UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Virtual milling Bélanger, Isabelle 2004

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-ubc_2004-0174.pdf [ 4.82MB ]
Metadata
JSON: 831-1.0080731.json
JSON-LD: 831-1.0080731-ld.json
RDF/XML (Pretty): 831-1.0080731-rdf.xml
RDF/JSON: 831-1.0080731-rdf.json
Turtle: 831-1.0080731-turtle.txt
N-Triples: 831-1.0080731-rdf-ntriples.txt
Original Record: 831-1.0080731-source.json
Full Text
831-1.0080731-fulltext.txt
Citation
831-1.0080731.ris

Full Text

V I R T U A L M I L L I N G B y Isabelle Be langer B . E n g . E c o l e Polytechnique de Mon t r ea l , Canada, 1996 A THESIS SUBMITTED IN PARTIAL F U L F I L L M E N T OF THE REQUIREMENTS FOR THE D E G R E E OF M A S T E R O F A P P L I E D S C I E N C E i n T h e Facu l ty of Graduate Studies Department o f M e c h a n i c a l Eng ineer ing W e accept this thesis as conforming to the required standard T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A A p r i l 2004 © Isabelle Belanger , 2004 Library Authorization In presenting this thesis in partial fulfillment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Title of Thesis: V/HTOAL MJU/fOG Degree: M/\^TFH OP APPLIED SCJF.A)C£ Y E A R : 2.D04-Departmentof Mf. CHAM CAL EK)C>>lh)£E.IUlOGr The University of British Columbia Vancouver, BC Canada Ic))o4-I'IOQ4-Name of Author (please print) Date (dd/mm/yyyy) Abstract M i l l i n g is used to manufacture a wide variety o f metal parts, f rom simple to complex geome-tries, i n smal l or large volumes . The requirements for these parts usual ly necessitate that the m i l l -i ng operation is accurate, but also the product ion rate must be as h igh as possible. These two requirements, w h i c h appear conf l ic t ing as first, are met i f the m i l l i n g operation is w e l l planned. W h i l e N C programming is s t i l l based i n many industries on past experience and practical k n o w l -edge, research in the areas o f cutting mechanics, mode l l i ng and s imulat ion are gradually changing the manufacturing practices. T h i s thesis investigates V i r tua l M i l l i n g , w h i c h is the integration o f m i l l i n g s imulat ion and C A D / C A M capabil i t ies . Ava i l ab l e m i l l i n g s imulat ion systems can simulate the process for one set o f cut t ing condi t ions. The objective wi th Vi r tua l M i l l i n g is to not on ly simulate the m i l l i n g operation for the whole N C program, but also to integrate features such as feedrate scheduling. A m i l l i n g s imula t ion for the who le part was developed based on the analyt ical c losed-loop m i l l i n g mode l presented by Spence[36]. The input to the s imula t ion is the cutter-workpiece inter-sections a long the tool path. The s imulat ion results include force, torque and power, and deflec-t ion along the tool path. The second part o f this thesis is the implementat ion of a V i r tua l M i l l i n g framework. The first step is the selection o f cutt ing condit ions wh ich is done dur ing the N C programming. C A D / C A M software do not provide tools to select appropriate cutting condit ions, therefore we established the requirements for such a tool using stabili ty lobe theory. A n interface was implemented i n a c o m -merc ia l C A D / C A M software to demonstrate this. The m i l l i n g s imula t ion is then used to identify cr i t ica l locations a long the tool path, and it is also used to perform feedrate scheduling. T w o off-l ine approaches for feedrate schedul ing were implemented, constraint-based feedrate schedul ing and off-l ine adaptive force control , and evaluated to see i f their use w o u l d lead to improved ii machin ing accuracy, better control o f cutt ing forces, and improved mach in ing time. Cut t ing tests were conducted and these approaches were also compared to an exis t ing onl ine adaptive force control . i i i Table of Contents Abstract i i Table of Contents i v List of Figures v i i Acknowledgements i x Nomenclature x 1. Introduction 1 2. Literature Review 3 2.1. O v e r v i e w 3 2.2. M o d e l l i n g o f M i l l i n g Forces 3 2.2.1. Or thogonal Cut t ing and Ob l ique Cut t ing 3 2.2.2. Cut t ing Force M o d e l s 4 2.2.3. Identification o f Cut t ing Coefficients 6 2.3. V i r tua l M i l l i n g 7 2.4. Research Focus 10 3. Modelling of the Milling Process 12 3.1. O v e r v i e w 12 3.2. M i l l i n g Process 13 3.3. Constraints 16 3.4. Cu t t ing T o o l - Workpiece Intersection 17 3.4.1. H e l i c a l E n d M i l l s 17 3.4.2. Intersection Cases 19 3.4.3. Ca lcu la t ion o f En t ry and E x i t A n g l e s 20 3.5. L i n e a r Edge Force M o d e l - A n a l y t i c a l C l o s e d - L o o p F o r m 21 3.5.1. Geometr ic Constants 24 i v 3.6. M a x i m u m Torque and P o w e r 26 3.7. Def lec t ion M o d e l s 27 3.7.1. Def l ec t ion a long the T o o l 28 3.7.2. M a x i m u m Def lec t ion 30 3.8. Val ida t ion o f the M i l l i n g Force M o d e l 31 3.8.1. Test Part and Se t -Up 31 3.8.2. Transformation to the X Y Z Cartesian Sys tem 35 3.8.3. S imula t ion and Exper imenta l Resul ts 36 4. Virtual Milling Implementation 43 4.1 . O v e r v i e w 43 4.2. V i r t u a l M i l l i n g A p p l i c a t i o n 44 4.3. Select ion o f Cut t ing Condi t ions i n C A D / C A M Software 45 4.3.1. Stabi l i ty Lobes 46 4.3.2. F lowchar t for the Select ion o f Stable Cut t ing Cond i t ions 49 4.3.3. Deve lopment o f an Interface in Ca t i a 51 4.4. Workp iece M o d e l and N C T o o l Path 52 4.5. Cu t t ing T o o l - Workp iece Intersection 53 4.5.1. Structure o f the Too l -Workp iece Intersection Output F i l e 54 4.6. M i l l i n g Process S imula t ion 55 4.6.1. Da ta Structure 55 4.7. Feedrate Schedu l ing 56 4.7.1. Const ra in t -Based Feedrate Schedul ing 58 4.7.2. Adap t ive Force Con t ro l 64 4.8. S imula t ion and Exper imenta l Results 67 4.8 .1 . Set-up 67 4.8.2. Tests 68 v 4.9. C o n c l u s i o n 75 5. Conclusion 76 Bibl iography 79 v i L i s t o f F i g u r e s 2 . 1 : M i l l i n g process - Force diagram. 5 3 . 1 : M i l l i n g process. 13 3.2 : U p m i l l i n g and d o w n m i l i n g . 14 3 . 3 : M i l l i n g process - Force diagram. 15 3.4 : Cu t t ing forces a long end m i l l . 16 3.5 : Geomet ry o f hel ica l end m i l l . 18 3.6 : Intersection cases and example o f entry and exi t angles. 19 3.7 : Ca lcu la t ion o f entry and exit angles. 21 3.8 : E n d m i l l - Static deflection mode l . 30 3.9 : E n d m i l l deflection model . 31 3.10: Toolpath . 32 3.11 : Test part w i th three features and dimensions. 33 3.12 : Transformation o f forces to machine coordinate system. 36 3.13 : Enve lope for the X and Y cutt ing forces -M a c h i n i n g o f the rectangular pocket. 37 3.14 : Enve lope for the Z cutt ing forces, and resultant cutt ing forces -M a c h i n i n g o f the rectangular pocket. 38 3.15 : E n v e l o p e for the X and Y cutt ing forces -M a c h i n i n g o f the triangular pocket. 39 3.16 : Enve lope for the Z cutt ing forces, and resultant cutting forces -M a c h i n i n g o f the triangular pocket. 40 3.17 : Enve lope for the X and Y cutt ing forces -M a c h i n i n g o f the c i rcular pocket. 41 v i i 3.18 : Enve lope for the Z cutt ing forces, and resultant cutt ing forces -M a c h i n i n g o f the c i rcular pocket. 42 4.1 : V i r t u a l M i l l i n g f lowchart . 44 4.2 : E x a m p l e o f stabili ty lobes. 48 4.3 : F lowchar t - Interface i n C A D / C A M software for the selection of cutt ing condi t ions. 50 4.4 : Ca t i a interface : selection o f cutt ing condi t ions. 52 4.5 : Ca t i a interface : stabili ty lobes. 52 4.6 : E x a m p l e o f tool -workpiece intersection output f i le . 54 4.7 : M i l l i n g process s imulat ion - Da ta structure for each step. 56 4.8 : Torque and power chart - M o r i S e i k i S H - 4 0 3 . 62 4.9 : B l o c k d iagram of a general adaptive control system i n machin ing . 65 4 . 1 0 : Test part - Toolpath. 68 4 . 1 1 : Test part - D imens ions . 69 4.12 : Feed curve - Off l ine adaptive force control . 71 4.13 : F e e d curve - Constraint-based feedrate schedul ing. 71 4.14 : S imula t ion o f peak forces. 72 4.15 : Feed curve - O n l i n e adaptive force control . 73 4.16 : Exper imenta l peak forces. 74 v i i i A c k n o w l e d g e m e n t s First , I w o u l d l i ke to thank D r Y u s u f Al t in tas for his supervis ion, encouragement and gu id-ance throughout this project. I w o u l d also l ike to thank the members o f the examin ing committee, D r Sassani and D r Y i p - H o i , for their feedback on the thesis. A l s o , m y colleagues f rom the M a n u -facturing A u t o m a t i o n Laboratory (Kaan , S i m o n , Jochem, Y u z h o n g , E v a , X u e m e i , C h i - H o , D i m a , and many others) for their support and for sharing wi th them the experience o f graduate studies. I w o u l d l i ke to thank speci f ica l ly Fuat Atabey, M e r h d a d N e v i s , S i m o n Park and D r X u e m e i H u a n g for their precious help dur ing the project. Je tiens egalement a remercier m a fami l le (Luc ide , Laurent , M a r c - A n d r e et sa conjointe Catherine) pour leur support et encouragement au cours des annees, mes amis a Mon t r ea l et V a n -couver, et finalement, un remerciement special a F l o r i a n pour son support au cours des derniers mois de redaction. i x Nomenclature a[im chatter-free axia l depth o f cut [mm] fa actual feedrate del ivered [mm/min] fc c o m m a n d feedrate [mm/min] h uncut chip thickness [mm] hmax m a x i m u m chip load [mm] i surface number j tooth number : 0 to N - l kt static stiffness [N/mm] k element k for deflection mode l /, L tool length [mm] n spindle speed [rad/s] or [rpm] st feedrate [mm/tooth] stchip adjusted feedrate for chip load constraint [mm/tooth] stidef adjusted feedrate for deflection constraint [mm/tooth] st,force adjusted feedrate for force constraint [mm/tooth] st o p t m a x i m u m al lowable feedrate [mm/tooth] st torque adjusted feedrate for torque constraint [mm/tooth] rc cutt ing tool radius [mm] vm, vk posi t ion of d isk m and disk k for deflection mode l z posi t ion of the elemental d isk in respect to the bot tom of the tool [mm] E Young ' s modulus [ M P a ] Fr reference force [N] Fa measured cutting force [N] x Ft> Fr Fa Cu t t ing force components i n tangential, radial and axia l directions [N] Fx, Fy Fz Cu t t ing force components in the X , Y and Z directions [N] Gm(z) transfer function o f the C N C Gp(z) transfer function o f the cutt ing process Gc(z) transfer function o f the C N C / c u t t i n g process / Inertia [mm4] Ktc, Krc, Kac Cu t t ing force coefficients i n tangential, radial and ax ia l directions [N/mm2] Kte, Kre, Kae E d g e force coefficients i n tangential, radial and axia l directions [N /mm] N number o f teeth on the cutt ing tool P> Pmax P o w e r and m a x i m u m power [hP] or [ k W ] Pij, Qij, Rij, Sij, Geometr ic constants for tooth j w i th respect to surface i Torque and m a x i m u m torque [N.m] tooth passing frequency [Hz] Cut t ing speed [m/min] normal rake angle [rad] orthogonal rake angle [rad] direct ional dynamic m i l l i n g force coefficients orthogonal f r ic t ion angle [rad] normal fr ict ion angle [rad] shear stress [ M P a ] deflection in y direct ion [mm] chatter frequency [rad/s] he l ix angle [rad] x i 1ij< "ij> ^ij T T x> A max Tf V (1 CL xx' yy Pa Pn 5, 1 ch ip f l ow angle [rad] 4> tool angle [rad] <t>c pi tch angle [rad] posi t ion o f tooth j [rad] entry angle, surface i [rad] exit angle, surface / [rad] A eigenvalue A / imaginary part o f the eigenvalue A * real part of the eigenvalue x i i 1 C h a p t e r 1 I n t r o d u c t i o n M i l l i n g is w ide ly used by companies i n the aerospace, automotive and m o l d and die indus-tries. It is used to produce parts wi th s imple or complex shapes as accurately as possible, i n smal l or large volumes , and to remove material as rapidly as possible wh i l e mainta ining tool and machine integrity. T h e m i l l i n g tool path is created using C A D / C A M software. C o m m o n manu-facturing practices i n N C programming are usual ly based on the programmer 's knowledge and experience, and tool proof ing is done using tr ial and error methods. O v e r the last decades though, research in the area o f m i l l i n g has produced significant advancements i n metal cutt ing mechanics , dynamics , mode l l i ng and s imulat ion o f the process. These projects are now being introduced in the industry and engineering practices are changing gradually. M o d e l l i n g and s imula t ion o f the m i l l i n g process provide tools to evaluate and improve the selection o f cutt ing parameters and the m i l l i n g operation. S imula t ions include cutt ing forces, tool deflections, torque and power requirements, and chatter vibrat ion stability check. O n the other hand, the current m i l l i n g process s imula t ion systems process one set o f specific cutt ing condit ions at a t ime. The objective o f V i r t u a l M i l l i n g is therefore to integrate i n one system, m i l l i n g process s imu-lat ion and C A D / C A M , offering the poss ib i l i ty to not on ly simulate the m i l l i n g process for one set of cutting condi t ions, but for the whole N C program. It offers several advantages to single cutt ing condi t ion m i l l i n g s imula t ion . It a l lows the identif icat ion o f c r i t ica l locations on the part w h i c h require special attention i n the N C programming . A l s o , it permits feedrate schedul ing for the whole part and for various mach in ing constraints, increasing machine performance, i m p r o v i n g machin ing cyc le t ime and producing quali ty parts. It w i l l also help to reduce the tool proofing t ime required before starting product ion. T h i s t ime should be greatly reduced or el iminated. T h i s thesis studies the development o f a Vi r tua l M i l l i n g appl icat ion for 2 1/2 D parts, i nc lud -in g the m i l l i n g s imulat ion and feedrate scheduling. The thesis outline is as fo l lows . Chapter 2 is the literature review conducted in the areas o f mode l l i ng o f m i l l i n g forces and Vi r tua l M i l l i n g . The m i l l i n g models developed to simulate cutt ing forces are first introduced. Research projects i n the area of Vi r tua l M i l l i n g are presented and the research objectives are stated. Chapter 3 defines the m i l l i n g process and describes i n more details the analytical c losed-loop m i l l i n g force mode l used in the m i l l i n g s imulat ion. There are many constraints that l imi t the mach in ing o f metals, and m i l l i n g s imulat ion is relevant in this context. T w o approaches for deflection calculat ions are presented. Cut t ing experiments were done to validate the models. Chapter 4 presents the implementat ion of the Vi r tua l M i l l i n g applicat ion. A new interface was developed and integrated i n a C A D / C A M software for the selection o f stable cutting cond i -tions. Feedrate schedul ing is then investigated. T w o approaches were implemented in the scheme of the V i r t u a l M i l l i n g appl icat ion and they were compared wi th an exis t ing onl ine adaptive force control a lgor i thm. Conc lus ions and summary of the results are presented in chapter 5. 