A Parametric Design of Ball End Mill. and Simulating Process

Transcription

1 A Parametrc Desgn of Ball End Mll and Smulatng Process Lyong Chang A Thess In the Department of Mechancal and Industral Engneerng Presented n Partal Fulfllment of the Requrements For the Degree of Master of Appled Scence at Concorda Unversty Montreal, Quebec, Canada March 2016 Lyong Chang, 2016 I

2 CONCORDIA UNIVERSITY School of Graduate Studes Ths s to certfy that the thess prepared By: Enttled: Lyong Chang A Parametrc Desgn of Ball end mll and Smulatng Process and submtted n partal fulfllment of the requrements for the degree of Master of Appled Scence comples wth the regulatons of the Unversty and meets the accepted standards wth respect to orgnalty and qualty. Sgned by the fnal examnng commttee: Dr. Onur Kuzgunkaya Char Dr. Langzhu Wang Examner Dr. Wenfang Xe Examner Dr. Z. C. Chen Supervsor Approved by Char of Department or Graduate Program Drector Dean of Faculty Date II

3 ABSTRACT A Parametrc Desgn of Ball End Mll and Smulatng Process Lyong Chang Ball end mll cutter s wdely used n precse CNC machnng as a hgh effcency processng tool for complex surface. On the bass of the lterature revew about mathematcal model, grndng machnng process, cuttng experment of ball end mlls, and the calculaton for a ball end mll, a ball end mll parametrc desgn system s bult by development technology wth CATIA 3D modelng software and Vsual Basc. Wth ths system obtanng the model of the ball end mll, the smulaton s processed n Thrd Wave AdvantEdge software. The man contents of ths paper are: 1. On the bass of creatng a mathematcal model of a ball end mll cuttng edge curve, we generate the 3D model of the cutter n CATIA. Moreover, the condtons of the engagement between the grndng wheel and rake surface to avod nterference are proposed. As a result, the grndng wheel center locaton and orentaton axs are defned. 2. A modelng program for ball end mlls s developed n Vsual Basc, and the 1

4 parameter modfcaton can be vsualzed n the nterface of ths program.in addton, the model s smulated n Thrd Wave AdvantEdge to analyze the temperature of the cutter and the cuttng force dstrbuton. KEY WORDS: Ball End Mll, Parametrc Desgn, CATIA Secondary Development, Smulaton 2

5 ACKNOWLEDGEMENTS I hereby would lke to thank my supervsor, Dr. Chevy Chen, for hs knd gudance and patent nstructons through all ths work. It really mproves me qute a lot gong through all ths research, I would not accomplsh thess wthout hm. Addtonally, I would lke to express my apprecaton to all my dear colleagues n our lab, for every generous help from everyone when I encountered any problems. Fnally, I gve my specal thanks to my parents, for all ther selfless love and contnuous support n every aspect all through my study. 3

6 Table of Contents Chapter 1. INTRODUCTION Ball End-mll Background Mathematcal Model Parametrc desgn Lterature Revew Objectve of Thess Thess Outlne Chapter 2. Mathematcal Model of Cuttng Edge Curve Parametrc Equaton Applcaton n Matlab Chapter 3. Mathematcal Model of Ball End Mll Introducton Toolbar Modelng and the Constructon of Coordnate System Mathematcal Model of Rake Face n Ball Part

7 3.3.1 Equaton for Bottom Curve of rake face Wheel Locatons for Rake Face n Ball Part Mathematcal Model for Clearance Face n Ball Part Constructon of the Clearance Face n Concave method Constructon of the Clearance Face n Flat method Calculaton Results Appled n Matlab and CATIA Chapter 4. Desgn and Modelng of Flute Surface Introducton Calculaton of the Flute Surface Flute Surface Constructon n CATIA Flute Surface n Ball Part Flute Surface n Cylnder Part Chapter 5. APPLICATION Introducton of the Smulaton Commercal Software Basc Settngs n Thrd Wave AdvantEdge

8 5.2.1 Tools and Workpece Materal Machnng Parameters Smulaton Example Chapter 6.Conclusons and Future Work Conclusons Future Work REFERENCES

9 Lst of Fgures Fgure 1.1 End Mll Tool Types... 1 Fgure 1.2 Ball End Mll Machnng on a Workpece... 2 Fgure 1.3 3D Ball End Mll Model n CATIA... 3 Fgure 2.1 Cuttng Edge Curve Vsualzed n MATLAB Fgure 2.2 Cuttng Edge Curve Vsualzed n Matlab(Top Vew) Fgure 3.1 Basc Components of Ball Part Fgure 3.2 Toolbar Locaton n Coordnate System Fgure 3.3 Geometrc Component on Cuttng Edge Fgure 3.4 Normal Plane of Cuttng Edge Fgure 3.5 Rake Face and Clearance Face Model I Fgure 3.6 Rake Face and Clearance Face Model II Fgure 3.7 Modelng Interface n Vsual Basc Fgure 3.8 Grndng Wheel for Rake Face Sketch

10 Fgure 3.9 Grndng Wheel Interference Stuaton Fgure 3.10 Grndng Wheel for Machnng Rake Face Fgure 3.11 Grndng Rake Face Vew n CATIA Fgure 3.12 Clearance Face Vew n Normal Plane Fgure 3.13 Grndng Wheel for Clearance Face Sketch Fgure 3.14 Axs Cross Secton Vew of the Grndng Wheel Fgure 3.15 x-o-z Plane Vew of Grndng Concave Clearance Face Fgure 3.16 Grndng Wheel Axs Orentaton Fgure 3.17Wheel Center Locaton of Flat-shaped Clearance Face Fgure 4.1 Generated Surface by the Movng Wheel Fgure 4.2 Grndng Wheel Coordnate System Fgure 4.3 Local Coordnate System Settng Fgure 4.4 Flute Surface Splt Fgure 4.5 Clearance Face Surface Fgure 4.6 Flute Profle on Cylnder Part

11 Fgure 4.7 Flute Surface by Sweepng Flute Profle along the Helx Fgure 4.8 Modelng the Flute surface wth Flute Profle Fgure 5.1 Thrd Wave AdvantEdge Interface Fgure 5.2 Materal Selecton of Tools and Workpece Fgure 5.3 Import the 3D Model of the Tool Fgure 5.4 Modfed Model For Smulaton Fgure 5.5 Meshng of the Ball End Mll and Workpece Fgure 5.6 Down-mllng Tool Feed and Moton Fgure 5.7 Up-mllng Tool Feed and Moton Fgure 5.8 Coordnate System of the Tool n AdvantEdge Fgure 5.9 Cuttng Force Fluctuaton Dagram Fgure 5.10 Cuttng Force Data Analyss n Excel Fgure 5.11 Temperature Dstrbuton of the Tool

