Vector modeling of robotic helical milling hole movement and theoretical analysis on roughness of hole surface

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J.Cent.South Univ.(2013)20：1818 1824DoI：10.1007/s11771-013-1678-5Vector modeling of robotic helical milling hole movement andtheoretical analysis on roughness of hole surface垒SpringerSHAN Yi-cai(单以才) -，HE Ning(何宁) ，LI Liang(李亮) ，ZHAO wei(赵威) ，YANG Yin.fei(杨吟飞)1.Colege of Mechanical and Electrical Engineering，Nanjing University ofAeronautics and Astronautics，Nanjing 210016，China；2.Nanjing Colege of Information Technology，Nanjing 2 1 0046，China◎Central South University Press and Springer-Verlag Berlin Heidelberg 20 1 3Abstract：To avoid the machine problems of excessive axial force.complex process flow and frequent tool changing during roboticdriling holes，a new hole-making technology fie.helical miling hole)was inoduced for designing a new robotic helical milinghole system，which could further improve robotic hole-making ability in airplane digita1 assembly.Atier analysis on thecharacteristics of helica1 milling hole.advantages and 1imitations of two typical robotic helica1 milling hole systems weresummarized.Then，vector model of helical milling hole movement was built on vector analysis method.Finaly.surface roughnesscalculation formula was deduced according to the movement principle of helical milling hole.then the influence of maintechnological parameters on surface roughness was analyzed.Analysis shows that theoretical surface roughness of hole becomespoor with the increase of tool speed ratio and revolution radius.Meanwhile，the roughness decreases according to the increase of toolteeth number.The research contributes greatly to the construction of roughness prediction modelin helical milling hole。

Key words：helical miling hole；robotic hole-making system；vector modeling；theoretical surface roughnessl Intr0ducti0nWith successful production of domestic regiona1airplane ARJ-700 and intensive study on big plane C9 1 9。

more concerns have been focused on how to improve thequality and eficiency of assembly hole.making in thestage of plane final assembly [2].Due to suchadvantages as high automation.good flexibility and lowcost，robotic hole-making system is gradually becomingthe main technology for future intelligent hole-making inlarge and super large plane[3-4]。

To meet the requirements of eficient and precisehole.making new robotic hole.making systems havesuccessively appeared. At present， the commontechnology is joint robot driling technology.On accountof inherent defects in serial robot of low rigid and poorbearing capacity，the application of this drilling system islimited.Recently，Boeing and Electroimpact iointlydeveloped flexible track automatic driling system inwhich vacuum chucks adsorb on the workpiece surfaceto realize hole-drilling.Now，the drilling system has beensuccessfully applied in the hole-making of Boeing 787，Boeing 777 and A3 80.Spanish M .To1TeS Companydesigned a climbing robot automatic drilling system.Inthis system，the drilling device was amounted on therobot and vacuum chucks on the robot foot completedadsorption function.So.special assistant tools can beavoided.Since the above systems both use vacuumadsorption technology，the two driling systems cannot fitfor occasion with large axial force.Therefore.bothsystems are only used in smal hole.W ith the continuousincrease of large holes in aviation subassembly made ofhard cuting materials(especialy，titanium aloy，carbonfiber reinforced polymer，and high strength aeronauticaluminum aloys). it is urgent to develop newhole-making systems with high eficiency and highprecision[5-7]。

Helical milling hole(i.e.，orbital milling hole)，is anew techn ology which utilizes the way of milling torealize hole making.Too1 movement of the techn ology isnot a simple combination of conventional drilling andmilling.but a relative motion of three-dimensiona1 screwfeed between tool and work-piece.In hole milling.thetool offsets from the axis of hole at a certain distance fi.c。

revolution radius).The process of helical miling holeincludes three movements of tool rotation around toolaxis，tool axial feed，and too1 revolution around hole axis。

