- Email: [email protected]
3D surface topography analysis in 5-axis ball-end milling
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CIRP-1579; No. of Pages 4 CIRP Annals - Manufacturing Technology xxx (2016) xxx–xxx
Contents lists available at ScienceDirect
CIRP Annals - Manufacturing Technology jou rnal homep age : ht t p: // ees .e lse vi er . com /ci r p/ def a ult . asp
3D surface topography analysis in 5-axis ball-end milling S. Ehsan Layegh K, Ismail Lazoglu (2)* Manufacturing and Automation Research Center, Koc University, Istanbul 34450, Turkey
A R T I C L E I N F O
A B S T R A C T
Keywords: Topography Surface Milling
This article presents a new analytical model to predict the topography and roughness of the machined surface in 5-axis ball-end milling operation for the first time. The model is able to predict the surface topography and profile roughness parameters such as 3D average roughness (Sa) and 3D root mean square roughness (Sq) by considering the process parameters such as the feedrate, number of flutes, stepover and depth of cut as well as the effects of eccentricity and tool runout in 5-axis ball-end milling. This model allows to simulate the effects of the lead and tilt angles on the machined surface quality in the virtual environment prior to the costly 5-axis machining operations. The effectiveness of the introduced surface topography prediction model is validated experimentally by conducting 5-axis ball-end milling tests in various cutting conditions. ß 2017 Published by Elsevier Ltd on behalf of CIRP.
1. Introduction 5-axis milling operations are widely used for high-performance machining of complex freeform parts in different industries such as aerospace, biomedical, power plants and automotive. Since the machined surfaces of the complex freeform parts are typically generated using ball-end mill tools, simulation of the surface generation mechanism is crucial for 5-axis ball-end milling operation. Moreover, the virtual realization of the machined surface prior to the machining, eradicates trial and error methods to achieve desired surface quality, thus reducing the cost of machining and boost the productivity. Significant amount of research has been dedicated to simulate the surface texture and topography in 3-axis milling operations considering the tool vibration [1,2], tool parallel axis offset [3], trochoidal motion of the tool [4] and tool deflection [5]. However, the topography of the machined surface in 5-axis milling operations cannot be modeled using those approaches because of the complexity caused by the inclination of the tool axis. Some research works have been performed to determine the chip geometry [6], cutting forces [7] and surface roughness [8,9] in 5axis milling operation. The effects of cutting parameters on the surface topography after re-contouring of the welded parts using 5-axis milling operation are also investigated [10]. Additionally, numerical approaches have been employed by some research works to predict the surface topography [11,12]. However, all of the available models which are able to predict the surface parameters in 5-axis milling do not analytically consider the trochoidal motion of the cutting edge. Therefore, the effects of
* Corresponding author. E-mail address: [email protected] (I. Lazoglu).
parameters such as runout and cutting edge defects cannot be analytically modeled. In this article, analytical equation of trochoidal motion of the cutting edge is derived considering the feedrate, inclination of the tool and runout. Finite number of parallel planes are defined perpendicular to the feed vector with a certain number of increments. The intersection between the trochoidal motion of each point on the cutting edge and the defined planes, represents the cross-section of the generated machined surface. The model is capable of considering the effects of tool orientation, feedrate, stepover, depth of cut, tool orientation and runout. The performance of the proposed strategy is validated by conducting experimental tests and measuring the surface texture using the white light interferometry (WLI). The novelty of the presented method is the analytical prediction of the effects of runout and tool orientation as lead and tilt angles on the machined surface topography for the 5-axis ball-end milling operation. The other novelty lies in the analytical prediction of the trochoidal motion of cutting flutes in multi-axis milling operation that can be utilized for static and dynamic simulation of the generated machined surface. 2. Toolpath geometry of 5-axis ball-end milling In order to model the topography of the machined surface in 5axis ball-end milling, the trochoidal motion of the cutting edge must be modeled considering the parallel tool axis offset and the orientation of the cutter. As an example, the swept volume by the tool and a toolpath sample in 5-axis ball-end milling operation are illustrated in Fig. 1. As is shown in this figure, the toolpath contains of several cutter location (CL) points. Generally, each toolpath segment between two consecutive CL points can be considered as a straight line and the rotation of the tool within the toolpath segments can be neglected. Fig. 1(c) depicts the feed direction and the feed coordinate frame represented as (XfYfZf).
http://dx.doi.org/10.1016/j.cirp.2017.04.021 0007-8506/ß 2017 Published by Elsevier Ltd on behalf of CIRP.
