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麻花 螺旋 加工 及其 成形 铣刀 设计

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麻花钻螺旋槽加工及其成形铣刀设计,麻花,螺旋,加工,及其,成形,铣刀,设计

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I麻花钻螺旋槽加工及其成形铣刀设计本资料由闰土机械外文大类翻译成品淘宝店整理，主营机械大类外文翻译成品，夹具，注塑、 冲压模具，机械设计成品参考资料。本科毕业论文（设计）题 目麻花钻螺旋槽加工及其成形铣刀设计II麻花钻螺旋槽加工及其成形铣刀设计麻花钻螺旋槽加工及其成形铣刀设计：麻花钻是日常生产与生活中最常用的孔加工刀具，需求量巨大，使用成形铣刀加工是其螺旋槽成形的重要方法之一，因此加工麻花钻螺旋槽应当设计合适的成形铣刀。本文主要研究了加工麻花钻成形铣刀的设计方法，并仿真模拟成形铣刀加工麻花钻。通过对成形铣刀的廓形与结构进行设计计算设计出合适的成形铣刀，提升加工螺旋槽的效率，从而提升了麻花钻的生产效率。关键词关键词：成形铣刀 ；麻花钻；运动仿真The machining of spiral groove and the design offorming milling cutterIII麻花钻螺旋槽加工及其成形铣刀设计:Twist drill is commonly used in the daily production and life of hole machining tool, and the huge demand, use forming milling cutter machining is one ofthe important methods of the spiral groove forming, so the processing of twist drill spiral groove shall be design suitable forming milling cutter. This paper mainly studies the design method of machining twist drill, and simulates the machining of twist drill. Through the design and calculation of the profile and structure of the formed milling cutter, the suitable forming milling cutter is designed to improve the efficiency of spiral groove, thus improving the production efficiency of the twist drill.Keywords：Forming milling cutter，Twist drill，Motion simulation目 录目 录IV摘要摘要 . 2 2AbstractAbstract.IIII第一章绪论第一章绪论.1 11.11.1 研究的目的及意义研究的目的及意义.1 11.21.2 国内外研究现状国内外研究现状.1 11.31.3 研究内容研究内容.2 21.41.4 小结小结.3 3第二章麻花钻第二章麻花钻.4 42.12.1 概述概述.4 42.22.2 标准麻花钻的结构标准麻花钻的结构.4 42.22.2 麻花钻基本参数与材料选择麻花钻基本参数与材料选择.5 52.32.3 小结小结.6 6第三章成形铣刀第三章成形铣刀.7 73.13.1 概述概述.7 73.23.2 成形铣刀的材料选择成形铣刀的材料选择.7 73.33.3 成形铣刀的廓形设计成形铣刀的廓形设计.7 73.43.4 成形铣刀的技术条件成形铣刀的技术条件.15153.53.5 成形铣刀工作图成形铣刀工作图.16163.63.6 小结小结.1616第四章麻花钻与成形的建模和仿真第四章麻花钻与成形的建模和仿真.17174.1ug4.1ug 的概述的概述.17174.24.2 刀具的建模刀具的建模.17174.2.14.2.1 麻花钻的建模麻花钻的建模.17174.2.24.2.2 成形铣刀的建模成形铣刀的建模.21214.2.34.2.3 其它部分的建模其它部分的建模.24244.34.3 工件的装配工件的装配.26264.44.4 运动仿真运动仿真.27274.54.5 小结小结.2828第五章总结第五章总结.29295.15.1 总体评价总体评价.29295.25.2 成果展望成果展望.2929参考文献参考文献.3030致谢致谢.3131附录附录 A A 外文文献外文文献.3232附录附录 B B 中文翻译中文翻译.46461麻花钻螺旋槽加工及其成形铣刀设计 第一章绪论第一章绪论1.1研究的目的及意义研究的目的及意义麻花钻是日常生活与生产加工中最常用的孔加工刀具，其工序占比达到总加工工序的四分之一左右。它的螺旋槽形成其前刀面，而其主切削刃由螺旋槽以及后刀面的交线形成，故麻花钻的螺旋槽直接影响其切削性能和它的主切削刃形状麻花钻工作时其螺旋槽提供排屑作用，其槽形以及大小决定了它排屑的能力，若排屑不畅，会导致切屑堆积在容屑槽内，严重时甚至会使麻花钻断裂。此外，容屑槽的形状与大小还会对麻花钻的强度与刚度有一定的影响。麻花钻的螺旋槽常设计专用的成形铣刀进行加工。通过设计合适的成形铣刀，能有效地提高麻花钻的精度以及生产效率。因此，设计专用的成形铣刀加工麻花钻的螺旋槽具有重要的研究意义。1.2国内外研究现状国内外研究现状近一个世纪来，麻花钻的结构形状变化很小，故钻头性能并没有较为大的提高。一些国内外的研究人员在麻花钻的结构上做出了一些改变，尽管不能在一般的加工中推广，但是却在一些特殊的生产环境中产生了较为良好的作用并引发人们对麻花钻结构改进进一步的思考。近百年以来，麻花钻的主刃一般被人们设计为直线，而当研究人员建立了主刃的数学模型并推导出麻花钻主刃前角的计算公式，便发现了由于采取的直线主刃的设计方式导致钻芯的前角出现较大的负值，因此降低了标准麻花钻的切削性能。十九世纪九十年代初期，FugelsoMA 发现，造成钻芯主刃附近的后角较小的原因是钻头的主刃为直线，故提出了将钻头的主刃设计为曲线的方案。在此之后，WangY（1990），LinC 和CaoZ（1991），RenKC 和NiJ（1999）等人相继提出了麻花钻曲线主刃的数学模型。在这之中，RenKC 和NiJ 通过使用向量分析的方法，建立了麻花钻后刀面的几何参数与刃磨参数之间的关系，并分析计算了麻花钻的切削角度。ShiHM 等一些人经研究发现了能够控制钻头主刃前角的方法，通过改进主刃的走向，可以使主刃前角达到可实现的最大值，之后在九十年代初成功地完成了这种能将主刃前角达到最大值的曲刃麻花钻。此外，KoehlerW尝试了一些有关于切削2性能实验，研究麻花钻的切削刃的轮廓与形状对切削性能的影响。通过以上的这些研究，充分表明曲刃麻花钻一定程度上降低了钻头的损耗并增强了切削性能。麻花钻螺旋槽的常用的方法有多种，例如铣削法，成形砂轮磨削法，四棍螺旋液压法以及四板搓制法等。每种工艺方法所用的沟成形关键工具虽不同，但都是为了保证麻花钻的主刃为直线，并使其排屑流畅，以及保证螺旋升角、刃宽等几何参数。设计专用的成形铣刀是加工麻花钻螺旋槽较为常用的方法之一。加工时，铣刀轴线与麻花钻轴线成一定的夹角，铣刀旋转，麻花钻作螺旋进给运动，当移动一个导程时，麻花钻旋转一周。成形铣刀廓形的常用设计方法一般有以下几种：（1）早期为求解铣刀廓形人们常采用作图法，该方法直观明了，但是由于采用的作图求解接触点坐标，误差较大。此外，该方法效率较低，无法满足当前社会的需求，故几乎已经被淘汰。（2）近些年来，由于计算机辅助设计的飞速发展，人们逐渐采用CAD 软件进行辅助设计，通过采用软件的一些设计模块，能够轻易地求解出铣刀的廓形。相比于作图法，这种方法的效率与精度都要高得多。（3）计算法是较为常用的一种求解铣刀廓形的方法。 首先应根据工件端面廓形和螺旋参数求出工件螺旋面方程，然后由螺旋面上的法线与刀具轴线相交的条件求出所有接触点，这些接触点的连线即为接触线。将接触线绕刀具轴线的平面与该回转面相交，截形即为铣刀的廓形。（4）对于一些标准件，铣刀的廓形可采用经验公式计算法，该方法是通过实际生产加工得出，效率高且较为实用。1.3 研究内容研究内容该研究围绕以下几方面展开：1、查阅国内外有关麻花钻螺旋槽加工及成形铣刀的相关文献和资料，掌握国内外研究现状和常用的技术路线；2、对麻花钻结构及加工工艺作出分析；3、设计一加工40麻花钻螺旋槽的成形铣刀；4、对螺旋槽的做出加工运动仿真。1.4 小结小结本章主要阐述了麻花钻与成形铣刀的一些基本研究情况，成形铣刀廓形的设计方法以及研究的目的及意义，此外描述了该设计的主要研究内容，为之后的成形铣刀的设计计算以及麻花钻的运动仿真做好铺垫。3麻花钻螺旋槽加工及其成形铣刀设计4第二章麻花钻第二章麻花钻2.1 概述概述麻花钻是最生产中最常用的孔加工刀具，既可以在实心的物体上进行钻孔也可以在原有的孔上进行扩大，可加工的范围为0.1mm至80mm。一般常用的麻花钻我的螺旋槽为两条，起导向切削以及排屑的作用。麻花钻主要加工精度较低或者粗糙度较高的孔，根据其材料不同可分为碳素钢麻花钻、高速钢麻花钻以及硬质合金麻花钻，现最常用的麻花钻为高速钢麻花钻。2.2 标准麻花钻的结构标准麻花钻的结构标准麻花钻由工作部分、颈部及柄部三部分组成，现分别介绍如下：工作部分该部分由导向部分与切削部分组成。其中导向部分负责引导刀具的进给方向并起到排屑的作用；而切削部分负责切削工件。麻花钻的直径应由切削部分图 2.1 麻花钻的基本结构逐渐减少，整体形状成倒锥形，其直径为每100mm减少0.030.12mm，以此减少麻花钻与工件内壁的摩擦。颈部该部分为工作部分与柄部的过渡区域，一般作为退刀时的空刀槽。柄部该处是机床夹持部分，并传递扭矩到麻花钻上。它的常用形状一般有两种（莫氏锥柄与圆柱直柄）。对于柄部形状的选择一般根据麻花钻的直径以及承5麻花钻螺旋槽加工及其成形铣刀设计受的轴向力与扭矩来选择。一般钻头直径小于20mm时选择圆柱直柄（短直柄麻花钻直径小于等于40mm），麻花钻直径大于等于3mm时即可选择莫氏锥柄。麻花钻的切削部分可看成是由两把镗刀所组成，它有两个前刀面、 两个后刀面、两个副后刀面、两个主切削刃、两个副切削刃和一个横刃。前刀面螺旋槽上临近主切削刃的部分，即切削流出时最初接触的钻头表面。后刀面钻孔时与工件加工表面相对的表面。副后刀面钻孔时与工件加工表面相对的表面。主切削刃前刀面与后刀面相交而形成的刃口。副切削刃前刀面与副后刀面相交而形成的刃口。横刃两个后刀面相交而形成的刃口。图2.2麻花钻的切削刃组成2.2 麻花钻基本参数与材料选择麻花钻基本参数与材料选择由设计题目麻花钻的直径为40mm，可知麻花钻的螺旋角为30，锋角为118，后角为8，横刃斜角为 4060，刃宽23.6mm，刃带宽2.1mm。