液压机械手设计方案

液压机械手设计方案1章液压机械手总体方案设计机械手总体设计方案拟定机械手能够独立地依据程序，自动重复操作。依据课题的要求，机械手需具备上料，翻转和转位等功能，并依据自动 承受直角坐标式，自动线呈直线布置，机械手在空中行走，依据增加，运动质量增大。1.1.1直角坐标式布局示意图 机身承受立柱式，机械手侧面行走，依据挨次完成上料、翻转、1.1.2立柱式机械手布局示意图 机身承受机座式，自动线围绕机座布置，挨次完成上料、翻转、工件等优点。1.1.3机座式机械手布局示意图总体方案选定液压缸通油，推动活塞带动杠杆机构合拢将工件加紧。其能够围着回转销轴转动。回转运动通过叶片式回转油缸的运动来实现。中掌握、反向运动敏捷等优点。0.5~1mm。具有构造简洁、传递扭矩大、传动效率高等特点。1.21液压机械手本设计的液压机械手有五个自由度，包括机械手的抓取、回转，手臂的拉而且编排和转变掌握程序简洁，使用便利。液压机械手主要参数设计：〔用于说明机械手主要性能的参数、规格参数〔标牌上标注的参数、液压参数〔液压系统设计参数。根本参数：1.抓重机械手的抓重是手臂所能抓取的物件的最大重量，而该液压机械手是用于R175外形参数250X170X140mm而柴油机机体选用的材料是铸铁，密度为0.01g/mm21.3，15Kg。自由度机械手的自由度标志着机械手所具有的功能大小，自由度越大，机械手动作3~4i

ipVii

ip65555即机械手的i5。运动速度0.1m/s。行程围机械手臂运动的行程围与机械手的抓重、坐标形式、驱动方式、运动精度等体的面域。位置精度重复定位精度。我们所说的位置精度是指重复定位精度。位置精度的凹凸取决于位置的掌握方式及机械书运动部件本身的精度和刚液压参数：油压设计校核液压系统参数是依据执行元件和泵的类型进展设计，依据拟加1.6MPa，液压泵的工作p1=0.3×106Pa，油液的泄漏系数取λ=1.1，抓取动作和回转动作所需的工作压力为p=1.1MPa，选用的流量为p4.5L/minppp1 1

MPaq q5L/minP P符合设计的要求。1.6MPa。2章执行机构的设计抓取机构的设计抓取机构的工作原理工业机械手的抓取机构又称手部，是用来直接抓取工件或握持工件的部件。完成抓取任务。夹持力的计算当机械手水平夹持工件时2.11水平夹持物体受力图依据手指受力分析，可得：M (F)0 NbRo1 2

H(b )6M (F)0 NbRbR

H(b )O2 1 2 6联立可解得：N(3L1)GH 2N 夹紧工件所需的力；G 工件的重力；L，H 尺寸。依据任务书的要求，代入G=15Kg,并取L=50mm,H=80mm。可得：N(3501)150356.25N80 2因工件在传输的过程中会产生惯性力，震惊等影响，故实际力1N NKK21实 机械效率，=0.85~0.95取=0.9K K1

=1.2~2 K1

=1.5K 工作状况系数，K2

1a/g1N NKK21

=356.25

1.51.5

890N实 0.9液压缸驱动力的设计计算2.12液压缸驱动手爪受力图P2RsinRhl RlCD由于hl COSl COS(180o)l COS()BC BC BCR”N实

cosP2Rsin

2lsincos Nlcos() 实由构造设计可得10o50o,120o,lCD

130mm，lBC

36mm。P2130sin10ocos50o890763N36cos160o10o,50o,120o,lCD

130mm，lBC

36mm。夹紧液压缸主要尺寸确实定D1.13 Pp1mP p1

系统工作压力取p1

1.6 N/mm2，m

机械效率取m

=0.97631.60.9D7631.60.9依据JB-826-66的标准，取D=30mm, d=10mm液压缸壁厚确实定pD依据

2pp 试验压力， p 8MPap p许用应力 压缸材料，可得=200MPa2.08300.15mm2200依据工艺的要求,取10mm液压缸外径及长度确实定：D D250mm0长度l(20~30)D0

取l60mm.液压活塞缸的设计：1.活塞液压缸D=30mm,d=10mm，10mml60mm3045d查机械材料手册可以得到：

=355MPa,b

=600MPa；s则b1.4

3551.4253.6MPa4F48904F4890253.6GB/T2348-1993D10mm4F

4890

10.5mmd2 102活塞杆的强度符合设计要求b活塞密封件承受标准件，所以活塞上开槽的尺寸就可以确定了。密封的作用。利用开槽圆螺母将其锁紧，圆螺母的选择：由于活塞杆的直径已确定为101mm，可以M8GB/T6179-1986可得：开槽圆螺母2x16Q215Q235。开口销本设计承受弹簧使抓取液压缸复位。依据弹簧设计计算公式：弹簧受力图依据弹簧的强度条件选择弹簧钢丝的直径：因弹簧在一般载荷条件下工作，可以依据第三类弹簧来考虑，现选用弹簧钢丝为C级，并依据D2