Please cite this article in press as: Layegh K SE, Lazoglu I. 3D surface topography analysis in 5-axis ball-end milling. CIRP Annals Manufacturing Technology (2017), http://dx.doi.org/10.1016/j.cirp.2017.04.021
G Model
CIRP-1579; No. of Pages 4 S.E. Layegh K, I. Lazoglu / CIRP Annals - Manufacturing Technology xxx (2016) xxx–xxx
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Fig. 1. (a) A sample toolpath in 5-axis milling. (b) Swept volume and (c) CL points in 5-axis milling.
Fig. 3. Trochoidal motion of two flutes for lead = 308, tilt = 308, feedrate = 5 mm/rev, runout offset = 0.5 mm, locating angle of offset = 458, local radius Ri = 4 mm and tool diameter = 12 mm.
next flute due to the runout. In order to visibly illustrate the effect of runout, the parallel offset and the feedrate are intentionally considered as 0.5 mm and 5 mm/rev respectively. 4. Simulation of surface topography
Fig. 2. Illustration of ball-end mill tool geometry.
The geometry of the tool and cutting flute for a ball-end mill tool is presented in Fig. 2. Point Pi,N represents an arbitrary point on flute N of the tool at the height of Zi measured from the tool tip. Due to the runout, the center of spindle system (Os) is different with the center of tool system (Ot). As it is shown in Fig. 2, this offset is defined using two parameters namely runout offset (r) and locating angle of offset (l). 3. Cutting edge trajectory model In freeform 5-axis ball-end milling operation, feed vector has a component along Zf direction. The trochoidal trajectory of point Pi,N, which is located at height level of Zi and on the Nth flute, can be written in the feed coordinate frame as the following: u þ rcosðuÞ þ Ri cosðzuÞ; xPi;N ¼ f x 2p yPi;N ¼ rsinðuÞ þ Ri sinðzuÞ; u zPi;N ¼ f z þ Zi; 2 p qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 2 Ri ¼ R ðRZ i Þ2 ; 2p z ¼ l þ c þ ðk1Þ Nt
The trochoidal trajectories are modeled for 5-axis ball-end milling operation considering the tool inclination and runout. Fig. 4 schematically illustrates the trochoidal trajectories and the intersection of the paths with a plane perpendicular to the feed direction. The obtained intersection points for each feed plane are stored as a point cloud file to be used for simulation of the machined surface cross sections. All the intersection points can be found for each feed plane as a point cloud by solving the system of equation given as Eq. (2). The first three equations represent the trajectory of the cutting edge as a function of angular position. The last equation is the feed plane equation considering the orientation of the tool. 8 u > > x ¼ f þ rcosðuÞ þ Ri cosðzuÞ > P x > i;N > 2p > > > > zPi;N ¼ f z þ Zi > > 2p > > : ax þ by þ cz ¼d P i;N
Pi;N
P i;N
The above nonlinear system of equations is solved to determine the intersection points for all the feed planes and all the trochoidal trajectories. The convex hull of the obtained intersection points found from Eq. (2) represents the cross section of the machined surface. Fig. 5 represents the strategy that is used to acquire the cross section of the machined surface. At each feed plane, a curve is fitted to the convex hulls and by trimming the extra sections, the cross section of the generated surface is obtained. The accuracy of the simulation is depended upon the number of planes perpendicular to the feed direction. Fig. 6 represents a schematic view of the proposed strategy to simulate the machined surface. The cross sections obtained from Fig. 5 are assembled side by side and a surface is fitted to the
(1)
where u, c, Nt, k, Ri and R are rotation angle of the tool, local helix angle, total number of flutes, number of the current flute, local tool radius and tool radius, respectively. Additionally, fx and fz are respectively the projection of the feed vector f in the x and z directions. Fig. 3 illustrates the trajectory of two points on the cutting edge of a typical two fluted ball-end mill. Considering the direction of the feed vector and spindle speed, upper and lower envelopes in the figure represent the feed-marks on the machined surface. As is shown in Fig. 3, one flute removes more material in contrast to the
Fig. 4. Schematic view of the intersection between cutter trajectories and a plane perpendicular to the feed direction.