12 Lst of Tables Table 3-1 Parameter Settng for Rake face Table 3-2 Parameters of the Grndng Wheel for Rake Face Table 3-3 Parameters of the Grndng Wheel for Clearance Face

13 Chapter 1. Introducton 1.1 Ball End-mll Background End mll cutter, s playng a vtal role n machnng process n ndustry world. Due to the hgh paces of manufacturng development, the contnuously growng varetes of materal and the complexty of component geometry, end mllng tools need to step nto a hgher level of condtons. In recent years, varous end mllng tools are adopted n ndustry, such as flat mll, ball end mll, fllet mll as shown n Fgure 1.1. Even f some Fgure 1.1 End Mll Tools Types 11

14 new manufacturng tools or even manufacturng methods sprng up, end mllng tools stll have rreplaceable advantages. Ball end mll used n a Computer Numercal Control (CNC) machne has been wdely appled n Hgh-Speed Machnng (HSM) process. Addtonally, ball end mll s an mportant knd of tool n machnng complex three-dmensonal surface. Due to ts unque cuttng edge shape (S-type, Helx-type, etc), ball end mll has the advantages of hgh machnng precson, long product lfe, low manufacturng process cost, and t s able to axally feed. In a word, t meets the requrements for automatc processng of complex spatal surfaces. Fgure1.2 Ball End Mll Machnng On a Work Pece As shown n Fg 1.2, a ball end mll can be used n manufacturng a sphere n a work 12

15 pece, and the surface s much better than the one manufactured by other knds of mll tools. Ths s just a sample, ball end mll can be wdely appled n mllng varous shapes. Defntely, all the expected advantages wll be realzed when the tools are well desgned. Desgnng ball end mlls has ts unque obstacles, whch wll be dscussed n next chapters. A model of ball end mll dsplayed n a 3D modelng software s shown n Fg 1.3. Fgure1.3 3D Ball End Mll Model n CATIA 1.2 Mathematcal Model The performance of a ball end mll n machnng process s determned by the shapes of rake face and clearance face. Based on the mathematcal model of the cuttng edge of the ball end mll, rake face and clearance face can be defned by rake angle and 13

16 clearance angle respectvely n the orthogonal sectons. Afterwards, the grndng wheel locatons can be determned by ths mathematcal model. It s necessary to create the mathematcal model of the cuttng edge and nspect t vsually n Matlab. Based on the rght mathematcal model, t s tme-savng to proceed the desgn. In desgn process, mathematcal calculaton s the bass. Compared wth featurebased desgn, because the cuttng edge mathematcal model s created at the very begnnng n ths method, t s more productve to calculate the data of manufacturng process. The basc connecton of CAD and CAM can be bult n ths way, and that wll be dscussed n Chapter Parametrc desgn In general, a mechancal part conssts of a couple of geometrc features related to ts functon and ts manufacturng method. Now, a kernel technque of the computer-aded desgn s parametrc part desgn and modelng. On the bass of a new trend of mechancal part desgn-the part feature optmzaton, feature-based parametrc part desgn s a dspensable advanced technque snce the parametrc CAD models of the part features can be easly modfed n the part desgn optmzaton process. Therefore, the parametrc part modelng functon n the commercal CAD/CAM software s very mportant. By defnton, the parametrc part desgn s to determne the crtcal feature dmensons as the parameters and to specfy the relatons among the parameters and other part dmensons. In the parametrc modelng functon of the CAD/CAM software, 14

17 the functons of defnng parameters and constrants are developed, and the parametrc part models can be constructed. By assgnng data to the feature parameters, all dmensons are calculated, and the sold model of the part can be changed and updated n seconds. Mechancal part desgn ncludes several decson-makng processes and actvtes, whch are nvolved n determnng the shape and dmensons of a mechancal part. Generally, the development of a mechancal part has fve sectons: formulaton, concept desgn, confguraton desgn, parametrc desgn, and detal desgn. Wth a parametrc desgn of a part, the sold model of a part desgn can be easly attaned, and the part can be analyzed to predct the part performance and functonalty. Ths can sgnfcantly reduce the leadng tme n the part desgn cycle and the cost of makng prototype. To mplement the parametrc part desgn and modelng, the followng four procedures are necessary, whch are 1) Defnng the key dmensons as the parameters, 2) Fxng the relatonshps or constrants between the parameters and the part dmensons, 3) Buldng the part model n CAD/CAM software, 4) Inputtng dfferent parameters and the constrants to nspect the models. 1.4 Lterature Revew There are a number of academc thess that have proposed the modelng process of 15

18 the ball end mll. Km and Park [1] have descrbed a desgn process of an end mll. In ther thess, the sold model of a specfc end mll s constructed together wth the computaton of the cutter s geometry, grndng wheel geometry, wheel postonng fabrcatng end mlls wthe the requred cutter geometry. Tandon and Khan [2] present a three dmensonal modelng and fnte element smulaton of a generc end mll. Ther paper descrbes n detal the methodology to model the geometry of a end mll n terms of three-dmensonal parameters. The geometrc defnton of the end mll s developed n terms of surface patches; flutes as helcodal surfaces, the shank as a surface of revoluton and the blendng surfaces as bcubc Bezer and bparametrc sweep surfaces. Lazoglu[3] developed a mechancal model of a ball end mll n the year of 2003, the model has the ablty to calculate the workpece/cutter ntersecton doman automatcally for a gven cutter locaton (CL) fle, cutter and workpece geometres, that helps to obtan experences about the cutter workng condtons. Altntas and Lee [4] have presented the mechancs and dynamcs of cutter wth helcal ball end mlls. The helcal ball end mll attached to the spndle s modeled by orthogonal structural modes n the feed and normal drectons at the tool tp. Vckers and Quan[5] showed how to gve a better match to the requred surface geometry and hence reduce the number of surface passes requred. Zhu and Kapoor [6] gave a mechancal modelng of ball end mll process, n addton, they present an dea of mult-axs machnng of free style surface. Wth regard to the smulaton of the end mlls, several papers are revewed. Iman, Sadegh and Elbestaw [7] developed a system that deals wth the geometry and mechancs of machnng wth ball-end mllng cutters. Moreover, ths system can 16

