0062 mm and 0.0061 mm, respectively. It was seen that the global tool path optimiza-tion approach improved the machining accuracy greatly. 1.3 Cutting process condition optimization The cutting process conditions such as the smoothness of the tool path and the rigidity of the whole cutting system are paid more attention in high speed machining. The tool path smoothness and tool overhang length affect the dynamics characteristics of five-axis NC machining. The cutter orien-tations would also influence the valid cutting parameters such as cutting speed and cutting area, and hence the cutting force and surface quality. Therefore, the cutting process conditions should be taken into account when planning the tool path. (i) Cutter orientation smoothness. The drastic change of the tool orientation must be avoided in a practical five-axis cutting process 29,30. Generally, the measure of cutter orientation smoothness can be defined in the machine tool coordinate system, the workpiece coordinate system and the process coordinate system. The three measures reflect the rotational motion of the machine tool, the transition of cut-ter orientations relative to the workpiece and the change of cutting conditions, respectively. The measure defined in the machine tool coordinate sys-tem is the commonly used one in current research works. Kersting et al. 31 proposed an interesting algorithm to smooth cutter orientations in the free C-space. Castagnetti et al. 29 defined a new measure in the machine tool coordi-nate system to improve the cutting efficiency and the even-ness of the rotational motions. Their results showed that the cutting time could be greatly shortened by optimizing cut-ting orientations. We 11,12 proposed a model to globally DING Han, et al. Chinese Sci Bull October (2010) Vol.55 No.30 3413 smooth cutter orientations in the feasible space. The con-straint on the angle between two orientations at two neighboring CC points was considered in the model. The global smoothness problem was formulated as a discrete minimization problem and solved by the shortest path algo-rithm in graph theory. The research works about smoothing cutter orientations in the workpiece coordinate system focus on the NURBS tool path generation. The researchers in Dassult Systmes company described a new tool path format composed of two NURBS curves 32. The distance between the two curves is constant and the smoothness of the cutter orientations is guaranteed. The format has been supported by the 840D NC system of Siemens company. We 33 proposed a new method to generate this kind of tool path for five-axis ma-chining based on the “point-line” kinematics. From the viewpoint of kinematics, a point-line is the abstract of a tool. By using the screw theory in kinematics, the mapping from the space of point-line in Euclidean three-dimensional space into the hyperplane in dual quaternion space was con-structed. The problem of point-line motion design was con-verted to that of projective Bzier or B-spline image curve design in the hyperplane of dual quaternion. The resulting point trajectory is a NURBS curve in Euclidean three- dimensional space and orientation curve is a NURBS curve on unit sphere. Such two NURBS curves, named dou-ble-NURBS curves, can describe the tool path in NC ma-chining. The measure defined in the process coordinate system indicates the change of cutting conditions. Optimizing cutter orientations according to this measure is helpful to smooth cutting force. Ozturk et al. 34 gave the relationship be-tween the cutter orientation and the cutting force and showed that the cutting force acting on a ball-end cutter depended greatly on the cutter orientation. We 30,35 pro-posed an algorithm to globally smooth cutter orientations based on a mesh-based model. The measures defined in the three coordinate systems were comprehensively considered. The approach has two advantages: (1) The cutter orienta-tions are smoothed along both the feed direction and the pick-feed direction; (2) only the accessibility cones of mesh points are required to compute and computation efficiency is improved. Simulations showed that the global smoothing of cutter orientations was helpful to improve cutting effi-ciency, evenness of feed velocity and smoothness of cutting force. (ii) Shorter tool length. The use of shorter cutters with-out collision is a key advantage of five-axis machining be-cause the magnitude of tool deflection and the stability of the cutting process are greatly affected by the slenderness ratio of the cutter. In the existing works, the shortest colli-sion-free cutter length is generally considered in the five-axis machining