D28253 估量弹簧的直径为3mm，查表可得B 1570MPa，可以算得0.80.5 628MPaBBC=6则由：K4C10.6154610.615

1.258001.2566284C4 C 48001.256628FKC2dFKC2

1.6

3.92选取d”=4mm，查得 不变，故不变，取D25mmB则C256.2548001.268001.266.25628FKC2FKC2

1.6

3.88与原值相近，所以取d=4mm弹簧的大径D2

25429mm21k FFF 2 121

80018067.8177.5取G82023MPa则n

Gd438Dk3F

820233.248253

4.6取n5F0

FkF 1” K

8FD00 d3综合上述两式可得：”0

=106.48MPa<150MPa符合设计的要求。极限工作应力：取” 0.56lim B” 0.5615700879.2MPalim极限工作载荷：F

lim

585MPalim

8DKGB/T1239.6-1992选取弹簧的截面直径为4mm，中径为28mm，自由11mm。有效圈数为5圈。选用弹簧的材料为65Mn，弹簧硬度要到达45~50HRC.弹簧抓取液压缸端盖：液压缸端盖O型密封圈具有构造简洁，截面尺寸小，密封性能好，摩擦系数小，简洁制安装便利，价格廉价，可在-40~120C温度围工作，使用的速度围是果。部可用铸造。管道尺寸的计算和确定：油管的径是依据管允许的流速和所通过的流量来确定的：4qv4qv0式中：q——通过油管的流量;v0——油管中允许的流速。而压力管道的流速取v0

5m/sGB/T1047-1995v 3mm0管接头的选择：55°GB/T3747.1-1983可得：管接头回转缸设计动。考虑到摇摆缸的容积效率cv

和机械效率cm

，叶片式摇摆缸轴输出扭矩TTZbD d8 2 2

p1

pcm 8qZbD cv2d22式中：Z 叶片数；b----------叶片宽度；D 缸体孔直径；d 叶片轴直径；p 缸的进口压力；1p 缸的出口压力；2q 缸的输入量。1.6MPa0.2MPa。为了便利固定叶片，叶片轴的直径初步定为d=25mm回转缸剖面图片与叶片轴之间承受销进展定位为了便利拆装和修理选用螺纹圆锥销，底部的螺纹孔可起到拔销的作用查GB/T118-2023选取A型螺纹圆锥销GB/T118 6X螺纹圆锥销的，这种设计构造紧凑，操作便利，特别是对于液压系统能够集中掌握。0机械手抓取机构如下图，液压叶片回转缸的回转轴与液压活塞缸做成一个整体，使得构造便于检修和维护。机械手手腕部设计：2.2.1机械手腕部外观图H7m6H8的协作。f7通过活塞杆的直线运动来驱动机械手腕部转动。伸缩缸选择：考虑到该设计手腕部所需的回转扭矩较小，拟选用 YY_CA_B32-100-0.0001活塞杆外端形式选择：2.2.2活塞杆接头安装的构造为铰制接头，孔径为20mm，活塞杆的直径为20mm。液压缸用双耳环支座安装：2.2.3液压缸安装支座双耳环支座的参数如下图。机械手臂设计俯仰运动时驱动力的计算2.3.1手臂受力图M=Pbcos(1

+)1AD BCtan1 1 1 (ADBC)OD OD 1 11 1BCbcos1 1

a ODcbsin1 1arctan

bcosa11 cbsin1M=Pbcos(arctan

bcos1

a+)cbsin 11而P 活塞上的驱动力；P液压缸的工作力；D活塞缸的径；P 密封装置的摩擦阻力封P 非工作缸的油压〔背压〕被当手臂处在俯角2

的位置时，驱动力矩为：M=Pbcos(2

-)2AE AEtan 2 22 OE OCEC1 1AEB2 2

COB2

OCbcos2aOCc1ECAB2 2 arctan

bsin2bcosa22 cbsin2M=Pbcos(arctan

bcos2

a-)cbsin 220，驱动力矩为M=Pbcos(arctanba)c的偏重力矩、手臂启动时的惯性力矩以及各回转副的摩擦力矩，即MM偏

M +M惯 摩M手臂作俯仰运动时的偏心力矩，手臂上仰为正，下俯为负；偏M 手臂做俯仰运动的惯性力矩；惯M 手臂作俯仰运动时，各运动副的摩擦力矩；摩可以初步确定机械手臂的尺寸。2.3.2手臂对手臂受力进展计算2.3.3手臂受力校核x0FFxT0hy0NFyGFv0OM0Fv0.476Fh