19 generate the model of workpece/cutter engagement. In Yucesan and Altntas[8] thess, Mechancs of mllng wth ball ended helcal cutters are modeled, whch s based on the analytc representaton of ball shaped helcal flute geometry, and ts rake and clearance surfaces. After that, ther work focused on the predcton of the cuttng forces. In Myaguch, Masuda, Takeoka and Iwabe [9] thess, the research focused on the effect of stffness upon tool wear n hgh spndle speed mllng, and t s appled n small sze of ball end mll. The specfc force coeffcents for a general end mll was dscussed n Gradš ek, Kalveram, and Wenert[10] thess. Mlfelner, Kopac, Cus and Zuperl [11] dd a reseach about a genetc equaton for the cuttng force n ball-end mllng n the year of Jn, Goto, Watanabe, Kurosawa,and Murakawa[12], developed a new cuttng edge of CBN ball-nosed end mll. In Sharman, Dewes, and Aspnwall [13] thess, tool lfe has been dscussed when hgh speed s appled on ball nose end mllng. Kangnn [14] bult a rgd Cuttng Force Model of Ball End Mll n the year of 1998, whch help us to analyze the cuttng force. In Jnlng [15] s study, the CNC Grndng of the Ball Nose End Mll, the grndng condtons have been ntroduced. Pa, Sarhan, and Shukor [16] showed a method of optmzng the cuttng parameters for better surface of ball end mll. In references [17], [18], [19] and [20], the smulaton for cuttng force and temperature dstrbuton on the end mll surface was studed. In Lazoglu and Lang s [21] thess, the modelng of ball-end mllng forces was appled wth cutter axs nclnaton, the result of ther experment helped to reconsder the ball end mll shape. Aoyama, Kshnam, and Sato [22] developed a knd of ball end mll named ellptc ball end mll. Wang s [23] thess, A new CAD/CAM/CAE ntegraton approach to modelng flutes of sold end-mlls, 17

20 helped us to calculate the flute profle ponts, whch s the foundaton of the flute modelng n cylnder part. 1.5 Objectve of Thess As the confguraton of the rake face and clearance face s qute decsve for a ball end mll, most works n ths thess wll be focused on them. Accordngly, we buld a mathematcal model of the cuttng edge curve, and program t n Matlab. In Matlab, ths model can be analyzed and verfed vsually. From the desgn of the rake face and clearance face, the flute surface can be generated by a fxed grndng wheel. Addtonally, t s a new method to determne the rake face by rake angle and the wdth of rake face n each cross sectons, clearance face can be defned n same way. It s tme wastng to buld dfferent models n 3D modelng software when we need to modfy a gven model or compare the performance of two models. A ball end mll modelng software s proposed n ths thess. Dfferent models can be generated automatcally n ths software by changng the values of the parameters. On the bass of mathematcal model of the cuttng edge, the flute surface can be generated by a grndng wheel n the lght of a tangency condton. Once we obtan the locaton coordnates of the wheel, Boolean operatons can be appled n the 3D modelng software. Our goal s to get a method to make the surface contnuous and precse. In the end, a fnte-element analyss smulaton s appled to compare the dfferent 18

21 models based on dfferent parameters. 1.6 Thess Outlne Ths thess conssts of several chapters. Chapter 1 ntroduces the basc knowledge of end mll tools, mathematcal model of the cuttng edge, parametrc desgn, and the lterature revews about ths thess topc. Chapter 2 represents the mathematcal model, the generaton of the rake face and clearance face. Then dscusson about the rake face parameters optmzaton s presented. Chapter 3 ntroduces the calculaton of the locaton coordnates of the grndng wheel, followed by the modelng by Boolean operatons. Then the method of optmzng flute surface s ntroduced. Chapter 4 shows smulaton n a FEA software compared wth two dfferent models. Chapter 5 concludes the research and ntroduces the future work about ths modelng method. 19

22 Chapter 2. Mathematcal Model of Cuttng Edge Curve 2.1 Parametrc Equaton The accuracy of the products manufactured by a ball end mll reles on the precson of the cuttng edge. Therefore, the cuttng edge need to be desgned and machned accurately. The goal of ths secton s to buld the equatons of the helx cuttng edge curve of a ball end mll. The cuttng edge curve goes from the top of the sphere through the ball part and cylndrcal part. A tool coordnate system OXYZ s bult n a bar, n whch the orgn O s placed at sphere center, and the OZ axs concdes wth the longtudnal axs of the bar. All of the followng calculatons are based on ths coordnate system. The cuttng edge curve s shown n Fg 2.1. edge curve, and ts coordnate can be presented as a vector M s a general pont along the cuttng OM as follows: OM cos R z,sn R z, z Eq.(2-1) In whch R s the radus of the ball and s the vrtual angle between the tool tp and the current M on the cuttng edge curve. 20

23 Helx angle s the angle between the tangent vector of the longtudnal axs Tˆ, and the tangent vector of the helx T. The angle represents the helx angle n ths model. A mathematcal model of the cuttng edge wth a constant helx or a constant ptch was developed prevously. In our research, the constant helx s appled to the cuttng edge curve. Thus, the relaton of the vrtual angle and helx angle can be descrbed as follows: tan d dz Eq.(2-2) R The vrtual angle s zero at tool tp where z R, and t can be obtaned by calculaton the ntegral of Eq.(2-2): tan z R R Eq.(2-3) Substtutng the n Eq.(2-3) nto Eq.(2-1), we can get the parameter equaton of the cuttng edge curve: x y z R cos 1 1 tan R sn 1 1 tan R 1 tan 2 2 Eq. (2-4) 2.2 Applcaton n Matlab In ths secton, the manpulaton of the parameter equaton of the cuttng edge 21

24 curve s descrbed. Addtonally, ths process contrbutes to obtanng the precse cuttng edge curve, and make t convenent n programmng n Matlab to get the vsualzed analyss. Frstly, the equaton can be added wth several condtons on the bass of foundatons of mathematcs. The condtons wll be presented as follows: 1) 0 2) 0 1 tan Applyng Eq.(2-4) and the condtons above n Matlab, the 3D confguraton of the cuttng edge can be descrbed n Fgure 2.1. In ths graph, there are four cuttng edges determned by four dfferent helx angles shown on the sphere surface. From left to rght, four curves n whte, yellow, green and black represent the cases n terms of varable helx angle, and the value s , , , , whte yellow green black respectvely. 22