Please cite this article in press as: Layegh K SE, Lazoglu I. 3D surface topography analysis in 5-axis ball-end milling. CIRP Annals Manufacturing Technology (2017), http://dx.doi.org/10.1016/j.cirp.2017.04.021
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CIRP-1579; No. of Pages 4 S.E. Layegh K, I. Lazoglu / CIRP Annals - Manufacturing Technology xxx (2016) xxx–xxx
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Table 1 Cutting conditions. Spindle speed Depth of cut Stepover Tilt Lead Nominal helix
Fig. 5. Simulated cross section of the machined surface.
collected cross sections. In order to clarify the employed approach, one of the plane perpendicular to feed direction and the simulated cross section of the machined surface corresponding to that plane are highlighted in Fig. 6. In order to model the machined surface, a 3D surface is fitted to the simulated cross sections. Knowing the peaks and valleys of the machined surface from the simulation, it is also possible to determine the surface quality parameters. Fig. 7 represents an example of 3D simulated machined surface from the convex hull points obtained for each cross section. The computation time for this simulation using Windows Intel1 Xeon 3.33 GHz, 32.00 GB Workstation and MATLAB R2015b is 5 h for 35 planes.
2500 rpm 0.2 mm 0.5 mm 0–308 0–308 308
The predicted and measured surface topographies in 5-axis ball-end milling operation are illustrated in some cases in Figs. 8– 10. The effect of runout can be seen clearly in these figures. In all the cases, one of the flutes overcut and the other one undercut the workpiece due to the runout. For the case, which is shown in Fig. 9, one flute does not have contribution to the final generated surface. The texture of predicted surface topography agrees the measured topography in all the cases. 3D average roughness (Sa) and 3D root mean square roughness (Sq) are simulated and compared with the experimental data in Figs. 11 and 12 for two different feedrates. As it can be deduced from the results, the surface roughness values are affected by the tool axis orientation, which is defined by lead/tilt angle values. These figures also illustrate the agreement between the value and the trend of the simulated and experimental surface roughness parameters. For the feedrate of 0.5 mm/rev, the maximum experimental surface roughness is 1.87 mm and the minimum experimental surface roughness is 1.49 mm. In other words, by choosing the appropriate tool orientation with lead and tilt angles, the surface roughness can be improved as much as 20% for 0.5 mm/rev feedrate. For the feedrate of 1 mm/rev, the surface roughness can be improved up to 18% by selecting the tool orientation using the proposed model.
Fig. 6. Illustration of the machined surface.
Fig. 7. Simulated machined surface topography for lead = 308, tilt = 308, feedrate = 0.5 mm/rev, runout = 20 mm.
Fig. 8. Surface topography for lead = 308, tilt = 08, runout = 20 mm: (a) simulated and (b) measured.
5. Experimental results and surface topography validations
As seen from the simulated surface parameters in Figs. 11 and 12, Sa and Sq values generally increase by increasing the lead and tilt angles. This trend is also observed in experimental results reported in the same figures. For the case of feedrate of 1 mm/rev, the agreement between the experimental observation and simulation results is not as close as the case in which the feedrate is 0.5 mm/rev. As the feedrate increases, the magnitude of cutting forces increases, which in turn leads to higher tool/tool holder and workpiece deflection. Additionally, higher magnitude of lead and tilt angles causes more vibration on the tool and workpiece [8]. In this study, tool, tool holder and the workpiece are considered as rigid bodies. Considering this, the prediction error for the case of 1 mm/rev feedrate and lead/tilt of (0/5), (5/5), (30/30) in Fig. 12 can be explained.