simulation process. For example, the minimal tool overhang length can be calculated by the simulation software such as Vericut. With this method, the shortest safe tool length (SSTL) can only be determined according to a predefined tool path. However, the SSTL along a tool path is essentially determined by the tool ori-entations in machining of a complex shape. Therefore, the SSTL should be considered in the process of the tool path generation. The tool length is usually ignored in the existing tool path generation algorithms. Morimoto et al. 10 proposed a novel algorithm to shorten the overhang length for 3+2 axis machining with a ball-end cutter by properly selecting cutter orientations. In this work, the offset surfaces of the ma-chined surface and the interference checking surface must be constructed, which is not an easy task. Furthermore, the estimated safe tool length is too conservative. We 36 pro-posed a GPU- based algorithm to compute the SSTL along a cutter orientation at a CL point based on the GPU-based accessibility detection method and developed an efficient method to generate the SSTL for 3+2 axis machining proc-ess. In succession, we 37,38 proposed a novel algorithm to determine the SSTL for 5-axis NC machining with a short ball-end cutter by optimizing the tool orientations under the constraints of global collision avoidance and tool orientation smoothness. The optimization problem was formulated as a constrained combinatorial optimization problem and solved by a dynamic programming technique. It would generate concurrently the SSTL and collision-free tool path. 2 Integrated geometric/mechanistic simulation As a foundation of physical simulation, the dynamic cutting force simulation plays an important role in feed-rate sched-uling, spindle speed optimization, chatter prediction, adap-tive control of machining process, monitoring of tool wear and broken, prediction of surface topographic, error analysis and compensation, and so on. The dynamic cutting force in the material removal process is usually predicted based on the instantaneous cutting conditions which mainly consist of the cutting geometry and the cutting force coefficients. The cutting force coefficients are usually determined by an ex-perimental calibration 39,40. So, modeling swept volume of cutter and cutter-workpiece engagement becomes a pri-mary work. 2.1 Integration of geometry simulation and cutting force prediction The computation of the envelope surface of cutter is critical for the modeling of swept volume. Numerical methods are usually used, including the Jacobian rank-deficiency method, swept-envelope differential equation algorithm, implicit modeling and Minkowski sum method 41. The high-order differential or transcendental equations are gen-erally needed to be solved in the numerical methods, which require great computation costs. Chiou et al. 42,43 re-3414 DING Han, et al. Chinese Sci Bull October (2010) Vol.55 No.30 ported two explicit (closed-form) expressions of the swept profile of a generalized APT cutter undergoing a five-axis tool motion. The one derived in 42 is directly related to the kinematical model of the machine tool due to the im-proper representation of the velocity of the cutter, and the machine-configu- ration independent one developed in 43 requires to define a instantaneous auxiliary frame at the CC point. Du et al. 44,45 simplified the derivations and com-putations in 42 by introducing a instantaneous auxiliary frame and rigid-body velocity. In our studies 13,14, two methods were proposed to analytically compute the swept envelope surfaces of the rotary tools. The first one was based on the observation that many surfaces of revolution can be treated as a canal surface, i.e. the envelope surface of an one-parameter family of spheres. The analytical expres-sions of the envelopes of the swept volumes generated by the commonly used rotary cutters undergoing general spa-tial motions were derived by using the envelope theory of sphere congruence. For the toroidal cutter, two methods for determining the effective patch of the envelope surface were proposed. With the present model, it was shown that the swept surfaces of a torus and a cylinder can be easily con-structed without complicated calculations, and that the mini-mum distance between the swept surface and a simple surface and the signed distance between the swept surface and a point in space could be easily computed without construct-ing the swept surface itself. The second one was based on the tangency condition in envelope theory and the body velocity representation in spatial kinematics. No additional moving frames or local frames