0.392N0.241T0.2910Fv353NF 143Nh机械手底座机身设计运动中不会偏转。机身的设计如下图：2.4.1机械手底座具体设计机身底座的参数如下：2.4.2底座回转工作台设计回转工作台安装：回转工作台的箱体设计有光孔，并安底座。因此机械手的底座可以安放在HT200器来调定的。挡铁的设置主要是保证回转角度的精度。齿轮传动：2.5.1圆锥直齿轮传动的一对圆锥直齿轮将扭矩由沿水平方向转换成竖直方向。4540~50HRC。承受直尺锥齿轮，它具有齿形简洁，制造简洁，本钱较低等特点。齿轮的轴向定位和紧固。2.5.2齿轮轴向定位〔弯曲，失稳，转角。假设刚度缺乏，轴上的零件如齿轮，轴承等将由于轴力状况，构造布置和有关尺寸，验算弯曲刚度。轴选用的材料为45钢，通过调质处理，使硬度到达200~240HBS轴1d 计算剖面处轴的直径(mm)轴的许用应力(MPa)T 轴传递的额定扭矩(N·mm2)pnpn595500005955000035000

=18mm取安全系数S=1.5所以d=27mm 将轴径进展圆整，取d=30mm按许用弯曲应力来校核该轴：M2TM2T2d3 计算面上的工作应力M 计算截面上的合成弯矩T 轴计算面上的转矩 依据转应力变化的校正系数1 许用疲乏应力PP5.50.975.3Kw158r/mini对于轴的受力状况，在轴向受到pn转应力为脉动循环，因此取-=0.7查手册可得1=60MPa Tpn40735020.795540735020.795502703依据刚度校核轴：轴的弯曲变形的条件和允许值机床的主传动轴的弯曲刚度验算，主要验算轴上装齿轮和轴承出的挠度y和倾角y，装齿轮和轴承处的倾角，应小于弯曲刚度的许用值y和， 即yy轴的弯曲变形的允许值：轴的类型轴的类型允许挠度变形部位允许倾角一般传动轴〔0.0003~0.0005〕0.0025 0.0001处刚度要求较高的0.00021装单列圆锥滚子0.0006轴轴轴承安装齿轮的轴〔0.01~0.03〕装滑动轴承处0.001孔和切制螺纹，因此不影响轴的疲乏强度，而且构造重量轻。2.5.3轴键，以其承载力量高、定心性及导向性好。矩形花键轴：平均直径d1

=〔D+d〕/264I4 当量直径64I4 2惯性矩：I=d46z(Dd)(Dd)264花键的校核：强度为：p

2T103zhldm8X32X36X6;8X42X46X8轮固定在花键上。a，寿命计算公式：滚动轴承的寿命计算公式如下：CL=P 式中：L—额定寿命〔x106〕转〔Kgf〕〔Kgf〕——寿命指数，对球轴承=3 对滚子轴承=10/3在实际计算中，一般承受工作小时数表示轴承的额定寿命，这时上试可变为：106hL=60nh Lh

—额定寿命〔h〕n—轴承的计算转速〔r/min〕P=XFr

+YFaFr

—径向负荷〔Kgf〕F—轴向负荷〔Kgf〕aX—径向系数Y—轴向系数〔2〕依据负载荷选择轴承按额定静负载选择轴承的根本公式如下：C=S P0 0 0式中：P—当量静负荷〔Kgf〕 按以下两式计算，取大值0p xF0 0 r

YF0

p F0 rC—额定静负荷〔kgf〕0S—安全系数0一般将电动机的选择分三个步骤选择电动机的类型和构造型式。选择电动机的容量。1〕步进电机的工作原理：步进电机有转子、定子和定子绕组。定子绕组分假设干相，每相的磁极上有步距角360/mzkm，z，k2〕步进电机的工作特点：数量和脉冲频率成正比，转变通电挨次可以转变步进电机的旋转方向；的力量，不需要机械制动；C、有肯定的步距精度，没有累积误差；〔步距角〕不能够太小、18000HZ。步进电机选择a、 计算步进电机的负载转矩Tm36FT p m

(N·cm)m 2b式中： ————脉冲当量〔mm/step；pF————进给牵引力〔N；m 0.75°；b————电机——丝杠的传动效率，为齿轮、轴承、丝杠效率之0.98，0.99，0.990.94。36FT p m

360.011799.134

152.307 N·cmm 2b

20.750.980.990.990.94b、估算步进电机的起动转矩TqmT Tm

152.307 507.69N·cmq 0.30.5 0.3c、计算最大静转矩Tjmax查表取五相十拍，则Tjmax

T q0.951

507.690.951

533.85 N·cmd、计算步进电机运行频率fe

和最高起动频率fk1000vsfe 60sp

10001.52500Hz600.011000vf maxk 60p

10002.44000Hz600.01试中：vs

————最大切削进给速度〔m/min〕1.5m/min；v ————最大快移速度〔m/min2.4m/min；max 0.01mm/step。pe、初选步进电机型号依据估算出的最大静转距T 查得110BF004最大静转距为784Ngcm>jmaxT ，可以满足要求，考虑到此经济型数控铣床有可能使用较大的切削用量，jmax130BF001130BF001校核步进电机转距a、等效转动惯量计算J