Simulations and experimental validations were conducted at different cutting tool orientations and feedrates. The cutting tests were carried on Mori Seiki NMV5000 DCG 5-axis milling center. The topography of the machined surfaces was measured using the white light interferometry (WLI). For all the experimental samples, the cut-off value of WLI is set as 0.25 mm. All the machining tests were conducted on Aluminum 7050. A two-fluted ball-end mill tool with 12 mm nominal diameter and 308 nominal helix angle was used for all the simulation and experimental cases. The simulation and experimental cutting conditions used in this article are given in Table 1. In all the cases, the runout offset was 20 mm and the runout angle was 908.
feedrate = 1 mm/rev,
Please cite this article in press as: Layegh K SE, Lazoglu I. 3D surface topography analysis in 5-axis ball-end milling. CIRP Annals Manufacturing Technology (2017), http://dx.doi.org/10.1016/j.cirp.2017.04.021
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Fig. 12. Surface quality values for feedrate of 1 mm/rev.
ball-end milling operation with the accuracy of 20% average error. The model is also able to predict the trend of the changes in surface quality values by changing the tool orientation. 6. Conclusion Fig. 9. Surface topography for lead = 08, tilt = 308, feedrate = 0.5 mm/rev, runout = 20 mm: (a) simulated and (b) measured.
This article presented a model for analytical prediction of the machined surface topography for 5-axis ball-end milling operation for the first time. The novelty of this research work lies in simultaneously considering the effects of tool orientation with lead and tilt angles, feedrate and tool runout for 5-axis ball-end milling operation. The model is able to predict the surface texture and roughness parameters of the machined surface with the average of 20% prediction error. The simulations and experimental results clearly show that the surface parameters are affected by tool axis orientation determined by lead and tilt angles. The model can help prior to the real machining to determine the surface topography and tool orientation in order to achieve desired surface quality in 5-axis ball-end milling. Acknowledgements The authors would like to thank the Turkish Aerospace Industries, Inc., Sandvik Coromant and Koc University Surface Science and Technology Center (KUYTAM) for their kind supports for the project. References
Fig. 10. Surface topography for lead = 58, tilt = 58, feedrate = 0.5 mm/rev, runout = 20 mm: (a) simulated and (b) measured.
The influence of the tool orientation, runout and the feedrate are studied for different cases. From the results shown in Figs. 11 and 12, it can be concluded that the surface generation prediction model is able to simulate the topography of the machined surface in 5-axis
Fig. 11. Surface quality values for feedrate of 0.5 mm/rev.
[1] Montgomery D, Altintas Y (1991) Mechanism of Cutting Force and Surface Generation in Dynamic Milling. Journal of Engineering for Industry 113(2):160. [2] Arizmendi M, Campa FJ, Ferna´ndez J, Lo´pez de Lacalle LN, Gil A, et al (2009) Model for Surface Topography Prediction in Peripheral Milling Considering Tool Vibration. CIRP Annals - Manufacturing Technology 58(1):93–96. [3] Arizmendi M, Ferna´ndez J, Lo´pez de Lacalle LN, Lamikiz A, Gil A, et al (2008) Model Development for the Prediction of Surface Topography Generated by Ball-End Mills Taking into Account the Tool Parallel Axis Offset. Experimental Validation. CIRP Annals - Manufacturing Technology 57(1):101–104. [4] Ehmann KF, Hong MS (1994) A Generalized Model of the Surface Generation Process in Metal Cutting. CIRP Annals - Manufacturing Technology 43(1):483–486. [5] Lim EM, Menq C-H (1995) The Prediction of Dimensional Error for Sculptured Surface Productions using the Ball-End Milling Process. Part 2: Surface Generation Model and Experimental Verification. International Journal of Machine Tools and Manufacture 35(8):1171–1185. [6] Bouzakis K-D, Aichouh P, Efstathiou K (2003) Determination of the Chip Geometry, Cutting Force and Roughness in Free Form Surfaces Finishing Milling, with Ball End Tools. International Journal of Machine Tools and Manufacture 43(5):499–514. [7] Lazoglu I, Boz Y, Erdim H (2011) Five-Axis Milling Mechanics for Complex Free Form Surfaces. CIRP Annals - Manufacturing Technology 60(1):117–120. [8] Layegh K. SE, Yigit IE, Lazoglu I (2015) Analysis of Tool Orientation for 5-Axis Ball-End Milling of Flexible Parts. CIRP Annals - Manufacturing Technology 64(1):97–100. [9] Chen X, Zhao J, Dong Y, Han S, Li A, et al (2012) Effects of Inclination Angles on Geometrical Features of Machined Surface in Five-Axis Milling. International Journal of Advanced Manufacturing Technology 65(9–12):1721–1733. [10] Nespor D, Denkena B, Grove T, Pape O (2016) Surface Topography after Recontouring of Welded Ti-6Al-4V Parts by Means of 5-Axis Ball Nose End Milling. International Journal of Advanced Manufacturing Technology 85(5): 1585–1602. [11] Quintana G, De Ciurana J, Ribatallada J (2010) Surface Roughness Generation and Material Removal Rate in Ball End Milling Operations. Materials and Manufacturing Processes 25(6):386–398. [12] Quinsat Y, Lavernhe S, Lartigue C (2011) Characterization of 3D Surface Topography in 5-Axis Milling. Wear 271(3):590–595.