麻花钻的材料采用碳素工具钢T10，该材料使用较为广泛，常用于制作各种对切削力要求较低，切削条件较差且具有锋利刀口的刀具，如麻花钻等。2.3 小结小结本章节主要介绍了麻花钻的一些概况以及基本结构，并对其的各个结构功能进行了相应的说明，再通过查找文献资料确定了麻花钻的一些基本参数以及材料，为之后的成形铣刀设计做好了铺垫。67麻花钻螺旋槽加工及其成形铣刀设计 第三章成形铣刀第三章成形铣刀3.1 概述概述成形铣刀的截面廓形是根据工件廓形设计的。用成形铣刀可以在通用铣床上加工复杂形状的表面，生产效率高，使用方便，故应用广泛。成形铣刀经常用于加工直沟与螺旋沟。标准成形铣刀一般分为凹半圆成形铣刀与凸半圆铣刀，并用来加工凸棱与凹槽。成形铣刀轴线相当于被加工表面的位置可以不同，但加工成形直槽时，总是将铣刀轴线放在垂直于进给方向的平面中。在某些情况下，成形铣刀轴线可以是工件廓形的对称轴，这对铣刀称为指形铣刀。用成形铣刀加工螺旋沟时，工件应作螺旋运动，其运动参数与工件螺旋参数相同。对于同一个螺旋沟表面，铣刀轴线位置不同时，切削刃廓形也不同，所以加工螺旋沟的成形铣刀在使用时一定要符合设计条件。按照齿背的加工形式，成形铣刀也分为尖齿形铣刀和铲齿型铣刀两大类。尖齿成形铣刀用钝后重磨后刀面，其耐用度和工件加工表面质量都比较高，但因后刀面是成形表面，制造和重磨这种铣刀都需要专门的靠模夹具，使用不便。铲齿成形铣刀用钝后重磨前刀面，由于前刀面是平面，刃磨很方便，所以铲齿成形铣刀应用最广泛。故本文采用铲齿成形铣刀。3.2 成形铣刀的材料选择成形铣刀的材料选择成形铣刀一般采用高速钢，根据文献1采用通用高速钢W18Cr4V，可磨削性好，耐热性中等，淬火范围较宽，不易过热，强度较好，刀刃锋利，适于加工一般的钢与铸铁，可制作各种刀具，如成形铣刀，HRC63。3.3 成形铣刀的廓形设计成形铣刀的廓形设计麻花钻的螺旋槽截形，是靠成形铣刀轴向剖面的廓形来保证成形铣刀的廓形计算方法有以下几种：（1）经验公式计算法；（2）理论分析并借助于计算机计算法。（3）作图计算法求截形。8本文采用经验公式计算法，通常按理论计算或作图法求出来的槽截形可以用两端圆弧代替，如图3.1。图3.1成形铣刀的截面廓形这时，由1R形成的切削刃是铣钻头一侧的螺旋表面，=10的斜线是铣钻沟另一侧面的螺旋面，两者之间的2R是连接两者之间的过渡圆弧，同时是铣刀顶刃，铣削横刃附近的沟底螺旋面。各参数的经验近似计算公式为：DCC3211CR式中 D钻头直径（mm）。1C由于钻头之顶角2及螺旋角 不同的影响系数：9麻花钻螺旋槽加工及其成形铣刀设计31220.26C2C钻头心厚K的影响系数：044. 02)14. 0(KDC（一般钻芯厚度K=0.14D，则2C=1）3C铣刀直径0D影响系数：0.903DD13C）（一般铣刀直径D13D0,则3C=1）D75. 02015. 0R211RRB根据以上公式求得：20.219mmR1,7.691mmR2，27.91mmB13.4铲齿成形铣刀的结构参数确定（1）铣刀齿形高度h和宽度B由上一小节求出的铣刀廓形参数可求得h=20mm，B=28mm（2）确定容屑槽底形式 如果工件齿形高度较大，为增加铣刀强度减少铣刀直径，可采用采用加强式槽底（见图3.2），反之可选用平底式容屑槽，故铣刀采用平底式。10过切削刃曲线的两极限点作直线，如图中点划线所示；再距切削刃为1H=K+r 作切削刃的平移曲线，也用点划线画出；进一步作与切削刃两端直连线平行并与平移曲线相切（型）或相交（型）的直线，即为容屑槽槽底。及2H可由图求得。显然，Hh+K+r其中 K铲削量；R容屑槽底圆弧半径；H铣刀的齿形高度。作距齿顶为H=h+r且平行于铣刀轴的直线，再距切削刃为1H=k+r作切削刃的平移曲线，如图中的点划线所示，进一步过平移曲线与端面的交点（对型，为齿形高度较大的那个端面的交点），作很很近但低于平移曲线的倾斜直线，与距齿顶为H的水平直线相交，即得铣刀槽底。其中倾斜直线的倾斜角由图求得。 由于Hh，因此磨前刀面时，可在一次调整机床的情况下磨出。若使容屑槽底距刀齿顶的距离大于1H而小于H+r亦可，但这时铣刀前刀面不能在一次调整机床的情况下进行重磨，对型，需要调整机床两次；对型需要调整机床三次。图 3.2 加强型容屑槽槽底的形状及画法（3）确定铣刀孔径用铣刀切削时，要求其刀杆直径足够大，以保证在铣削力作用下有足够的强度和刚度。 因此，铣刀孔径应按强度或刚度条件计算决定。 在一般情况下，可根据铣削宽度和切削条件选取。表3.1为根据生产经验推荐的数值，因此选取d=32mm。表 3.1 成形铣刀的孔径（mm）铣削宽度铣刀孔径一般切削重切削613136121622122522272540273240603240601004050（4）初选铣刀外径在保证铣刀孔径足够大和铣刀刀体强度足够的条件下，应选取较小的铣刀外径。铣刀的外径应符合下式11麻花钻螺旋槽加工及其成形铣刀设计2H2mdd0式中 d铣刀孔径；m铣刀刀体壁厚，一般取m=（0.30.5）d：H容屑槽高度。由于H 的计算又需依据外径0d，因此，在设计铣刀时，可先用下式估算外径，待确定了有关参数后再按上式校验铣刀强度。mmhd)62(2 . 2)2 . 22(d0对加强型容屑槽，铣刀外径可取得略小，即mm622)26 . 1 (0）（hdd由于铣刀高度较大，可取较大直径故160mmd0。（5）初选铣刀齿数 在保证刀齿强度和足够的重磨次数的条件下，应尽力取齿数多些，以便增加铣削的平稳性。齿数z 与铣刀直径之间有如下关系：tdz0式中 t铣刀的圆周齿距。粗加工时，可取 t=（1.82.4）H；精加工时，可取t=（1.31.8）H。 由于H 的确定需根据齿数，所以在设计铣刀时，可以根据生产经验按铣刀的大小预选铣刀齿数，在设计计算出铣刀的其它结构后，再校验所选齿数是否合理。表 3.3 是根据生产经验推荐的铲齿成形铣刀的齿数。此表适用于平底式容屑槽的不铲磨铣刀。对于加强式容屑槽，齿数可适当增加，对铲磨铣刀，齿数可适当减少。表 3.2 铲齿成形铣刀齿数铣刀外径0d4040455055607580105110120130140150230铣刀齿数0z18161412111098为了测量方便，一般宜将齿数取为偶数。但在铣刀齿数较少的情况下，若增加或减少一个刀齿，将对刀齿强度及可磨次数产生较大影响。在这种情况下，可取齿数为奇数。12由于铣刀的初选外径为160mm，再根据表格得8z0。（6）铣刀的后角及铲销量的计算铲齿成形铣刀通常给出进给方向的后角fa，一般可取fa=1015。确定后角后，可按以下公式确定铲销量：f0tanazdK故取后角。，12mmK12af（7）确定容削槽尺寸容削槽槽底半径可按下式计算：2AzKh2-d0）（r式中A一般不铲磨齿背的成形铣刀，或齿廓高度 h 不大的成形铣刀，可取 A=6 。计算出的r 应圆整为0.5mm 的倍数。容屑槽角 值应按加工容屑槽所用的角度铣刀的系列选取，一般取为 22、 25、 30等。 当铣刀齿数少时选大值。少数情况下，可取 为 45, 如梳形螺纹铣刀即是。容削槽深度H 应能保证铲齿时铲刀或砂轮不致碰到容削槽底。 对于平底式容屑槽，铣刀的容屑槽深度可用下式计算：H=h+K+r故取r=3mm，=25 ，H=35mm 容屑槽槽底的形式和深度如图 3.3 所示图3.3成形铣刀容屑槽槽底（8）确定分屑槽的尺寸当铣刀宽度B20mm 时，可按表3.4推荐的尺寸和数目在切削刃上做出分屑槽。由于相邻刀齿的分屑槽需交错排列，因此，取铣刀齿数为偶数，铲削时，隔一齿铲削一次。故分屑槽R=2，数量为 2。13麻花钻螺旋槽加工及其成形铣刀设计表 3.3 成形铣刀分屑槽尺寸和数目铣刀宽度/B分屑槽距/至端面距离/1p分屑槽数2084222942241042251052281162301262321362（9）检验铣刀刀齿强度对于平底式容屑槽，可以根据下式进行计算齿根宽度c：k0z2H-d2.5c）（要求Hc0.8，经上式计算，c=0.8040.8。（10）校验刀体强度为保证刀体强度，要求m0.3d。m可按下式计算：220dHdm故 m=290.3d，刀体强度符合要求。（11）确定内孔空刀尺寸及键槽尺寸内孔空刀尺寸如表3.5所示，键槽尺寸如表3.6 所示。表 3.4 刀具内孔空刀尺寸公称尺寸 d131619222732405060以上14公称尺寸 L1l225677882467788882667799910286779991130789910101112357891010111213408991111121314459101012121314155091111121314151618表 3.5刀具内孔心轴及键的尺寸公差dbl1lr1r尺寸偏差尺寸偏差尺寸偏差尺寸偏差826.700.10-8.90.1000.400.10-0.1600.08-1038.211.51311.214.616413.217.70.600.20-15麻花钻螺旋槽加工及其成形铣刀设计19515.621.11.000.30-0.2500.09-22617.624.127722.0 00.20-29.80.2001.232827.034.8401034.542.50.4000.02-3.4 成形铣刀的技术条件成形铣刀的技术条件（1）表面粗糙度刀齿前面、 内孔表面、 端面及铲磨铣刀的齿背表面不大于0.8；m铲齿铣刀的齿背面不大于1.6；m其余部分不大于6.3m。（2）尺寸公差铣刀主要结构尺寸见表3.7。表 3.6 铣刀主要结构尺寸公差序号名称符号公差1铣刀外径0dh152铣刀宽度Bh123铣刀孔径dH7（3）成形铣刀的形状位置公差铣刀的形状位置公差见表3.8。表 3.7成形铣刀的形状位置公差序号项目铣刀尺寸公差1切削刃的径向及端面跳动100d0100d00.030.042刀体端面跳动100d0100d00.020.03163零度前角铣刀前端面的径向性30H30H2020H1010H0.040.060.090.12（4）齿形公差铣刀的齿形公差可大致取工件廓形的1/21/3。（5）材料及热处理成形铣刀材料采用高速钢W2Mo9Cr4VCo8。热处理后硬度66HRC。在铣刀的工作部分，不得有脱碳层和软点。3.5 成形铣刀工作图成形铣刀工作图见附件。3.6 小结小结本章节主要介绍了加工麻花钻螺旋槽的成形铣刀廓形的设计方法，确定了铣刀廓形的计算方法，并根据铣刀的廓形确定了其基本的结构与参数，最后确定了铣刀的技术条件，并根据设计的形状与参数绘制了成形铣刀的工作图。17麻花钻螺旋槽加工及其成形铣刀设计第四章麻花钻与成形的建模和仿真第四章麻花钻与成形的建模和仿真4.1ug 的概述的概述Unigraphics 该软件目前在国内外应用极其广泛，其功能十分强大，包括了设计，分析，加工等各个领域，并且可以在各种系统环境下使用。它是一个交互式的计算机辅助设计和计算机辅助制造系统，含有当下机械加工所需绝大多数制图和工程设计功能。 此外，它也是一个双精度、 全三维的造型系统，让使用者能够轻松得绘制出各种物体，通过对这些物体的组合，可以对产品进行设计分析。Ug 还可以为工程师提供机完整的械设计与模具设计方案，其中包括设计，分析以及制造。除此之外，该软件实现了完全参数化，能为工件的系统化建模提供巨大的支撑。当一个产品在开发时，它可以管理该产品的所有数据，并根据这些数据实现并行工程与逆向工程。