Simulation-aided Design of Thread Milling Cutter

Transcription

1 Available online at Procedia CIRP 1 (2012 ) th CIRP Conference on High Performance Cutting 2012 Simulation-aided Design of Thread Milling Cutter Seok Won Lee a *, Andreas Nestler a a Institute of Forming and Cutting Manufacturing Technology, Dresden Univeristy of Technology, George-Bähr-Str. 3c, Dresden, Germany * Corresonding author. Tel.: ; fax: address: seokwon.lee@tu-dresden.de. Abstract Thread milling has become quite oular in recent years as an alternative to taing or other forms of threading because of diversity and comlexity of arts and flexibility of the rocess in industries such as biomedical alications, aerosace and die-mold manufacturing. Today the design of the tooth rofile is, however, redominantly feasible by the exertise and trial and error rincile. Presented in this aer are a novel methodology to design the tooth rofile of the thread mill by comaring the to-be thread rofile and the as-is thread rofile which is analyzed by means of NC cutting simulation. The simulation kernel enables to continually subtract the swet volume of thread milling cutter undergoing helical movement from the workiece and to calculate the virtual workiece (VWP). Combined with the standardized to-be thread rofile, the tooth rofile of to-be-designed thread mill is adatively modified until the thread rofile on VWP and the to-be thread rofile become congruent with each other. The roosed methodology could be integrated into CAD/CAM systems The Published Authors. by Published Elsevier BV. by Elsevier Selection B.V. and/or Selection eer-review and/or eer-review under resonsibility under resonsibility of Prof. Konrad of Professor Wegener Konrad Wegener Oen access under CC BY-NC-ND license. Keywords: Design, Simulation, Thread milling, Tool Design 1. Introduction Helical surface machining (either grinding or milling) is a widely adoted rocess used to generate helicallyswet surfaces for drill flutes, end mill cutters, helical geaeeth, screw mechanisms, and so on [1-2]. It is extremely comlex due to the helical motion of the disktye (grinding wheel, slab mill) or axial-tye (mounted wheels, end mill) cutters along the helical tool ath on cylindrical stocks. During machining of a helical surface, the rotating cutter moves along the axis of the workiece, while the workiece rotates about its own axis. The combined relative motion of the cutter and workiece results in a helical motion [3]. The roblem of helical surface machining, however, is that it is still usually aroached by many manufacturers with an emirical trial-and-error method. The geometry of the helical surface not only deends on the geometry of the tool, but also on the oerating (machine setu) arameters. Identical surfaces can be manufactured under radically different conditions with resect to the machine setu and tool geometry used. For that reason, the choice of oerating arameters and cutter rofiles deends on the machine oerator and his know-how about the rocess [4]. Classical alication areas of form-milling cutters are, among othehings, the gear cutting and the roduction of helical slots, for examle, those of threads. Fohread milling by using form-milling cutters (generally referred to as thread milling cutter) as well as fohe fast develoment of secial threads, there arises a need for comuter-based construction and simulationsuorted functional verification of thread cutters. When it comes to the fabrication of threads, threadmilling is advantageous in comarison to taing for several reasons. Firstly, thread-milling roduces far sueriohreads as comared to taing due to a much higher cutting seed. Secondly, thread milling is a ractical solution fohreading large holes. However, it demands a careful, deliberate aroach, as well as several other rerequisites. At first, u-to-date CNC machine tools are a necessity. To erform thread milling, The Authors. Published by Elsevier B.V. Selection and/or eer-review under resonsibility of Professor Konrad Wegener Oen access under CC BY-NC-ND license. htt://dx.doi.org/ /j.rocir