25 Fgure 2.1 Cuttng Edge Curve Vsualzed n Matlab In Fgure 2.2, the curvature n dsperse helx angle determnng stuatons can be clearly detected. Wth the helx angle ncreasng, apparently, the performance of a ball end mll wll be nfluenced. The specfc nfluences wll be dscussed n the smulaton chapter, Chapter 5. 23

26 Fgure 2.2 Cuttng Edge Curve Vsualzed n Matlab (Top Vew) 24

27 Chapter 3. Mathematcal Model of Ball End Mll 3.1 Introducton In ths chapter, the basc components of the ball part wll be modeled mathematcally. It s dvded n rake face desgn and clearance face desgn. In each part, Fgure 3.1 Basc Components of Ball Part 25

28 The equatons wll be determned frst, and then verfed n CATIA by codng n VB.NET. The ball part components are shown n Fg 3.1. Wheel locatons for the rake face part and clearance part are defntely mportant for machnng. Thus, they wll be calculated and analyzed n ths chapter. 3.2 Toolbar Modelng and the Constructon of Coordnate System Our purpose s to precsely machne a ball end mll, and the basc parameters of the product,.e. radus of the ball part, length of cutter, are determned by the toolbar parameters settngs. In ths paper, the radus of the bar R, and the length of the bar L are set as follows: R 6mm, L 80mm The calculatons of the ball end mll components,.e. cuttng edge, rake face, clearance face, are on the bass of coordnate system OXYZ. The center of the hemsphere of the ball part s defned as the orgn of ths coordnate system OXYZ, and the axs of the toolbar s determned as the Z-axs. They can be descrbed n Fg

29 Fgure 3.2 Toolbar Locaton n Coordnate System The radus and length can be edted n desgned Vsual Basc nterface, and that wll be ntroduced n next chapter. 3.3 Mathematcal Model of Rake Face n Ball Part In ths secton, the tangent and normal vectors to the sphercal surface along the cuttng edge are ntroduced as the basc components of the cuttng edge curve. As shown n Fg

30 Fgure 3.3 Geometrc Component on Cuttng Edge On the bass of desgned depth of cut n the normal plane of cuttng edge, a bottom curve s defned, whch s mportant for determnng the wheel locatons for the rake face, and t wll be ntroduced n Secton 3.3. The tangent vector of the Cuttng edge Tˆ, the normal vector of the ball surface and the vector Ĉ, whch s the cross product of the vector Tˆ and vector Nˆ. Pont Nˆ, M s defned as a general pont of the cuttng edge. On the bass of the poston vector m x,y,z of a general pont along the cuttng edge, the vectors Tˆ, Nˆ and Ĉ can be 28

31 descrbed by Eq(3-1): Tˆ Nˆ Ĉ m Tx,Ty,Tz m m N x,n y,n z m Tˆ Nˆ C,C,C x y z Eq.(3-1) The normal rake angle s measured n the normal plane P n, whch s normal to the cuttng edge. The rake face s a contnuous surface wth a cross sectons n the normal plane that conssts of the lne segment M K, as shown n Fg 3.4. Fgure 3.4 Normal Plane of Cuttng Edge 29

32 For a pont on the cuttng edge, the depth of cut can be descrbed as M K, the depth M K h s fxed. It equals zero at the tp and ncreases n the negatve drecton of the Z-axs. The hghlghted lne n red ndcates the bottom lne of the rake face. The rake face shows n dfferent patterns when the defnton dffers. As shown n Fg 3.5, t s the model correspondng to the depth M K beng descrbed as Eq.(3-2). M K / R R z h where, 0 z R Eq.(3-2) Fgure 3.5 Rake Face and Clearance Face Model I As shown n Fg 3.6, t s the model correspondng to the depth Eq.(3-3) M K beng descrbed as M K h R max h z hmax Eq.(3-3) 30

33 Fgure 3.6 Rake Face and Clearance Face Model II In ths case, h max s a assumed parameter that s determned by the user of the modelng software. The relaton between M and K z s lnear, and hmax s the maxmum value of the cut depth. Fg 3.7 shows the nterface of modfyng the hmax n Vsual Basc. 31

34 Fgure 3.7 Modelng Interface n Vsual Basc Equaton for Bottom Curve of rake face In order to accurately machne the rake face of the ball part wth a fxed rake angle and a desgned cut depth, the bottom lne, whch affects the wheel locatons, s needed to be determned. n ths secton, the prncple normal vector of the bottom curve and the normal vector of the rake face along the lne segment n the normal plane are calculated, whch are used n next secton to make sure the rake face can be machned wthout any nterference. 32

35 The vector of the pont K on the bottom curve to the pont s ndcated n Fg 3.2, and t can be calculated as follow: M on the cuttng edge m OK m OC M K x k,y k, z k Eq.(3-4) Where, M K h cos Nˆ h sn Ĉ The bottom curve of the rake face s defned as Eq.(3-4), and t can be parameterzed as Eq.(3-5) m m OK OK x,y, z k k k Eq.(3-5) The prncple normal vector of the bottom curve of the rake face descrbed as follows, whch wll be used n next secton, Nˆ K at pont K s Nˆ K dm dm 2 OK 2 OK d d 2 2 N K x,n K y, N K z Eq.(3-6) Therefore, the parameter equaton for the rake face based on the equatons of the cuttng edge and bottom curve can be determned as follows: S, 1 m m r h Nˆ cos Ĉ sn OC OK OC Eq.(3-7) Where, Wheel Locatons for Rake Face n Ball Part In ths secton, the condtons of engagement between the rake face and grndng wheel are proposed, whch can ensure the grndng wheel machnng the rake face wth ts sde face precsely avod nterference. 33

36 Therefore, the coordnates of the center of the grndng wheel and the vectors of the orentaton of the grndng wheel are determned along the cuttng edge to machne the rake face of the ball part. The radus of the grndng wheel s R w, as shown n Fg 3.8. Fgure 3.8 Grndng Wheel for Rake Face Sketch The rake face s machned by grndng each lne segment M K, usng the sde face of the grndng wheel. The sde face of the grndng wheel wth the center poston of s perpendcular to the wheel axs. In order to avod nterference n machnng the rake face wth the defned cuttng edge, the tangent vector T of the cuttng edge at the G, 34

37 current grndng pont M must be coplanar wth the sde face of the grndng wheel. However, there are many qualfed locatons of the wheel exst that can realze the lne segment Fg 3.9. M K can be ground wthout nterference along the cuttng edge, as shown n Fgure 3.9 Grndng Wheel Interference Stuaton However, the grndng wheel at locaton-1 nterferes the defned bottom curve of the rake face. In other words, only the grndng wheel at locaton-2 can grnd the defned rake wthout any nterference. Moreover, to avod nterference between the grndng wheel and the defned bottom curve, the vector grndng wheel sde face G, as shown n Fg Nˆ K must pass though the center of the 35

