Five-axis milling mechanics for complex free form surfaces

CIRP Annals - Manufacturing Technology 60 (2011) 117–120

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CIRP Annals - Manufacturing Technology jou rnal homep age : ht t p: // ees .e lse vi er. com/ci rp/ def a ult . asp

Five-axis milling mechanics for complex free form surfaces I. Lazoglu (2)a,*, Y. Boz a, H. Erdim b a b

Koc University, Manufacturing and Automation Research Center, Rumeli Feneri Yolu, Sariyer, Istanbul 34450, Turkey Mitsubishi Electric Research Laboratories, 201 Broadway, Cambridge, MA 02139, USA

A R T I C L E I N F O

A B S T R A C T

Keywords: Computer aided manufacturing (CAM) Milling Force

Accurate and fast prediction of machining forces is important in high performance cutting of free form surfaces that are commonly used in aerospace, automotive, biomedical and die/mold industries. This paper presents a novel and generalized approach for prediction of cutting forces in five-axis machining of parts with complex free form surfaces. Engagement simulations between cutter and part are performed precisely along the tool path by a recently developed boundary representation method. Moreover, mathematical model for five-axis milling mechanics is developed for any given solid model of parts with complex free form surfaces. Theoretical simulations and experimental validations show that cutting forces are predicted fast and precisely for five-axis machining of complex free form surfaces. ß 2011 CIRP.

1. Introduction Five-axis machining technologies are used in the production of complex parts in aerospace, die-mold, automotive and biomedical industries. With five-axis machining, parts can be machined in a single setup which reduces cycle times. Improved tool accessibility allows the use of shorter tools that provide more accurate machining. The main focus of using five-axis machining in industry is to reduce cycle times, dimensional and surface errors in its nature. However, these desired points cannot be achieved satisfactorily without modeling of five-axis milling mechanics. Consequently, this paper aims to help exploring potential improvements on five-axis machining processes based on scientific analysis rather than trial and errors in practice. Throughout the evolution of the machining processes very limited portion of the research have been dedicated to five-axis milling process mechanics mainly due to its complexity. Most of the research on five-axis machining focused on the geometric and kinematic aspects of this process such as toolpath generation, geometric verifications and control strategies. In addition, the existing five-axis models that consider process mechanics can handle relatively simple part geometries and mostly plain flat surfaces only. Various approaches were used in the literature in order to improve the performance of five-axis machining process. Sorby et al. [1] proposed an empirical method for selection of cutting tool and machining data for flank milling based cutting tool life and cutting forces. Lauwers et al. [2] developed a five-axis tool path generation algorithm based on faceted or tessellated

* Corresponding author. 0007-8506/$ – see front matter ß 2011 CIRP. doi:10.1016/j.cirp.2011.03.090

models. Becze et al. [3] introduced an analytical chip load model for five-axis high-speed milling. Biermann et al. [4] showed effects of workpiece vibrations on five-axis milling of turbine blades. Budak et al. [5] presented models for milling stability analysis where the process geometry is extracted using a semianalytical engagement method. Ferry and Altintas [6] developed a semi-discrete solid modeler based simulation system for fiveaxis flank milling. This article presents an enhanced and generic five-axis milling force model for any given complex free-form surfaces fast and precisely. In the newly developed model, boundary representation (B-rep) based exact Boolean method is introduced for extracting complex cutter-workpiece engagements at every cutter location point due to its efficiency and speed over other discrete methods. Developed engagement model is proved to calculate complex concave and convex engagement regions between tool and workpiece efficiently and accurately. Comprehensive formulation of the cutting force system is presented and the validity of the proposed model is demonstrated on the five-axis machining of impeller. The developed model is unique to allow simulating multiprocess operations including roughing, semi-finishing and finishing. The features of the model allow the first time the literature to simulate cutting forces fast and precisely for the five-axis milling of complex free form surfaces. 2. Cutter-workpiece engagement model In sculpture surface machining, the cutter/workpiece engagement region does vary along the cutter path and in general, unless some specific and very simple workpiece geometry is machined, it is difficult to find an exact analytical representation for the engagement region. Chip load and force calculations are

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Fig. 1. Cutter-workpiece engagement geometry extraction.