2 3 Chapter 2 Literature Review 2.1. Overview M i l l i n g is one o f the most ly used metal cutt ing process . In order to understand the physics o f the process and increase its efficiency, many research projects have focused on cutt ing mechanics , mode l l i ng and s imula t ion of the m i l l i n g process. V i r tua l s imula t ion o f the process, i.e, V i r tua l M i l l l i n g , is based on the integration in one system of m i l l i n g process s imulat ion and C A D / C A M capabil i t ies to extract geometric informat ion f rom the part mode l and the toolpath. Firs t , the major contributions i n the area o f mode l l i ng o f m i l l i n g forces are presented. Then , past and cur-rent research i n the area o f V i r tua l M i l l i n g is covered. F ina l ly , the research objectives o f this project are formulated. 2.2. Modelling of Milling Forces T h i s section covers the mode l l i ng o f m i l l i n g forces. Firs t , orthogonal and obl ique cutt ing are introduced, then the two ma in force models and two approaches to identify cutt ing coefficients are described. 2.2.1. Orthogonal Cutting and Oblique Cutting The cutt ing operations are d iv ided into two types o f operations: orthogonal cutt ing and obl ique cutt ing. In orthogonal cutt ing, the straight cut t ing edge is perpendicular to the relative mot ion o f the tool w i th respect to the workpiece and two forces are generated on the cutt ing edge: feed force and tangential force. In the case o f obl ique cutting, the relative veloci ty o f the work -piece is not perpendicular to the cutt ing edge anymore. F o r the m i l l i n g operation, w h i c h falls into the category o f obl ique cutting, the inc l ina t ion angle is equal to the hel ix angle o f the cutter. Ob l ique cutt ing w i l l produce 3 components o f forces ident i f ied as tangential, radial and axia l forces. It w i l l be shown later that assumptions f rom the c lass ica l obl ique cutt ing mode l can be used to s impl i fy the calculat ions o f cutt ing coefficients for m i l l i n g using an orthogonal cutt ing database [18]. 2.2.2. C u t t i n g F o r c e M o d e l s M a n y research works have focused on the understanding o f the force generation dur ing the m i l l i n g operation. T h e relationship between the uncut ch ip thickness and m i l l i n g force was first reported by Koenigsberger and Sabberwal [29][34]. In this thesis, the ma in models based on the uncut ch ip thickness, average chip thickness model [42] and linear edge force mode l [11][42][46], are presented. Average C h i p Thickness M o d e l The average ch ip thickness mode l [42] relates the uncut ch ip thickness h to the cutt ing forces through the use o f cutt ing coefficients. A force d iagram is shown on figure 2.1. F o r an elemental s l ice o f the m i l l i n g tool at height z and for a specific cutt ing tooth j, the tangential dFtj(§,z) and radial dFrj$,z) force components are g iven as : dFtJW,z) = KrhjW,z)-dz (2.1) dFrJW,z) = Kr-hjW,z)-dz (2.2) 4 where hfi$,z) is g iven by: hj(<$>,z) = stsmtyj(z) (2.3) and where the angular posi t ion o f tooth j at the height z, W z ) is [36]: <t>,(z) = (l)+7(t>1 tan\|/ (2.4) 0 be ing the angular posi t ion o f the reference tooth, s t : the feed per tooth, <|>c : the tooth angu-lar spacing or p i tch angle, \|/ : the he l ix angle and rc : the cutter radius. The cutt ing coefficients Kt and Kr are obtained by experiments and we w i l l present two ways o f ident i fying those coefficients i n section 2.2.3. F o r a specific angular posi t ion 0 o f the tool , the total forces Ft and Fr are obtained by summing the elemental forces for a l l the teeth along the z axis , consider ing the sec-tions o f the cutt ing edges that are i n cut. d F v Yk T,0 Feed F i g u r e 2.1 : M i l l i n g process - Force diagram. 5 L i n e a r E d g e Force M o d e l The average ch ip thickness mode l was improved by the addi t ion o f the edge force compo-nents f o l l o w i n g the w o r k o f T lus ty and M a c N e i l [42], Y e l l o w l e y [46] and Armarego [11][13]. The edge force components represent the contact of the flank face o f the tooth on the machined surface dur ing the m i l l i n g operation. The cutting coefficients Kte and Kre are added to the equa-tions and the force mode l is g iven by Armarego [11] as : dFtJW, z) = (Ktc • hjW, z) + Kte)dz (2.5) dFrJW, z) = (Krc • hjW, z) + KJdz (2.6) The l inear edge force mode l w i l l be used in this project for the m i l l i n g s imulat ion. 2.2.3. Identification of Cutting Coefficients Cut t ing coefficients can be identif ied using two approaches. T h e first approach is ca l l ed mechanist ic mode l . T h i s approach consists i n conduct ing a series o f cutt ing tests on a m i l l i n g machine wi th the m i l l i n g tool for a same immers ion condi t ion but at several feedrates. U s i n g l i n -ear regression on the experimental data, the cutting coefficients are identif ied, Ktc and Krc be ing the slope o f the corresponding l inear regression curves and Kte and Kre the ordinates. T h i s approach yie lds cutt ing coefficients w h i c h are specific to the cutt ing tool and the workpiece mate-r ia l [18]. The other approach relies on the orthogonal to obl ique transformation proposed by Armarego [12]. Or thogonal cutt ing tests are first performed on a lathe wi th a series o f inserts o f different rake angles for several cutt ing speeds and feedrates. The cutt ing forces Ft and Fr are measured wi th a dynamometer and functions are statistically determined to represent shear stress, shear 6 angle and fr ic t ion angle respectively, consider ing as w e l l tool geometry and cutting condi t ions. T h e orthogonal to obl ique cutt ing transformation is then used to calculate the cutt ing coefficients. The first approach, mechanist ic mode l , is useful and fast to identify cutt ing coefficients that are specific to one combinat ion tool -workpiece material . O n the other hand, i n the case o f m u l t i -ple end m i l l s used for the same material , the second approach w i l l require more t ime for exper i -ments but w i l l produce a database that is suitable for a l l the end m i l l s . 2.3. Virtual Milling A v a i l a b l e N C mach in ing modules i n C A D / C A M systems offer a wide selection o f options to create complex tool paths. O n the other hand, the selection o f cut t ing condit ions is left to the pro-grammer, w h i c h specifies the cutting condit ions according to his knowledge , his experience as w e l l as mach in ing data available i n handbooks. Current C A D / C A M software systems do not mode l the mach in ing process physics and do not provide tools to select appropriate cutt ing cond i -tions i n respect to the tool , cutt ing geometry, tool and workpiece materials, and machine tool l i m -itations. M i l l i n g process s imula t ion is used to select stable cutt ing condi t ions. T o o l geometry, work-piece material , cutt ing geometry, and dynamic parameters o f the tool-machine system as w e l l as the workpiece , are required to simulate the m i l l i n g operation. W h e n using a software l ike C u t P r o [10], developed i n the Manufac tur ing Au toma t ion Labora tory at the Un ive r s i t y o f B r i t i s h C o l u m -b ia , the user is able to simulate cutting forces, torque and power requirements, tool vibrations and d imensional surface f in ish . A chart o f the axia l depth o f cut as a function o f the spindle speed can also be obtained for a specific width o f cut, i.e. stability lobes, w h i c h provide the user wi th a graph o f stable cutt ing condit ions to choose f rom. T h i s is generated for a specific set o f cutt ing geometry, not for the who le part. The objective o f V i r t u a l M i l l i n g is therefore to simulate the pro-cess for the who le part, as w e l l as to opt imize the cutt ing condi t ions. 7 One o f the first groups to work on a system that is a imed at s imula t ing the m i l l i n g process is Takata et al.[44] at the O s a k a Univers i ty . The i r m i l l i n g s imulat ion system is based on an appl ica-t ion interacting wi th a s o l i d modeller. T h e geometric information required by the m i l l i n g s imula -t ion is extracted f rom the so l id model ler and the tool -workpiece intersections are calculated us ing the Z-buffer approach. Then , a discrete mechanist ic mode l is used for force calculat ions and the elemental forces are computed along the edges o f the tool and summed up. T o o l displacements and regenerative effect are also considered in the calculat ion o f the uncut ch ip thickness. The i r s imula t ion system is used for both the predict ion o f cut t ing forces a long the tool path as w e l l as for the predict ion o f chatter vibrations. F o r chatter predict ion, a s impl i f i ed stability crite-r ion proposed by M e r r i t [32] is used first. I f this cri ter ion is met, then the current case is stable and further calculat ions are not necessary. Otherwise , numer ica l s imulations are performed and the occurence o f chatter is identif ied by changes i n cutt ing forces or tool displacements over sev-eral revolut ions o f the tool . However , as stated by the authors then, the s imula t ion t ime is too long to be used i n a pract ical appl icat ion. In addit ion, M e r r i t ' s stabili ty cr i ter ion is not suitable to use i n m i l l i n g since it is based on single point mach in ing models . Al t in tas and Spence [2][36][38] w o r k e d on a so l id model ler based m i l l i n g s imulat ion system for 2 1/2 D workpiece . In this system, the workpiece is mode l l ed us ing Const ruct ive S o l i d G e o m -etry ( C S G ) s o l i d mode l l i ng . In order to calculate the static cutt ing forces as w e l l as torque, power and tool deflections, a pre-processing step is done i n w h i c h a semi-c i rcular arc is swept i n the feed direct ion and intersected wi th the part geometry i n order to calculate the entry and exit angles o f the cutter. W i t h the immers ion condi t ions, the cutting forces are calculated us ing an analytic c losed fo rm solut ion. Therefore, d ig i ta l integration along the z axis is not necessary. The advan-tage o f this method is a reduced computat ion t ime compared to methods us ing discret ization o f the tool a long the z axis . T h e m i l l i n g s imula t ion also includes feedrate schedul ing w h i c h is per-formed based on constraints such as m a x i m u m force, m a x i m u m power and torque, m a x i m u m tool 8 deflection and m a x i m u m chip load. T h i s s imulat ion system was developed for straigth paths and for c y l i n d r i c a l end m i l l s only. Al t in tas and Spence also developed a C A D assisted adaptive control [37]. T h i s adaptive force control helps prevent force overshoots by feeding informat ion to the control ler ahead o f t ime regarding sudden geometry changes so that the control ler adjusts the feed before its actual occurrence. T h e a lgor i thm uses an adaptive pole placement approach to maintain the peak cutt ing force to a reference force leve l . Exper imenta l results showed that force overshoots were e l i m i -nated. Spence [35] cont inued research i n the area o f m i l l i n g process s imula t ion and developed an appl icat ion based on the A C I S S o l i d M o d e l e r K e r n e l . The appl icat ion is now based on B - R e p mode l l i ng . W h i l e the Z-buffer method offers advantages such as s impl ic i ty , robustness, re lat ively h igh computat ional t ime, the author suggests that Z-buffer approach is better fit to applications such as v isua l inspection o f N C tool paths for co l l i s ions and for feedrate schedul ing based on material r emova l rate. O n the other hand, the B - R e p approach is more exact for calculat ions o f tool -workpiece intersection, but the computat ional t ime is longer. Therefore, Spence et a l . [39] w o r k e d on implement ing methods to increase the computat ional speed o f the B - R e p approach. T h e y focused on paral lel processing implementat ions, us ing round rob in paral le l processing, dual C P U , ne tworked solutions and neighbor groups. The latter reduces the B o o l e a n subtraction t ime through grouping o f related pr imit ives and gives better results than the round robin approach. T h e y also w o r k e d on on-l ine moni tor ing and control o f the m i l l i n g process [35]. A new concept was also introduced : departure paths. T h e use o f departure paths provides a way to remove the tool smoothly f rom the workpiece without l eav ing d w e l l marks on the part i f the cutt ing cond i -tions are generating h igh cutt ing forces and the control ler is not able to adjust the feedrate accord-ingly. Once the tool is m o v e d away f rom the part, the toolpath is reinit iated wi th appropriate cutt ing condi t ions . 