38 Fgure 3.10 Grndng Wheel for Machnng Rake Face The vector Nˆ K s the projecton of the prncple normal vector Nˆ K n the plane of the sde face of the grndng wheel. The condtons for machnng the rake face of the ball part wthout nterference can be descrbed as follows: 1. The lne segment M K must be n the plane of the sde face of the grndng wheel. Moreover, the tangent vector of the cuttng edge at the grndng pont contaned n the plane of the sde face as well. M must be 2. The projecton of the prncple normal vector Nˆ K of the bottom curve, Nˆ K must contan the center of the sde face of the grndng wheel G. 36

39 Based on the condtons shown above, the wheel axs Î can be presented as follows: Î Tˆ KM Tˆ K M I x,i y, I z Eq.(3-8) As the Secton 3.3 mentoned, M K h cos Nˆ h sn Ĉ Tˆ T x,t y, T z Where, Nˆ N,N, N and Ĉ C,C, C x y z x y z Therefore, K M h cos h sn Ĉ, and Tˆ KM Nˆ can be presented as follows: x y z g g g Tˆ Tˆ Tˆ y z x h cos N h sn C Tˆ h cos N h sn C h cos N h sn C Tˆ h cos N h sn C h cos N h sn C Tˆ h cos N h sn C z x y z x y On the bass of the condtons1 and condtons 2 above, the poston of the wheel center s determned by Eq.(3-10) z x y y z x y z x m OG m OK Nˆ K R w Eq.(3-10) There s only one common pont K between the grndng wheel and the bottom curve of the rake face. And we can get the concluson from the condtons above that I and Nˆ K, these two vectors are ntersected, thus, I, Nˆ K and Nˆ K are coplanar. The vector Nˆ K can be obtaned as follows: Nˆ K Î Nˆ K Î Î Nˆ K Î Eq.(3-11) 37

40 When the sde face of the grndng wheel contans the lne segment M K, the wheel axs orentaton s defned to be equvalent to the normal of the rake face at the grndng pont M. Then the contact lne between the desgned rake face and the sde face of the grndng wheel s ths lne segment. The poston of the wheel center and the orentaton of wheel axs that are requred for accurate machnng of the rake face are determned by Eq.(3-10) and (3-8), respectvely. Moreover, Eq.(3-12) s to prove the normal of the rake face s constant along the lne segment M K. I S S, S,, S, cos Ĉ sn Nˆ Nˆ Nˆ h cos Nˆ sn Ĉ m mtˆ h cos Tˆ kn sn F R m m h cos kn sn sn h R Eq.(3-12) Where, Nˆ F s the prncple normal vector, kn s the normal curvature, and s the angle between the prncple normal vector grndng pont M. Nˆ F and the normal of the sphere Nˆ at the current Fg 3.11 shows the grndng status n CATIA, the volume n blue represents the grndng wheel, and the other volume s the tool bar. The grndng wheel s machnng the tool bar and the wheel sde face profle s tangent to the bottom curve of the rake face. 38

41 Fgure 3.11 Grndng Rake Face Vew n CATIA 3.4 Mathematcal Model for Clearance Face n Ball Part In machnng process, the clearance angle of the ball end mll affects the cuttng force, chps removal and some other condtons whch sgnfcantly determnes the cuttng performance and the tool lfe. Moreover, the clearance face shape s an 39

42 mportant component of a ball end mll, and t can be dfferent pror to the grndng method. In ths paper, the frst and second clearance face calculaton wll be presented n ths secton. And the clearance face and clearance angle defnton s shown n Fg Fgure 3.12 Clearance Face Vew n Normal Plane The clearance angle, s defned as the angle between the tangent vector at pont M and the drecton of the vector Ĉ n the normal plane. The clearance face s machned by the outer crcle face of the grndng wheel n the concave method and by the sde face of the grndng wheel n the flat method. The parameters of the grndng 40

43 wheel for the clearance face are shown n Fg 3.13: Fgure 3.13 Grndng Wheel for Clearance Face Sketch Constructon of the Clearance Face n Concave method In ths secton, the grndng wheel locaton can be determned by the cuttng edge and ts basc components. Once the grndng wheel center poston and axs orentaton are calculated, the concave-shape clearance face wth a constant clearance angle can be 41

44 obtaned along the cuttng edge. The locaton of the grndng wheel for machnng the concave-shape clearance face s shown n Fg 3.14 and Fg The clearance face s formed by the crcle face of the grndng wheel, and the axs of the grndng wheel s perpendcular wth the tangent vector of the cuttng edge. Moreover, to ensure the clearance angle beng constant, the tangent vector of the grndng wheel outer crcle at the grndng pont angle of the value of clearance angle wth the drecton of Ĉ. M make a Therefore, the relatve poston of the grndng wheel center and the orentaton of wheel axs are determned as follows: m OG m OM M G Where, M G R sn Ĉ cos Nˆ c Eq.(3-13) The orentaton of the wheel axs can be presented as follows: Î Ĉ Nˆ Eq.(3-14) 42

45 Fgure 3.14 Axs Cross Secton Vew of the Grndng Wheel 43

46 Fgure 3.15 x-o-z Plane Vew of Grndng Concave Clearance Face Constructon of the Clearance Face n Flat method In ths secton, the grndng wheel locaton can be determned by the cuttng edge and ts basc components. Once the grndng wheel center poston and axs orentaton 44

47 are calculated, the concave-shape clearance face wth a constant clearance angle can be obtaned along the cuttng edge. The model for grndng flat-shape clearance face s shown n Fg The clearance face s machned by the sde face of the grndng wheel movng along the cuttng edge. The orentaton of the wheel axs makes a angle of the value of the clearance angle. The grndng wheel ntersects the ball part at each grndng pont, and that ntersecton presents as a lne segment. The length of ths lne segment s defned as the wdth of the clearance face. Therefore, the poston of the center of the grndng wheel s obtaned as follows: m OG m OM M G Eq.(3-15) 2 2 Where, MG R sn cos Ĉ sn Rc R sn The orentaton of the grndng wheel axs can be calculated as follows: Nˆ Tˆ Î cos Nˆ sn Ĉ Eq.(3-16) 45