The technology can make diferent holes withoutchanging tool，and satisfy requirements of positionalFoundation item：Projects(50975141，51005118)supposed by the National Natural Science Foundation of China；Pr0jects(2009l652018，2010352005)supported by Aviation Science Fund of China；Project(YKJ11-001)supported by Key Program of Nanjing Colege of InformationTechnology Institute，ChinaReceived date：2012--03--28；Accepted date：2012--06--30Corresponding author：LI Liang，Professor；Tel：86-25-84896040；E-mail：liliang###nua.edu.cnJ.Cent.South Univ.(2013)20：1818-1824 1819precision，geometrical precision，ana surface roughness8-91.Therefore，the new robotic hole.making systembased on helical miling hole technology has a broadapplying prospect in the fields of aviation，aerospace andshipbuilding，etc[10-13].However，the cuting processof robotic helical milling hole has not been deeplystudied.In this work.a vector modeling ofrobotic helicalmilling hole is built and an in.depth research on holetheoretical surface roughness is conducted。

2 Characteristics of helical milling hole andtwo typical m achining methods based onjoint robot2.1 characteristics of helical miling holePrinciple of helical milling hole is shown in Fig.1[14].In helical miling hole，primary motion ishigh.speed rotation of the tool and feed motion is screwfeed of the tool relative to workpiece.The feed motion isa combined movement of revolution feed and axia1 feedbe een tool and workpiece.Thus.helica1 milling holehas folowing characteristics：HS：TOO”∞：Tool：Feed iP：Tbo1 revolution radius-上IFig.1 Schematic diagram of helical miling hole1 1 As revolution radius exists，the hole diameter isdetermined by too1 diameter and revolution radius.So。

helical milling can generate not only cylindrical bore andtapered bore，but also correct position eror.Further，itimproves processing accuracy of the hole。

31 The discontinuous helical milling achieves shortchips， which helps to realize automatic chiptransportation and improve hole quality。

4 The discontinuous helical milling guaranteesenough cooling time for too1.Meanwhile，the smallertool diameter contributes to heat dissipation of too1.So。

51 Compared to conventional drilling hole，helicalmiling hole greatly decreases axial force.Therefore.themiling method is suitable for making precise holes inhard cuting materials。

2.2 Two typical machining methodsAccording to realization fornls of screw feed，robotic helical milling hole has two typical machiningmethods.In the first machining method.screw feed isrealized through too1 axial feed and workpiece rotation。

as shown in Fig.2fa1.Another method uses too1 axia1feed and tool revolution to achieve helical milling.andthe principle is shown in Fig.2fb1。

fa1/ 、 /，1：/(b)Fig.2 Two typical machining methods for helical milling hole(a)Workpiece movement interpolation；(b)Tool revolutionIn Fig.2(a)，workpiece rotation is realized by theinterpolation of two linear motions.To ensure goodprecision，this machining method has high requirementson the processing platform characteristics of feed drivingacceleration， rigidity and stiffness. So， worldwidescholars usually choose high speed precision machiningcenter for helical milling hole is usually chosenworldwide.Since the screw feed is accomplished by theworkpiece loading platform and spindle，the process ofhelical milling hole is easy to be realized.However，theworkpiece volume is restricted by the dimension ofloading platform 。

The revolution movement of helica1 milling holeshown in Fig.2(b)is accomplished by tool revolutionaround hole axis.The second machining method canavoid the machining errors caused by interpolationmovement.As the spindle realizes rotation，axial feedand revolution simultaneously，it is unnecessary to adjustworkpiece posture inline.Therefore.the second methodis very suitable for automatic hole-making in large andsuper large workpieces.But，it requires complicatedmovement mechanism。

1820 J.Cent.South Univ.(2013)20：1818-18243 Vector modeling of robotic helical millinghole3.1 Work procedure of robotic helical milling systemRobotic helical miling system is mainly composedof robot platform， end efector for hole-making，automatic measuring equipment for seeking hole markedpoint and control platform.End effector and automaticmeasuring equipment are amounted on robot platform。

Before helical milling，end effector is sent to specificposition by robot platform under the guidance ofautomatic measuring equipment. The detectionalgorithms for determining the hole marked point areshown in Ref.[15].In the end，the end effector is torealize the movement of helical milling.The workingprocedure of robotic helical miling system is shown inFig.3。