9 Anothe r group o f researchers, Fusse l l and Jerard, also developed a m i l l i n g process s imula t ion system to opt imize feedrates for 3-axis m i l l i n g o f sculptured surfaces us ing bal l end mil ls[23][24][26][33]. T h e y used a combinat ion o f off-l ine feedrate opt imiza t ion schemes wi th on- l ine adaptive force control to maintain a peak force dur ing end m i l l i n g for safe, accurate and efficient mach in ing . T h e feedrate opt imizat ion is based on constraints such as machine power, shank failure, tooth failure and surface f in ish . The addit ion o f adaptive force control is to ensure that force overshoots are avoided. A l s o , the authors suggest that this approach w i l l compensate for the inaccuracies caused by variations in the force predict ion mode l or occurences that can not be predicted due to variations i n material , tool condi t ion , c o o l i n g f lu id , tool runout, etc... T h e i r system is also based on a Z-buffer representation o f the geometric mode l for the tool -workpiece intersection calculat ions. T h e cutt ing force mode l is a discrete mechanist ic model . They tested two types o f controllers : a d iv i s i on control ler and an adjustable P I controller. B o t h controllers g ive better results than the use o f off-l ine feedrate opt imizat ion only, but the adjustable P I control ler is s lower than the d iv i s i on controller. In average, for roughing, semi-f in-ish ing and f in i sh ing , the experimental results us ing the combina t ion o f off-l ine opt imizat ion and on-l ine control show a decrease i n cutt ing times by about 15% when compared to cutt ing times obtained f rom "standard practice" N C toolpaths. However , on a pract ical point o f v iew, the sys-tem used for on- l ine control includes a dynamometer. Dynamometers as w e l l as many sensors are adequate for laboratory experiments, but they can not be used as is i n an industr ial context. 2.4. Research Focus T h i s project focuses on the s imulat ion o f the m i l l i n g process for the whole part. Static cut t ing forces, torque and power, deflections are calculated a l l a long the tool path. In order to do so, the intersection between the tool and workpiece , specif ied by entry and exit angles, is required. T h i s is obtained f rom another appl icat ion developed in the Manufac tu r ing Au toma t ion Laboratory. 10 The second objective is to develop an interface to suggest the selection of stable cutting con-ditions at the level of the N C programming, i.e. in the C A D / C A M software. With the specifica-tions of the workpiece material, width of cut, frequency response functions of the tool, stability lobes are generated. The N C programmer can therefore select appropriate cutting conditions for the mill ing operation. The last part of this project consists in feedrate scheduling. Two approaches have been used, constraint-based feedrate scheduling and offline virtual adaptive force control. The latter approach was developed in a previous research project. These 2 approaches are compared with online adaptive generalized predictive control [3] [9] . 11 1 2 Chapter 3 Modelling of the Milling Process 3.1. Overview The objectives o f mach in ing are to produce parts as accurately as possible i n order to obtain the right geometry and to meet the specif ied part tolerances, but also on an economica l aspect to remove excess material as rapidly as possible wh i l e avo id ing damages to the cutt ing tool and the machine tool . T o control the process, it is important to have the capabil i t ies to simulate and con-trol cutt ing forces, tool deflections, and torque and power requirements. Unders tanding the in f lu -ence o f the cutt ing parameters and the cutt ing geometry is also relevant in order to improve and opt imize the m i l l i n g operations. A s an example, increasing the cutter immers ion or the depth o f cut may result i n force overshoots and eventually i n tool breakage. The predict ion and avoidance o f such occurences us ing m i l l i n g s imulat ion w i l l help improve the m i l l i n g process. The f o l l o w i n g sections present the models used in the m i l l i n g s imulat ion. Fi rs t , the m i l l i n g operation is described. Second, constraints in the mach in ing o f metals are discussed as these are the reasons why m i l l i n g s imulat ion is relevant. Then , the basic concepts behind the calculat ions of tool -workpiece intersections required for the m i l l i n g s imulat ion are g iven . F o l l o w i n g , the l i n -ear edge force mode l i n an analyt ical c losed- loop f rom is presented i n more details. Then , two approaches for deflection calculat ions are stated. F i n a l l y , experiments were conducted to validate the models and the results are shown. 3.2. Milling Process Milling is an intermittent cutting process. The cutter teeth are successively entering and exit-ing the workpiece and generating the finished surface at a direction normal to the feed. The work-piece is fed towards a rotating tool with a linear feed speed. In many milling machine configurations, the workpiece is mounted on a table moved by feed drives while the cutting tool is mounted in the stationary spindle shaft which rotates using the spindle motor. Rotational speed (»J Feed direction Figure 3.1 : Milling process. Source : Manufacturing Automation, Altintas [9]. The programmed feedrate is relatively small compared to the spindle speed. Therefore, the assumption formulated by Martellotti [30] can be used : it states that the trochoidal path followed by the cutting teeth can be approximated as a circular motion. This commonly used assumption leads to the following equation for the chip thickness: h(ty) = stsm§ (3.1) 13 M i l l i n g can be d i v i d e d into two types o f operations: face m i l l i n g and peripheral m i l l i n g . In face m i l l i n g , the tool diameter is usual ly larger than the wid th o f cut and the ax ia l depth o f cut is relat ively smal l . Face m i l l s are usual ly large tools wi th m i l l i n g inserts. In peripheral m i l l i n g , the cutting tool is smaller and the flank and tip o f the tool are s imultaneously used to remove material . There are several types o f cutting tools for peripheral m i l l i n g : c y l i n d r i c a l end m i l l s , wi th or w i th -out a corner radius, tapered end m i l l s , ba l l end m i l l s , etc. Per ipheral m i l l i n g can also be d i v i d e d i n end m i l l i n g and f lank m i l l i n g . It is used to machine pockets, slots, sculptured surfaces, etc. Per ipheral m i l l i n g operations can also be d iv ided into d o w n m i l l i n g and u p m i l l i n g . F igure 3.2 illustrates these 2 methods. T h e difference is i n the way the ch ip is generated. In u p m i l l i n g , the ch ip thickness is zero when the cutt ing tooth enters the material and it increases as the tool rotates. In d o w n m i l l i n g , the ch ip thickness is the greatest when the cutt ing tooth enters the material and it becomes zero as it leaves the workpiece . Upmilling Downmilling Figure 3.2 : U p m i l l i n g and d o w n m i l l i n g . F igure 3.3 shows a section of the cutt ing tool dur ing a m i l l i n g operation. A s the cutt ing tool rotates, forces w i l l vary i n regards to the immers ion o f the cutt ing tooth and as a function o f the ch ip thickness, ax ia l depth of cut and the material properties. A s ment ioned earlier, the path o f 14 each cutt ing tooth is often approximated as h(§) = st • sin<|). In this work , we w i l l use this equa-t ion for the ch ip thickness as it is sufficient for static cutting force calculat ions and for process p lanning purposes. Cu t t ing forces as shown on figure 3.3 are present a l l a long the cutt ing edges w h i c h are i n cut. F igure 3.4 shows the distr ibution o f cutting forces a long the cutt ing edges o f an end m i l l . T h i s distr ibution is a function o f the cutting geometry, i.e. the axia l and radial depths o f cut, as w e l l as the cutter geometry, i.e. the hel ix angle, cutter radius, and specific cutter geometry such as taper angle. T h e resultant tangential force, as w e l l as the resultant planar force and the X , Y and Z forces are obtained by summing al l the force components along the cutting edges. Feed Figure 3.3 : M i l l i n g process - Force diagram. 15 X F i g u r e 3.4 : Cut t ing forces along end m i l l . 3.3. C o n s t r a i n t s There are l imitat ions to the m i l l i n g process. The selection o f cutting condit ions has to be done consider ing the f o l l o w i n g constraints. Mach ine tool dependent constraints The spindle drives have l imi ted capacity in terms o f torque and power. It is therefore essen-tial to check that the m a x i m u m torque and power do not exceed the spindle specifications. 16 T o o l and workpiece dependent constraints T h e ch ip load must not exceed the pr inc ipa l tensile stress i n the cutt ing wedge beyond the ultimate tensile strength o f the tool material . A l s o , the m a x i m u m static deflections left on the f in -i shed surface must be wi th in the tolerance o f the workpiece . F i n a l l y , the m a x i m u m resultant cut-t ing force must be kept safely be low a l imi t value to prevent fracture o f the shank 3.4. Cutting tool - Workpiece Intersection The cutt ing tool -workpiece intersection is the first step in the calcula t ion of static cutt ing forces us ing the analyt ical mode l developed by Spence [36]. The geometry o f he l ica l end m i l l s is first expla ined. Then , the intersection cases encountered dur ing the m i l l i n g operation are i l l u s -trated. In the last section, we discuss the calcula t ion o f the cutt ing tool - workpiece intersection and the ca lcula t ion o f entry and exit angles. 3.4.1. Helical End Mills F o r he l ica l end m i l l s as shown on figure 3.4, the he l ix angle is such that the tooth engagement changes along the tool axis. The intersection o f a g iven disk element a long the z axis must be c a l -culated. Therefore, the exact posi t ion o f this disk element for each flute can be calculated. If we start w i th the bot tom end points o f the flutes, their posit ions are g iven by [36] : tyO) = $ +j$c f o r j = 0 , l , 2 , . . . J V - l (4.1) 17 where N is the number o f teeth and (j)c = (2n)/N is the pi tch angle. Then , at an axia l depth of cut z for an elemental d isk element, the posi t ion o f tooth j is g iven by: tyz) = <\>+j$c-kyZ f o r j = 0 , l , 2 , . . . 7 V - l (4.2) A s seen in the equation, i n the case o f end mi l l s , the hel ix angle needs to be considered and the angular posi t ion a long the z axis w i l l vary wi th /c^ the lag angle. Therefore, ky is defined as: kw = ^ (4 .3) V rc where (3 is the hel ix angle and rc the tool radius. X F i g u r e 3.5 : Geometry o f a hel ical end m i l l . 18 3.4.2. In t e r sec t i on Cases D u r i n g the m i l l i n g operation, as the cutting tool is rotating, each tooth engagement changes. T h e engagement o f an elemental d isk a long a tooth w i l l depend on the z pos i t ion, the hel ix angle and the geometry of the workpiece . There are f ive possible intersection cases, as ident i f ied by Spence [36]. F igure 3.6 illustrates these cases. A s an example , the surface defined by the axia l depth o f cut a and between the entry angle tyst and the exit angle <|)ex is the developed surface o f a cut section o f the workpiece shown i n figure 3.6 and defined by (|>st 0 and (|)ex o On the graph, each l ine represents a possible intersection between a cutt ing edge and the workpiece . It is necessary to ment ion that these lines can not belong to the same cutt ing tool . In fact, the inc l ina t ion o f the cutt ing edges w o u l d a l l be the same as the he l ix angle is constant. Therefore, these lines w o u l d be long to different tools wi th different tool geometries. F i g u r e 3.6 : Intersection cases and example o f entry and exit angles. 19 A s the tool rotates the cutt ing edge intersection case wi th the surface w i l l change. Case 4 represents a l l the cases where cutting edges are out o f cut. T h e ident if icat ion o f the intersection cases at each rotation o f the cutting tool w i l l be essential to calculate the geometric constants required for the cutt ing forces calculat ions. 3.4.3. Calculat ion of E n t r y and E x i t Angles The ca lcula t ion o f entry and exit angles is performed assuming the cutt ing tool geometry is a cyl inder . T h e output w i l l be a set o f entry and exit angles. F igure 3.7 shows an example o f entry and exit angles. In end m i l l i n g , i n most operations there is one i n cut section, but it can occur that there are mul t ip le engagements. F o r the case o f d o w n m i l l i n g , the entry angle w i l l be (|>st, depending on the workpiece geome-try, and the exi t angle w i l l be n. F o r the case o f u p m i l l i n g , the entry angle is 0 and the exit angle is (|) e x, again depending on the workpiece geometry. In the case o f slott ing, the entry angle is 0 and the exit angle is n. 20 F e e d Figure 3.7 : Ca lcu la t ion o f entry and exit angles. 