它也能实现复杂曲面或者螺旋面的建模，并且对图形显示采用了区域化管理方式，有效地减少了系统的使用率，节约了系统资源。ug的装配功能及其丰富与强大，通过各种约束关系能轻松得完成各种装配，极大地减少了设计时间，提高了设计的效率。 Ug的运动仿真模块十分便捷，通过对各个工件进行连杆特性的定义，能做出各种复杂的运动。Ug 的操作界面十分得简洁明了，处处透露着以人为本的设计理念，对于初学者十分友好，能使用户很快得掌握该软件的一些常用操作，极大得提高了工作与学习的效率。 Ug含有建模，装配，加工，仿真，有限元分析等多种模块，通过这些模块用户可以方便地进行机械设计。4.2 刀具的建模刀具的建模4.2.1 麻花钻的建模麻花钻的建模（1）打开ug8.0选择新建，在模板中选择模型，将基座标系调整为显示，并选择拉伸指令，任选一个面为草绘面绘制一个直径为40的圆形，如图4.1 所示。18图 4.1 麻花钻草绘截面（2）使用编辑指令中的螺旋线指令，选择圈数为2，螺距为138mm，半径为20mm，选择完成创建出螺旋线如图 4.2所示。图 4.2 螺旋槽螺旋线（3）垂直于螺旋线创建一基准平面并绘制麻花钻螺旋槽截面草图如图4.3所示。19麻花钻螺旋槽加工及其成形铣刀设计图4.3，麻花钻螺旋槽截面（4）在插入指令中选择扫掠，以草绘图为截面，螺旋线为引导线，并勾选保留截面形状，矢量方向选为z 轴方向，完成扫描图形如图 4.4所示。4.4螺旋槽扫描截面（5）选用插入指令中的布尔运算求差，目标体设置为圆柱，刀具体设置为扫描截面，求得图形如图5.5所示。204.5扫描截面与圆柱进行求差运算图形（6）选择草图绘制指令在圆柱面上绘制草图，倒出前刀面的118角，草图如图4.6 所示。4.6 前刀面草绘图（7）使用旋转指令，并以草绘图形为截面z 轴为矢量轴，对其进行旋转，并选择布尔运算求差，得出的几何图形如图4.7所示。21麻花钻螺旋槽加工及其成形铣刀设计4.7 前刀面的绘制（8）通过阵列特征模块，选择螺旋槽截面为阵列特征，矢量方向选择麻花钻的轴向，阵列定义布局选择圆形，数量选择为2，节距选为180度，最后进行布尔运算求差将目标体设置为圆柱，刀具体设置为阵列截面，得出图形如图4.8所示。4.8 螺旋槽的阵列4.2.2 成形铣刀的建模成形铣刀的建模（1）打开ug8.0选择新建，在模板中选择模型，将基座标系调整为显示，选择草绘指令，任选一个基准面为草绘平面绘制铣刀的旋转截面如图4.9所示。22图 4.9成形铣刀总体旋转截面草绘图（2）使用旋转指令，将草绘图形设置为旋转截面，并以z 轴为矢量方向，布尔运算为无，创建出旋转体如图4.10所示。图 4.10草绘图形旋转截面（3）使用草绘指令，以铣刀端面为草绘平面创建草绘图形，并在此面上绘制草绘图形，创建出铣刀刀背与容屑槽的基本形状，草绘图如图4.11所示。23麻花钻螺旋槽加工及其成形铣刀设计图4.11铣刀刀背与容屑槽草绘图（4）选用拉伸指令并将草绘面作为拉伸面，z 轴作为矢量方向并选择反向，然后选择布尔运算为差，拉伸出的图形如图4.12所示。图4.12 铣刀容屑槽与刀背截面的拉伸图形（5）通过功能表中的阵列功能，选择阵列的特征为拉伸特征，布局为圆形，旋转轴的矢量方向设置为z 轴，并将数量和节距分别设置为 12与30度，得出的阵列特征如图 4.13所示。（6）选择草绘指令创建刀具内孔截面，内孔半径为16，然后选择拉伸指令以草绘截面为拉绳面，z 轴为矢量方向，并进行布尔求差计算，创建出内孔图形如图4.14所示。24 图 4.13铣刀总体形状 图 4.14 铣刀内孔（7）使用边倒圆指令选择内孔的两条边 进行倒圆角处理，圆角半径设为1;再使用倒斜角指令，选择内孔两段面的边，并将参设设为斜角边为1，角度为45度，最后得出的铣刀的内孔的几何图形如图4.15所示。图4.15铣刀内孔的圆角与倒角4.2.3 其它部分的建模其它部分的建模由于要对成形铣刀加工麻花钻进行运动仿真，故建立了工作台以及铣刀轴。（1）铣刀轴的建模：使用旋转指令并在旋转指令中绘制草图，草图绘制完成后选择垂直轴为矢量方向，获得铣刀轴如图4.16所示。25麻花钻螺旋槽加工及其成形铣刀设计图 4.16 铣刀轴（2）工作台的建模：先在平面上使用拉伸指令建立一个底座，并在两侧使用拉伸指令创建出分度机构的外形，最后在分都机构的内侧拉伸出麻花钻与其配合的内孔，完成工作台的建模如图4.17所示。图 4.17 工作台4.3 工件的装配工件的装配（1）麻花钻与工作台的装配：创建一个新的文件选择并装配模块，在装配模块中添加组件工作台，将其约束设置为绝对原点创建到装配界面中，之后添加新26的组件，将麻花钻添加到装配组件中，并使用同心约束将其与工作台装配（如图4.18）。4.18麻爪钻与工作台的装配（2）铣刀与铣刀轴的装配：新建一个装配文件，在该文件中添加组件铣刀轴，将其以绝对远点进行定位，之后将铣刀导入到文件中并将铣刀的定位设为同心，装配图如图4.19所示。4.19 铣刀与铣刀轴的装配（3）铣刀与麻花钻的装配：新建一个装配文件，将铣刀与铣刀轴装配文件导入，选择其为绝对原点，并将麻花钻与分度机构的装配文件导入并进行约束，装配图如图 4.20。27麻花钻螺旋槽加工及其成形铣刀设计图4.20 麻花钻与成形铣刀的装配4.4 运动仿真运动仿真ug 的运动仿真模块十分强大，通过对工件的设定不同的连杆特性与参数，可以模拟各种复杂的三维运动，以下为铣刀加工麻花钻螺旋槽的运动仿真具体过程。（1）使用先前的麻花钻与铣刀的装配模型，进行仿真。（2）新建一个连杆将铣刀轴设置为固定连杆（3）新建连杆将成形铣刀设置为连杆。（4）新建连杆将麻花钻设置为连杆。（5）新建连杆将工作台设置为连杆。（6）新建运动副，并将运动副设为旋转副，并选择铣刀，指定x轴为方位，并勾选咬合连杆，将铣刀的中心点设为原点，并制定x轴为方位。（7）选择驾驶员将并速度设为恒定600。（8）新建运动副将麻花钻设置为圆柱副，并选择其端面中心为原点，其法向为方位。（9）选择驾驶员将速度定为恒定3000。（10）新建运动副滑动副并选择工作台，设计工作台中心为原点，指定工作台端面法向为方位，然后选择铣刀轴为咬合连杆，设计工作台中心为原点，指定工作台端面法向为方位。（11）选择驾驶员速度恒定为 1400。（12）新建运动副选择麻花钻为螺旋副，设计麻花钻端面中心为原点，指定麻花钻端面法向为方位，设置螺纹模数比为-138.5640-确认。（13）选择插入解算方案然后将时间设置为0.22，步数为20。28（14）选择结算中的系统自动计算。（15）选择动画播放并将其保存。以上步骤为成形铣刀加工麻花钻的运动仿真具体步骤，具体视频可点寄该链接进行播放。（播放视频）4.5 小结小结本章主要介绍了ug的一些基本概况以及其一些常用功能的使用方法，并通过这些功能完成了成形铣刀、 麻花钻、 工作台、 铣刀轴等工件三维模型的创建。 之后又使用了 ug中的运动仿真功能，通过对麻花钻等工件连杆特性的定义，完成了成形铣刀加工麻花钻的运动仿真。29麻花钻螺旋槽加工及其成形铣刀设计第五章总结第五章总结5.1 总体评价总体评价通过对麻花钻螺旋槽加工及其成形铣刀设计，深入了解了加工麻花钻成形铣刀的结构与形状，并通过对成形铣刀的设计，学习了成形铣刀廓形以及其结构参数的设计方法。此外，通过使用ug对麻花钻以及成形铣刀的建模，熟练掌握了拉伸、旋转、扫描等ug的基本建模功能。此外，通过对成形铣刀加工麻花钻的运动仿真，深入学习了ug的运动仿真模块，熟练掌握该软件的运动仿真操作方法。 在设计过程中，遇到了各种各样的难题，通过查找文献学习了他人的经验以及设计方法解决了设计难点，并明白了查找文献的重要性，通过他人的知识总结，能极大得提升设计效率，并学得他人的知识与经验。在设计成形铣刀的期间，多次运用了大学期间学习到的课程知识，并复习了互换性，机械设计，机械制图，creo，cad等课程。 通过这些课程的学习，毕业设计的能力有了极大的提高，并加深了我对该课题的理解。此外，暴露了自己专业课程的缺陷，并且缺少将各个课程综合应用的能力，软件运用也很不熟练，因此更应该在以后的工作中努力学习，成为一个对社会有贡献的人。总的来说，在这一次毕业设计中，我的个人设计能力得到了巨大的提升，并且查找文献能力的以及三维软件的运用水平得到了巨大的提高。5.2 成果展望成果展望麻花钻是大家日常工作与生活中最常用的孔加工刀具，其需求量极其巨大，设计合适的成形铣刀来加工麻花钻的螺旋槽能极大得提高麻花钻的生产效率，增加麻花钻的产量。由于采用的是铲齿型成形铣刀，刃磨十分方便，进一步提高了麻花钻的生产效率。然而，本设计的不足之处在于未能解决麻花钻螺旋槽尾部的加工方法，有待进一步的设计合适的刀具或者加工方法加工麻花钻螺旋槽的尾部。30 参考文献参考文献1王明华.麻花钻优化设计的发展现状J.工程技术 .2010：55-602王凯.标准麻花钻螺旋槽的三维建模及虚拟加工研究J.机械研究与应用.2011：45-673朱凌云,高阳.基于UG的麻花钻螺旋槽曲面数控仿真加工研究J.甘肃农林大学学报.2013：105-1434孙业龙，姚斌.麻花钻螺旋槽的虚拟加工仿真J.机械设计.2011：23-375杨佳.麻花钻螺旋结构的性质J.丹东纺专学报.2000：65-706梁萍.成形铣刀廓形的精确设计和制造J.机床与液压.2008：23-247奚威.设计螺旋槽铣刀的cad方法J.工具技术.1995：23-448戴俊平.麻花钻前刀面的研究J.煤矿机械.2011：88-899刘世瑶.深孔麻花钻的端截形及螺旋面的加工j.河北冶金.2002：13-2510S.L.Xiao,Z.X.Zhou.Parameter-design and experimental study on small-diameter solid carbide deep-hole twist drillJ.Trans Tech.2012：3-1031麻花钻螺旋槽加工及其成形铣刀设计致谢致谢在本次论文设计过程中，感谢我的学校，给了我学习的机会，在学习中，指导老师周老师从选题指导、论文框架到细节修改，都给予了细致的指导，提出了很多宝贵的意见与推荐，老师以其严谨求实的治学态度、 高度的敬业精神、 兢兢业业、孜孜以求的工作作风和大胆创新的进取精神对我产生重要影响。 他渊博的知识、 开阔的视野和敏锐的思维给了我深深的启迪。这篇论文是在老师的精心指导和大力支持下才完成的。感谢所有授我以业的老师，没有这些年知识的积淀，我没有这么大的动力和信心完成这篇论文。感恩之余，诚恳地请各位老师对我的论文多加批评指正，使我及时完善论文的不足之处。谨以此致谢最后，我要向百忙之中抽时间对本文进行审阅的各位老师表示衷心的感谢。