based on the cutter/workpiece engagements; therefore the output of the engagement model is very critical. The basic idea is mathematically removing the swept volume generated by cutter movements along the NC trajectory from the model of the raw stock, and thus obtaining in-process or final machined workpiece. In this work, boundary representation based method is developed to find the cutter/workpiece engagement (CWE). The tool movements are subtracted from the workpiece model by using Boolean operations in order to find the in-process machined surface. Once the in-process workpiece is obtained for each cutter location (CL) point, the contact patch surface between the tool and workpiece can be extracted. Then, the resulting 3D contact surface, as illustrated in Fig. 1, is projected to the plane perpendicular to the cutter axis. The cutter was discretized into slices along the tool axis. In order to perform force calculation for each slice, the engagement domain is determined. The engagement domain is the combination of start and exit angles of each discrete disc located on the cutter. The next step is to assign the start and exit angles to each respective projected disc by intersecting the discs with the boundaries of the contact patch in plane. The procedure described above is implemented in the Parasolid kernel. Engagement regions at two different CL points (CL points

[()TD$FIG]

132 and 164) are shown in Fig. 2 as the examples for instantaneous CWE model outputs. It is seen in this figure that the engagement is convex domain at CL point 132 (Fig. 2c). However, at CL point 164, engagement is concave (Fig. 2c). The concave domain generates multiple start and exit angles for the discrete discs in the contact region. Therefore, one of the advantages of this newly developed boundary representation based engagement domain calculation method over the existing techniques is that the new method allows determining concave engagement domains (multiple contact) regions precisely. Precise determination of the engagement regions naturally helps to enhance the force predictions. Moreover, the newly developed boundary representation based contact workpiece engagement (CWE) model is very fast. In a typical computer, CWE computation time for the impeller machining toolpath with 1572 CL points, 6 mm diameter tool and 50 mm disk thickness is less than 1 min. 3. Cutting force model In milling, cutting forces depend on the instantaneous uncut chip thickness. Hence, accurate calculation of the chip thickness is quite critical for five-axis machining cutting force predictions. The uncut chip thickness can be quite complicated since the tool can rotate as well as translate within a toolpath segment. In free-form surface machining, the effects of the lead and tilt angles on the cut geometry, and horizontal and vertical feed components must be considered. For ball-end mill tool, instantaneous uncut chip thickness is obtained as follows; ðt c Þk ¼ t x  sinðuÞ  sinðcÞ  cosðaÞ  t x  cosðcÞ  sinðaÞ

(1)

where (tc)k is the chip thickness, tx is the feed per tooth, u is the immersion angle of the cutting point, c is the cutting element position angle and a is the feed inclination angle. For a differential chip load in the engagement domain, the differential cutting forces (Fig. 3) in radial, axial, and tangential directions (r, C, t) is written as follows; dF r ¼ K rc  ðt c  dzÞ þ K re  dz dF c ¼ K cc  ðt c  dzÞ þ K ce  dz dF t ¼ K tc  ðt c  dzÞ þ K te  dz

(2)

where Krc, KCc and Ktc are radial, axial and tangential cutting force coefficients and Kre, KCe and Kte are edge force coefficients, respectively. They can be determined from the orthogonal to oblique transformations or mechanistically, dz is the thickness of the discrete disks. Cutting force measurement in five-axis machining is performed using rotary dynamometer. In Fig. 4, XD–YD–ZD represents the rotary dynamometer coordinate frame. Considering a two fluted ball-end mill where one of the cutting flute is be aligned with the XD-axis. The angle between YD-axis and the reference cutting flute is represented as the reference rotation angle VR. The rotation

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Fig. 2. Illustration of convex (on the left column) and concave (on the right column) engagement domains for two different CL points in impeller machining. (a) Workpiece and 3D engagement regions (blue region on tool), (b) projections of engagements domains (in red color) to the plane perpendicular to the cutter axis, (c) engagement angles (start and exit angles) for each discrete disc along the depth of cut.

Fig. 3. Illustration of (a) cutting force components, (b) angle definitions.

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Fig. 6. (a) Simulated five-axis impeller machining including blank workpiece and tool path, (b) Illustration of the part after five-axis machining.

[()TD$FIG] Fig. 4. Rotating coordinate frame transformation angles.

angle V is the angle between the cross feed direction (Yf) and the cutting flute. In order to obtain the transformation from the (r–C–t) coordinate frame (Fig. 3) to feed coordinate frame transformation matrix A is given as, 2 3 sinðcÞ  sinðu Þ cosðcÞ  sinðuÞ cosðuÞ 4 A ¼ sinðcÞ  cosðu Þ cosðcÞ  cosðuÞ (3) sinðuÞ 5 cosðcÞ sinðcÞ 0 Transformation from the feed coordinate system to rotating dynamometer coordinate frame can be obtained as follows; 2 3 cosðVR þ VÞ sinðVR þ VÞ 0 4 B ¼ sinðVR þ VÞ cosðVR þ VÞ 0 5 (4) 0 0 1 Cutting forces in rotary dynamometer coordinate frame are calculated from the following transformations; 2 3 2 3 dF X dF r 4 dF Y 5 ¼ ½B½A  4 dF c 5 (5) dF Z D dF t 4. Simulation results and experimental validations Proposed approach is validated on various free from geometries. In this article, simulation results and experimental validation