3.5. Linear Edge Force Model - Analytical Closed-Loop Form The l inear edge force mode l was introduced i n chapter 2. T h i s mode l incorporates force components generated by the action o f the ch ip on the rake face o f the tool and the rubbing o f the flank face on the new machined surface. A s mentioned, the tangential, radial and axia l force c o m -ponents are given as [36]: dFtJW,z) = (KTC-hj(<b,z) + KTE)dz dFrJ(<\>,z) = (KRC-hj(ty,z) + KRE)dz dFaJW,z) = (KAC-hjW,z) + KAE)dz where = ty+jtyc-kyZ. 21 T h e equations are usual ly so lved us ing integration along the z axis w h i c h translates i n discret-iza t ion i n the z d i rect ion. In terms o f computat ion t ime, this is a t ime consuming operation. F o r flat end m i l l s , Spence [36] proposed to solve these equations as a closed- loop analyt ical force mode l . T h i s approach has the advantage o f e l imina t ing the need to compute the forces a long the z axis. Instead, the integration o f the force components results i n equations consis t ing o f geometric terms and these terms are represented as geometric constants calculated for each specific posi t ion o f the tool and are dependent on the intersection cases, as we w i l l see later. To obtain the forces i n the machine directions, x, y and z, the force components are projected [ 3 6 ] : dFxJWj(z)) = - dFtJco^j(z) - dFrJsmtyz) (3.4) dFyJWj(z)) = dFtjsm$j(z)-dFrJcos$jfz) (3.5) dFzJWj(z)) = dFaJWj(z)) (3.6) The cutt ing force components result ing f rom the intersection o f a flute w i th a surface are obtained by integrating between the boundaries zi , and z(. . 2 . These l imi t s for each case are [36]: Case 0 : zijX = 0 zij2 = a C a s e l : zijX = 0 zij2 = (l/*v)[<|> +j$c - tysti] Case 2: zijX = (l /* v ) [< | )+;< | ) c -<!>„, . ] zij2a = a Case3 : ztjl = (l/*v)[<|> +j$c-tyeJ zij2 = (l/ky)[<$>+jtyc-<bsti] Case 4 : flute j is not cutt ing face i. 22 Integrating (3-7) (3.8) (3.9) The analyt ical force equations become : 1 T st Fx, ijW) = f\_KTEsm$j ~ KREC0S§j + 4 lKRcWj ~ s i n 2 ( t>y] " KTCcos2$j] -ijl st -i -KTEcos§j - KREsin§j + — [KTC[2tyj - sin2(|) ;] - KRCcos2fyj] F z , i j ^ = - r i K A C ^ o s ^ - K A E ^ ] \ i J 2 K\y zij\ R e p l a c i n g i n equations 3.10, 3.11 and 3.12 ,we can rewrite these equations : •iJ2 (3.10) (3.11) (3.12) st 1 KTESij - KREUij + 4 [KRCTij ~ KTCRij] J zij\ t ~KTEUij ~ KRESij + 4 [KTCTij ~ KRCRij\ <-ij\ -«2 •yi (3.13) (3.14) (3.15) where i?;- = COS 20 • Su = s infy 23 Tij = 2^--sin2<|) ; -The total forces are obtained by summing for a l l surfaces and al l teeth : FxW = X E F * . V ( 3 - 1 6 ) i i The planar resultant force is obtained us ing the equation: F(<t>) = [Fx2W) + Fy2W)]1/2 (3.19) 3.5.1. G e o m e t r i c C o n s t a n t s Refer r ing to figure 3.6, there are 5 possible intersection cases. The integration boundaries are Ziji and ztj2 • F o r each intersection case, the geometric constants are defined as [2] [36] : C a s e 0 : zin = 0 zij2 = a Py = cos(Q>+j$c-kya) Qy = cos(<>+7<>c) Rij = cos2(§+jtyc-k a ) -cos2(< | ) + 7<|)c) 24 Stj = sin((t)+7(t) c -^a)-sin((|)+;0 c) Ttj = sin2(0 +;(j) c) - {2k^a + sin2(<> +j^c-k^a)) Uu = cos(<\> +j$c - kyd) - cos((|) +jtyc) Zij = a C a s e l : zin = 0 zij2 = (l/k^M+j<\>c-$sti] Pij = C0^sti Qu = cos((|)+7'0c) Ry = cos2(|) J, |.-cos2(<|)+7<|) c) su = s i n $ s t i - s i n ( ( l ) + ; ( t ) c ) 7. . = sin2(0 +;(j) c) - (2(0 +j$c - tysti) + sin 2 ^ . ) uij = cos<|>Jf,.-cos(<|>+./<|>c) C a s e 2 : z y i = ( l /* v ) [< |>+ . /< |> c -< !>„ , . ] z , 7 2 a = a P y = cos((j>+./<j>c-&xj,a) Qij = C0S<$>exi Ry = cos2(<b+j$c-kwa)-cos2<$>exi Sy = sin(<t> +jtyc - kyd) - sin<|) e j d Ttj = 2 ( ( | ) + ; ( l ) c - ^ a ) + s i n 2 ^ , . - ( s i n 2 ( 0 + ; ( t ) c - / : v a ) + 2 ( | ) e J f / y = cos((j) +/(|>c - * v a ) - cos<|>ejcl-Z / ; - = a - ( l / V W + # c - * « , - ) 25 Case 3 : * ^ = (1/* V)M> +j<\>c-<$>exi] zij2 = (l/*v)[<|> +j$c-$sti] Pij = C 0 ^ s t i sij = sin <!>,,,•-sin <|>ejci Ti} = 2(|) a n .+ s i n 2 ( | » „ I . - ( 8 i n 2 0 , / I . + 2 i |>„ i ) uij = c o s <t>^-cos( | ) e ; c , . ztJ = C a s e 4: flute j is not cutting face / pij = Qij = Rij = 5 y = Tij = u i j = zij = 0 3.6. M a x i m u m T o r q u e a n d P o w e r M a x i m u m torque is calculated us ing the f o l l o w i n g equation: Tmax = Ft,maXxrc (3-20) The tangential force Ft is calculated analyt ical ly us ing geometric constants. F , . . ( 0 ) = fi2dFtJ(Q>)dz (3.21) The tangential force component was g iven i n equation 3.4: 26 dFtJW,z) = (KTC-hj(hz) + KTE)dz fan FT,ij(§) = J (KTC- stsm§j(z) + KTE)dz FT,i/^ = - ^ r c ^ [ ^ ( c o s « | » + ; < | > c - y / 7 . 2 ) ) - ^ - ( c o s ( ( t ) + ; 0 C - + ( - « 7 - £ ) [ Z y 2 - z i / i ] F r , y(4>) = ( " T ^ ) ^ ^ - 0-22) ^(*) = I I F u ; ( 3 - 2 3 ) Once the m a x i m u m torque is found, the m a x i m u m power i n h P is calculated us ing P m a x = - J ^ ( h P ) (3.24) where n is the spindle speed expressed i n rad/s. 3.7. D e f l e c t i o n M o d e l s In this appl icat ion, the assumption is that tool deflections are solely the result o f cutt ing forces act ing on the f lexib le cutter. Parameters such as run-out, deflection o f the workpiece are therefore not considered. T h e model assumes static deflection o f the cutt ing tool . T w o approaches are used to calculate deflections. F o r the calcula t ion o f deflections a long the tool , static deflection is calculated using the canti levered beam formulat ion for forces appl ied a l l 27 along the tool . F o r the calcula t ion o f m a x i m u m deflect ion, an analyt ical approach is used. In this approach, the force is appl ied on the tool at halfway the axia l depth o f cut. It was demonstrated that this s impl i f i ed , concentrated m a x i m u m normal force deflection mode l is appropriate for r i g i d parts [36]. 3.7.1. D e f l e c t i o n a l o n g the T o o l We assume that the cutt ing force is appl ied at the tool tip o f the endmi l l and that it causes the tool to deflect statically. T h e deflection is g iven by: 5 , = Ff (3.25) , , 3EI , , net where k = and / = — , ;3 64 W e observe that the surface generation is not the same for u p m i l l i n g and d o w n m i l l i n g . In the case o f u p m i l l i n g , the cutter teeth enter in the material and cause overcutt ing. In d o w n m i l l i n g , the forces act ing on the tool push it out o f the workpiece therefore result ing i n undercutting. The f inished surface is generated by the section o f the tooth that is in contact wi th it. In u p m i l l i n g , this occurs at §st = 0 , whi le i n d o w n m i l l i n g at § e x = n. The surface is either gener-ated by a single contact point for a posi t ion o f the too l , or by many contact points. A s fo rmu-lated earlier in equation 4.2, the angular posi t ion o f tooth j for a depth o f cut z is g iven by : fy(z) = Q+Mc-kyZ f o r j = 0 , l , 2 , . . . A ' - l where /c... = 1^11$ . V rc 28 Therefore, the contact points for u p m i l l i n g and d o w n m i l l i n g are der ived by setting (|>. = 0 for u p m i l l i n g and <|> • = n for d o w n m i l l i n g : '"upmilling («>) = ^downmilling ( ^  ) <1>+;<1>C (3.26) (3.27) The cutter is d i v i d e d into M smal l d isk elements. The axia l depth o f cut is a, so the height o f one element is Az = a/M. I f a large number o f elements is used, the influence o f the he l ix angle can be neglected. The differential cut t ing force at element m is [9] : &Fym(Q>) = Kts,Az £ [sm^(z)-Krcos<\,j(z)]sm^ (3.28) / = o The deflection at z^ caused by the force appl ied at element m is obtained us ing the canti le-vered beam equation [17] : o (zk,m) = A F v mVk 6EI K m k ) A F v 2 y,m m , 3 . 6E1 K k m ) (3.29) where vk = l - z k and vm = l - z n 29 AF, y,m 5v(z F i g u r e 3.8 : E n d m i l l - Static deflection mode l . Source : Manufac tur ing Au toma t ion , Al t in tas [9]. 3.7.2. M a x i m u m D e f l e c t i o n Def lec t ion o f the tool w i l l cause overcutt ing i n u p m i l l i n g and undercutting in d o w n m i l l i n g . B o t h situations, the deflection is m a x i m u m when the normal force F y reaches its m a x i m u m and there is a contact point i n cut. A s proposed by Spence [36], we assume the m a x i m u m deflect ion occurs at the tool tip and that the force distr ibution can be approximated as the resultant force i n y being appl ied at one point corresponding to half o f the axia l depth o f cut. F r o m figure 3.9, we observe that: A = L-a/2 (3.30) and the m a x i m u m deflection is : F ^ \ A - 3 L ) 30 7 L a " y.max Figure 3.9 : E n d m i l l deflection mode l . 3.8. Validation of the Milling Force Model 3.8.1. Test Part and Set-Up A test part featuring 3 different pockets, figure 3.11, was designed to verify the accuracy o f the predict ion o f cutting forces. T h e test consists i n mach in ing the three pockets and to measure the cutt ing forces a long the toolpath. These 3 pockets a l low for different sets o f entry and exit angles a long the tool path as w e l l as cases where there are more than one set o f entry and exit angles for the same tool posi t ion. A l s o , the direct ion o f the cutt ing forces vary a long the tool path. The cutt ing tool is a two-flute c y l i n d r i c a l end m i l l w i th a 12 m m diameter, a he l ix angle o f 30 degrees, and a rake angle o f 8 degrees. W e assumed no corner radius. F i n a l l y , the workpiece is mounted on a K i s t l e r dynamometer wi th sensors to measure F x , F y and F z . The cutt ing forces are recorded us ing the M A L - D A Q module f rom C u t P r o [10]. 31 The depth o f cut is 4 m m , the spindle speed is 2500 r p m and the feedrate is 500 m m / m i n . F igure 3.10 shows the toolpath. F o r the rectangular pocket, a hel ica l i nward toolpath was used wi th p lung ing entrance o f the tool i n the center o f the pocket. F o r the triangular toolpath, a he l ica l i nward toolpath was used as w e l l . F o r the c i rcular toolpath, an he l ica l outward toolpath was used. Figure 3.10 : Toolpath. 32 Figure 3.11: Test part wi th three features and dimensions. 33 The workp iece material is A17050-T7451 . T h e cutting coefficients for this material are obtained us ing an orthogonal to obl ique cutt ing mode l presented by Budak , Al t in tas and A r m a r -ego [18]. Or thogonal to Ob l ique Cut t ing Transformation The cutt ing coefficients are transformed f rom shear stress, shear angle, f r ic t ion angle and edge coefficients measured i n orthogonal cutt ing tests us ing a c lass ica l obl ique cutt ing mode l . It was found that this material behavior is a function o f ch ip thickness and spindle speed. The cut-t ing coefficients are therefore updated along the tool path as the ch ip thickness varies. The relations for the shear stress TS , shear angle § n , f r ic t ion angle (3n and the edge coeff i -cients are for A17050-T7451 : xs = 297.0528 + 1.0474 • an tyn = 24.2013 + 36.6678 • h + 0.0049 • V+ 0.2995 • a n P„ = 18.7883 -6 .7008 /1 - 0.0076 V + 0 . 2 5 8 l a „ KTE = 23.4071 - (0.0014 • V) - (0.2555 • a n • 180/TT.) KRE = 35.1607 - (0.0011 • V ) - (0.5076 • a„ • 180/TT.) KAE = 0 where a n is the normal rake angle i n degrees, h[mm] is the ch ip thickness and V is the cut-t ing speed i n [m/min] . In the c lass ical orthogonal to obl ique cutt ing transformation mode l , the f o l l o w i n g assumptions are made [12] : 1) the orthogonal shear angle (|>c is equal to the normal shear angle tyn in obl ique cutt ing; 2) the normal rake angle a n is equal to the orthogonal rake angle ar; 34 3) the ch ip f low angle i is equal to the obl ique cutt ing angle r ) ; 4) the fr ic t ion coefficient B Q and the shear stress xs are the same in orthogonal and obl ique cutt ing for a combina t ion o f speed, ch ip load and tool-material pair. The equations for the cutt ing coefficients are [12] : T c o s ( B „ - cc„) + t a n i • tanri • s i n B KTC = -r± — • — (3.32) i L s i n ^ c x. s i n ( 6 - a „ ) KRC = — — ^ — (3.33) s in <pw cos t c x. c o s ( B „ - a „ ) t a n i - tanri • s i n 6 „ KAr = —x — n- ! — (3.34) A C sin(j)n c I 2 2 2 where c = ^ c o s ( ( ^ + B n - an) + tan r| • sin B n . 3.8.2. Transformation to X Y Z Cartesian System D u r i n g m i l l i n g s imula t ion , the forces are first calculated i n their loca l axis system. The X and Y forces must be transformed to obtain forces i n the machine X and Y directions, as shown in figure 3.12, the Z direct ion being the same. T h e y are projected as fo l lows : [dFxdFy] = [T][dFxJocaldFyJoJ (3.35) where T is jjrj cosG - s i n 0 s i n 0 c o s 0 (3.36) where 0 is the angle between the loca l coordinate system and the machine coordinate system. 35 Figure 3.12 : Transformation o f forces to machine coordinate system. 3.8.3. Simulation and Experimental Results The envelope o f the experimental and s imulated results are presented for the X , Y , Z and resultant cutt ing forces for each part pocket i n figures 3.13 to 3.18. F r o m the results, we can make the f o l l o w i n g observations: 1) F o r the rectangular and triangular pockets, the trend o f the simulated results generally f o l -l o w the experimental results, except for the resultant force and the Z force for the rectangular pocket. The resultant force being the combinat ion o f X and Y results, this is expla ined by the fact that we are adding the slight deviations f rom both curves. In the case o f the Z force, there is an offset o f about 50 N that is not observed later dur ing the mach in ing o f the two other pockets. 2) T h e experimental results exhibi t a magnitude that is higher than the simulated results by about 50 N , w h i c h is an error o f about 10%. The results present noise and drift f rom the measure-ment equipment, but this deviat ion is probably due to the material cutt ing coefficients. The analysis of the results shows that the m i l l i n g force mode l is accurate. 