48 Fgure 3.16 Grndng Wheel Axs Orentaton 46

49 Fgure 3.17 Wheel Center Locaton of Flat-shaped Clearance Face 3.5 Calculaton Results Appled n Matlab and CATIA The mathematcal model of the cuttng edge, rake face, and clearance face are bult n last several sectons. Our goal s to create the 3D model n CATIA, and then the analyss and smulatons work can be done. Therefore, buldng a brdge between the mathematcal equatons and the software s defntely mportant. Frst of all, the equatons requre to be mported to MATLAB. Once the program s 47

50 created, several parameters need to be fxed to calculate the data. Table 3-1 shows the parameters that need to be set before the calculaton n MATLAB. Table 1-1 Parameter Settng for Rake face Settng Values Radus of ball Helx angle 6mm 57 degrees Number of the dscrete ponts 80 Number of flutes 2 Helx length Rake angle max Wdth max 80mm 3 degrees 1.85mm Table 1-2 Parameters of the Grndng Wheel for Rake Face Settng Values 1 st Radus Rw 56.45mm 2 nd Radus Rc 58.76mm Wdth L 7.6mm 48

51 Table 1-3 Parameters of the Grndng Wheel for Clearance Face Settng Values 1 st Radus Rw 57.1mm 2 nd Radus Rc 59mm Wdth L 8.5mm Wth the calculaton n MATLAB, we can code the program to produce the.txt fle n specfed folder. The data n ths fle wll be specfed amount of coordnates. These coordnates can be appled n VB program to control CATIA creatng ponts. For the cuttng edge of the ball part, the dssocated ponts can be connected as a splne n CATIA, whch s the way to obtan the cuttng edge curve. In terms of the grndng wheel locaton, the data produced by MATLAB ndcates the dssocated center ponts of the grndng wheels at each locatons, and the orentatons of the axs of the grndng wheel. Table 3-2 and Table 3-3 shows the parameters of the grndng wheels for machnng the rake face and clearance face, respectvely. 49

52 Chapter 4. Desgn and Modelng of Flute Surface 4.1 Introducton After the equaton of the cuttng edge and the normal rake angle and clearance angle are gven, wth the cut depth s set n the program, the rake face can be modeled n CATIA. Meanwhle, the postons of the grndng wheel center and the orentatons of the grndng wheel axs are calculated n MATLAB n prevous sectons, whch makes t possble to obtan the flute surface of the ball part. However, ths surface s ground by the revoluton surface of the grndng wheel. In ths secton, the generated surface of the flute wll be calculated wth the goal of vsualzaton and smulaton. The flute surface s calculated by the tangency condton at each grndng pont of the wheel surface. The flute surface s mportant for a ball end ml, because t determnes the cuttng performance and the chp removal. Although t s possble to obtan the flute surface by Boolean operaton n commercal software, for the precse smulaton purpose, t s requred to present a drect calculaton of the surface. 50

53 4.2 Calculaton of the Flute Surface The flute surface s determned by envelopng the surface of the movng grndng wheel along the cuttng edge. And t conssts of three factors: 1. The surface of the grndng wheel at the startng poston. 2. Swept surface of the movng grndng wheel. 3. The surface of the grndng wheel at the fnal poston. Fgure 4.1 Generated Surface by the Movng Wheel The ponts on the swept surface are determned by an mportant condton, whch s 51

54 the grndng wheel s always tangent to the swept envelope along a sweepng profle, as shown n Fg Thus, the unt normal vector N I, s parallel to the vector normal to the swept surface at any pont I on the swept surface. Moreover, the velocty vector V I, of pont I s constraned to be tangent to the swept surface. Therefore, the swept surface can be determned based on the tangency condton as follows: N I VI 0 Eq.(4-1) But the rear surface and the front surface are parts of the flute surface as well, n ths case, the condtons shown as follows wll be appled: For rear surface, N I VI 0 Eq.(4-2) For front surface, N I VI 0 Eq.(4-3) The wheel locaton center trajectory calculated n prevous secton can be parameterzed as follows: G t m,m, m m Eq.(4-4) follows: OG x OG y OG z And the unt vector of the orentaton of the wheel axs can be parameterzed as t I,I, I Î Eq.(4-5) x y z Therefore, the movement of the grndng wheel can be determned by the trajectory the wheel center locatons m G t, and the wheel axs orentaton s gven. A coordnate system of the grndng wheel can be founded at the wheel center, whch s presented as 52

55 follows: Xˆ Ŷ Ẑ W W W I I Ẑ Î W Xˆ W Eq.(4-6) Fg 4.2 ndcates the coordnate system vsually. Fgure 4.2 Grndng Wheel Coordnate System The axal cross-secton of the grndng wheel wth the wdth, L, n the X W ZW plane 53

56 of the grndng wheel coordnate system s created n Fg The parametrc equatons of the revoluton surface of the wheel can be obtaned by rotatng a curve along the axs, and t can be presented as follows: ZW - S W s,,t mg t rs cos Xˆ W rs sn ŶW s ẐW Eq.(4-7) Here, the normal vector N I and the velocty vectorv I are requred to be calculated. In the cross-secton of the wheel surface whch normal to the wheel axs Î, offset from the wheel center a dstance s n the angle,, measured from the axs Z W axs, takng a pont I n that cross-secton at an X L. The velocty of pont I and the normal of wheel surface at pont I are determned n workpece coordnates as follows: 54

57 V I r G Î Ŷ W GI Fgure 4.3 Grndng Wheel Coordnate System V G r s cos Xˆ W rs sn ŶW s ẐW m G Eq.(4-8) Where, G s the nstant angle velocty of the wheel. Therefore, the velocty vector V I can be smplfed as follows: V I m G s I Xˆ W I r s cos Ẑ W Eq.(4-9) Moreover, the normal vector of the wheel surface at general pont I can be calculated as follows: 55

58 N I SW SW cos Xˆ s,,t S s,,t s,,t S s,,t W W W sn Ŷ 1 r 2 s s W s r s Ẑ W Eq.(4-10) For the swept surface of the movng wheel, N V 0, we can get the followng equaton: I I m Xˆ I rs r s I scos m Ŷ sn r s m Z 0 G W G W G W Eq.(4-11) Therefore, we can obtan the contact lne between the grndng wheel surface and the swept surface. For the case of the ntal poston and fnal poston, as stated prevously, the condton N V 0 and N V 0 must be satsfed, respectvely. I I I I Above all, the flute surface machned by the movng grndng wheel can be determned. 4.3 Flute Surface Constructon n CATIA Flute Surface n Ball Part After the Boolean operaton for the grndng wheel and ball part workpece, the flute surface can be obtaned. But the surface s shown hackly n CATIA because of the dsadvantage of Boolean operaton. Even though, we can calculate the wheel locatons ntensvely n MATLAB, the surface s not smooth enough. Here, we wll show the operaton method to obtan a smooth flute surface. 56