Please cite this article in press as: Layegh K SE, Lazoglu I. 3D surface topography analysis in 5-axis ball-end milling. CIRP Annals Manufacturing Technology (2017), http://dx.doi.org/10.1016/j.cirp.2017.04.021
CIRP-1579; No. of Pages 4 CIRP Annals - Manufacturing Technology xxx (2016) xxx–xxx
Contents lists available at ScienceDirect
CIRP Annals - Manufacturing Technology jou rnal homep age : ht t p: // ees .e lse vi er . com /ci r p/ def a ult . asp
3D surface topography analysis in 5-axis ball-end milling S. Ehsan Layegh K, Ismail Lazoglu (2)* Manufacturing and Automation Research Center, Koc University, Istanbul 34450, Turkey
A R T I C L E I N F O
A B S T R A C T
Keywords: Topography Surface Milling
This article presents a new analytical model to predict the topography and roughness of the machined surface in 5-axis ball-end milling operation for the first time. The model is able to predict the surface topography and profile roughness parameters such as 3D average roughness (Sa) and 3D root mean square roughness (Sq) by considering the process parameters such as the feedrate, number of flutes, stepover and depth of cut as well as the effects of eccentricity and tool runout in 5-axis ball-end milling. This model allows to simulate the effects of the lead and tilt angles on the machined surface quality in the virtual environment prior to the costly 5-axis machining operations. The effectiveness of the introduced surface topography prediction model is validated experimentally by conducting 5-axis ball-end milling tests in various cutting conditions. ß 2017 Published by Elsevier Ltd on behalf of CIRP.
1. Introduction 5-axis milling operations are widely used for high-performance machining of complex freeform parts in different industries such as aerospace, biomedical, power plants and automotive. Since the machined surfaces of the complex freeform parts are typically generated using ball-end mill tools, simulation of the surface generation mechanism is crucial for 5-axis ball-end milling operation. Moreover, the virtual realization of the machined surface prior to the machining, eradicates trial and error methods to achieve desired surface quality, thus reducing the cost of machining and boost the productivity. Significant amount of research has been dedicated to simulate the surface texture and topography in 3-axis milling operations considering the tool vibration [1,2], tool parallel axis offset [3], trochoidal motion of the tool [4] and tool deflection [5]. However, the topography of the machined surface in 5-axis milling operations cannot be modeled using those approaches because of the complexity caused by the inclination of the tool axis. Some research works have been performed to determine the chip geometry [6], cutting forces [7] and surface roughness [8,9] in 5axis milling operation. The effects of cutting parameters on the surface topography after re-contouring of the welded parts using 5-axis milling operation are also investigated [10]. Additionally, numerical approaches have been employed by some research works to predict the surface topography [11,12]. However, all of the available models which are able to predict the surface parameters in 5-axis milling do not analytically consider the trochoidal motion of the cutting edge. Therefore, the effects of
* Corresponding author. E-mail address: [email protected] (I. Lazoglu).