36 600 n Rectangular Feature - X Peak Force Experimental Simulated -6001 20 25 30 35 40 Time [s] 45 50 600, 4001 g 200 r o LL CO u CD > Rectangular Feature - Y Peak Force 200 -400 -6001 Experimental Simulated 20 25 30 35 40 Time [s] 45 50 F i g u r e 3.13 : Enve lope for the X and Y cutt ing forces - M a c h i n i n g o f the rectangular pocket. 37 Rectangular Feature - Z Peak Force -200 ' ' • ' 1 1 20 25 30 35 40 45 50 Time [s] Rectangular Feature - Resultant Peak Force _ , , , , , Time [s] Figure 3.14 : Enve lope for the Z cutt ing forces, and resultant cutt ing forces - M a c h i n i n g o f the rectangular pocket. 38 600 400 g 200 Triangular Feature - X Peak Force -600 -I 1 1 T" Experimental Simulated _J I I I l_ 152 153 154 155 156 157 158 159 160 161 162 Time [s] 600 Triangular Feature - Y Peak Force -200 [ -600 ~i 1 1 1 1 1 1 1 1 r~ Experimental Simulated _j i t i i i i i i L_ 152 153 154 155 156 157 158 159 160 161 162 Time [s] F i g u r e 3.15 : Enve lope for the X and Y cutt ing forces - M a c h i n i n g o f the triangular pocket. 39 200 150 — 100 CD O 0 50 1 0 N - 5 0 -100 -150 -200 Triangular Feature - Z Peak Force -i r-Experimental Simulated ^ i.*- r *• - /• I r*f| I / _J i i i i i i i i_ 152 153 154 155 156 157 158 159 160 161 162 Time [s] ftnn Triangular Feature - Resultant Peak Force DUUi—i 1 1 1 1 1 1 1 1 1 500 r CD O i £ 400 CD i 300 c 05 I 200 CD 0C 100 0 152 153 154 155 156 157 158 159 160 161 162 Time [s] F i g u r e 3.16 : Enve lope for the Z cutt ing forces, and resultant cutt ing forces - M a c h i n i n g o f the triangular pocket. 40 Circular Feature - X Peak Force -6001 ' 1 1 1 ' 1 1 1 1 1 1 ' 249 250 251 252 253 254 255 256 257 258 259 260 Time [s] 6 0 0 ^ Circular Feature - Y Peak Force Experimental — - Simulated J i i i i i i i i 1— 249 250 251 252 253 254 255 256 257 258 259 260 Time [s] F i g u r e 3.17 : Enve lope for the X and Y cutting forces - M a c h i n i n g o f the c i rcular pocket. 41 600 400 ^ 200 CD O Circular Feature - Z Peak Force o Q_ N o y •200 -400 -600 —\ 1 1 1 1 1 1 r -Experimental — — Simulated _i i i i i i i u 249 250 251 252 253 254 255 256 257 258 259 260 Time [s] F i g u r e 3.18 : Enve lope for the Z cutt ing forces, and resultant cutt ing forces - M a c h i n i n g o f the c i rcu lar pocket. 42 43 Chapter 4 Virtual Milling Implementation 4.1. Overview In chapter 3, the details o f the m i l l i n g s imulat ion were g iven . In this chapter, the imp lemen-tation o f the m i l l i n g s imula t ion wi th in the f ramework o f the V i r t u a l M i l l i n g project is presented. V i r t u a l M i l l i n g offers several advantages to single cutt ing condi t ion m i l l i n g s imulat ion. W i t h V i r -tual M i l l i n g , the m i l l i n g s imulat ion is done for the whole part w h i c h a l lows the N C programmer to identify c r i t i ca l situations occur ing dur ing the operation. A l s o , feedrate schedul ing and op t imi -zat ion is performed for the whole part and for various mach in ing constraints, therefore m a x i m i z -ing machine performance, reducing cyc le t ime and produc ing qual i ty parts. Ano the r major advantage o f V i r t u a l M i l l i n g is that the t ime spent on the machine tool to improve the N C pro-gram c o u l d be greatly reduced, i f not e l iminated. The overa l l appl icat ion is presented i n the first sections, wi th the details o f the interface developed for the selection o f cutt ing condit ions i n C A D / C A M software, as w e l l as the type o f input required and the f lowchart o f the appl icat ion. The f o l l o w i n g sections are dedicated to fee-drate schedul ing. Three approaches are used and experiments are conducted to validate the m o d -els and compare these approaches. 4.2. V i r t u a l M i l l i n g A p p l i c a t i o n The flowchart shown i n figure 4.1 illustrates the steps for the Vi r tua l M i l l i n g project. T h e software components are the f o l l o w i n g : - N e w interface i n the C A D / C A M software for the selection o f cutt ing condi t ions; - C A D / C A M system to create the workpiece geometry and the N C tool path; - A p p l i c a t i o n developed i n A C I S to calculate tool -workpiece intersection; - M i l l i n g process s imula t ion; - Feedrate schedul ing. Input Lii«f°lMpij£mr Tool-Workpiece Intersection • Selection of Stable Cutting Conditions CATIA + CLFile __, (NC Tool Path) ACIS Tool -W6rkpiece_ Intersection Output File • • Immersion Angles • • Feed • Depth of Cut • Spindle Speed Milling Process Simulation and Optimization Input _ • Oiitput; File • Workpiece Material • Cutter Properties • Limits for Optimization Force Calculation (Statlc^ Model) Optimization Feed Constraints Maximum Torque Maximum Power Maximum Deflection! Maximum Force Maximum Chip Load! * Static Forces: Instantaneous Forces, Tangential Force, ResuitaritForce; . •torque and Power I • Deflection ^ Optimized CL File F i g u r e 4 . 1 : V i r t u a l M i l l i n g f lowchart . 44 4.3. Selection of Cutting Conditions in C A D / C A M Software During the creation of N C tool paths, the programmer must specify cutting conditions such as spindle speed, feedrate and depths of cut. Available C A D / C A M software do not provide tools for the selection of these cutting conditions. Most commercial N C packages offer interfaces where cutting parameters are entered but there is no knowledge or help available specifically for the selection of cutting conditions. The programmer therefore defines cutting conditions based on his knowledge and experience, and/or on information available in handbooks. The proposed system integrates knowledge for the selection of these parameters. This is a new feature added to C A D / C A M software and it is the first step in the Virtual M i l l i n g . It allows for the selection of stable conditions for spindle speed, depth of cut and width of cut. The N C programming is done using these selected conditions and wi l l therefore lead to stable operation. The feedrate is first selected using data available from tool manufacturers or handbooks, but wi l l later be optimized in Virtual M i l l i n g using mill ing simulation and feedrate scheduling techniques. This part is presented in section 4.4. To illustrate this idea, a new interface is developed and integrated in C A T I A , a widely used commercial C A D / C A M software, especially by companies in the aerospace industry and in the automotive industry. The purpose of this new interface is to display stability lobes for specific tool and workpiece material combination and for a given width of cut during the N C program-ming. The programmer is then able to select the appropriate set of spindle speed and axial depth of cut to ensure stable cutting operation. The following sections introduce the theory of stability 45 lobes, and describe the requirements and functionalit ies o f the system, as w e l l as present the inter-face developed speci f ica l ly i n C A T I A . 4 .3 .1 . S t a b i l i t y lobes Chatter vibrations are caused by a self-excitation mechanism i n the generation o f ch ip thick-ness dur ing the m i l l i n g operation. One o f the structural modes o f the tool -workpiece-machine system is first exci ted by cutt ing forces. The machined surface presents osci l la t ions. The suc-ceeding tooth is also osc i l la t ing due to the vibrations, therefore generating an osci l la tory ch ip thickness. The ch ip thickness being oscil latory, the cutt ing forces become osci l la tory as w e l l . T h e self exci ted cutt ing system becomes unstable, and chatter vibrations grow unt i l the tool jumps out o f the cut or breaks under the excessive cutting forces. Thus , the chatter vibrations continue to be the major l i m i t i n g factor in increasing the metal removal rates o f the machine tools. [9] In order to avo id condit ions where chatter vibrations w o u l d develop, many researchers have w o r k e d i n this area. T lus ty [41] and Tobias [43] first presented stabili ty theory for orthogonal cut-t ing. M e r r i t [32] also presented Nyqu i s t stability based solut ion. Al t in tas and B u d a k [8] later pre-sented an analyt ical solut ion applicable to the m i l l i n g operation. T h i s solut ion is used here to generate stabili ty lobes. The reader should refer to [8],[9] for more details about the theory and equations. The analyt ical stabili ty lobes are obtained f rom the f o l l o w i n g characteristic equation [8] [9]: a 0 A 2 + a j A + 1 = 0 (4.1) where 46 a0 = ^Xx(i(ac)^yy(i(ac)(aXXayy-axyayx) (4-2) fli = a A ( ' f f l c ) + W ' 1 0 ^ <4-3) ® x x and Q>yy are the direct transfer functions in the x and y directions. axx and a are the direct ional dynamic m i l l i n g force coefficients. co c is the chatter frequency. The eigenvalue A is then so lved by : A = ~2cT0^ai±^a^''~4ao) (4.4) The transfer functions o f the orthogonal modes i n x and y are complex , so the eigenvalue is complex as w e l l . A = AR + iA} (4.5) The expression for chatter-free axia l depth o f cut is g iven as : 271 A , , 2 fl«» = H v * f ( 1 + K ) ( 4 ' 6 ) where K = — . K, is the tangential cutt ing coefficient and N the number o f teeth. The spindle speed is obtained by f inding the corresponding tooth passing frequency : Tf = — (E + 2/C7T) k=0, l ,2 , . . . (4.7) and then the spindle speed n [rev/min] : n = ^ . (4.8) B y l o o k i n g at the equation for a/ i O T , it is apparent that stability lobes are function o f the trans-fer functions o f the system, the wid th o f cut (through the direct ional dynamic m i l l i n g coeff i -47 cients), the number of teeth N and the cutting coefficient Kt, which correspond respectively to the dynamic parameters of the tool-machine system, the cutting geometry, the cuting tool geometry and the workpiece material. Stability lobes are presented as a graph that relates the axial depth of cut to the spindle speed. Figure 4.2 shows an example of stability lobes. The region under the curve is the stable region while cutting conditions above the curve correspond to chatter conditions. Stability Lobes (Analytical) 0 1 1 1 1 1 1 1 0 2000 4000 6000 8000 10000 12000 Spindle Speed [rpm] Figure 4.2 : Example of stability lobes. 48 4.3.2. Flowchart for the Selection of Stable Cutting Conditions A s ment ioned in the previous section, ca lcula t ion o f stabili ty lobes requires that some ele-ments o f the cutt ing process be specif ied by the user. The f o l l o w i n g parameters and cutting con-dit ions are selected or entered v i a the interface: workpiece material , selection o f the cutt ing tool , tool and workpiece frequency response functions, and the radial depth o f cut. The interface must be integrated i n the C A D / C A M software and must a l l ow for the selection o f a l l the parameters and cutting condit ions previously mentioned. T h e f lowchart presented in figure 4.3 illustrates the steps that the user fo l lows in the selection/entry o f these parameters. The boxes on the right side correspond to tasks performed by the applicat ion according to the selections made by the user. 49 Steps: Selection/Entry of Parameters Tasks Performed by the Application Select Workpiece Material Select Tool J K] Read Cutting Coefficients from Database Ktc,Krc, Kac,Kte,Kre,Kae Read Cutter Geometry from Database Number of teeth, Helix Angle, Diameter Display Recommended Cutting Speed Display Recommended Feedrate 4-Select Machine/Tool Dynamics Select Workpiece Dynamics Read Transfer Functions from Database FRFs for Machine/Tool and Workpiece Enter Radial Depth of Cut 1 > Read Radial Depth of Cut Entered by the I ' User 1 Display Stability Lobes 1 Calculation of Stability Lobes fo r : r - Specified Cutting Conditions - Selected Cutting Tool - Selected Workpiece Material - Selected Machine/Tool and Workpiece Dynamics Figure 4.3 : F lowchar t - Interface in C A D / C A M software for the selection o f cutt ing condi t ions. The first step is the selection o f workpiece material i n a l ist o f materials avai lable. Once the material is selected, a list o f tools for w h i c h mechanist ic cutt ing tests have been performed is shown. 50 The second step is the selection o f the appropriate cutt ing tool for the operation. W i t h the workpiece material and cutt ing tool selected, the associated m i l l i n g cutt ing force coefficients are extracted f rom the database. R e c o m m e n d e d cutt ing speed and feedrate range are then displayed. T h e user uses this informat ion as a reference to program the feedrate. The th i rd step is the selection o f the machine/ tool and workp iece dynamics . T h e frequency response function o f the cutt ing tool is necessary to calculate the stability lobes, wh i l e the fre-quency response function of the workpiece is selected on ly for the case o f a f lex ib le workpiece . The fourth step is the entry o f the radial depth o f cut used i n the operation. W i t h a l l the informat ion extracted f rom the database and entered by the user, the stability lobes are calculated and d isp layed to the user i n order to select appropriate spindle speed and axia l depth o f cut for the operation. 