59 At each locaton, the grndng wheel ntersects the workpece as a contact curve. The ntersecton can be easly obtaned n CATIA wth the functon ntersecton. In geometrc shape desgn, we can use the functon mult-secton surface to connect these contact lne to a surface. Thus, by splttng the workpece wth the mult-secton surface, the smooth flute surface can be obtaned, as shown n Fg 4.4. Fgure 4.4 Flute Surface Splt It can be also appled to the clearance surface, as shown n Fg

60 Fgure 4.5 Clearance Face Surface Flute Surface n Cylnder Part For the flute surface n cylnder part, we take the method n the thess A New CAD/CAM/CAE Integraton Approach to Modelng Flutes of Sold End-mlls. By calculatng the coordnates of the ponts n the axal cross-secton of the toolbar, the ponts can be obtaned n CATIA as shown n Fg

61 Fgure 4.6 Flute Profle on Cylnder Part By usng the splne functon, all of the ponts can be connected to a splne curve, whch s defned as the object to be swept. As stated prevously, the helx angle and radus of the toolbar has been defned. Therefore, we can obtan the flute surface by sweepng the splne curve shown n Fg 4.7 along the helx, as shown n Fg

62 Fgure 4.7 Flute Surface based on sweepng the Flute Profle along Helx 60

63 Fgure 4.8 Modelng the Flute surface wth Flute Profle 61

64 Chapter 5. APPLICATION 5.1 Introducton of the Commercal Smulaton Software The modelng process of ball end mll and flute surface s demonstrated n two chapters prevously. By gatherng all of the modelng features, the whole ball end mll can be bult n 3D modelng commercal software,.e. CATIA, SOLIDWORKS etc. In ths paper, we apply all the modelng work n CATIA. To verfy the desgn standard and performance of the model, t s requred to conduct a smulaton n a software. FEA technque s wdely used n many smulaton software. Fnte element analyss can obtan approxmate solutons to engneerng smulaton problems whch transfers a whole part nto smpler parts to get a close result. Thrd Wave Advantedge s a software for optmzaton of metal cuttng wth valdated fnte element technque to analyze machnng processes n 2D and 3D envronments. The model of ball end mll n CATIA can be mported nto Advantedge for further analyss. By defnng geometres and materals of tools and workpece, n addton, settng the cuttng condtons, the results of cuttng process are generated, such as: temperature, stress, chp formaton and power consumpton. The nterface of the Thrd Wave Advantedge s shown n Fg

65 Fgure 5.1 Thrd Wave AdvantEdge Interface 5.2 Basc Settngs n Thrd Wave AdvantEdge Tools and Workpece Materal Cuttng tools are mostly operated at hgh temperature and under heavy loads. Several major requrements for cuttng tools are: good physcal and chemcal propertes under hgh temperature, especally hot-hardness. Hgh wear resstance and hgh resstance to brttle fracture [24]. However, sngle materal cannot satsfy all of the propertes. For nstance, f the hgh-temperature resstance and wear resstance of a knd of materal are hgh, the resstance to brttle fracture wll probably be reduced. Most knds of tool materal n ndustry are carbon steels, hgh-speed steels, cast 63

66 alloys, cemented carbde and ceramcs. Cemented carbdes s the knd of the most wdely used materal n ndustry. Cemented carbdes vares three categores: P, M and K. As shown n Fg 5.2. Cemented carbdes P deals wth materal that produce long chps, ncludng most steels; M for stanless and heat resstant alloys; K for cast rons, nonferrous alloys and hardened steels. In Thrd Wave Advantedge software, all types of carbde are provded. Carbde-Grade-M s selected as the materal of the ball end-mll, because end mlls are always used for multple purposes. Fgure 5.2 Materal Selecton of Tools and Workpece In Advantedge, varous workpece materals are avalable. As ttanum alloy s one of the most hgh performance metals wth hgh tensle strength and toughness, t s 64

67 preferable for smulaton whch could gve contrastng results. Ttanum alloy are dvded nto numbers of categores among whch Grade 5(T-6Al-4V) s the most frequently used Fgure 5.3 Import the 3D Model of the Tool knd of alloy. So T-6Al-4V s set as the materal of the workpece n the smulaton. After determnng the materals of the tools and workpece, we can mport the cutter to the software as shown n Fg 5.3. For the reason of that FEA s a tme 65

68 consumng work, f the entre cutter were mported, there would be too much useless calculaton process. Therefore, we wll select part of the tool as the model whch s mported to the software for smulaton as shown n Fg 5.4. Fgure 5.4 Modfed Model for Smulaton 66

69 5.2.2 Machnng Parameters There are several categores of machnng operaton optons n the software, and corner mllng matches the condtons to verfy the performance of ball end mll. Moreover, both up and down mllng s appled for smulaton. The dmenson of workpece s 6mm*6mm*4mm. Adaptve remeshng technque s appled n meshng procedure. The secton that s approached the more the elements, the more detaled element gets. The mnmum element sze s 0.15 mm. Fgure 5.5 Meshng of the Ball End Mll and Workpece The meshng of ball end mll s shown n 5.5. Mnmum tool element sze s 0.1 mm. Runout s not appled n the smulatng process, that s because only cuttng force 67

70 and temperature are tested wthn 180 degrees that runout of cutter can be neglected. Fgure 0.1 Meshng of fllet end-mll model Spndle speed can be calculated by SFM RPM 1 D 12 Eq.(5-1) Where RPM s the spndle speed (revoluton per mnute), SFM s the lnear speed of cutter whch s recommended accordng to dfferent materal (160 SFM), Dc s the dameter of cutter stock. After transferrng to metrc system, the spndle speed for smulaton s 1500 r/mn. And feed per tooth (FPT) of ths cutter for machnng Ttanum alloy s recommended as 0.1mm/tooth. Fg 5.6 and Fg 5.7 shows the orentaton of tool feed and drecton of tool moton n terms of down-mllng and up-mllng, respectvely. 68