〔kgcm2〕可以按下Σ试计算：J JΣ M

J(1

z1)2[(Jz 22

G LJ) ( 0)2]s g 2

Kg·cm2 ⑴JΣ

——步进电机转子转动惯量(Kg·cm2)G——工作台及工件等移动部件的重量〔N；J，J1 2

zz1,2

的转动惯量；130BF001，JΣ

=4.65Kg·cm2对于轴、轴承、齿轮、联轴节等圆柱体的转动惯量计算公式为：cJMD2c

(Kg·cm2)8对于钢材，材料密度为7.8105(kg/cm3),代入上式，有：J0.78D4L103Kg/cm2式中：Mc

——圆柱体质量〔kg；D——圆柱体直径L——圆柱体长度〔cm；J1

0.78103dL1 1=(0.781037.242)4.2 Kg·cm2J 0.78103dL2 2 2=(0.78103942)10.2 Kg·cm2J 0.78103dL3 3 3=(0.7810344132.5)26.4 Kg·cm2代入式⑴J JΣ M

J(1

z1)2[(Jz 22

G LJ) ( 0)2]s g 24.654.2(35.2

40 4892.16 0.6 )2[(10.2 26.4) ( )2] 50 9.8 2考虑步进电机与传动系统惯性匹配问题：J ／JM Σ

4.65/35.20.132根本满足惯性匹配的要求。3章液压驱动、掌握系统的设计3.1液压系统回路分析调压回路〔防〕在系统正常工作的状况下，阀关闭不溢流，系统的压时系统的压力就是阀的调定压力。3.1.1调压回路调速回路2%~5%。此时，溢间缸活塞二边的运动保持两缸的流量根本相等。3.1.2调速回路保压回路本设计承受复合式泵的保压回路，当系统压力较低时，低压大泵和位移，仅用小泵供给，便削减系统发热，减低能耗。3.1.3保压回路换向回路O液压缸锁紧。由于液压缸布满液压油，故能从静止到启动较平稳，且换向冲击小，换向复位精准。3.1.4三位四通换向阀阀转变油路的变化。缓冲回路应急动力源，向回路释放压力油，使工件不会脱落。3.15缓冲回路掌握系统方案设计该设计承受的是机械在反响开环掌握系统方案。的。以下图为反响校正框图：3.2.1反响框图开环系统的优点是系统简洁、本钱低，但缺点是精度不高。液压泵及液压原件选择液压泵选择泵可以通过溢流阀调定的压力来掌握。选用双联叶片泵，其型号为5.5Kw.同步转速1500r/min。25L。在油箱处还应设置滤油器，滤油器在1.6~2.5MPa，为一般液压系统，液压25~50μm简洁拆换等特点。溢流阀：Y6-60;单向阀：Y10B;调速阀：Q63B;节流阀：L-25B；换向阀：34E-63B。驱动缸的选定：驱动缸的径和活塞杆外径的计算由方案设计得驱动缸的径即为回转缸直径，设此工作压力P=6.3Mpa则：4FP47777.8/4FP47777.8/6.3按JB2183-77,选取D=40mm；d=0.45D=0.4540=18mm。JB2183-77,d=20mm。驱动缸外径及行程：GB1068-67D’=60mm；。强度校核：A、壁厚校核：D/50/510,故可视为薄壁，PD=1.56.350≈2.4mm；200明显=10>2.4mm,故壁厚安全。B、活塞杆的稳定性校核：nn=1；n故瘦长比l/k=630/7=90,而m