are required, and the computational formulas are independent of the types of the machines. The modeling of cutter-workpiece engagement is the foundation for the cutting force simulation in five-axis milling. The usual method used so far can be classified into three types. The first is the solid geometry method, used by Altintas et al. 46 to identify the instantaneous cutter- workpiece intersection and chip load distribution in the ACIS solid modeling environment. The second is the ana-lytical method. Elbestaw et al. 47,48 employed a NURBS curve to represent the cutting edge profile and then deter-mined the instantaneous in-cut segments and chip load by computing the intersection between the NURBS curve and the locally defined surface. The third is the discrete geome-try method. Jerard et al. 40 used the extended Z-buffer model to represent the workpiece. The instantaneous contact area and chip load were obtained by computing the intersec-tions of the cutter envelope with Z-buffer elements. 2.2 Feed-rate optimization based on cutting force model On the basis of the integration of geometry simulation and cutting force prediction for the five axis milling process, the feed-rate can be optimized according to the predicted cut-ting force. Nowadays, the feed-rate optimization algorithms in the commercial softwares are mostly based on the vol-ume (or material removal rate) analysis. In this common method, the feed-rate is set in inverse ratio to the instanta-neous removed material. The main drawbacks of this me-thod lie in two aspects. Firstly, to a certain degree, the ma-terial removal rate is in the ratio of the magnitude of the instantaneous cutting force, but it cannot predict the direc-tion of the force. Secondly, it is difficult to keep the magni-tude of the instantaneous cutting force at a near-constant level. To overcome these problems, Elbestawi et al. 47,48 proposed a feed-rate optimization method for five axis ma-chining via the cutting force model. Lazoglu et al. 49 com-pleted a comparative study of the force-based feed-rate scheduling strategies. In our work 50, we proposed a feed-rate optimization method for five axis flank milling considering the constraint on the cutting force. Based on the cubic interpolation technique, the optimization model is established by using the time series assigned to the corre-sponding cutter locations as the design variable, the sum of the total time series as the objective function, the machine kinematical performance indices (i.e., velocity, acceleration and jerk of each axis) as the constraint functions, and the maximum magnitude of the instantaneous cutting force as the constraint of the whole milling process. The feed-rate can be calculated via the optimization model. This method is applicable to rough milling of free-form surfaces and semi-finish milling of ruled surfaces or ruled surface-like free-form surfaces. 3 Dynamics simulation The dynamics simulation for five-axis machining is used to obtain the time-varying status data of the cutting process, which are the foundation of the cutting process optimization. The essential work of dynamics simulation includes dy-namics modeling, cutting process stability analysis and cut-ting parameter optimization. 3.1 Dynamics modeling There are three kinds of cutter-workpiece dynamics models: (1) The coupled vibration model of the cutter and the work-piece. The model is often employed in the machining of the thin-wall workpiece. Ratchev et al. 51 proposed a coupled vibration model of the thin-wall workpiece and the cutter based on the FEM. Kovecses et al. 52 studied the analyti-cal vibration model of the thin-wall workpiece. However, the workpiece vibration model and the coupled vibration model for the machining of the sheet workpiece are usually ignored in the existing works. (2) The contact dynamics model of the workpiece and the fixture. Hu et al. 53 ana-lyzed the dynamic stability of the fixture based on the lumped parameter model that comes from the flexible mul-tibody dynamics theory. Kapoor et al. 54 studied the con- DING Han, et al. Chinese Sci Bull October (2010) Vol.55 No.30 3415 tact dynamics model that considers the friction between the fixture and the workpiece. The contact rigidity matrix was identified by the experimental method 55. (3) Melkote et al. 56 investigated the relationship between the dynamic fixture stability and the dynamic actions between the cutter and the workpiece (the time-varying characteristics of the workpiece inertia, rigidity and natural frequency in the process of material removing). 