32附录附录A 外文文献外文文献Geometry design model of a precise form-milling cutter based on the machiningcharacteristicsAbstract This paper presents a new approach to design a form milling cutter forprecisely obtaining the complex free-form surfaces. In this study, the intersection point ofthe rake surface, helix flute and clearance flank is appropriately defined due to itssignificant role in the design and grinding performance. The angle-solid-block analysis isdeveloped to establish the new cutter geometry model. Hence, a new form-milling cuttersatisfying the requirements of machining characteristics of workpiece can be designed. Inaddition, the cutter geometric model can be adopted to map out the measuring strategywith minimum measured points to attain the exact geometric feature of cutter.1 Introduction1.1 Motive of researchA multifacet drill (MFD) with multifacet and multiflanks has been distinguishedfrom its significant characteristics such as lower cutting forces, better heat transfer, moreaccuracy, longer tool life, higher productivity, etc 1. A three-axis milling machine with aball-nosed milling cutter is the familiar method in the free form surface milling process.However, its precision has less refinement than a five-axis milling machine with an endmill. In every milling location, the coincidence between tool axis and surface normal forfive-axis milling process has better performance than three-axis process. If thecoincidence between tool axis and surface normal is identical, it is referred to as beingalways normal; the term “quasi-normal” is proposed to describe the relative normaldegree. In this case, the consideration of milling characteristics and application to multi-axis degree of freedom has to be taken into account to help design a ball-nosed millingcutter with multifacet and multiflanks. Accordingly, it leads to better geometric precisionand geometric compatibility of workpieces, and this milling cutter is called a formmilling cutter in this study. Therefore, a geometric design model for precise form millingcutter is the main purpose of this study.This study probes into the modeling research of cutting edge geometry to drive offthe problems of surface normal vectors, which are different from point to point based onthe concepts of always normal and quasi-normal. Accordingly, the inspection method isdeveloped to verify the theory and performance of modeling.1.2 Review33麻花钻螺旋槽加工及其成形铣刀设计In order to exactly solve the above problems, both the cutter and workpiecesgeometric characteristics have to be verified and unified at first. Glaeser, Wallner andPottmann 2 made a concept definition for workpiece characteristics, but thecorresponding cutter characteristics have not been well defined. The method of alwaysnormal (named as axis milling by Baptista and Simoes 3), proposes that the spindle isnormal to the free-form surface on the cutting point in the workpiece. Baptista andSimoes showed some larger scallops were left and then replaced the ball-nosed end millby an end mill inclined in the feeding direction to reduce the scallop dimension.However, it was not suitable for 3-axis milling.Lee and Chang 4 used the 2-phase approach with 4-th and 5-th axis postures toavoid the global cutter interfer-ence caused by the cutter and its holder. A method byYoon et al. 5, presented locally optimal cutting positions for cutting directions on the 5-axis sculptured surface machining. The cutter positions can guarantee local gougingavoidance. Both 4 and 5 briefly described the limitation of cutter posture in the 3-axismilling processes. Glaeser 2 offered an idea on selecting a cutter of collision-free 3-axismilling for free-form surfaces, but the cutter design has never been studied. Regardingthe suitable tool-path of 3-axis milling on free-form surface, Park and Choi 6 describeda direction-parallel method and Park 7, 8 proposed both characteristic contour and z-map methods. Nevertheless, the geometric relationship between the cutting edge and theworkpiece was not fully described.Tsai and Wu 9 showed the quadratic surface flanks for drill point design andgrinding. Fujii et al. 10 defined the cutting edge of drill geometry as wire framealgorithm. Wu and Shen 1 derived the configuration of the multifacet drill. All of theabove cutter geometric models were analyzed by the analytic geometry method. Then,Wang et al. 11 investigated the geometry of a multifacet drill with a new approach - theangle-solid-blocks method. This study analyzed the relationship of the geometry of thedrill-tip, flanks and straight cutting edges and then found the relationships of the cuttingparameters, which depend upon one another. However, the approach 11 has not yetdeveloped the angles-relation of the cutter geometry for the generation of curved cuttingedges, multi-segments edges and flutes. So a new modeling method for the form millingcutter is still required.Bradley and Chan 12 used reverse engineering in the inspection of a ground cutterwith a touch probe and laser scanning. But they still lacked the better