4.3.3. Development of an Interface in C A T I A F o l l o w i n g the f lowchart presented above, an interface is developed us ing V i s u a l B a s i c pro-g ramming language. T h i s interface is integrated in the Pr ismat ic M a c h i n i n g module o f the soft-ware C A T I A V 5 . The interface is d i v i d e d i n two w i n d o w s . T h e ma in w i n d o w is shown in figure 4.4. In this w indow, the user specifies information regarding the process, i.e. workpiece material , cutting tool selection, cutt ing tool and workpiece frequency response functions and wid th o f cut. The second w i n d o w is shown i n figure 4.5. It is used to display the stability lobes for the cutt ing parameters and the selections previously made. 51 Tool and workpiece FRFs Radial Depth of Cut Stability lobes F i g u r e 4.4 : C A T I A interface : selection o f cutt ing condit ions. Stability lobes • Stable cutting conditions • The user will transfer the information to the CAD system, but eventually it can be automated. Stable zone F i g u r e 4.5 : C A T I A interface: stability lobes. U s i n g the stability lobes, the N C programmer selects a set o f spindle speed and depth o f cut under the curve i n order to avo id chatter condit ions. 4.4. W o r k p i e c e M o d e l a n d N C T o o l P a t h The geometry o f the blank and f inal part are created in the C A D / C A M software. In order to be read by the applicat ion in A C I S for the cutting tool - workpiece intersection calculat ions, they 52 are converted to the S T E P format. The N C tool path is p rogrammed i n the C A D / C A M software. The corresponding A P T fi le is generated and transferred to the appl icat ion i n A C I S . U s i n g S T E P files for the part geometry and A P T fi le for the N C toolpath means that any c o m -merc ia l package capable o f convert ing to these formats can be used, therefore it is independent of the C A D / C A M software. 4.5. Cutting Tool - Workpiece Intersection In order to simulate the m i l l i n g operation, the vir tual m i l l i n g appl icat ion requires input regarding the process. T o calculate the cutting forces as w e l l as the torque and power, and tool deflection, it is necessary to k n o w for each step along the tool path the f o l l o w i n g parameters: the entry and exit angles w h i c h define the radial wid th o f cut, the feedrate, the spindle speed and the axia l depth o f cut. T h e appl icat ion developed in A C I S by H u a n g [25] to calculate the intersection between the tool and the workpiece reads the A P T fi le generated by the C A D / C A M software. T h i s f i le con-tains A P T instructions descr ibing the motions o f the tool programmed. It is necessary to dis-cretize the tool path i n order to catch the geometry changes. Therefore, the current version o f the appl icat ion calculates the intersection along the tool path at smal l intevals, such as 0 .5 ,1 or 2 m m , or as specif ied by the user. A later vers ion o f the appl icat ion w i l l recognize automatical ly areas where it is necessary to discretize the tool path and other areas where it is not. T h i s improvement w i l l reduce greatly the computat ion t ime. 53 Anothe r informat ion required is the angle between the tool path and the machine X axis. T h e cutt ing forces are measured i n the X , Y and Z directions. The entry and exit angles are g iven according to the local coordinate system for a specific locat ion on the tool path. The cutt ing forces are calculated i n this system and they are projected on X and Y , as seen i n section 3.8.2. 4.5.1. Structure of the Tool-Workpiece Intersection Output File The applicat ion i n A C I S generates an output file w h i c h is read by the m i l l i n g process s imula -t ion. T h i s output f i le has the f o l l o w i n g fo rmat : 1 : number o f pairs o f entry-exit angle; 2 : sets o f entry-exit angles [radians]; 3 : X , Y and Z coordinates [mm]; 4 : angle between loca l coordinate system and X - Y machine system [radians]; 5 : depth o f cut [mm]; 6 : spindle speed [rpm]; 7 : feedrate [mm/min] . 1|2|0.00000|0.00000|-42.998|49.039|-7.000|0.000|7.0|2500.0|500.0| 0|-40.998|49.039|-7.000|0.000| 1|2|1.55241|1.58918|-9.998|49.039|-7.000|0.000|7.0|2500.0|500.0| 1|2|0.92701|2.21458|-7.998|49.039|-7.000|0.000|7.0|2500.0|500.0| 1|4|0.00000|1.13028|1.36782|3.14159|1.002|49.039|-7.000|0.000|7.0|2500.0|500.0| Figure 4.6 : E x a m p l e o f tool -workpiece intersection output f i le . 54 4.6. M i l l i n g Process Simulat ion The m i l l i n g process s imulat ion appl icat ion can be d i v i d e d into two components. The first component is the engine that calculates the instantaneous cutt ing forces, m a x i m u m forces, m a x i -m u m torque and power, as w e l l as deflection and m a x i m u m deflection. The second component is used to perform feedrate scheduling. Funct ions f rom the m i l l i n g process s imulat ion applicat ion are ca l l ed to calculate m a x i m u m force, m a x i m u m torque and power, m a x i m u m deflection, i n order to schedule the feedrate according to these constraints. T h e output o f the m i l l i n g process s imulat ion is an op t imized C L fi le . 4.6.1. Data Structure The m i l l i n g process s imulat ion is p rogrammed i n C++. The ma in class provides methods to calculate forces, torque and power, deflection, and perform feedrate scheduling. F o r each step along the tool path, information is read from the tool -workpiece intersection output fi le and results are stored. F igure 4.7 shows the structure used to store this information. 55 H T No • + - • INFORMATION READ FROM OUTPUT FILE - Element number - Type of operation: roughing, finishing - Coordinates x, y, z [mm] - Lists of entry and exit angles - Table of intersection cases - Depth of cut [mm] - Spindle speed [rpm] - Feed rate [mm/min] FORCE CALCULATIONS - Geometric constants: Pt, Qt, Rt, St,Tt, Ut - Maximum resultant force [N] - Maximum power [hP] and torque [Nm] - Maximum tangential force - Instantaneous X,Y,Z forces - Instantaneous tangential forces - Instantaneous resultant forces - Average force DEFLECTION CALCULATIONS - Maximum deflection using conventional discretization approach - Maximum deflection using analytical model FEED RATE SCHEDULING 1) Constraint-Based Feed Rate Scheduling - New feed rate - New feed rate after smoothing 2) Offline Adaptive Force Control - New feed rate - New feed rate after smoothing F i g u r e 4.7 : M i l l i n g process s imulat ion - Da ta structure for each step. 4.7. F e e d r a t e S c h e d u l i n g Op t imiza t ion o f the mach in ing tool path can be performed either off-l ine or on-l ine dur ing the mach in ing operations. On- l ine moni tor ing o f the forces, etc... i n order to modi fy the spindle speed and feedrate, requires the use o f addit ional measuring equipment and modif icat ions to the machine tool and its controller. It is usual ly used once to opt imize the parameters and register the new N C program. Off - l ine methods are based on models w h i c h try to represent as accurately as 56 possible the physics o f the process. M o r e cutt ing condit ions can be mod i f i ed us ing off-l ine approach, as w i th the on- l ine method it is rather diff icul t to modi fy the tool path itself, wh i l e wi th off-l ine it is a lways possible to modi fy the depths o f cut, etc... In this research project, we are go ing to compare 3 approaches, two off-l ine approaches and one on- l ine approach. In a l l cases, on ly the feedrate can be adjusted. Since there is no exis t ing l i n k between a m i l l i n g s imulat ion system and a commerc ia l C A D / C A M software, it w o u l d be rather diff icult to modi fy the cutting geometry, i.e. the axia l and radial depths o f cut. O u r appl ica-tion provides options that are readily usable in a commerc ia l setting. Therefore, on ly the feedrate can be adjusted. The 2 off-l ine methods are constraint-based feedrate schedul ing and off-l ine adaptive force control . On- l i ne approach is done us ing an applicat ion programmed and avai lable i n the M a n u -facturing Au toma t ion Laboratory [3]. D u r i n g the mach in ing operation, sudden changes i n the workpiece geometry may result i n increase i n the depth o f cut or immers ion . These changes might cause force overshoots, creating situations where the forces and stresses exerted on the cutt ing tool may exceed the tool capacity as w e l l as exceed the spindle motor power. These situations are potential r isk o f severe damage to the tool and machine and should be avoided. Other objectives of feedrate schedul ing is to reduce the mach in ing cyc le t ime and improve the workpiece surface f in ish and accuracy. In the f o l l o w i n g sections, we w i l l expla in a l l three approaches and complete this part w i th the approach used to smooth the new op t imized feed curve. 57 4.7.1. Constraint-Based Feedrate Scheduling R o u g h i n g and f in i sh ing operations do not have the same requirements. D u r i n g roughing, the objective is to achieve the highest material removal rate, as it is economica l to reduce the mach in -ing t ime as m u c h as possible, whi le the objective i n f in ish ing is to meet close part tolerances and achieve good surface f in ish . F o r feedrate schedul ing, the f o l l o w i n g constraints w i l l be cons id -ered: m a x i m u m force, m a x i m u m torque and power, m a x i m u m chip load and m a x i m u m deflec-t ion. R o u g h i n g In roughing, large forces and tool deflections are a l l owed as the focus is on the vo lume o f material removed. The m a x i m u m force, m a x i m u m torque and power, and m a x i m u m chip load w i l l be checked. T h e loads on the cutt ing tool w i l l be high consider ing aggressive cutt ing condit ions are selected to machine the part as q u i c k l y as possible. It is important to verify that the m a x i m u m cutting force w i l l not be exceeded, w h i c h c o u l d result i n tool shank breakage, and to adjust the feedrate accordingly. The machine tool and its spindle motor are designed for certain types o f mach in ing appl ica-tions. Sp ind le motors specifications are defined in a chart o f the m a x i m u m torque and power available versus the spindle speed. M a x i m u m torque and power need to calculated in order to assure that the cutt ing condit ions w i l l not over load the machine spindle, causing important dam-age and possible failure o f this component. 58 The cutt ing tool edges are submitted to large stress and the a l lowable tooth stress is expressed by the tool manufacturer i n the form of ch ip load. Therefore, we need to check that the ch ip load is not exceeded. F i n i s h i n g In f in i sh ing , deflections should be m i n i m i z e d and we want to achieve close tolerances and meet the surface f inish requirement. The same constraints as for roughing w i l l be considered, as w e l l as the m a x i m u m deflection constraint. M a x i m u m Force The m a x i m u m force constraint F R E S M A X is evaluated i n order to avo id shank breakage. A s stated earlier i n equations 3.13 and 3.14, the forces i n X and Y are g iven by : ,zij2 Fy.uW = {-Y)[-KTEUirKRESij + S^^KTcTirKRcRij\ The resultant force in the X - Y plane is g iven by : •ij2 F D u c _ = JFS + F, 2 2 RES, max ~ x + Fy W e can define FX and FY as : FX = A + sLJORCEB (4.9) FY = C + sLJORCED (4.10) 59 where the variables A, B, C and D, are : A = T~{KTEST-KREUT) B = -^-(KRCTT-KTCRj) C = (-1?\(-KREST- KTEUT) D = (^-7jA(KTCTT + KRCRT) The cutt ing coefficients KTC, KTE, KRC and KRE are k n o w n for a g iven posi t ion o f the tool as w e l l as the geometric constants. F R E S is the m a x i m u m a l lowable force on the tool . The feed per tooth stforce is the unknown . The resultant force F R E S M A X takes the fo rm : FRES, max = + st, forced + ( C + st, forced The f o l l o w i n g quadratic equation is obtained : s t J o r c e 2 ( B 2 + D2) + sTJORCE(2AB + 2CD) + A2 + C2-F2RES,max = 0 (4.11) and i n a s impl i f i ed fo rm : where J, K and L are : J s t, force2+ K s , , force+ L = 0 2 2 J = B +D K = 2A5 + 2CD 60 L = A2 + C 2 - F R ' The feed per tooth is obtained by so lv ing for stjorce, the unknown . W = - " " f 1 ^ (4-12) W e only consider the posit ive values o f s t j o r c e and keep the lowest value. M a x i m u m Torque and P o w e r It is important to verify that the torque and power requirements do not exceed the machine spindle capacity and to adjust the feedrate accordingly to use the m a x i m u m torque and power available at a g iven spindle speed. The m a x i m u m torque and power were g iven by equations 3.20 and 3.24 : T = F x r max t, max c P m a x = iTmax-n)[kW] T h e m a x i m u m torque and power are function o f the spindle speed. Typ ica l ly , the machine tool bui lder provides a torque/power chart. A s an example o f this type o f chart, the chart for the horizontal m i l l i n g machine M o r i S e i k i S H - 4 0 3 is presented i n figure 4.8. If we do not consider its direct ion, the tangential force Ft is g iven : K <i p _ Y 7 TC°t, torque T r rt,max ~ "-TE T~ u T The torque is T = I KTFZT - K t c S ' ' t o r c i u e — (4.13) Lmax \"-TE T k V 1000 61 20,000 min' 18.5/15 kW (24.7/20 HP) High-speed (option) 200 100 SO 100 200 1000 Spmal» spauK) (mm j • n' • n 11 /, I,  i rr, • ISOQ -~ <3Q miri> CWWEBCC * 1 15 mifvconl *2 30 mirvtonl F i g u r e 4.8 : Torque and power chart - M o r i S e i k i S H - 4 0 3 . Source : M o r i S e i k i Company . The feed per tooth sttorque is : ( T m a x • 1000 \ k9 W . - ^ K ^ ) l ^ T T ( 4 ' 1 4 ) c M a x i m u m C h i p L o a d The m a x i m u m chip load corresponds to the m a x i m u m recommended ch ip load by the tool manufacturer or found in handbooks. The m a x i m u m chip load is found wi th : hmax = St,chip^j Calcula t ions are done for the values o f § s t and § e x for each set o f entry-exit angles. If n/2 is part o f one o f the intervals, then the m a x i m u m chip load w i l l occur at this angle and is equal to the feed per tooth since s in n/2 is equal to 1. 62 /, chip p — Zi t, chip max n (4.15) s*,cWp = min(hmax/(sin^ = <t>Jt>0, <|>ejt>0, <|>sU> ...)