parameters such as runout and cutting edge defects cannot be analytically modeled. In this article, analytical equation of trochoidal motion of the cutting edge is derived considering the feedrate, inclination of the tool and runout. Finite number of parallel planes are defined perpendicular to the feed vector with a certain number of increments. The intersection between the trochoidal motion of each point on the cutting edge and the defined planes, represents the cross-section of the generated machined surface. The model is capable of considering the effects of tool orientation, feedrate, stepover, depth of cut, tool orientation and runout. The performance of the proposed strategy is validated by conducting experimental tests and measuring the surface texture using the white light interferometry (WLI). The novelty of the presented method is the analytical prediction of the effects of runout and tool orientation as lead and tilt angles on the machined surface topography for the 5-axis ball-end milling operation. The other novelty lies in the analytical prediction of the trochoidal motion of cutting flutes in multi-axis milling operation that can be utilized for static and dynamic simulation of the generated machined surface. 2. Toolpath geometry of 5-axis ball-end milling In order to model the topography of the machined surface in 5axis ball-end milling, the trochoidal motion of the cutting edge must be modeled considering the parallel tool axis offset and the orientation of the cutter. As an example, the swept volume by the tool and a toolpath sample in 5-axis ball-end milling operation are illustrated in Fig. 1. As is shown in this figure, the toolpath contains of several cutter location (CL) points. Generally, each toolpath segment between two consecutive CL points can be considered as a straight line and the rotation of the tool within the toolpath segments can be neglected. Fig. 1(c) depicts the feed direction and the feed coordinate frame represented as (XfYfZf).
http://dx.doi.org/10.1016/j.cirp.2017.04.021 0007-8506/ß 2017 Published by Elsevier Ltd on behalf of CIRP.
Please cite this article in press as: Layegh K SE, Lazoglu I. 3D surface topography analysis in 5-axis ball-end milling. CIRP Annals Manufacturing Technology (2017), http://dx.doi.org/10.1016/j.cirp.2017.04.021
G Model
CIRP-1579; No. of Pages 4 S.E. Layegh K, I. Lazoglu / CIRP Annals - Manufacturing Technology xxx (2016) xxx–xxx
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Fig. 1. (a) A sample toolpath in 5-axis milling. (b) Swept volume and (c) CL points in 5-axis milling.
Fig. 3. Trochoidal motion of two flutes for lead = 308, tilt = 308, feedrate = 5 mm/rev, runout offset = 0.5 mm, locating angle of offset = 458, local radius Ri = 4 mm and tool diameter = 12 mm.
next flute due to the runout. In order to visibly illustrate the effect of runout, the parallel offset and the feedrate are intentionally considered as 0.5 mm and 5 mm/rev respectively. 4. Simulation of surface topography
Fig. 2. Illustration of ball-end mill tool geometry.
The geometry of the tool and cutting flute for a ball-end mill tool is presented in Fig. 2. Point Pi,N represents an arbitrary point on flute N of the tool at the height of Zi measured from the tool tip. Due to the runout, the center of spindle system (Os) is different with the center of tool system (Ot). As it is shown in Fig. 2, this offset is defined using two parameters namely runout offset (r) and locating angle of offset (l). 3. Cutting edge trajectory model In freeform 5-axis ball-end milling operation, feed vector has a component along Zf direction. The trochoidal trajectory of point Pi,N, which is located at height level of Zi and on the Nth flute, can be written in the feed coordinate frame as the following: u þ rcosðuÞ þ Ri cosðzuÞ; xPi;N ¼ f x 2p yPi;N ¼ rsinðuÞ þ Ri sinðzuÞ; u zPi;N ¼ f z þ Zi; 2 p qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 2 Ri ¼ R ðRZ i Þ2 ; 2p z ¼ l þ c þ ðk1Þ Nt
The trochoidal trajectories are modeled for 5-axis ball-end milling operation considering the tool inclination and runout. Fig. 4 schematically illustrates the trochoidal trajectories and the intersection of the paths with a plane perpendicular to the feed direction. The obtained intersection points for each feed plane are stored as a point cloud file to be used for simulation of the machined surface cross sections. All the intersection points can be found for each feed plane as a point cloud by solving the system of equation given as Eq. (2). The first three equations represent the trajectory of the cutting edge as a function of angular position. The last equation is the feed plane equation considering the orientation of the tool. 8 u > > x ¼ f þ rcosðuÞ þ Ri cosðzuÞ > P x > i;N > 2p > >