method formeasuring the geometry of cutting edge.1.3 Guidance of researchThe intersection of rake surface, helix flute and clearance flank is defined as PN andalso the connected point of the cutting edge and side cutting edge. It plays an important34role in the design and grinding of the milling cutter. The first step of the research is todefine the nominal relationship of the cutting tool as shown in Fig. 1. The correlationbetween PN and the adjoining cutter geometry has to be taken precisely into account,otherwise it results in inaccurate geometry for grinding due to the parameters interferencementioned by Wang et al. 11. Therefore, PN is taken as the prerequisite key point for thefollowing designing, grinding and measuring methods.Fig. 1 The defined characteristic points along the cutting edge of a precise form-milling cutterOne of the key terms of the precise milling is that form accuracy can be improved ifthe cutter point on the cutting path is kept as normal to the cutting surfaceas possible. If any cutting position of the cutter allows the workpiece to be quasi-normal in the3-axis machining process, then some strategies need to be studied. The 4-th axisinclination has an important effect on the geometry of the cutter projection-profile so thatthe manner of 4-th axis is incorporated directly into the cutter design. For improving thecutter precision of 3-axis precise milling, it is attempted to impose both 4-th and 5-thaxes movement degrees of freedom and the relative characteristics on the cuttersgeometric design. An inspection method verifies the geometric quality of the cutter with the measuredcharacteristic points through reverse engineering. Additionally, the angular-solid ap-proach 11 for proving the relationships among the cutters design parameters isrequired. Then it has been realized that once the minimum of measured characteristicpoints have been defined, where the accuracy of the design parameters of N-segments-edge form the milling cutter, can be verified by the re-modeling process of reverseengineering. A new approach is developed in this work based on the specification of machiningcharacteristics. In this research, some workpieces geometries are taken as practicemachin-ing characteristics. A precise form milling cutters CAD solid geometry model is35麻花钻螺旋槽加工及其成形铣刀设计designed according to the geometrical characteristics as described above. The cuttergeometric models are then constructed by the rapid prototype (RP) method called 3Dprinting. Finally, the accuracy is verified by the least amount of measured characteristicpoints satisfying the requirement and fitting in the relationship among design parameters.Hereby, a cutter with more complicated features is designed, based on the research so thatthe geometrys reliability is advanced concretely and feasibly. Furthermore, for the total solution oriented objects, there must be an effectiveapproach to develop a model for design, grinding and inspection. 2 Normal algorithm Based on the machining characteristics of the workpiece, the major normal vectorinterval is defined, and a multi-segment cutting edge by the utilization of fewcharacteristic points, such as a threshold point or control point in the interval, isaccordingly designed. The characteristic point has to be always normal and regarded asthe basis information for forming the cutting edge, according to the adoption of thisstudy. However, the projection-profile of each adjoining characteristic point has to fit inwith the condition of quasi-normal and becomes the major issue of this section. 2.1 Classification of always normal 2.1.1 Hermite curve Faux and Pratt 13 demonstrated the advantage of piecewise Hermite interpolationto easily get the first-derivative continuity without causing severe oscillation problems.They also mentioned the main disadvantage that the gradient values is hard to find. Whilein this paper, each characteristic point can actually define the normal condition on the 2D(two dimensional) projection-profile of the cutter and the tangent vector which isperpendicular to the normal vector. 2.1.2 Arc The arc, similar to Hermite curve, also has the first-derivative continuity, but itcauses a severe oscillation problem. Its main advantage is suitable for defining the multi-arc edge milling cutter 14. The normal vector is derived by linking the arc center to thetarget cutting point. 2.2 General equations available for quasi normal 362.2.1 Brief expressions of projection-profile and cutting edge The milling cutter can be formed by grinding or turning as a revolved-body 15.Then, flutes, rake surfaces, clearance surfaces and the other surfaces of the cutter areground sequentially. The continuous projection-profile of the cutting edge is divided intosome segments as piecewise continuously in the next step - called N-segments edge. Thedefinition of N-segments edge profile is shown in Fig. 2 - a 2D half projection-profile ofcutter in XProf, YProf coordi-nate system (local coordinate system). The more N-seg-ments,the larger the database of cutter model, and the better the accuracy of the geometry. 