3.2 Vector modeling of helical milling hole withworkpiece movement interpolationThough deeD studies have been made on thekinematics of helical milling hole，research on motionvector modeling is stil lacking at present.To developrobotic hole.making system based on helical millingtechnology， a vector equation should be foun d todescribe the movement of helical milling hole.Therefore，a fundamental vector mode1 needs to be established inspace coordinates system。

Figure 4 gives a basic vector model of helicalmilling hole when workpiece is moving.For being easyto study，workpiece interpolation motion is substitutedwith workpiece rotation.According to the pose of holemarked point detected by automatic measuringequipment， a new absolute coordinate systemD -x z is established in the mode1.The two relativecoordinate systems o4- z and o5- z areboth related to workpiece.The two coordinate systemsare transiation and rotation coordinate systems betweenhole marked point and end effeetor.The other tw orelative coordinate systems related to tool are too1 axia1feed coordinate system o -x y z and tool rotationcoordinate system o -x；y z；. The translationcoordinate system o4- z is formed by thetranslation of 0 -x y z along vector E and .InD - z ，the origin point of o - z is describedby tool axia1 feed vector .The tool rotation vector Tdescribes the position vector of cuting edge ino -呓 during machining movement.The positionvector P of cutting edge in o5- z is synthesizedby tool axial feed vector F 、tool rotation vector Tand two axial deviation vectors E and 。

Fig.3 Working process of robotic helical miling holeJ.Cent.South Univ.(2013)20：1818-1824 1821Fig.4 Vector model of helical milling hole with workpiece movement interpolationIn Fig.4，the tool rotatesThe tool rotation vector inaScounter clockwise by s。

0 - ； z is expressed(1) where h is the tool safety height。

The transformation matrix from 0 -呓 z to0 - z is given as； II，zw，甜] 0- 。 。 。 。 。 。 。 。 。 。 - - apnw. where口P denotes axial feed distance when workpiecerevolutes a circle.n ∞is workpiece revolution speed. ∞means workpiece revolution angle。

W hen transform ing O4- z to 0 - z ，new translation matrix iS needed：.z e， ) (3)The transformation matrix from 05- z toO4- z is described bycos s sin s 0；M ( s)l-sin s cos s 0l 0 0 1(4)where 0s is workpiece rotation angle。

In O5- ，the cuting edge position vector P isgained：P(CPs， )[54 ( )- (-H -E )t4M ( )]- (-H -E )[54 ( )]- (- -E 十 十 ( )) (5)The above expression is the basic vector model ofhelical milling hole when workpiece makes ainterpolation movement。

3.3 Vector modeling of helical miling hole with toolrevolutionIn Fig.2(b)，it is unnecessary to adjust workpiecepose in helical milling hole.Therefore，a vector model ofhelical milling hole with tool revolution is established inFig.5.In this model，a new absolute coordinate system0 - z is also established based on the pose of holemarked point in robot coordinate system .Theoriginal point of 0 - z is hole maed point.Tosatisfy requirements of the relative pose between endeffector and marked point，the working coordinatesystem of end effector Ow-x is established.Theother three relative coordinate systems are toolrevolution coordinate system Ol-XlYlZ1，tool axial feedcoordinate system 02-x2Y2Z2，and tool rotate coordinatesystem 03-x3Y3Z3. In Oo-xoYoZo， the origin point of0 x is described by tool safety height vector H。

The tool revolution vector E describes the origin point of02-x2Y2Z2 in Ol-XlYlZ1.Tool axial feed vector Fa androtation vector T correspond to the vector and T0 O .n C S-.......。，.....L -2J 1822 J.Cent.South Univ. (2013)20：1818-1824。0 (z0Fig.5 Vector model of helical miling hole with tool revolutionshown in Fig.4.We define P as the position vector ofcutting edge in Oo-XoYoZ0.Here，P is the combination offourvectors asH，E，Fa，andT。

The transformation matrix from Ow-xwy rw toOo-XoYoZo is given as0waz(h)l 0 (6)When transforming Ol-XlYlZl to Ow-x 7 ，newtranslation transformation matrix iS needed：M( )cos(Pco sin 0- sin cos(po 00 0(7)： ㈣；00唧 H(o(9)The cuting edge position vector P in Oo-xoyozo isexpressed asP(Os， ) [0、vuzL，zJ十W1 ( ) ][0wG( )( )( (e) )]0wG( ) ( ) G ce ；Gz( 口 ] c ]、 c 。Expression(10)is a basic vector model of helicalmilling hole with tool revolution。