Pi;N
P i;N
The above nonlinear system of equations is solved to determine the intersection points for all the feed planes and all the trochoidal trajectories. The convex hull of the obtained intersection points found from Eq. (2) represents the cross section of the machined surface. Fig. 5 represents the strategy that is used to acquire the cross section of the machined surface. At each feed plane, a curve is fitted to the convex hulls and by trimming the extra sections, the cross section of the generated surface is obtained. The accuracy of the simulation is depended upon the number of planes perpendicular to the feed direction. Fig. 6 represents a schematic view of the proposed strategy to simulate the machined surface. The cross sections obtained from Fig. 5 are assembled side by side and a surface is fitted to the
(1)
where u, c, Nt, k, Ri and R are rotation angle of the tool, local helix angle, total number of flutes, number of the current flute, local tool radius and tool radius, respectively. Additionally, fx and fz are respectively the projection of the feed vector f in the x and z directions. Fig. 3 illustrates the trajectory of two points on the cutting edge of a typical two fluted ball-end mill. Considering the direction of the feed vector and spindle speed, upper and lower envelopes in the figure represent the feed-marks on the machined surface. As is shown in Fig. 3, one flute removes more material in contrast to the
Fig. 4. Schematic view of the intersection between cutter trajectories and a plane perpendicular to the feed direction.
Please cite this article in press as: Layegh K SE, Lazoglu I. 3D surface topography analysis in 5-axis ball-end milling. CIRP Annals Manufacturing Technology (2017), http://dx.doi.org/10.1016/j.cirp.2017.04.021
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CIRP-1579; No. of Pages 4 S.E. Layegh K, I. Lazoglu / CIRP Annals - Manufacturing Technology xxx (2016) xxx–xxx
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Table 1 Cutting conditions. Spindle speed Depth of cut Stepover Tilt Lead Nominal helix
Fig. 5. Simulated cross section of the machined surface.
collected cross sections. In order to clarify the employed approach, one of the plane perpendicular to feed direction and the simulated cross section of the machined surface corresponding to that plane are highlighted in Fig. 6. In order to model the machined surface, a 3D surface is fitted to the simulated cross sections. Knowing the peaks and valleys of the machined surface from the simulation, it is also possible to determine the surface quality parameters. Fig. 7 represents an example of 3D simulated machined surface from the convex hull points obtained for each cross section. The computation time for this simulation using Windows Intel1 Xeon 3.33 GHz, 32.00 GB Workstation and MATLAB R2015b is 5 h for 35 planes.
2500 rpm 0.2 mm 0.5 mm 0–308 0–308 308
The predicted and measured surface topographies in 5-axis ball-end milling operation are illustrated in some cases in Figs. 8– 10. The effect of runout can be seen clearly in these figures. In all the cases, one of the flutes overcut and the other one undercut the workpiece due to the runout. For the case, which is shown in Fig. 9, one flute does not have contribution to the final generated surface. The texture of predicted surface topography agrees the measured topography in all the cases. 3D average roughness (Sa) and 3D root mean square roughness (Sq) are simulated and compared with the experimental data in Figs. 11 and 12 for two different feedrates. As it can be deduced from the results, the surface roughness values are affected by the tool axis orientation, which is defined by lead/tilt angle values. These figures also illustrate the agreement between the value and the trend of the simulated and experimental surface roughness parameters. For the feedrate of 0.5 mm/rev, the maximum experimental surface roughness is 1.87 mm and the minimum experimental surface roughness is 1.49 mm. In other words, by choosing the appropriate tool orientation with lead and tilt angles, the surface roughness can be improved as much as 20% for 0.5 mm/rev feedrate. For the feedrate of 1 mm/rev, the surface roughness can be improved up to 18% by selecting the tool orientation using the proposed model.