71 Fgure 5.6 Down-mllng Tool Feed and Moton Fgure 5.7 Up-mllng Tool Feed and Moton 69

72 5.3 Smulaton Example After settng the materal of tool and workpece and gettng the preparaton done, smulatng process gets started. Cuttng force s one of the most crtcal results that reflect the cuttng condtons. Besdes, by usng the cuttng force predcton software, we can compare the predcton wth the smulaton results n order to modfy the model avod stress concentraton. Fg 5.8 shows the coordnate system of whch the ball end mll s located. Fgure 5.8 Coordnate System of the Tool n AdvantEdge Cuttng forces are derved from smulaton on the orentaton of X, Y and Z axs. Fg 5.9 ndcates that the cuttng force varaton wthn seconds. Obvously, n the X- 70

73 axs drecton, the value of cuttng force fluctuate gently. In terms of Y-axs and Z-axs, the value of cuttng force changes sgnfcantly. Fgure 5.9 Cuttng Force Fluctuaton Dagram Fgure 5.10 Cuttng Force Data Analyss n Excel We can extract the pont of the cuttng force dagram, and mport the data to Mcrosoft Excel to obtan the average cuttng force on each axs orentaton. 71

74 Thus, the average cuttng force of the cutter s obtaned. On the drecton of X-axs, the cuttng force s N. On the drecton of Y-axs, the cuttng force s N. On the drecton of Z-axs, the cuttng force s N. Compared wth the revews n the thess of cuttng force predcton [25], the cuttng force of ths model s too hgh. Therefore, ths wll be a consderaton of ths model n the future work. Moreover, temperature s an mportant factor that s effected by the geometry of end mll model. As shown n Fg 5.11, hgh temperatures are generated n the area of the clearance face. The reason s that the clearance angle we set prevously s too small. As a result, there s not enough space for chps evacuaton. Hence, the desgned clearance angle s requred to modfy larger. Fgure 5.11 Temperature Dstrbuton of the Tool 72

75 Chapter 6.Conclusons and Future Work 6.1 Conclusons In ths paper, we buld a model of ball end mll, fnsh the calculaton of the basc features of the ball end mll, whch are cuttng edge curve, bottom curve of rake face, rake face surface. In addton, we ntegrate the process nto a program to obtan the model. The method of modelng a ball end mll has been ntroduced, ncludng the determnaton of the mathematcal equatons of the basc features of the cutter, the calculaton of the grndng wheel locaton whch can lead to NC code generaton for the machnng process, and the verfcaton of the model va smulaton. It follows the prncple of current computer aded desgn, whch s combnng the mathematcal knowledge wth computer system to conduct the desgn coverng creaton, modfcaton, sold modelng and optmzaton. Moreover, n the premse of ensurng the modelng geometrc parameters precsely matched wth the desgn parameters, a modelng program s developed to buld the model automatcally and effcently. Ths program saves tme sgnfcantly so that the new model can be appled to smulaton and experment quckly. It s a way to ncrease the productvty. 73

76 In the smulaton part, some problems have been found. The cuttng force of desgned model s too hgh, and the clearance angle needs to be modfed n order to reduce the temperature on the clearance face. 6.2 Future Work For the future research, there are several ponts requres to be consdered. In ths research, the desgned model s n a two flutes shape. Actually, the amount of the flutes can be modfed n the rake face and clearance face modelng program. The multple flutes ball end mll grndng wheel locaton wll be calculated. For ths model, because the grndng wheel locaton calculaton has been fnshed, we are able to obtan the NC code by the data of wheel center coordnates and wheel axs orentaton vectors. So that further research n machnng area wll be done n the future. In the part of smulaton, the smulatng process wll be further dscussed by puttng nto more knds of materal, ncludng more knds of materal match of tools and workpece. Moreover, the model wll be appled nto the smulaton of freestyle surface machnng n the future. 74

77 REFERENCES 1. Km, J. H., Park, J. W., & Ko, T. J. (2008). End mll desgn and machnng va cuttng smulaton. Computer-Aded Desgn, 40(3), Tandon, P., & Khan, M. R. (2009). Three dmensonal modelng and fnte element smulaton of a generc end mll. Computer-Aded Desgn, 41(2), Lazoglu, I. (2003). Sculpture surface machnng: a generalzed model of ball-end mllng force system. Internatonal Journal of Machne Tools and Manufacture, 43(5), Altntas, Y., & Lee, P. (1998). Mechancs and dynamcs of ball end mllng.journal of Manufacturng Scence and Engneerng,120(4), Vckers, G. W., & Quan, K. W. (1989). Ball-mlls versus end-mlls for curved surface machnng. Journal of Engneerng for Industry, 111(1), Zhu, R., Kapoor, S. G., & DeVor, R. E. (2001). Mechanstc modelng of the ball end mllng process for mult-axs machnng of free-form surfaces.journal of Manufacturng Scence and Engneerng, 123(3), Iman, B. M., Sadegh, M. H., & Elbestaw, M. A. (1998). An mproved process smulaton system for ball-end mllng of sculptured surfaces.internatonal Journal of Machne Tools and Manufacture, 38(9), Yucesan, G., & Altntas, Y. (1996). Predcton of ball end mllng forces.journal of engneerng for ndustry,118(1),

78 9. Myaguch, T., Masuda, M., Takeoka, E., & Iwabe, H. (2001). Effect of tool stffness upon tool wear n hgh spndle speed mllng usng small ball end mll. Precson engneerng, 25(2), Gradšek, J., Kalveram, M., & Wenert, K. (2004). Mechanstc dentfcaton of specfc force coeffcents for a general end mll. Internatonal Journal of Machne Tools and Manufacture, 44(4), Mlfelner, M., Kopac, J., Cus, F., & Zuperl, U. (2005). Genetc equaton for the cuttng force n ball-end mllng. Journal of Materals Processng Technology, 164, Jn, M., Goto, I., Watanabe, T., Kurosawa, J. I., & Murakawa, M. (2007). Development of CBN ball-nosed end mll wth newly desgned cuttng edge.journal of materals processng technology, 192, Sharman, A., Dewes, R. C., & Aspnwall, D. K. (2001). Tool lfe when hgh speed ball nose end mllng Inconel 718. Journal of Materals Processng Technology, 118(1), Kangnn, M. W. L. Z. C. (1998). Rgd Cuttng Force Model of Ball End Mll [J]. MECHANICAL SCIENCE AND TECHNOLOGY, Jnlng, X. (1995). The CNC Grndng of the Ball Nose End Mll. TOOL ENGINEERING, Pa, N. M. N., Sarhan, A. A. D., & Shukor, M. H. A. (2012). Optmzng the cuttng parameters for better surface qualty n 2.5 D cuttng utlzng ttanum coated carbde ball end mll. Internatonal Journal of Precson Engneerng and Manufacturng, 13(12),