4 Calculation and analysis of hole surfaceroughnessIn the process of helical milling hole，hole surfaceroughness Rz directly affects workpiece characteristics ofwear resistance，fatigue property，and stress corrosionresistance.Therefore，great attention should be paid onsurface roughness.According to tool movement principle，theoretical analysis can be made on hole surfaceroughness。

Figure 6 shows a model for calculating hole surfaceroughness. W hen tool rotates one tooth. the toolrevolution angle iS2nn∞ 2nwhere Z is tool teeth number， is the speed ratio of toolrotation and too1 revolution。

From Fig.6，hole surface roughness Rz is expressedaS： D- z 01 十dt- where lo，A means the distance from point Ol to point A，which iS described asdt lo，A -- inin ] 2When substituting Eq.(1 1)and Eq.(13)intoEq.(1 2)，we gain the folowing equation：、/ P 口2 -兀，. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .- /nJ.Cent.South Univ.(2013)20：1818-1824 l823of aU the diferent tools iS 2.and the holes to bemachined al1 have the same diameter of 23 mm。

Conclusions can be drawn as follows： 1、 Whenrevolution radius iS gradually increased.the hole surfaceroughness folows increasing trend；2)Under largerevolution radius and low speed ratio，hole qualitybecomes poor。

These conclusions from Figs. 7-9 have greatsignificance in optimizing control parameters duringhelical milling。

e [siI1(尢- -arcsin n㈨ )]/sin (14a( ·in e 0· - - - - - - ㈦(14b IFig.6 Theoretical calculation model of hole surface roughnessEquation(1 41 iS a theoretica1 formula of surfaceroughness in helical milling hole.Roughn ess Rz isdetermined by severa1 parameters of tool teeth numbegtoo1 diameter，rotation speed.revolution speed andrevolution radius。

W hen tool diameter iS 1 2 rain and hole diameter iS23 mm，the relationship of surface roughness with toolteeth number and speed ratio iS shown in Fig.7.Surfaceroughness increases with the decrease of tool teeth andspeed ratio.Here.the influence of tool teeth number onsurface roughn ess is obvious.The two parameters havesignifcant influence on hole surface roughnessespecially when machining with low speed ratio andsmal tool teeth number。

Figure 8 shows the relations among threeparameters of surface roughness，revolution radius andspeed ratio.when tool diameter is set as 1 2 min and too1teeth are 2.Here.hole diameter increases with theenlargement of tool revolution radius.Under high speedratio.hole surface roughness increases a litle.However，it decreases obviously with small speed ratio.Thesmaller the speed ratio iS.the faster the hole surfaceroughness decreases。

Figure 9 reflects the efrect of revolution radius androtate speed ratio on surface roughn ess when differenttools are used to machine holes.Here.the teeth numberg≈ 50Fig.7 Relationship ofRz with Z and (D23 mm，dt12 mm)重Fig.8 Relationship ofRz with e and (dt12 mm，Z2)gFig.9 Relationship ofRz with e and (D23 mm，Z2)5 Conclusions001)According to the principle of helical milling hole，characteristics of two typical methods in robotic helicalmiling are discussed and working process of roboticD-2， 、 .m ，r1824 J.Cent.South Univ.(2013)20：1818-1824helical milling is designed.After analysis on movementof robotic helical miling，vector equations of two typicalhelical miling methods are deduced.which helps torealize the movement control in helical milling hole。

21 An analytical model of hole surface roughness isbuilt upon the movement features of helical milling hole。

then influence of cutting parameters on roughness isstudied.The research gives good reference for choosingproper parameters of tool teeth number，tool radius，revolution radius and speed ratio in the process of helica1miling。

3)In helical milling hole，the surface roughness isalso influenced by actual process factors of cuttingenvironment，chip types，and chip transportation，etc。

Thus.how to find a precise roughness model based on ane衔cient combination of theory and experiment wil1become an important research direction。

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