Fig. 6. Illustration of the machined surface.
Fig. 7. Simulated machined surface topography for lead = 308, tilt = 308, feedrate = 0.5 mm/rev, runout = 20 mm.
Fig. 8. Surface topography for lead = 308, tilt = 08, runout = 20 mm: (a) simulated and (b) measured.
5. Experimental results and surface topography validations
As seen from the simulated surface parameters in Figs. 11 and 12, Sa and Sq values generally increase by increasing the lead and tilt angles. This trend is also observed in experimental results reported in the same figures. For the case of feedrate of 1 mm/rev, the agreement between the experimental observation and simulation results is not as close as the case in which the feedrate is 0.5 mm/rev. As the feedrate increases, the magnitude of cutting forces increases, which in turn leads to higher tool/tool holder and workpiece deflection. Additionally, higher magnitude of lead and tilt angles causes more vibration on the tool and workpiece [8]. In this study, tool, tool holder and the workpiece are considered as rigid bodies. Considering this, the prediction error for the case of 1 mm/rev feedrate and lead/tilt of (0/5), (5/5), (30/30) in Fig. 12 can be explained.
Simulations and experimental validations were conducted at different cutting tool orientations and feedrates. The cutting tests were carried on Mori Seiki NMV5000 DCG 5-axis milling center. The topography of the machined surfaces was measured using the white light interferometry (WLI). For all the experimental samples, the cut-off value of WLI is set as 0.25 mm. All the machining tests were conducted on Aluminum 7050. A two-fluted ball-end mill tool with 12 mm nominal diameter and 308 nominal helix angle was used for all the simulation and experimental cases. The simulation and experimental cutting conditions used in this article are given in Table 1. In all the cases, the runout offset was 20 mm and the runout angle was 908.
feedrate = 1 mm/rev,
Please cite this article in press as: Layegh K SE, Lazoglu I. 3D surface topography analysis in 5-axis ball-end milling. CIRP Annals Manufacturing Technology (2017), http://dx.doi.org/10.1016/j.cirp.2017.04.021
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S.E. Layegh K, I. Lazoglu / CIRP Annals - Manufacturing Technology xxx (2016) xxx–xxx
Fig. 12. Surface quality values for feedrate of 1 mm/rev.
ball-end milling operation with the accuracy of 20% average error. The model is also able to predict the trend of the changes in surface quality values by changing the tool orientation. 6. Conclusion Fig. 9. Surface topography for lead = 08, tilt = 308, feedrate = 0.5 mm/rev, runout = 20 mm: (a) simulated and (b) measured.
This article presented a model for analytical prediction of the machined surface topography for 5-axis ball-end milling operation for the first time. The novelty of this research work lies in simultaneously considering the effects of tool orientation with lead and tilt angles, feedrate and tool runout for 5-axis ball-end milling operation. The model is able to predict the surface texture and roughness parameters of the machined surface with the average of 20% prediction error. The simulations and experimental results clearly show that the surface parameters are affected by tool axis orientation determined by lead and tilt angles. The model can help prior to the real machining to determine the surface topography and tool orientation in order to achieve desired surface quality in 5-axis ball-end milling. Acknowledgements The authors would like to thank the Turkish Aerospace Industries, Inc., Sandvik Coromant and Koc University Surface Science and Technology Center (KUYTAM) for their kind supports for the project. References
Fig. 10. Surface topography for lead = 58, tilt = 58, feedrate = 0.5 mm/rev, runout = 20 mm: (a) simulated and (b) measured.
The influence of the tool orientation, runout and the feedrate are studied for different cases. From the results shown in Figs. 11 and 12, it can be concluded that the surface generation prediction model is able to simulate the topography of the machined surface in 5-axis
Fig. 11. Surface quality values for feedrate of 0.5 mm/rev.
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Please cite this article in press as: Layegh K SE, Lazoglu I. 3D surface topography analysis in 5-axis ball-end milling. CIRP Annals Manufacturing Technology (2017), http://dx.doi.org/10.1016/j.cirp.2017.04.021