> M a x i m u m Def lec t ion The m a x i m u m deflection is calculated using the model presented in section 3.7.2. The con-straint is set as the tolerance a l lowable for the part. The m a x i m u m deflection was given i n equa-t ion 3.31 : y,max g £ / The constants A, E, I and L depend on the geometry of the cut and the tool material . W e set 5^ m a x , so we can f ind stdej-. F y t n a x can be expressed as earlier as : Fy,max = C + St,defD where C - [~)(-KREST-KTEUT) D - (^-^-j(KTCTT + KRCRT), So, the feed per tooth st ^ b e c o m e s *t,def VA2(A - 3L)J D~ (4.16) 63 Identif ication o f m a x i m u m al lowable feedrate The m a x i m u m al lowable feedrate is the m i n i m u m o f a l l feedrates calculated : st, opt = min(st,force' st, torque' st, power' st, chip' st, def> (4-17) The new feedrate commands might not produce a smooth feedrate curve. In order to get a smoother curve, we use a 5-point average smoothing method where the 4 previous feed values (st)k_4, st)/(_3, stk_2, st,k-l) a n a " t n e current feed stk are used, and the average over these 5 points is calculated to obtain the new feed for step k. st,k-4 + st,k-3 + st,k-2 + st,k- \ + st,k ,A , 8 x st,k,new ~ 5 V*-*-°) The N C program is then updated wi th new F commands for each step. 4.7.2. A d a p t i v e F o r c e C o n t r o l W h e n mach in ing , the quali ty o f the workpiece and the performance o f the machine are related largely to the C N C feed dr ive dynamics and the cutt ing process dynamics . U s i n g adaptive control i n mach in ing provides improved mach in ing parameters by adapting to the changes in the cutting operation, such as depth o f cut and wid th o f cut. In this research project, both approaches, off-l ine and onl ine adaptive force control , are based on the adaptive general ized predict ive control developed by Al t in tas [9] and are used to mainta in the peak force at a specif ied reference cutt ing force by updating the feedrate command . T h i s 64 adaptive control a lgor i thm is based on Genera l ized Predic t ive C o n t r o l method presented by C l a r k e et al[20]. The b l o c k diagram presented i n figure 4.9 shows the general adaptive control system. In this b l o c k diagram, we can see that the input to the m i l l i n g process is the feed c o m m a n d / c wh i l e the output is the resultant cut t ing force Fa appl ied at the tool t ip. Reference Force Fr[N], H > 1 Feed Command fc [mm/s] CNC/MIIIIng Process Adaptive Control Algorithm Adjust Control Parameters CNC F e e d Dr ive, Motors, and Amplifiers CNC Machine Tool Measured |Cutting Force fa actual Gm feed delivered Cutting P roc ess , Gp i I Fa[N] Estimation of Machining Process Transfer Function F i g u r e 4.9 : B l o c k diagram o f a general adaptive control system i n machin ing . Source : Al t in tas [9]. The C N C and feed dr ive dynamics can be mode l l ed as [6]: Gm(z) = fa(z) _ (8o + 8iz 1 + 8 2 z ) (4.19) where fc is the feed c o m m a n d to the C N C a n d / a is the actual feed del ivered by the drives. The parameters g0, gj, g2 and h1 vary wi th the feedrate and spindle speed. The m i l l i n g process can be expressed by the transfer function [6]: - l r (^ - - fc Ja\z> \+az (4.20) where 65 1 + LI M n ( l + Li) where M is the number o f teeth, n is the spindle speed [rps], Ks is the cutt ing coefficient and kt is the stiffness o f the tool . Therefore, the transfer function o f the plant is g iven by [9]: -1 -1 -2 F„(z) R(7\ z (bn + biZ + b0z ) Gc(z) = GmxGp = f^ = m= 0 I (4.21) where bQ - g0 x B , bx = gx x B , /3 2 = g 2 x (3, a j = - hx + a and a 2 = - / i j x a . T h e plant dynamic parameters can be estimated using a Recurs ive Least Square ( R L S ) algo-r i thm [9]. On l ine Adap t ive Force Cont ro l F o r the onl ine approach, the X and Y forces are measured dur ing the mach in ing using a dyna-mometer and transferred to the adaptive control ler w h i c h adapts the parameters and generates a new feedrate command . T h e new feedrate c o m m a n d is sent to the C N C and the new resultant force is measured. 66 Off- l ine Adap t ive Fo rce Con t ro l The adaptive general ized predict ive control developed by Al t in tas [9] was also implemented i n the V i r t u a l M i l l i n g project. The difference wi th the onl ine adaptive control is that i n this case, the resultant cutt ing force is not measured during the mach in ing but calculated by the m i l l i n g s i m -ulat ion. 4.8. Simulation and Experimental Results 4.8.1. Set-up Exper imen ta l cutt ing tests were performed on a Fada l ver t ical mach in ing center equipped wi th both a K i s t l e r dynamometer and the Open Archi tec ture R e a l - T i m e Operat ing Sys tem ( O R T S ) . O R T S is a general purpose real-time operating system running on a D S P board con-nected to a P C . T h i s system was developed in the Manufac tu r ing A u t o m a t i o n Laboratory at the Un ive r s i t y o f B r i t i s h C o l u m b i a [4]. The cutt ing forces i n X and Y are measured using the K i s t l e r dynamometer. F o r the cutt ing tests for constraint-based feedrate schedul ing and offline adaptive force control , the cutt ing forces are recorded us ing the M A L - D A Q module f rom C u t P r o [10]. F o r the onl ine adaptive force control , the cutt ing forces are fed into the interface board o f O R T S . F o r a l l three approaches, N C programs were transferred to the machine tool controller. F o r constraint-based feedrate schedul ing and offline adaptive force control , s imulations us ing the m i l l i n g s imula t ion module and the corresponding feedrate schedul ing a lgor i thm are first run. Feedrate curves and mod i f i ed N C programs are obtained. 67 F o r onl ine adaptive force control , the or iginal N C program is fed to the controller and the adaptive force control a lgor i thm implemented in O R T S adjusts the feedrate according to the cut-t ing forces and control ler parameters. O R T S is connected direct ly to the control ler ' s feed over-ride potentiometer. 4.8.2. Tests The tests were performed for the m i l l i n g operation shown in figure 4.10. The three pockets were previously machined at a depth o f cut of 8 m m and the test consists in the linear tool path shown by the segment f rom point A to B . The axia l depth of cut is 2 m m . The dimensions o f the workpiece and its features are g iven i n figure 4.11. F i g u r e 4.10 : Test part - Toolpath. 68 F i g u r e 4 . 1 1 : Test part - D imens ions . The workpiece material is A17075-T7451 . The cutt ing tool is a two-flute cy l i nd r i ca l end m i l l w i th a diameter o f 12mm, a rake angle o f 8 degrees and a he l ix angle o f 30 degrees. The spindle speed used is 2500 r p m and the depth o f cut is 2 m m . T h e parameters used for the tests were as fo l lows : the m a x i m u m al lowable feedrate is set to 2000 m m / m i n and the reference cutt ing force is 350 N . 69 Simula t ion Results Firs t , s imulat ions us ing constraint-based feedrate schedul ing and off-l ine adaptive force con-trol are conducted to obtain feed curves that are used for the experimental m i l l i n g tests. The feed curves are shown in figures 4.12 and 4.13. These curves show the feedrate as a function o f the posi t ion o f tool a long the toolpath. F igure 4.14 shows the corresponding s imula t ion results for the resultant peak force. W e choose to display these curves using posi t ion instead o f t ime as posi t ion refers direct ly to the N C code that is generated and sent to the machine tool controller. F r o m these curves, we can observe some differences. A t posi t ion 35 m m , both algori thms detect a force increase as the cutt ing tool enters the workpiece . T h e constraint-based approach decreases the feedrate faster and i n the s imulat ion results, it reaches the desired reference cutt ing force at 40 m m . B o t h approaches give s imi la r feedrates for the segment o f the tool path where the tool machines the side o f the rectangular feature. A t posi t ion 80 m m , the algori thms detect again a change i n the geometry as the cutt ing tool enters the section between the rectangular and trian-gular features. A g a i n , constraint-based approach brings the s imula t ion force back to the reference value faster than the offline adaptive force control . A s the tool is go ing through the triangular fea-ture, both algori thms increase the feedrate in a s imi la r manner w i th a very s imi la r peak feedrate at posi t ion 120 m m . A s the cutt ing tool is go ing through the last c i rcu lar feature, we observe a smooth peak wi th the offline adaptive force control . The s imula t ion results for peak forces using those feed curves gave good results wi th slight deviations f rom the reference cutting force o f 350 N . 70 Constraint-Based Feedrate Scheduling 100 150 200 250 Position [mm] Figure 4.13 : Feed curve - Constraint-based feedrate scheduling. 71 500 £ . 4 0 0 o o 300 $ 200 Q_ Offline Adaptive Force Control - Simulation Results 100 h 0 500 2-400 o o 300 $ 200 Q_ 100 0 Constraint-Based Feedrate Scheduling - Simulation Results 100 120 140 Position [mm] Figure 4.14 : S imula t ion o f peak forces. Exper imenta l Resul ts Exper iments are conducted for the 3 approaches. F o r the constraint-based approach and the off-l ine adaptive force control approach, the N C programs are defined us ing the feed curves obtained by s imulat ion. F o r onl ine adaptive force control , a N C program is first fed to the 72 machine control ler and the O R T S and the adaptive control a lgor i thm adjusts the feedrate i n order to meet the process specifications, that is the reference force and m a x i m u m feedrate. F igure 4.15 shows the feed curve obtained when using onl ine adaptive force control . The feedrate is g iven as a function o f t ime, but we can observe a s imi la r trend as for the s imulat ion feed curves obtained wi th the off-l ine approaches. Online Adaptive Force Control 1000 28 30 32 34 36 38 40 Time [s] Figure 4.15 : F e e d curve - On l ine adaptive force control . The experimental results for the peak force measurements are presented i n figure 4.16. A s we can see, a l l three approaches give good results. F o r a l l three approaches, there is an overshoot when the cutt ing tool enters the workpiece and between features. The overshoot is about 2 0 % for the onl ine adaptive force control as the tool enters the workpiece , w h i c h is s l ight ly higher than wi th the off- l ine approaches. A l s o , between the rectangular pocket and the triangular pocket, the 7 3 onl ine adaptive force control gives a higher overshoot. O n the other hand, this approach gives a smoother peak force curve than the other approaches. In terms o f cyc le t ime, the onl ine adaptive force control is the method that gave the best results w i th a t ime o f 8 s. F o r off-l ine adaptive force control , the cyc le t ime was 9 s and for con -straint-based feedrate schedul ing it was 9.9 s. ^ 5 0 0 I 400 § 300 ^ 200 j> 100 0 O f f l i n e A d a p t i v e F o r c e C o n t r o l - E x p e r i m e n t a l R e s u l t s 32 33 34 35 36 37 38 39 40 41 C o n s t r a i n t - B a s e d F e e d r a t e S c h e d u l i n g - E x p e r i m e n t a l R e s u l t s 35 36 37 38 39 40 41 42 43 44 O n l i n e A d a p t i v e F o r c e C o n t r o l - E x p e r i m e n t a l R e s u l t s Figure 4.16 : Exper imenta l peak forces. 74 4.9. Conclusion Based on the analyt ical m i l l i n g force mode l developed by Spence [36] and presented i n chap-ter 3, a f ramework for the implementat ion of Vi r tua l M i l l i n g was developed. Th i s appl icat ion comprises a new interface for the selection o f stable cutting condi t ions. T h i s interface is inte-grated i n a C A D / C A M software, w h i c h is new since current C A D / C A M systems do not offer such options. T h i s is the first step in the Vi r tua l M i l l i n g project. T h i s interface was developed and integrating i n the m i l l i n g module o f C A T I A V 5 . The val idat ion o f the force mode l was presented i n the previous chapter. T w o approaches for feedrate schedul ing, constraint-based feedrate schedul ing and off-l ine adaptive force control , were implemented. These 2 approaches were tested and compared wi th a third approach, onl ine adaptive force control . Cu t t ing tests were done and al l three approaches prove to give good results. On- l i ne adaptive force control seems to be the most efficient approach since it gives good results for peak force and the lowest cyc le t ime, but it requires testing on the machine. The two off-l ine approaches are an interesting alternative and even though they d i d not perform as w e l l as the onl ine adaptive force control , they provide an improvement i n terms of force control and cyc le t ime compared to tradit ional N C programming practices. 