2 Seok Won Lee and Andreas Nestler / Procedia CIRP 1 ( 2012 ) the machine must be caable of helical interolation. Second to none, a thread milling cutter, the rofile of which is to be designed slightly different from the thread rofile due to the helical movement of the cutter, is required. Other asects to consider in relation to thread milling are the issues of right-handed/left-handed threads, internal/external threads, and multi-start threads [5-6]. This aer resents a novel aroach to the rerofiling of rotating thread milling cutters. The rerofiling of cutter rofile is based on the enveloe rofiles [8-9] of the moving cutter and the helical motion that results from the relative motion between the cutter and workiece. To demonstrate the validity of the roosed method, an ISO metric screw thread is chosen as an examle in this work [7]. Fig. 1 shows the sectional view of ISO metric screw thread defined by two design arameters, itch and major diameter D, in the lane which goes through the axis of screw thread. Additionally, H is the height of the fundamental triangle, D2 is the itch diameter and D1 is the minor diameter of the external thread. The basic rofile is the theoretical rofile of the thread. An essential rincile is that the actual rofiles of both the internal/external threads must never cross oransgress the theoretical rofile. So, external threads will always be equal to, or smallehan, the dimensions of the basic rofile. Internal threads will always be equal to, or greatehan, the basic rofile [7]. method exemlarily. Section 6 concludes and summarizes the work. 2. Helical Projection A (linear) rojection is the maing of threedimensional (3D) oints onto a two-dimensional (2D) lane by connecting corresonding oints with arallel lines. On the other hand, a curvilinear rojection of 3D oints onto a 2D lane along a helix with an axis and a itch is called helical rojection. In contrast to linear rojection, helical rojection connects the corresonding oints along helical curves that could have a common itch but different radii of helix. Helical rojection is very useful in the formulation of the helical surfaces or grooves embedded in rotor, milling or boring cutters, worm gear ohreaded screws, etc. Hereafter, any mention of rojection refers to helical rojection if it is not secified. The family of Euclidean congruence transformations, which is arameterized by the angle arameter [rad], and mas oints in a suitable Cartesian coordinate system according to (1) is called a one-arameter grou of helical motions if. If, it is called a one-arameter grou of rotations, or a uniform rotation. A uniform helical motion is the suerosition of a uniform rotation and a translation by the vector. The line is called its axis, and is called its itch (see Fig. 2). If an arbitrary oint as in Eq. (2) Fig. 1 Cross sectional view of ISO metric screw thread after [7]. This aer is organized as follows: Section 2 resents the helical rojection which is the foundation fohe roosed aroach. The aroach to the calculation of enveloe rofile of the thread milling cutter and the method of the simulation-aided design of the thread milling cutter are resented in Section 3 and Section 4, resectively. Section 5 resents the imlementation and two demonstration-examles by using the roosed where (2),, is given, the helix with itch through could be rewritten from Eq. (1) and Eq. (2) as Eq. (3), or, where. (3)

3 122 Seok Won Lee and Andreas Nestler / Procedia CIRP 1 ( 2012 ) Then, the helically rojected oint of the helix onto lane is found by substituting Eq. (3) into the lane equation as in Eq. (4) (see Fig. 2). that cuts raw stock and forms a thread. Given a itch of the to-be thread, that of the corresonding thread cutter, and that of the helical trajectory should be identical with (see Fig. 3). z Workiece D Thread milling tool : itch R = (l 2 +m 2 ) : ax+by+cz = d r helix t x() = Q Z b /2 R x(0) = P (l,m,n) Helix X Y x y Fig. 3 Relative ositioning of thread milling tool to workiece at thread milling. Fig. 2 Helical motion and helical rojection of the helix onto lane. where, and,,. (4) Then, the solution could be found aroriately by restricting the valid rojection angle interval. 