2.2.2 Quasi normal for the cutter geometry with N-segments edge The general design model can be derived from the relationship between the cutterdesign parameters and the projection-profile of N-segments edge. The fundamentalgeometry of the N-segments edge described in Fig. 2 can be illustrated in the form ofFergusons parametric cubic curves. Each segment of cutting edge can be expressed as 13, 16:)(1 ()2)(0()32)(1 () 132)(0()(23232323ttrtttrttrttrtrFig. 2 Definition of the half projection-profile in the x-y profile coordinate system (local coordinate system). n: normal vector. Pprof i: characteristic point i on half projectionprofile3 The geometry characteristics of both workpiece and cutter 37麻花钻螺旋槽加工及其成形铣刀设计To choose or design a suitable cutter by both analyzing and surveying the geometriccharacteristic of the workpiece is much more beneficial for precisely milling the free-form surfaces. 3.1 Definition of the geometrical characteristics between workpiece and cutter There are some assessments and definitions obtained by the following procedures.By studying on the definition for the geometry characteristics of workpiece, a propershape of cutting edge will be developed for promoting the precision in 3-axis milling upto the 4-axis or 5-axis milling has, and the cutting edge will be designed as properlypiecewise division. For a case the 3-axis milling on free-form surfaces, Fig. 3a shows the existingmethod without the spindle tilt axis. Regarding the conditions in Fig. 3a, it is necessary todefine as a milling characteristic for designing a proper cutter. For a cutter without thetraditional concept, as shown in Fig. 3b, its projection-profile can be determined byscaling up or down from the workpieces projection-profiles, which are suitable in thefinish milling. 3.2 Main approach of designing the high-accuracy form milling cutter 3.2.1 Definition of the characteristic points of cutter projection-profile The sketch map in Fig. 4 shows the position on the cutting location of the 3-axismilling with normal vectors of workpiece and cutter. This is an improved type z-constantcontour machining from the methods of Park 7, 8. By this machining approach, asuitable projection-profile of cutter is regarded as the design goal. The basic position-calibration points including the cutter tip (coordinate origin) andthe point PN, and the character-istic points on the projection-profile of the cutter, greatlyinfluence the cutting efficiency. The normal vectors or tangent vectors are defined on thecutters characteristic points.38Fig. 3 Schematic illustration of the 3-axis milling on the freeform surface: (a) theexisting method; (b) the cutter projection-profiles designed based on the characteristics ofworkpiece geometry3.2.2 Projection-profile of cutter mapped by the workpieces characteristic points A significant goal of this research is dedicated to satisfying the requirements - theleast characteristic points of cutter and the minimum workpieces geometry error. Anavailable mathematical model is herein developed for finding the interval coordinatevalue between any two neighbouring characteristic points. And also be applicable forverifying the inspection stratagem. The characteristic points of the workpiece can be mapped to the 2D projection-profile of cutter. For always normal, any two adjacent characteristic points will be linkedby a Hermite curve. 3.2.3 Determination of tangent vector on the characteristic point The projection-profile of cutter is expressed as a piecewise continuous type ofHermit curves in the x-z 2D coordinatesystem. From the numerical method and theassumption of dx0, the 2D coordinate of the characteristic point on projection-profilehas a general form of (x, z(x). The point (x+dx, z(x+dx) is near to the characteristicpoint at the designed Hermite curve. The derivative is set as x=dx, )()(xzdxxzz.Therefore, the tangent vector on the i-th characteristic point is39麻花钻螺旋槽加工及其成形铣刀设计LzxztzLzxxtxiitiiii2222)(,)( (2)where, L is the average chord length among the three characteristic points),(),(),(1111iiiiiizxzxzx,as given by21212121)()()(21Liiiiiiiizzxxzzxx）（ Fig. 4 Modified z-constant contour machiningSubstituting Eq. (2) into the general Eq. (1) yields a simplified 2D projection-profile, and the tangent vectors of the two ends of a Hermite curve are obtained as ) 1 (),1 (),0(),0(11iiiiiiiiizzzxxzzxx.As mentioned above, the equations of the