3.2 Stability analysis for machining process Up to now, based on the structural dynamics of the “cut-ter-workpiece” system, considerable attention has been de-voted to stability analysis (or chatter analysis) in the field of dynamic analysis of the milling process. The regenerative chatter and mode coupling chatter are the two main kinds of self-excited chatter. And the former one occurs earlier than the later one in most cases. Altintas and Budak 57 pre-sented an analytical method (ZOA method) for predicting milling stability lobes based on the mean of the Fourier se-ries of the dynamic milling coefficients. This method is ef-ficient and fast, but it cannot predict the existence of the additional stability regions and period doubling bifurcations in the case of low immersion milling. Recently, Altintas and his co-workers 58 explored the multi-frequency solution of chatter stability, which can predict stability lobe diagram accurately in low radial immersion milling. Bayly et al. 59 proposed the temporal finite element analysis (TFEA) for milling stability prediction. This method is efficient and accurate for small times in the cut, but not quite suitable in full and near-full immersion cases. Insperger and Stpn 60 developed the semi-discretization (SD) method. The key point of this method is that only the time-delay term of the dynamical system is discretized while the time domain terms are all unchanged. The multi-frequency and SD me-thods take into account the effect of higher harmonics mostly due to multiple mode excitation or highly interrupted cutting. However, their computational efficiencies are not high 61. In our work 62, a full-discretization (FD) method for prediction of milling stability was introduced. The response of the system of the dynamic milling process considering the regenerative effect is calculated via a direct integration scheme with the help of discretizing the time period. Then, the Duhamel term of the response is solved using FD method, i.e., the involved system state, time-pe- riodic and time delay items are simultaneously approxi-mated by means of linear interpolation. After obtaining the discrete map of the state transition on one time interval, a closed form expression for the transition matrix of the sys-tem is constructed. The milling stability is then predicted based on Floquet theory. Compared with SD method, FD method has much higher computational efficiency without loss of any numerical precision. For one degree of the free-dom milling model, the computation time of the proposed method can be reduced nearly 75%; and for two degrees of freedom milling model, the computation time can be re-duced about 60%. A summary of the methods for stability analysis is listed in Table 4. 3.3 Cutting parameters optimization The existing research on the chatter-free cutting parameters optimization concentrates on the three-axis machining. Bu-dak et al. 63 developed a method to compute the optimum axial and radial depth. In their studies, the optimization ob-ject was to maximize the material removal rate and the con-straint condition was to guarantee the chatter-free machin-ing. Altintas et al. 64 proposed a method to optimize the spindle speed and feed rate based on the milling process simulation and stability prediction. The existing works on the stability prediction and cutting parameter optimization are based on the deterministic parameter model. However, the deterministic model cannot account for the parameter uncertainties in a practical milling process. Usually there are physical and geometrical uncertain parameters in the cutter-workpiece structures. The former includes the elastic module and Poisson ratio, and the later consists of the workpiece thickness and other geometry dimensions. As a result, the chatter-free machining cannot be guaranteed. In the previous studies 65, uncertainties in the milling proc-ess were handled from the perspective of feedback control. The uncertainties in the cutting process were accommodated using a control system, and complex controllers were de-signed to compensate for the known process effects and accounted for the force-feed nonlinearity inherent in the cutting operations. To our best knowledge, the milling process dynamics taking account of the uncertain parame-ters are addressed little. We presented a robust optimization model for selecting cutting parameters in five-axis milling 6668. The interval algebra was introduced to characterizeTable 4 Comparison of methods for stability analysis Scope of application Methods Low radial immersion High radial immersion Computational load ZOA method 57 No Yes Lowest Frequency domain Multi-frequency method 58 Yes Yes High TFEA method 59 Yes No Low Semi-discretization method 60 Yes Yes High Time domain The proposed method 62 Yes Yes Low 3416 DING Han, et al. Chinese Sci Bull October (2010) Vol.55 No.30 the parameters uncertainties. The upper and lower bounds of the stability lobe diagram and cutter dynamics response were obtained using the sensitivity analysis technique. In comparison with the deterministic model, the stability of the milling process was guaranteed by adopting the results de-rived from the robust optimization model. 