=85；n故l/k>m ,因 30156.56mm4nk

n2l2

=101130156.5610-12=1005kN；0.632而实际使用时，为了保证活塞杆不产生纵向弯曲，≤kPP/n=1005/4=251.3kN〔n=4〕≤kF F参考文献天津大学《工业机器手设计根底》编写组.工业机器手设计根底[M]，天津；天津科技，1980华东纺织工学院,工业大学, 天津大学, 主编.机床设计图册［M；学技术，1981.5何存兴.液压元件[M]，;机械工业，1982王占林.近代液压掌握[M]，;机械工业，1997《机械设计手册》编辑组编.机床设计手册［M］.：机械工业，1986.12雷天觉.编液压工程手册[M]，;理工大学，1998濮良贵，纪名刚．机械设计第七版[M]2023．5卜炎．机械传动装置手册[M]．1998．12宏钧．有用机械加工工艺手册其次版[M]．机械工业，2023．1工业大学理论力学教研室编．理论力学第六版[M]2023．4鸿文．材料力学第四版[M]，2023．3马纲，王之栎，松元．一种型搬运码垛机械手的设计[J学，100083章跃，国生．机械制造专业英语[M]．机械工业，1999．12叔子克冲．机械工程掌握根底第五版[M2023．7桓，作模，文杰.机械原理第七版[M]2023．5广弟，朱月秀，冷祖祁.单片机根底[M].：航空航天大学，2023.6建勇.机电一体化[M].：科学，2023辞的标准来衡量一切事物的方法论。感颜竟成教师对我的细心指导。英文翻译ModificationMethodfortheReductionofNon-linearityErrorsinFive-AxisCNCMachiningABSTRACTInthemachiningofsculpturedsurfaces，five-axisCNCmachinetoolsprovidemoreflexibilitytorealizethecutterpositionasitsaxisorientationspatiallychanges.Conventionalfive-axismachiningusesstraightlinesegmentstoconnectconsecutivemachiningdatapoints,anduseslinearinterpolationtogeneratecommandsignalsforpositionsbetweenendpoints，Duetofive-axissimultaneousandcoupledrotaryandlinearmovements,theactualmachiningmotiontrajectoryisanon-linearpath.Thenon-linearcurvesegmentsdeviatefromthelinearlyinterpolatedstraightlinesegments,resultinginanon-linearitymachiningerrorineachmachiningstep. Thesenon-linearityerrors,inadditiontolinearityerror,commonlycreateobstaclestotheassuranceofhighmachiningprecision.Inthispaper,anovelmethodologyforsolvingthenon-linearityerrorsprobleminfive-axisCNCmachiningispresented.Theproposemethodisbasedonthemachinetype-specifickinematicsandthemachiningmotiontrajectory.Non-linearityerrorsarereducedbymodifyingthecutterorientationswithoutinsertingadditionalmachiningdatapoints.Anoff-lineprocessingofasetoftoolpathdataformachiningasculpturedsurfaceillustratesthattheproposedmethodincreasesmachiningprecision.KeywordNon-linearerror;Machinekinematics;Machiningmotiontrajectory.INTRODUCTIONInconventionalfive-axismachining,atoolpath,representedbythecutterlocationsdata(CLDATA),consistsofthespatiallyvaryingcutterpositionsanditsaxisorientations.TheseCLDATAaregeneratedbasedsolelyonthegeometricalpropertiesofthemachinedsurfacesandthecutter.TheseCLDATAarefurtherprocessedintoNC-codeswhichisspecifictoaparticularmachineconfiguration.Linearinterpolationisthenusedtogeneratetherequiredcommandsforpositionsalonglinesegmentconnectingthemachiningdatapoints.Thesimultaneouslinearandrotarymovementsareinvolvedinfive-axismachiningsinceevernewcutteraxisorientationrequiresthemotionatleastoneotheraxis.Therearealsocouplingeffectsofthecutteraxiswillaffectthepositionofthecutter.Thesesimultaneousandcoupledmovementscausethecuttercontractpoint(CCpoint)tomoveinanon-linearmanner.Asaresult,themachiningerrorineachmotionstepismadeupofnotonlythelinearsegmentationapproximationerrorbutalsoanadditionalmachiningerror. Asshowninfigure1formachiningiseitheraconcavesurfaceoraconvexsurface,alinesegmentisusedtoconnecttwoconsecutivemachiningdatapoints(thespindlechunkisthemachinecontrolpointMCP).Linearinterpolationgenerateintermediatepositionsalongthelinesegment.Thedesiresurfaceisdesigncurve(eitherconcaveorconvex).Thelinearsegmentapproximatestodesigncurveresultinginthelinearityerror,δt.Apartfromthelinearityerror.Thenon-linearCCpointtrajectorydeviatesfromthestraightlinesegment(thecuttergagelengthisconstantandMCPisinterpolatedalongthelinesegment)resultinanadditionalmachiningerror,referredtoasthenon-linearityerror,δn.Inthecasethatthedesiresurfaceisconcave(seefigure1a),thetotalmachiningerrorisdifferenceofthenon-linearityerrorandthelinearityerror:δtotal=δt-δn.Thenon-linearityerror,inthiscase,compensateforthetotalmachiningerror(AIGPPost-processor,1996;Liu,1994).Onthecontrary,forthemachiningofconvexsurfaceasshowninfigure1b,thenon-linearityerroraddsontothelinearityerrorandenlargesthemachiningerror:δtotal=δt+δn(AIGPPost-processor,1996;Liu,1994).figure1.Themulti-axisCNCmachiningerrorConsequentlythenon-linearityerrorhavecauseddifficultiesforensuringultra-precisionmachiningrequirements.Inthemachiningofairfoilsurface,forexample,themachiningofthecontoursurfaceofairfoiltotheedgesisproblematic.Thesurfacecurvatureontheseareachangesabruptly,andthusthecutterorientationvariesinconsistentlyfromonecuttertothenext.Theseabruptcutterorientationvariationsinconsistentlyfromonecutterlocationtothenext.Theseabruptcutterorientationareatypicalnon-linearityerrorproblem.Inordertosolvethefive-axisCNCmachiningerrorproblem,effortshavebeenmadetotreatnon-linearityerrorsingenerateNCcodes.Someproducersused“linearizationprocesses”forthispurpose.Thebasicfunctionof“linearizationprocesses”areinsertingmachiningdatapointsbetweenNCcodeswherethetotalmachiningerrorisoutofthespecifiedtolerancerange.Takeuchietal.