N-segments Hermite projection-profile arenecessary for precisely designing a quasi-normal form-milling cutter. Therefore, thedefinitions are extremely important in the processes of designing, grinding, inspectionand tool path simulation.4 Design processes and computer-aided modeling of cutter geometry The flow chart, as shown in the left part of Fig. 8, illustrates the continuousprocesses from the projection-profile defi-nition of the cutter to the NC path decision forgrinding the clearance surfaces. It is less easy for searching the gradient values of 3DHermite curves. The gradient values of the Hermite curves, including 3D cutting edgeand NC grinding path, must be able to be calculated only by the 2D projection-profiledefinition. Therefore, a series of program-ming processes needs to be developed.4.1 Cutting edge geometry 40For describing the accuracy of the cutting edge, the coordinate value needs to beobtained from any position of the cutting edge. From the given characteristic point Pi(xi,0, zi) of the projection-profile, a relationship mapped on the cutting edge for developingcharacteristic point Qi(Xi, Yi, Zi) is expressed in the following equations:Fig. 5 Combination of angle-solid-block OPNO1Q and tool solid model for performing coordinate transformation into a inspection gestureFig. 6 Flow chart of the design processes and the geometry constructionBased on the developed equations of projection-profile and rake surface (Eq. (4), itis possible to derive the Hermite equations of the cutting edge.41麻花钻螺旋槽加工及其成形铣刀设计 A more close neighboring point approaching to Qi on the cutting edge is defined as Qi(Qix, Qiy, Qiz), and the tangent vector of the i-th characteristic point is expressed asLdLQZLiziiyiixi,dLQ-YLdLQ-X， （11）where dL is the length of iQQi and 1iiQQLi is chord length.Accordingly, the coordinate values and tangent vectors, described by Eq. (11), of thetwo adjacent characteristic points are substituded into the general Eq. (1) of Hermitecurve. The geometry equations of the piecewise continuous cutting edge can be derivedexactly and piecewisely. 4.2 Grinding path for cutting edge with quasi normal The matrix form is suitable for representing the coordinate transformation. The relationships between different forms of coordinate systems XYZ (globe) and XgYgZg (grinding), need to be developed. The coordinate systems XgYgZg is the same as XMYMZMshown in Fig. 7. Thus, the key matrix M is the product of two coordinate transformation matrixes, RZ (S) and RX ().The transformation matrixes are useful in the jug-calibration process for grinding theclearance surfaces. The askew plane OPNQ on the angle-solid-block OO1PN Q, as shown in Fig. 6a, canbe set for being coincident with orthogonal plane y=0 after the angle-solid-block OO1PNQis rotated twice. The angle-solid-block QPOON1，as shown in Fig. 6b, is obtained byrotating the angle-solid-block QPOON1 an angle s about Z-axis. The angle-solid-block42QPOON 1an angle about X-axis. In the Fig. 6c, the Y-coordinate values of pointQPN and are equal to zero.From the above verification illustrated in Fig. 6, any point or vector (e.g., acharacteristic point and tangent vector on cutting edge) on the rake surface can betransformed to locate on the plane y=0 according to Eq. (12). Therefore, a group of new2D Hermite curves (y=0) for NC grinding paths of clearance surfaces can be successfullydesigned. 4.3 Computer-aided modeling The flow chart, as shown in the right part of Fig.6, shows the feature-based solidmodeling processes, taking into the grinding sequence of the cutter. The main processesincluding the grinding sequence are described as follows. 4.3.1 Parameters selection The cutter design parameters, as shown in a template of Fig. 7, are classified intoexternal and internal parameters. 1.External parameters for constructing N-segments cutting edgeA N-segments cutter, consisting of characteristic points (P0(x0, z0), P1(x1, z1), P2(x2, z2),.,PN,(XN, ZN) and normal vectors and diameter D, is similar to the main projection-profile as shown in Fig. 2.2. Internal geometry parametersThe parameters are classified as design and grinding parameters (as shown in thelocal left part of Fig. 7) for constructing various features of cutter model.43麻花钻螺旋槽加工及其成形铣刀设计Fig. 7 Geometry parameters of a quasi-normal form-milling cutter with fourcharacteristic points (N=3)4.3.2 Angle-solid-blocks for computer-aided modeling Because the internal parameters cannot be straightly measured, the internalparameters for CAD modeling need to be obtained by using the angle-solid-blocksapproach. 1. Angle-solid-block of rake surfaceThe tetrahedron body OO PNQ is shown in Fig. 5. 