4 Future work The five-axis NC machining provides a valid and efficient way to manufacture the mechanical parts with complex shapes, which are widely used in aerospace, energy and national defense industries. Its technology innovations have attracted much attention in recent years. The involved fun-damental theories and key technologies have become the major topics of many national projects. Some emerging trends for future studies in this field are as follows: (i) The development of the full dynamics model for simulating the five-axis cutting process. Dynamics simu-lation is the foundation of high-efficiency and high-precise NC machining. The cutting system is composed of the ma-chine tool, the cutter and the fixture. Most of the existing works focus on the individual sub-systems, however, the full dynamics model should be considered. For example, the coupling between the large overall rigid motion and the vibration of the milling cutter is usually ignored in the pre-vious studies. However, the cutter feed-rate is time-varying during the five-axis machining process because of the addi-tional rotational motion. According to the multibody dy-namics theory, the elastic deformation of the cutter is af-fected by the acceleration of its large overall rigid motion. Therefore, the relationship between the cutting parameters and the machined surface quality should be investigated based on a full dynamics model taking into account this coupling effect. (ii) The development of the intelligent closed-loop manu-facturing methodology that integrates design, machining and measurement. Due to the time-varying cutting condi-tions and a lot of uncertain factors in the five-axis machin-ing, open-loop machining sometimes cannot satisfy the high quality requirements in both geometry precision and physi-cal performance. The closed-loop machining is a valid way to solve this problem and will be an important research area. The closed-loop machining consists of three fundamental steps: (1) Planning and simulating the cutting process; (2) Measuring the machined surface and analyzing the meas-ured data. (3) Evaluating the machined surface quality and re-designing the nominal surface. The challenging issues include the efficient online measurement to obtain the data about the geometry precision and physical performance, the re-design of the nominal surface based on the requirement of the physical performance, the accurate computation of the material volume to be removed in the compensation machining process and the process planning that considers the dynamics characteristics and physical constraints of the cutting process. (iii) The development of the multiphysic model for simu-lating the surface forming process. Higher surface quality is more and more desired by high-performance parts. The surface quality is affected by the cutting force, the cutting heat, the cutting deformation, and so on. The multiphysic modeling of these coupling effects is the foundation of cut-ting process control and cutting parameter optimization. The existing multiphysic models mainly apply to turning and the three-axis milling processes. The multiphysic simulation of the five-axis milling process becomes a challenging prob-lem because of the time-varying cutting conditions. The key issues in multiphysic simulation include the quantitive de-scription, prediction and control of the physic field, the mapping between the cutting parameters and the physical performance of the machined surface, and the new cutting process optimization approaches. This work was supported by the National Basic Research Program of China (2005CB724103) and the National Natural Science Foundation of China (50835004). 