(1990)insertedpointsbysubdividingthelinesegmentwithequallyspacedinterval.Choetal.(1993)inserteddatapointsbylimitingthemaximummachiningerrorwithinthelineintervalfromthestartpointtotheinsertedpointtobethetolerance.And,bothofthemsetthecutterorientationsvaryinglinearlyinsuccessivepositions.IntheAutomationIntelligence Generalization Postprocessor (AIGP)(1996), a“linearizationprocesses”calculatesthemiddlepoint(MP)betweenadjacentNC-codesandinsertstheMPasanadditionaldataintheNCcode.TheinsertioncanbeperformedfurtherbetweentheconsecutiveNC-codeduntileitherallpointsarewithinthemachiningtoleranceoruntilamaximumof63pointsareinsertedbetweentheconsecutivedatapoint.Thecurrentpost-processors,suchastheVanguardCustomPost-processorGenerator(1996),theOminimillCustomPostprocessor(1992),theAIXNumericalControlPostGenerator(1996),areallhavingthesimilar“linearizationprocesses”asintheAIGP.InthecurrentCAD/CAMsoftware. Unigraphics(2023),theUG/postpostprocessorsinsertsdatapointsbetweenadjacentNC-codes,therebysimulatingastraightlinewithseriesofsmallcurves.Thenumberoftheinsertedpointsisdeterminedbasedonthemaximumallowabledeviationandaniterationmethodisusedifthedeviationbetweenthesegmentedarcsandthelinearestilloutofthespecifiedtolerancelimit,theprocessisaborted.“linearizationprocesses”discussedabovemanipulateNC-codesbyinsertingextramachiningdatapoints.AlthoughtheproducedNC-codessatisfythemachiningrequirement,theymaycontaindensesetsofnon-equallyspaceddatawithconstantorlinearlyvaryingcutterorientation.Consequently,thelinearizationprocesshasraisedthefollowingproblems.Inthemachiningofcomplexcontoursurface,thecutterorientationvariesfromonecutterlocationtothenext.Thecutterpositionchangesinthiscasecannotbetoosmallsincethemachinewillproduceeitherjerkmotionorrandomrotarymovements.Asinanindustrialprocedureofmachiningairfoilsurfaceofanimpeller,alinearizationprocesswasusedtoreducethenon-linearityerrors.ManydatapointswereinsertedbetweenapairofNC-codes.Theinsertionofmanydatapointscausedthecutterpositionchangetobenearlyequaltozerowhilethecutterorientationchangedabruptly.Asaconsequence,themachinerotarymovementswererapidwithinfinitefeedrate.Randomrotarymovementsresultedandtheworkpiecewasdamaged.Theinsertionofmachiningdatapointscanalsocausenon-constantfederatealongthecuttingcurve.Theinsertionofadditionaldataresultsinnon-equallyspacedsegment,whileaccelerationanddecelerationstepsarerequiredforeachsegment.Thus,thefeederatevariesineachsegmentandmayneverreachthedesiredvalue.Theresultofvaryingfeederatecausesanonsmoothsurfacefinishandtheunreachablefeedrateincreasesoverallmachiningtime.Inaddition,theinsertionofconstantcutterorientationvariationalsocausessevereroughnessaroundtheendpointsalongthesurface.Linearlyinaccuratelysincethechangeincutterorientationisnotnecessarilylinear.Thenon-linearityerrorproblemarisesfromthefactthatfive-axismachiningmotiontrajectoriesarenon-linearcurvesegments.Thesimultaneousandcoupledrotaryandtranslationmovementsgeneratethenon-linearitymotiontrajectory,andthelinearinterpolationtechniqueisnotcapabletocurvefitthenonlinearpath.Onesolutiontoistodesignnewinterpolationmethods.Liangetal.(2023)presentedacombine3Dlinearandcircular(3DL&C)interpolationtechnique.Thenew3DL&Cinterpolationcanon-linedrivetherotationmovementpivotalongapre-designed3Dcurvepath,sothattheCCpointmotiontrajectoryisaviaastraightlineconnectingmachiningdatapoints,thus,thenon-linearityerrorcanbeeliminated.Five-axismachiningmovementsarekinematicallyrelatedtothecutterlocationdata.Inotherword,thenon-linearmotiontrajectorydependsonthecutterorientationchangesandnon-linearityerrorsarerelatedtothetoolpathgeneration.Thus,anothersolutiontothenon-linearityerrorproblemcanbeapproachedfromtoolpath(CLDATA)generationwiththerequirementsthatthemachiningerrorsareminimizedandthereisnointerferencebetweentheworkpieceandthecutter.Intoolpathgeneration,varioustechniquesfordifferentsurfacerepresentationshavebeenusedbytheCAD/CAMpackageproducers1990)andresearchers.HuangandOliver(1992).Bedietal.(1997)presentedaprinciplecurvaturealignmenttechniqueforfive-axismachiningusingatoroidalshapedtool.Liu(1995)presentedthesinglepointoffsetandthedoublepointoffsetalgorithmsforfive-axisflankmillingtoolpathgenerationbasedondifferentialgeometryandanalyticalgeometry.Morishgeetal.