2. Angle-solid-block of flute The cross section profile of the flute on plane z=h is defined based on the rakesurface. Figure 10a shows the angle-solid-block of flute. The grinding parameter (contain DD1PN angle DD1P2 of plane and) as a function of , LC,s D, , 0 can bedetermined from the angle-solid-block. 3. Angle-solid-block of clearance surfaceThe angle-solid-block based on the point PN, as shown in Fig. 10b, presents therelationship between the clearance angle 0 (for computer-aided modeling) and themeasured-clearance angle .44Fig. 8 Analysis diagram of angle-solid-blocks for creating primitives of the cuttermodel: (a) construction of the flute angle-solid-block based on the rake surface, thetriangle PND1D2 is recommanded for creating a basic cross-section of flute; ( b) angle-solid-block for creating side clearance angle45麻花钻螺旋槽加工及其成形铣刀设计Fig. 9 CAD solid model obtained by the subtraction operation: (a) half projection-profile and rough model; (b) rake surface; (c) flute and side clearance surface; (d) firstand second clearance surfaces, some modified surfaces, and fillet surfaces4.3.3 Boolean operation The processes are similar to those defined by Wang et al. 11. The modelingprocesses of the cutter model with the subtracting operation as shown in Fig. 11 areperformed through modeling a cutter solid by constructing as shown from Fig. 11ad.5 Conclusions 1.The unified geometry model is developed for the design, grinding andinspection of form-milling cutters. The model potentially satisfies the specifica-tionsof the geometric characteristics for various free-form surfaces. 2.For precision, each geometric checkpoint (PN) for designing, grindingand measuring cutters needs to be set on the same point. In addition, the rake surface should include the primary characteristic point PN. 3.Adding the 4-th and 5-th machining axis into the cutter design strategycan improve the accuracy. The accuracy achieved in the cutter of 3-axis machiningadapting this design strategy is higher than that of the conventional cutters.4.The geometries of cutting edges derived by the piecewise continuousHermite equations may fulfill the goal for constructing a cutter model.5.This research enables the cutting edges of existing cutters to be preciselyreconstructed, using the method of reverse engineering. Based on a fewcharacteristicpoints and the derivative values, the cutting edge of the existing cutter can be measured. 6.A derived unified model in the present study reveals that the projection-profile of the cutter can be more precisely obtained from the correct key parameters, S, h. This model is very useful for the quality management of the form millingcutter as well as the other tools. 7.The 3-axis form milling cutter is designed by the proposed methodincorporating the cutting behavior of 4-th axis. Accordingly, it can reduce theindentation effects caused by the dead point of the cutter. 8.More importantly, the coordinate values of any point on the cutting edgecan be obtained in the present study, being very useful for developing the forcemodel.46附录附录 B 中文翻译中文翻译基于加工特性的精密铣刀几何模型基于加工特性的精密铣刀几何模型设计设计摘要摘要：本文提出了一种设计一种形状铣刀的新方法，用于精确地获得复杂的自由曲面。在本研究中，由于其在设计和磨削性能上的重要作用，可以适当地定义耙面、 螺旋槽和间隙面的交点。 提出了一种新的刀具几何模型。 因此，设计了一种满足工件加工特性要求的新型铣刀。此外，还可采用刀形几何模型，以最小测点绘制测量策略，以达到刀具的精确几何特征。1 1介绍介绍1.11.1研究的动机研究的动机多面和多侧面的多面钻(MFD)具有较低的切削力、 更好的传热、 更准确、 更长的刀具寿命、 更高的生产率等特点。 三轴铣刀是在自由曲面铣削过程中常见的一种铣刀。 然而，它的精度比五轴铣床的精度要低。 在每一个铣削位置，五轴铣削加工过程中刀具轴与表面法线的重合性能优于三轴铣削加工。如果工具轴与表面法线的重合是相同的，则称其为常态;“准正常”一词是用来描述相对正规度的。 在这种情况下，考虑铣削特性和应用到多轴自由度的考虑，有助于设计多面和多侧面的球头铣刀。因此，它能提高工件的几何精度和几何相容性，而这种铣刀在本研究中称为成形铣刀。因此，该研究的主要目的是为精确成形铣刀的几何设计模型。本研究探讨了切削刃几何的建模研究，以消除表面法向量的问题，这些问题与点到点的不同，是基于始终正常和准正态的概念。因此，建立了检验方法，验证了模型的理论和性能。1.21.2审查审查为了准确解决上述问题，刀具和工件的几何特性必须首先得到验证和统一 。Glaeser、Wallner 和Pottmann2对工件特性进行了概念定义，但其对应的刀具特征没有得到很好的定义。 通常的方法(以巴普提斯塔(Baptista)和西莫(Simoes)3命名为轴铣3)，建议在工件上的切削点上的自由曲面上的主轴是正常的 。Baptista 和Simoes展示了一些更大的扇贝，然后用一个末端的铣刀在进给的方向上取代了球型的端铣刀，以减少扇贝的尺寸。但是，它不适合三轴铣削。Lee 和Chang4采用了四、五轴姿态的两相方法，避免了刀具及其支架造成的全球刀具干涉。一种由 Yoon等5提出的方法，提出了在5轴雕刻曲面加工中切削方向的局部最优切削位置。 刀具位置可以保证局部的刨削避免。 4和5简要描述了三轴铣削过程中刀具姿态的限制。Glaeser2提出了一种选择无碰撞三轴铣刀自由曲面铣刀的想法，但从未研究过刀具的设计。关于自由曲面3轴铣削的合适工具路径，Park 和Choi6描述了一个方向平行的方法和Park7, 8提出了特征轮廓和 z-map方法。然而，切削刃与工件之间的几何关系并没有得到充分的描述。Tsai 和Wu9展示了钻点设计和磨削的二次曲面侧翼。 Fujii等10定义了钻形几何的切削刃为线框算法。 Wu和Shen1推导了多面钻头的结构。 用解析几何方法对上述所有刀具几何模型进行了分析。然后，Wang等11用一种新方法研究了多面钻的几何结构角-固体块法。本研究分析了钻尖、侧翼和直切边缘的几何关系，并发现了切削参数之间的关系。然而，该方法11还未开发出刀具几何形47麻花钻螺旋槽加工及其成形铣刀设计状与曲线切割边缘、 多段边和长笛的关系。 因此，还需要一种新的成形铣刀建模方法。Bradley 和Chan12使用了反向工程，在地面切割机的检查中使用了探针和激光扫描。但是他们仍然缺少更好的方法来测量切削刃的几何形状。1.31.3指导的研究指导的研究耙齿面、螺旋槽和间隙面的交点定义为PN，也定义了切削刃和侧边切削刃的连接点。 它在铣刀的设计和磨削中起着重要的作用。 研究的第一步是定义切割工具的名义关系，如图 1所示。PN与邻接刀的几何关系必须精确地考虑，否则，由于Wang 等11所提到的参数干扰，会导致磨削的几何形状不准确。因此，PN被作为以下设计、磨削和测量方法的先决条件。图 1.精密铣刀切削刃上的特征点精确铣削的一个关键术语是，如果切割路径上的刀具点保持与切割面尽可能的保持正常，则可以提高成形精度。如果刀具的任何切削位置允许工件在三轴加工过程中是准正常的，那么就需要研究一些策略。四轴倾角对刀形轮廓的几何形状有重要影响，使四轴的方式直接与刀具的设计相结合。为了提高三轴精密铣削刀具的精度，尝试将 4