3. Enveloe Profile of a Thread Milling Cutter The enveloe rofile is a line of contact along which the thread milling cutteouches the generated thread surface [9]. This rofile roduces the contour on the workiece and is therefore also referred to as a generator, deending exclusively on the geometry and the motion of the tool. Accordingly, in ordeo calculate re-rofiling of a tool rofile, the kinematics of a thread milling cutter needs be examined first. Then, enveloe rofiles are to be determined from the analysis of the velocity distribution of the tool. During thread milling, the cutter moves along a helical trajectory around the cylindrical geometry. Fig. 3 shows the relative ositioning of a thread milling cutter Because the tool moves with a fixed tool axis along the helix, the velocity vectors and of the cutter at the bottom and on the to are identical with the feed vector. As denoted in Fig. 4, is calculated from the relationshi between itch of the screw thread and the distance, which is measured from the axis of the workiece to the axis of the cutter. Due to the fact that the tool undergoes the three-axis motion, the velocity vector of any oint P on the tool surface is congruent with ( ). Tool D r helix 2 r helix D External thread Fig. 4 Definition of a feed vector. Z Fig. 5 schematically illustrates the fundamental rocedure used to determine the geometrically exact rofile of the thread milling cutter. Because the teeth of the thread milling tool are connected with each other, just one tooth is considered here and the rincile is alied to otheeeth reeatedly. It is assumed that a oint P of interest is laced on the tooth. At first, the unit surface normal vector is obtained for any given oint P on the tooth surface ( can fall into one of both and ) and maed onto a unit shere. Then, small (= v b = v t ) O 2 r D 2 r helix = tan -1 where is the itch of thread. 2 r for examle, ISO M24 = 3 mm D = 24 mm = 2.27º r helix = 36 mm = 1.52º = - = 0.72º B B` circumference

4 Seok Won Lee and Andreas Nestler / Procedia CIRP 1 ( 2012 ) circles can be built by using and (see Fig. 5 (a)-(b)). Secondly, since is already given, the unit circle that is erendiculao is maed onto the unit shere as the great circle, so that the intersection oints and between the circles and are calculated (see Fig. 5 (c)-(b)). Consequently, both oints P on the tool surface, which corresond to the intersection oints and on the unit shere, satisfy the tangency condition which enables finding the enveloe rofile on tooth surface (see Fig. 5 (d)). n u n d a) Initial Tool Tooth h t f) Design Profile / 8 c g Comare & Caculate max error max c u c d b) Overlaing of T-Ma and C-Ma n u n d n 2 e) Projected Profile max Fig. 5 Schematic flow diagram fohe calculation of otimal thread milling cutteooth design from thread data and helical tool ath. Fig. 6 shows in detail the enveloe rofile that is calculated by the roosed method. The thread milling tool is a double frustum of a cone which has the height and the radius. Please note that and according to the definition of the screw thread in Fig. 1. Thus, the enveloe rofile of the thread milling tool is comrised of the arc segment and both line segments and. h t T n1 z P 3 (0,0,H) c) Helical Tool Path n 2 Helix n 1 d) Enveloe Profile a = (a,b,c) 4. Simulation-aided Design of the Thread Milling Cutter The modification of the tool shae leads to the deformation of the thread rofile because the enveloe rofile is modified corresondingly. Fig. 5 (e) shows the rojected view of the enveloe rofile in the section AA which goes through the tool axis (see Fig. 7 in detail). The rojected enveloe rofile is shown as a dotted curve and the sectioned rofile of the thread surface is deicted bold in Fig. 7 (b). On the section AA, the rojected enveloe rofile can be comared with, and be modified to the sectioned thread surface. For examle, a oint P lies on an enveloe rofile and the rojected oint P AA onto the section AA can be transformed slightly by changing the osition of P along the surface normal. P is adjusted such that P AA could coincide with the to-be oint T AA on a sectioned thread surface. It imlies that the fundamental analytical condition of engagement between the generating cutter and generated helical surface is established, which in turn says that the surface normal of the thread milling tool at P AA is arallel to the surface normal of the thread at T AA when the thread milling tool is in contact with the oint T AA. Please note that the direction of of the cutter is inverted in AA because the thread surface is the conjugated surface of the cutter surface. n P h t a) Initial dimension of cutteooth Fig. 7 Transformation of