(1999)presentedatoolpathgenerationmethodforfive-axisCNCmachining,whichappliestheC-space(a3Dconfigurationspace)todeterminecollision-freecutterpositionsanditsorientation.Theseresearchworkontoolpathgenerationareallbasedexclusivelyonthegeometricofthemachinedsurfacesandthecutter,withoutconsideringthemachining-specificmachiningkinematics.Asaresult,thegeneratedtoolpaths(themachiningNC-codestransformedfromtheseCLDATA)commonlycauseobstaclesformeetingtheultra-precisionmachiningrequirements,particularlyforthecutterorientationgenerationinfive-axismachining.Thus,theproblemwithpresentoff-linetoolpathgenerationapproachesisthattherealmachiningkinematicsisnotdirectlyincorporated.Toensuremachiningprecision,cutterorientationgenerationshouldbebasednotonlyonthegeometryofthemachinedsurfacesbutalsoonthemachinetype-specifickinematics.Inthispaper,anovelmethodologyforsolvingthenon-linearityerrorprobleminfive-axismachiningispresented.ThemethodoptimizestheCLDATAbasedonmachine-specifickinematicsandmachiningmotiontrajectory,wherebythecutterorientationsaremodifiedtoreducethenon-linearityerrorsprovidedthatthereisnointerferencebetweenthecutterandtheworkpiece.Asoftwareprogramforimplementingtheproposedmethodispresented.Asanapplicationofproposedmethod,acasestudyispresented,whichshowsanincreaseinmachiningprecisionascomparedwiththoseprocessedbytheexistingAIGP’smethod.PROPOSEDTOOLPATHGENERATIONMETHODThemachiningnon-linearityerrorsdependupontheactualCCpointtrajectory,sinceaCCpointtrajectoryisafunctionofthemachinerotaryvariables,eachactualCCpointtrajectorycanbemanipulatedwithinthetolerancelimitbychangingthemachinerotaryvariables,providedthatthereisnointerferencebetweentheworkpieceandthecutter.Furthermore,becauseofthemachinerotaryvariablesarekinematicallyrelatedtothecutterorientationchanges,thenon-linearityerrorproblemcanbeapproachedbymanipulatingcutterorientations.Toproposedmethodreducesthenon-linearityerrorsbydeterminingtheacceptablemachinerotaryvariablesemployingthemachinemotiontrajectorymodel,andbymodifyingthecutterorientationthroughthemachinekinematicrelations.Itmustbeemphasizedthatthemachinekinematicpropertiesandmotiontrajectoryaremachinetype-specific.Hence,themodificationofCLDATAhastobecarriedoutinteamsofmachinevariablesandsubsequentuseofthekinematictransformationtodeterminethemodifiedCLDATA.TheprocedureoftheproposedmethodstartswiththetransformationoftheCLDATAtomachiningNC-codesbyemployingthemachine-typespecificinversekinematicmodel.Inteamsofmachinevariables,theactualmachiningmotiontrajectoryisdeterminedbyusingthespecificmachinemotiontrajectorymodel.Then,themachiningerrorsaredetermined.Thelinearityerrorisafunctionofsurfacelocalcurvatureonthecuttingcurveandthestep-forwarddistance.Fromthecubicsplinecuttingcurvefunction,thesurfacelocalcurvaturecanbedetermined.ThelinearityerrorforeachmovethencanbecomputedfromtheadjacentCCpointdataandthesurfacelocalcurvature.Byknowingthelinearityerror,theallowablenon-linearityerrorcanbedeterminedasthedifferenceofthelinearityerrorfromthespecifiedmachiningtolerance.Usingthemachinetrajectorymodelandthelinesegmentequation,themaximumdeviationcanbedetermined.BytakingsamplepointsonbothoftheCCnon-linearcurveandthelinesegments,themaximumchorddeviationisthemaximumnon-linearityerror.Inthestepswherethemaximumnon-linearityerrorexceedstheallowablenon-linearityerror,theproposedmethodmodifiesthemachinerotaryvariablechanges.Themodificationiscarriedoutbyincreasing/decreasingamachinerotaryvariablevariationasmallangleintheplanecontainingthetwooriginalcuttervectors,andbyadding/subtractingtheangletotheoriginalmachinerotaryvariables.Thenewrotaryvariablesarethenusedtocalculatetheresultantnon-linearityerror,whichinturniscomparedagainwiththeallowablenon-linearityerror.Thus,byusingthedifferencebetweentheallowablenon-linearityerrorandmodifiednon-linearityerrorasthecriterion,theacceptablemachinerotaryvariablescanbedeterminediteratively.Finally,fromthemodifiedmachinerotaryvariables,thecorrespondingcutterorientationscanbedeterminedbyperformingtheforwardkinematictransformation.Inordertoavoidinterferencebetweentheworkpieceandthecutter,therotaryangleswereadjustedsuchthattheanglechangesarelessthanhalfoftheorientationanglechangesarelessthanonehalfoftheoriginalcutterorientationchanges.Comparingtotheexisting“linearizationprocesses”,theadditionaldatapointsareinsertedwithcutterorientationseithervaryinglinearlyorastheaveragevariation(i.e.,theonehalf)oftherotaryanglechange,andtheinterferenceproblemisnotconsidered.Alternatively,themodifiedmachinerotaryvariablesanglechangefromtheproposedmethodaresmallerthanonehalfofangelchange,whichthusensuresthecorrespondingcutterorientationarewithintherangesuchthatnointerferenceoccurs.ForasetofCLDATA,themodificationprocedurecanbeperformedbyusingthefollowingalgorithm.TOOLPATHMODIFICATIONALGORITHMTransformtheinitialCLDATA,intoitscorrespondingmachiningNC-codesbyusingthespecificmachineinversekinematicmodel;DeterminetheCCpointcoordinatesbyemployingthemachinemotiontrajectorymodel;ComputethedesiretoolpathbyusingcubicsplinefunctionbasedontheCLDATAandcalculatethelocalsurfacecurvaturesKoftheftoolpathatthemachiningpoints;errorbyusingtheformulagivenbyFauxandPratt(1979):δt=1/8Kf