75 76 Conclusion M i l l i n g process s imula t ion is becoming part o f engineering practices in advanced manufac-turing faci l i t ies . The next step is to integrate the m i l l i n g process s imula t ion and the C A D / C A M capabil i t ies to simulate the mach in ing operation for the whole N C program. T h i s is k n o w n as V i r -tual M i l l i n g and offers many advantages such as the capabi l i ty to identify cr i t ica l cutting cond i -tions, to calculate cutt ing forces and deflections a long the tool path i n order to improve part quali ty and meet part tolerances, to reduce the mach in ing cyc le t ime by performing feedrate schedul ing, and to reduce or el iminate the tool proof ing t ime before product ion start. T h i s thesis presents an appl icat ion for V i r tua l M i l l i n g developed and tested for 2 1/2 D parts. The first section o f this work , the m i l l i n g s imula t ion , i n v o l v e d mode l l i ng o f the m i l l i n g pro-cess for the who le part and was done by implement ing the analyt ical c losed- loop fo rm m i l l i n g force mode l developed by Spence [36]. T h i s analyt ical model has the advantage o f requir ing less computat ion t ime since integration along the tool axis is not required. The input is a f i le gener-ated by the tool -workpiece intersection applicat ion developed i n A C I S by H u a n g [25]. T h i s f i le contains the tool -workpiece intersections along the discret ized tool path. T h e output of the m i l l -i ng s imulat ion include instantaneous forces, resultant forces, m a x i m u m forces, m a x i m u m torque and power, deflections a long the tool axis and m a x i m u m deflection, for each step along the tool path. In order to validate the mode l , experimental cutting tests were performed on a 2 1/2 D part. The test part featured different geometries and different intersection cases. Exper imenta l results were compared wi th s imula t ion results and showed that the m i l l i n g force mode l is relat ively accu-rate, with an error of about 10%. The principal source of error is the modelling of the material cutting coefficients. Then, the Virtual Milling flowchart was presented. The first step in Virtual Milling is the selection of appropriate and stable cutting conditions during the NC programming. Once the NC program is completed, it is more difficult to modify the axial depth of cut as it requires to modify the tool path itself. If the user is guided in the selection of the axial depth of cut that will provide stable cutting, the NC program will not require subsequent modifications. Current C A D / C A M systems do not offer tools for the selection of cutting conditions. Therefore, the requirements of such a tool were estalished and a new interface was developed and integrated in the Prismatic Machining module of the C A D / C A M software CATIA V5. This interface provides the user with a chart of the axial depth of cut as a function of the spindle speed, known as stability lobes. The user must first select the cutting tool geometry and workpiece material in a database, then select the tool-machine transfer functions, and specify the radial width of cut used in the program. These input are necessary for the calculation of stability lobes. The NC programmer can then select a proper combination of axial depth of cut and spindle speed using the stability lobes. The second step in the Virtual Milling is the milling simulation. The milling simulation is used for two purposes : to evaluate the milling operation and check its validity, and to perform feedrate scheduling. The first purpose allows the user to identify problematic sections of the tool path. The second use for milling simulation is to perform feedrate scheduling. Two off-line approaches were implemented: constraint-based feedrate scheduling and off-line adaptive force control. These approaches were used to generate feed curves for a specific tool path in order to evaluate the gain from using off-line approaches. Experimental cutting tests were conducted. 77 Anothe r approach, onl ine adaptive force control developed by Al t in tas [9] was also used dur ing the tests i n order to compare the three methods. A l l three methods gave good results. There were overshoots at transient cuts i n a l l cases, the m a x i m u m overshoot o f about 2 0 % was observed wi th the onl ine adaptive force control . O n the other hand, the mach in ing t ime was lower wi th this approach and the constraint-based feedrate schedul ing was the slowest method. O v e r a l l , the off-l ine approaches can be used to adapt the feedrate to specific mach in ing constraints and w i l l pro-v ide good control of the cutt ing forces w h i l e i m p r o v i n g the mach in ing time. Future Research T h i s thesis focused on Vi r tua l M i l l i n g for 2 1/2 D parts us ing c y l i n d r i c a l end m i l l s . Future w o r k should include complex geometries, such as sculptured surfaces and 5-axis mach in ing , as w e l l as different tool geometries. The m i l l i n g s imula t ion should provide the user wi th information regarding locations o f c r i t i -ca l constraints a long the tool path. Ideally, it should be integrated i n the C A D / C A M software and c o u l d run i n real-t ime wi th the visual isat ion o f the metal r emova l . 78 79 Bibliography [1] Al t in tas Y . , Y e l l o w l e y I., T lus ty J . , 1988, The Detection of Tool Breakage in Milling Oper-ations, A S M E Journal o f Engineer ing for Industry, Vo l .110 , pp.271-277. [2] Al t in tas Y . , Spence A . D . , 1991, End Milling Force Algorithms for CAD Systems, A n n a l s o f the C I R P , V o l . 4 0 (1), pp.31-34. [3] Al t in tas Y , 1994, Direct Adaptive Control of End Milling Process, International Journal o f M a c h i n e Tools and Manufac tur ing , Vo l .34 , N o . 4 , pp.461-472. [4] Al t in tas , Y , Munas inghe W . K . , 1994, A Hierarchical Open-Architecture CNC System for Machine Tools, A n n a l s o f the C I R P , V o l . 4 3 / 1 , pp.349-354. [5] Al t in tas Y , B u d a k E . , 1995, Analytical Prediction of Stability Lobes in Milling, A n n a l s o f the C I R P , V o l . 4 4 / 1 , pp.357-362. [6] Al t in tas Y , Munas inghe W . K . , 1996, Modular CNC design for Intelligent Machining, Part 2: Modular Integration of Sensor based Milling Process Monitoring and Control Tasks, Journal o f Manufac tur ing Science and Engineer ing , Vol .118 , pp.514-521. [7] Al t in tas Y , L e e P., 1996, A General Mechanics and Dynamics Model for Helical End Mills, A n n a l s o f the C I R P , V o l . 4 5 ( l ) , pp.59-64. [8] Al t in tas Y , E n g i n S., B u d a k E . , M a y 1999, Analytical Stability Prediction and Design of Variable Pitch Cutters, A S M E Journal o f Manufac tu r ing Science and Engineer ing , V o l . 1 2 1 , p p . l 7 3 - 1 7 8 . [9] Al t in tas Y , 2000, Manufacturing Automation, Cambr idge Un ive r s i t y Press. [10] Al t in tas Y . , 2000, Modelling Approaches and Software for Predicting the Performance of Milling Operations at MAL-UBC, M a c h i n i n g Science and Technology, Vol .4(3) , pp.445-478. [11] A r m a r e g o E . J . A . , E p p C . J . , 1970, An Investigation of Zero Helix Peripheral Up-Milling, International Journal o f M a c h i n e T o o l D e s i g n and Research, V o l . 1 0 , pp.273-291. [12] A r m a r e g o E . J . A . , W a n g J . , Deshpande N . R , 1995, Computer-Aided Predictive Cutting Model for Forces in Face Milling Allowing for Tooth Run-Out, A n n a l s o f the C I R P , Vo l .44 (1), pp.43-48. [13] A r m a r e g o E . J . A . , Deshpande N . P . , 1993, Force Prediction Models and CAD/CAM soft-ware for Helical Tooth Milling Processes, i. Basic Approach and Cutting Analyses, Interna-t ional Journal o f Product ion Research, Vol .31(8) , pp. 1991-2009. [14] B a i l e y T., E lbes t awi M . A . , E l -Ward an y T.I . , F i tzpa t r ick P., 2002, Generic Simulation Approach for Multi-Axis Machining, Part 1: Modeling Methodology, Transactions o f the A S M E , pp.624-633. [15] B a i l e y T., E lbes t awi M . A . , E l -Ward an y T.I . , F i tzpa t r ick P., 2002, Generic Simulation Approach for Multi-Axis Machining, Part 2: Model Calibration and Feed Rate Scheduling, Transactions o f the A S M E , pp.634-642. [16] B u d a k E . , 1994, Mechanics and Dynamics of Milling Thin Walled Structures, Un ive r s i t y o f B r i t i s h C o l u m b i a , P h . D . Thesis . [17] B u d a k E . Al t in tas Y . , 1994, Peripheral Milling Conditions for Improved Dimensional Accuracy, International Journal o f M a c h i n e Tools and Manufacture , Vol .34(7) , pp.907-918. 80 [18] B u d a k E . , Al t in tas Y . , Armarego E . J A . , 1996, Prediction of Milling Force Coefficients From Orthogonal Cutting Data, Transactions o f the A S M E , Vo l .118 , pp.216-224. [19] B u d a k E . , 2000, Improving Productivity and Part Quality in Milling of Titanium Based Impellers by Chatter Suppression and Force Control, A n n a l s o f the C I R P , V o l . 4 9 ( l ) , pp.31-36. [20] C l a r k e D . W . , M o h t a d i C , Tuffs P.S. , 1987, Generalized Predictive Control - Part I, The Basic Algorithm, Au tomat i ca , Vol .23(2) , pp.137-148. [21] E n g i n S., Al t in tas Y , 1999, Generalized Modeling of Milling - Mechanics and Dynamics: Part I: Helical End Mills, A S M E International M e c h a n i c a l Engineer ing Congress and E x p o s i t i o n S y m p o s i u m , M a c h i n i n g Science and Technology. [22] E n g i n S., Al t in tas Y , 1999, Generalized Modeling of Milling - Mechanics and Dynamics: Part II: Inserted Cutters, A S M E International M e c h a n i c a l Engineer ing Congress and E x p o s i t i o n S y m p o s i u m , M a c h i n i n g Science and Technology. [23] Fusse l l B . K . , Jerard R . B . , Hemmet t J . G , M a y 2001 , Robust Feedrate Selection for 3-Axis NC Machining Using Discrete Models, Transactions o f A S M E , V o l . 123, pp.214-224. [24] Fusse l l B . K . , Jerard R . B . , R ichards N . , Y a l c i n C , 2002, NC Machining Feedrate Optimiza-tion Using On-Line Model Tuning and Adaptive Control, Proceedings o f the 2002 N S F D e s i g n and Manufac tu r ing Research Conference. [25] H u a n g X , 2003, Internal Report at UBC MAE [26] Jerard R . B . , Fusse l l B . K , Hemmet t J . G , E r c a n M . T . , 2000, Toolpath Feedrate Optimiza-tion: A Case Study, Proceedings o f the 2000 N S F D e s i g n & Manufac tu r ing Research C o n -ference. 81 [27] K a n g M . , L e e S . - K . , K o S . - L . , Optimization of Cutting Conditions Using Enhanced Z Map Model, A n n a l s o f the C I R P , Vol .51 (1), pp.429-432. [28] K o J . H . , Y u n W . - S . , C h o D . - W . , E h m a n n K . H . , 2002, Development of a virtual machining system, part 1: approximation of the size effect for cutting force prediction, International Journal o f M a c h i n e Tools & Manufacture , V o l . 4 2 , pp.1595-1605. [29] Koenigsberger E , Sabberwal A . J . P . , 1961, An Investigation into the Cutting Force Pulsa-tions during Milling Operations, International Journal o f M a c h i n e T o o l D e s i g n and Research, V o l 1, pp.15-33. [30] Mar te l lo t t i M . E . , 1941, An Analysis of the Milling Process, Transactions o f A S M E , pp.677-700. [31] Mar te l lo t t i M . E . , 1945, An Analysis of the Milling Process Part II: Down Milling, Trans-actions o f A S M E , V o l . 67, pp.233-251. [32] M e r r i t H . E . , 1965, Theory of Self-Excited Machine-Tool Chatter, Trans. A S M E Journal o f Enginee r ing for Industry, V o l . 8 7 , pp.447-454. [33] Richards N . D . , Fusse l l B . K . , Jerard R . B . , 2002, Efficient NC Machining Using Off-Line Optimized Feedrates and On-Line Adaptive Control, Manufac tur ing Engineer ing D i v i s i o n : S y m p o s i u m on Process P lann ing and Process Opt imiza t ion , 2 0 0 2 I M E C E . [34] Sabberwal A . J . P . , 1961, Chip Section and Cutting Force during the Milling Operation, C I R P A n n a l s , V o l . 1 0 , pp.197-203. [35] Saturley P.V. , Spence A . D . , 2000, Integration of Milling Process Simulation and On-Line Monitoring and Control, International Journal o f A d v a n c e d Manufac tur ing Technology, pp.92-98. 82 [36] Spence A . D . , 1992, Solid Modeller Based Milling Process Simulation, Un ive r s i ty o f B r i t -ish C o l u m b i a , P h . D . Thesis . [37] Spence A . D . , Al t in tas Y . , 1991, CAD Assisted Adaptive Control for Milling, Journal o f D y n a m i c Systems, Measurement and Con t ro l , Transactions o f the A S M E , Vol .113 , pp.444-450. [38] Spence A . D . , Al t in tas Y , K i r k p a t r i c k D . , 1990, Direct Calculation of Machining Parame-ters from a Solid Model, Journal o f Computers in Industry, Vo l .14 . , N o . 4 , pp.271-280. [39] ***Spence A . D . , L i Z . , X X X X , Parallel Processing for 2-1/2 D Machining Simulation, [40] Suh S . - H . , C h o J . - H . , Hascoet J . - Y , 1996, Incorporation of Tool Deflection in Tool Path Computation: Simulation and Analysis, Journal o f Manufac tu r ing Systems, V o l . 1 5 , no.3, pp. 190-199. [41] T lus ty J . , Po lacek M . , 1963, The Stability of Machine Tools Against Self Excited Vibrations in Machining, International Research in Product ion Engineer ing , A S M E , pp. 465-474. [42] T lus ty J . , M a c N e i l P., 1975, Dynamics of Cutting Forces in End Milling, A n n a l s o f the C I R P , V o l . 2 4 , pp.21-25. [43] Tobias , S . A . , 1965, Machine Tool Vibration, B l a c k i e . [44] Tsa i M . D . , Takata. S. et a l . , 1990, Prediction of Chatter Vibrations by Means of a Model-Based Cutting Simulation System, A n n a l s o f the C I R P , V o l . 3 9 ( l ) , pp.447-450. [45] van Luttervel t C . A . , C h i l d s T . H . C . , et a l . , 1998, Present Situation and Future Trends in Modelling of Machining Operations, C I R P S T C Cut t ing K e y n o t e Paper. 83 [46] Y e l l o w l e y I., K u s i a k A . , 1985, Observations on the Use of Computers in the Process Plan-ning of Machined Components, Transactions o f the A S M E , Vol .9(2) , pp.70-74. [47] Y u n W . - S . , K o J . H . , C h o D . - W . , E h m a n n K . H . , 2002, Development of a virtual machining system, part 2: prediction and analysis of a machined surface error, International Journal o f M a c h i n e Tools & Manufacture , V o l . 4 2 , pp.1607-1615. [48] Y u n W . - S . , K o J . H . , L e e H . U . , C h o D . - W . , E h m a n n K . H . , 2002, Development of a virtual machining system, part 3: cutting process simulation in transient cuts, International Jour-nal o f M a c h i n e Tools & Manufacture , V o l . 4 2 , pp.1617-1626. 84 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0080731/manifest

Comment

Related Items