a oint P on the cutter surface in surface normal direction. Enveloe rofile max P -n T 60 / 8 b) Projected enveloe rofile P 1 = ( sin, cos,0) P 2 = ( sin,- cos,0) t 1 = (-cos,sin,0) t 2 = (cos,sin,0) d 1 = (- sin,- cos,-h t )/T d 2 = (- sin, cos,h t )/T n 1 = (h t sin,h cos,- )/T n 2 = (h t sin,-h cos, )/T Y n 2 d 2 P 5 o P 1 P 2 t 2 t 1 x d P 1 4 n 1 P 0 (0,0,-H) Fig. 6 Enveloe rofile on the thread milling tool. Z X O Workiece CS y Cutter CS By comaring the modified thread rofile with the design rofile of the thread, a reformed rofile of the thread milling cutter is calculated (Fig. 5 (e),(f)). The initial dimension of the thread milling cutter is and, which can be derived from the definition of the screw thread in Fig. 1. is modified iteratively until the sloe of the rojected enveloe rofile becomes arallel with the basic rofile in the interval under rescribed tolerance (see Fig. 5(a),(e)). After has been determined, is modified, keeing the ratio until the rojected enveloe rofile coincides with the

5 124 Seok Won Lee and Andreas Nestler / Procedia CIRP 1 ( 2012 ) basic rofile in Fig. 1 (see Fig. 5 (e),(f)). The same solving rocedure can be alied to internal screw threads. 5. Imlementation and Results The NC simulation kernel (NCSK) fohread milling machining has been develoed with C++, OenGL version 2.0 [10] and the standard temlate library. The simulation module runs on AMD Athlon II X4 630 CPU 2,81 GHz and 8 GB RAM which is equied with an nvidia Quadro FX 580 PCI-E grahics accelerator with 512 MB RAM. Based on the enveloe rofile calculation and the helical rojection of the enveloe rofile, some results are resented hereafter. Fig. 8 shows the 3D model of a virtual thread milling cutter which is designed for cutting the external ISO M24 x 3 metric screw thread. Because the rofile design of a thread milling cutter is focused on in this work, the slots along the tool axis are ignored in the visualization. Fig. 9 Simulated-aided design of ISO M24 screw thread. Fig. 10 shows the virtual measurement of the simulated ISO M24 x 3 thread, which is virtually cut by the virtual thread milling tool that is designed in the framework of the NCSK (comare the dimensions in Fig. 1) [11]. As a result of the simulation, the itch is roven to be exactly 3 mm aftehe ISO standard, and the as-is angle in the fundamental triangle is 59,986 with 0.012% deviation from the to-be angle (60 ). The as-is thread band-width at the major diameter is mm with 0.16% deviation from the to-be value (0.38mm). As a result, the simulation-aided design of the thread cutter enables generation of the rofile of the thread milling cutter, which corresonds to the design rofile of the thread with high recision. Fig. 8 Virtual thread milling cutter: simulated-aided design of a thread milling cutter fohe screw thread ISO M24 x 3. The surface of thread is the conjugate surface of the thread milling cutter. Therefore, by alying the tool rofile designed in Fig. 8, the thread of ISO M24 x 3 can be virtually machined [11]. Fig. 9 shows some examles of the internal and external ISO M24 x 3 metric screw threads of the major diameter D = 24mm and the itch = 3 mm which are simulated by NCSK. Fig. 9 (a) denotes the external M24 screw thread and the cross sectional view with heightened sectional curve. Fig. 9 (b) shows the internal M24 screw thread, which is the counterart of the external M24 screw thread, and the cross sectional view with heightened sectional curve. Fig. 10 Virtual measurement of to-be external M24 thread rofile in cross section. Practically, to make a thread, tolerances must be alied to ensure that the actual rofiles of both the external/internal threads must never cross oransgress the theoretical rofile. As a result, clearances must be alied to the basic rofile of the threads so that an external thread can be screwed into an internal thread aroriately, which inevitably influences the geometry of the tool [12]. Fig. 11 shows the external/internal ISO M24 x 3 thread aiaking a clearance of 260 μm into consideration. Firstly, both thread rofiles are calculated by making the external/internal thread rofiles congruent with the basic thread rofiles. Aftehat, the external (internal) rofile is translated radially outward (inward) so that the total clearance between both rofiles amounts to 260 μm.