(Δs)2where,K-thesurfacelocalcurvaturedeterminedfromstep(3);fΔs-thesegmentlengthbetweenconsecutiveCCpointsfromstep(2).Computetheallowablevalueofthenon-linearityerror:δa,n=tolerance-δt.Determinedthepointsonthestraightlinesegmentandonthemachinemotiontrajectorysegmentthatcorrespondtothemaximumchordaldeviation.Computethemaximumnon-linearityerror,δmax,usingthepointsfromstep(6);Modifythemachinerotaryanglechangeifδmax>δa,n,thatis,andΔCmsuchthatthenon-linearityerror,δn1,willsatisfy(δn1-δa,n)<0;ComputerthemachiningNC-codesofBm,i+1andCm,i+1basedonthemachinerotaryanglevariationfromstep8:Bm,i+1=Bm,iΔBmCm,i+1=Cm,iΔCmWhere,Bm,i,Cm,iarethei-throtaryvariables,Bm,i+1Cm,i+1arethei+1-throtaryvariablesandΔBmΔCmaremodifiedrotaryThe+and–signdependsonwhethertheanglesinstepi+1increaseordecrease,DeterminetheoptimumcutterorientationsbytransformingthemodifiedmachiningNC-codesusingthespecificmachineforwardkinematicmodel.TheproposedmethodcanbeimplementedwithasoftwareasshowninFigure2.Thepre-postprocessoracceptstheinitialδtCLDATA.Then,bypassingthemodifiedCLDATAtoapostprocessor,theobtainedNC-codeswillresultinacceptablemachiningerrors.TheproposedmethodconsidersnotonlythegeometrycalculationofthecomplexsurfacesbyacceptingtheinitialCLDATA,butalsothefive-axismachiningkinematicsbyapplyingthemachiningmotiontrajectoryandtheprocessofdynamicpropertiesinthepostprocessor.Therefore,theproposedmethodprovidesasolutiontothenon-linearityproblemwithoutrequiringthedesignofanewinterpolators,andthemethodovercomesthedrawbacksoftheexistingmethodsasdescribedin“introduction”.CAMSystemCAMSystemToolGenerationPathBasedonofthegeometryThesurfacesmachinedPre-ProstprocessorModifyPre-ProstprocessorModifycutterorientationbasedonmachinekinematics&motiontrajectoryTransformCLDATAtoMachiningNC-codesbyProprocessorPostprocessingProprocessorPostprocessingAnoveltoolpathgenerationmethodologyforsolvingthefive-axisCNCmachiningerrorproblemisproposed.Thenewmethodsoff-linemodifiesthecutterorientationsbasedontheallowablechangeinmachinerotarymovements,whichinturnreducesthenon-linearityerrortobewithinthemachiningtolerance.Theproposedmethodemploysmachinetype-specifickinematicmodelsandthemachiningmotiontrajectory.ComparingwiththedatafromtheAIGP’s“linearizationprocesses”,theproposedmethodensuresthemachiningprecisionwithoutinsertingadditionalcutterpositionpoints.ThesoftwareforimplementingtheproposedmethodcanbeusedtoprocessCLDATAsthatwillbeusedontheOM-1five-axismillingcentre,anditcanalsobeextendedtootherfive-axisCNCmac