1 Ding H, Xiong Y L. Computational manufacturing. Prog Nat Sci, 2002, 12: 816 2 Wang Q H, Li J R, Zhou R R. Graphics-assisted approach to rapid collision detection for multi-axis machining. Int J Adv Manuf Tech, 2006, 30: 853863 3 Ilushin O, Elber G, Halperin D, et al. Precise global collision detec-tion in multi-axis NC-machining. Comput Aided Design, 2005, 37: 909920 4 Morishige K, Takeuchi Y, Kase K. Tool path generation using C-space for 5-axis control machining. J Manuf Sci E-T ASME, 1999, 121: 144149 5 Wang J, Roberts C A, Danielson S. Local and global accessibility evaluation with tool geometry. Comput Aided Des Appl, 2007, 4: 1929 6 Yin Z P, Ding H, Xiong Y L. Visibility theory and algorithms with application to manufacturing processes. Int J Prod Res, 2000, 38: 28912909 7 Yin Z P, Ding H, Xiong Y L. Accessibility analysis in manufacturing processes using visibility cones. Sci China Ser E-Tech Sci, 2002, 45: 4757 8 Yang W Y, Ding H, Xiong Y L. Manufacturability analysis for a sculptured surface using visibility cone computation. Int J Adv Manuf Tech, 1999, 15: 317321 9 Balasubramaniam M, Laxmiprasad P, Sarma S, et al. Generating 5-axis NC roughing paths directly from a tessellated representation. Comput Aided Design, 2000, 32: 261277 10 Morimoto K, Inui M. A GPU based algorithm for determining the optimal cutting direction in deep mold machining. In: ISAM - IEEE Int Symp Assem Manuf, Michigan USA, 2007, 203208 11 Ding H, Bi Q Z, Wang Y H, et al. Collision-free and orienta-tion-smooth tool path generation method for five-axis NC machining. Chinese Patent, Grant No. ZL200710045183.9, 2007-08-23 12 Bi Q Z, Wang Y H, Ding H. A GPU-based algorithm for generating collisionfree and orientation-smooth five-axis finishing tool paths of a ball-end cutter. Int J Prod Res, 2010, 48: 11051124 13 Zhu L M, Zheng G, Ding H. Formulating the swept envelope of ro-tary cutter undergoing general spatial motion for multi-axis NC ma-chining. Int J Mach Tool Manu, 2009, 49: 199202 14 Zhu L M, Zhang X M, Zheng G, et al. Analytical expression of the DING Han, et al. Chinese Sci Bull October (2010) Vol.55 No.30 3417 swept surface of a Rotary cutter using the envelope theory of sphere congruence. J Manuf Sci E-T ASME, 2009, 131: 4456 15 Wang X C, Wu X T, Li Y B. Second order curvature catering-a new approach in manufacture of sculptured surfaces. Acad J XJTU, 1992, 26: 5158 16 Rao A, Sarma R. On local gouging in five-axis sculptured surface machining using flat-end tools. Comput Aided Design, 2000, 32: 409420 17 Gong H, Cao L X, Liu J. Second order approximation of tool enve-lope surface for 5-axis machining with single point contact. Comput Aided Design, 2008, 40: 604615 18 Zhu L M, Ding H, Xiong Y L. Third Order Point Contact Approach for Five-Axis Sculptured Surface Machining Using Non-ball End Tools -Part I: Third Order Approximation of Tool Envelope Surface. Sci China: Tech Sci, 2010, 53: 19041912 19 Zhu L M, Ding H, Xiong Y L. Third order point contact approach for five-axis sculptured surface machining using non-ball end tools-Part II: Tool positioning strategy. Sci China: Tech Sci, 2010, 53: 2190 2197 20 Lartigue C, Duc E, Affouard A. Tool path deformation in 5-axis flank milling using envelope surface. Comput Aided Design, 2003, 35: 375382 21 Gong H, Cao L X, Liu J. Improved positioning of cylindrical cutter for flank milling ruled surfaces. Comput Aided Design, 2005, 37: 12051213. 22 Ding H, Zhu LM. Global optimization of tool path for five-axis flank milling with a cylindrical cutter. Sci China Ser E: Tech Sci, 2009, 52: 24492459 23 Ding Y, Zhu L M, Ding H. Semidefinite programming for Chebyshev fitting of spatial straight line with applications to cutter location planning and tolerance evaluation. Precis Eng, 2007, 31: 364368 24 Zhu L M, Zheng G, Ding H. Global optimization of tool path for five-axis flank milling with a conical cutter. Comput Aided Design, 2010, doi: 10.1016/j.cad.2010.06.005 25 Zhang X M, Zhu L M, Zheng G, et al. Tool path optimisation for flank milling ruled surface based on the distance function. Int J Prod Res, doi: 10.1080/00207540902993019 26 Chiou C J. Accurate tool position for five-axis ruled surface machin-ing by swept envelope approach. Comput Aided Design, 2004, 36: 967974 27 Redonnet J M, Rubio W, Dessein G. Side milling of ruled surfaces: Optimum positioning of the milling cutter and calculation of inter-ference. Int J Adv Manuf Tech, 1998, 14: 459465 28 Menzel C, Bedi S, Mann S. Triple tangent flank milling of ruled sur-faces. Comput Aided Design, 2004, 36: 289296 29 Castagnetti C, Duc E, Ray P. The Domain of Admissible Orientation concept: A new method for five-axis tool path optimisation. Comput Aided Design, 2008, 40: 938950 30 Bi Q Z, Wang Y H, Zhu L M, et al. Wholly smoothing cutter orienta-tions for five-axis NC machining based on cutter contact point mesh. Sci China: Tech Sci, 2010, 53: 12941303 31 Kersting P, Zabel A. Optimizing NC-tool paths for simultaneous five-axis milling based on multi-population multi-objective evolu-tionary algorithms. Adv Eng Softw, 2009, 40: 452463 32 Langeron J M, Duc E, Lartigue C, et

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