6 Seok Won Lee and Andreas Nestler / Procedia CIRP 1 ( 2012 ) Acknowledgements This investigation is suorted by the research grant 16467BR funded by the German Federal Ministry of Economics and Technology (BMWi) via Arbeitsgemeinschaft industrieller Forschungsvereinigungen Otto von Guericke e.v. (AiF). References Fig. 11 Tolerance design via simulated-aided design. 6. Conclusion and Outlook Presented in this aer is a novel methodology to design the tooth rofile of the thread milling cutter by comaring the to-be thread rofile and the as-is thread rofile which is simulated by a virtual thread milling cutter in the framework of the NC simulation kernel (NCSK). The NCSK enables continual subtraction of the swet volume of the thread milling cutter from the workiece and calculation of the virtual workiece (VWP). Intermediate outut of NCSK is the simulated thread which is virtually cut with the virtual thread milling cutter in NCSK. Combined with the standardized to-be thread rofile, the tooth rofile of the virtual thread milling cutter is iteratively modified until the as-is rofile of the simulated thread becomes congruent with the to-be thread rofile. The roosed aroach is roven to be ractically alicable to design tooth rofile of thread milling cutters in a virtual machining environment. The roosed methodology could be integrated into CAD/CAM systems to design the thread tool geometry by using the threading simulation, which is deficient in modern CAD/CAM systems. The following subjects are left oen for further research goals: Current cutter rofile is the double frustum of a cone which forms a shar edge at the minor diameter of the thread. The corner art could be furtheruncated for functionally stable threads, for which the enveloe rofile is to be calculated. Design of the thread milling tool for secial thread tyes; e.g., dental imlants in the healthcare industry is an emerging interest. A series of cutting tests could be conducted to verify the roosed methods in a real cutting environment. [1] Ko S-L. Geometrical analysis of helical flute grinding and alication to end mill. Transactions of NAMRI/SME Vol.22:165 72, [2] Ehmann, KF. Grinding wheel rofile definition fohe manufacture of drill flutes. Annals of CIRP 1990;39/1: [3] Kang SK. Ehmann KF, Lin C.A CAD aroach to helical groove machining I. mathematical model and model solution. Int. J. Machine Tools and Manufacture, 1996;36/1: [4] Kang JK, Suh SH. Machinability and Set-U Orientation for Five- Axis Numerically Controlled Machining of Free surfaces. In Int. J. Advanced Manufacturing Technology, 1997;13, [5] Handbuch der Gewindetechnik und Frästechnik: Anwendungen, Tis, Tabellen. Lauf/Rückersdorf, Publicis Cororate Publishing, ISBN , [6] Halas D. Taing vs. thread milling--where's the dividing line? Tooling & Production, November 1, [7] ISO 68-1:1998, ISO general urose screw threads -- Basic rofile -- Part 1: Metric screw threads. [8] Lee SW. An Aroach to Swet Volume Generation for NC machining using Gauss Ma, IN: Proceedings of 11th IEEE International Conference on Emerging Technology and Factory Automation (ETFA), Prague, Czech Reublic, Page , ISBN: , Setember 2006 [9] Lee SW, Nestler A. Comlete Swet Volume Generation - Part I: Swet Volume of a Piecewise C1-Continuous Cutter at Five-Axis Milling via Gauss Ma, Comuter-Aided Design (2011), 43/4: [10] Shreiner D, Woo M, Neider J. OenGL(R) Programming Guide: The Official Guide to Learning OenGL(R), Version th ed, Addison-Wesley, ISBN , [11] Lee S.W, Nestler A. Virtual Workiece: Workiece Reresentation for Material Removal Process, International Journal of Advanced Manufacturing Technology 2012, Volume 58, Numbers 5-8, , DOI /s [12] ISO 965-1:1998, ISO general-urose metric screw threads -- Tolerances -- Part 1: Princiles and basic data.