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Fig. 7. Variation of lead and tilt angles along cutter location points of tool path during the impeller machining.

of mechanic model for the five-axis machining is demonstrated on an impeller (Fig. 5). In the validation tests, Al7075 workpiece with 50 mm diameter and 18 mm height was used. Cutting tool was Sandvik carbide ball-end mill with 6 mm diameter. Experimental tests were performed on five-axis Mori Seiki NMV 5000 DCG machine tool (Fig. 6). Spindle speed and the feedrate are selected as 5000 rpm and 500 mm/min, respectively. Cutting force measurements are performed using Kistler 9123 rotary dynamometer. Simulated tool path consists of 1572 CL points employing zigzag toolpath strategy. The complete cutter-workpiece engagement domain and force calculations all along the tool path for the impeller were performed in less than two minutes in a standard computer. Simulation results and tool paths for five-axis machining of impeller and machined workpiece are shown in Fig. 6. Variations

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Fig. 5. Experimental five-axis machining setup.

Fig. 8. Comparison of predicted and measured cutting forces for the whole toolpath: (a) and (b) X direction; (c) and (d) Y direction.

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5. Conclusion An enhanced and unique mathematical model for the fast and precise prediction of cutting forces is introduced for the mechanics of five-axis milling. Due to variable tool axis orientation, free form surfaces of workpiece and tool geometry, engagement regions between the tool and the workpiece all along the tool path are very complex and irregular. A novel boundary representation method is used for determining the complex cutter-workpiece engagements. Hence, developed engagement model provides an efficient and accurate solution for extracting the information on contact region at CL points from the in-process workpiece. Another distinctive point of the developed model is that it allows especially for multistage process simulations including roughing, semi-finishing and finishing. The unique features of the model allow the first time the literature to simulate cutting forces fast and precisely for the fiveaxis milling of parts with complex free form surfaces. Acknowledgement Fig. 9. Comparison of cutting force predictions with experiments: (a) and (b): two tool passes; (c) and (d) close-up view in two tool revolutions.

of the lead and tilt angles along the cutter location points of the tool path during the impeller machining are shown in Fig. 7. In five-axis impeller machining, comparison of the cutting forces for full toolpath and comparison of the cutting force closeups are illustrated in Figs. 8 and 9, respectively. It is observed that the simulations predict the waveforms and the amplitudes of the cutting forces all along the tool paths very well. Although the engagements between the tool and workpiece change instantaneously during the five-axis machining of complex free form geometries, validation tests show that simulated and measured cutting forces match quite well within 12% error band. The small discrepancy on the cutting forces is observed especially in the low axial immersion regions. This is likely due to low resolution at smaller depth of cuts. Hence, increasing the simulation resolution may increase the simulation accuracy at the cost of computation time.

The authors acknowledge the Machine Tool Technologies Research Foundation (MTTRF), the Mori Seiki Co., DP Technology Corporation and Sandvik Coromant Company for their kind supports on this project. References [1] Sorby K, Tonnessen K, Torjusen JE, Rasch FO (2000) Improving High Speed Flank Milling Operations in Multi-Axis Machines. Annals of the CIRP 49:371– 374. [2] Lauwers B, Kiswanto G, Kruth J-P (2003) Development of a Five-axis Milling Tool Path Generation Algorithm based on Faceted Models. Annals of the CIRP 52(1):85–89. [3] Becze CE, Clayton P, Chen L, El-Wardany TI, Elbestawi MA (2000) High-speed Five-axis Milling of Hardened Tool Steel. International Journal of Machine Tools and Manufacture 40:869–885. [4] Biermann D, Kersting P, Surmann T (2010) A General Approach to Simulating Workpiece Vibrations during Five-Axis Milling of Turbine Blades. Annals of the CIRP 59(1):125–128. [5] Budak E, Ozturk E, Tunc LT (2009) Modeling and Simulation of 5-axis Milling Processes. Annals of the CIRP 58:347–350. [6] Ferry WB, Altintas Y (2008) Virtual Five-Axis Flank Milling of Jet Engine Impellers—Part I: Mechanics of Five-Axis Flank Milling. Journal of Manufacturing Science and Engineering 130. 011005-1:11.