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Analysis of tool orientation for 5-axis ball-end milling of flexible parts
G Model
CIRP-1334; No. of Pages 4 CIRP Annals - Manufacturing Technology xxx (2015) 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
Analysis of tool orientation for 5-axis ball-end milling of flexible parts S. Ehsan Layegh K., I. Enes Yigit, 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: Milling Modeling Tool posture
This article investigates the effects of lead and tilt angles in 5-axis ball-end milling of flexible freeform aerospace parts by considering process mechanics. In current CAM technology, tool posture is determined by geometrical analysis only. However, in high-performance 5-axis milling, not only the geometry, but also the mechanics of the process is critical. Therefore, a new and comprehensive mechanics-based strategy is proposed for selection of tool postures considering process parameters such as cutting force, torque, part vibration, and surface quality. Effectiveness of the proposed strategy is validated by conducting experiments on 5-axis ball-end milling of flexible freeform structures. ß 2015 CIRP.
1. Introduction In today’s competitive world, there is a significant demand for high-performance 5-axis milling of flexible parts in the aerospace industry. In the current state of the art of CAM technology, tool postures (lead and tilt angles) in 5-axis milling are determined only by geometrical concerns and the mechanics of the process has not been included yet. Ignoring the mechanics of the process may lead to the risks of suboptimal performance, such as undesired forces, tool/workpiece deflection, excessive vibration, poor surface quality, longer machining cycle time and relatively higher machining costs especially for freeform parts such as turbine blades, blisks and impellers. Nowadays, only geometry-based analysis for the selection of tool postures is not sufficient for competitive machining industries. In order to explore the full potential of 5axis machining for higher performance, current selection strategy of tool orientation must be enhanced by considering mechanical constraints of the process. Significant amount of research has been dedicated to gouge-free and geometry-based tool posture identification [1,2]. On the other hand, little research has been conducted to illustrate the effects of tool posture on mechanical parameters. Some studies considered the effects of tool orientation on wear [3], scallop height, workpiece accuracy, surface roughness [4] and the chatter stability [5]. The effects of tool orientation on multi-axis ball-end milling cutting forces were modeled in the frequency domain analytically using the convolution integration technique in rigid part machining [6]. Cutting forces for multi axis ball-end milling were modeled numerically in the time domain for rigid parts and did not focus on the effects of tool posture [7]. As indicated in all above-mentioned studies, 5-axis ball-end milling of freeform parts is challenging due to the fact that there are nonlinear relations between tool orientation and mechanical parameters of the process.
* Corresponding author. E-mail address: [email protected] (I. Lazoglu).
Despite all the research work have been carried out in this field, up to today, there is still a lack of mechanics-based strategy that is able to predict the ideal tool posture in 5-axis milling of flexible workpieces. Therefore, the aim of this article is to investigate the effects of lead and tilt angles on cutting force, torque, deflection and surface quality in 5-axis ball-end milling of flexible parts such as turbine blades. The novelty of the proposed strategy lies in presenting a mechanics-based reference map that suggests the appropriate tool orientation considering above-mentioned parameters. The effectiveness of the approach is demonstrated experimentally.
2. Effects of tool orientation on ball-end milling mechanics A cutting force model for 5-axis ball-end milling developed already [7] is utilized here to estimate the cutting force and torque at each cutter location (CL) point. Fig. 1 depicts 5-axis ball-end milling of a flexible freeform part. In this figure, l and t represent lead and tilt angles respectively. dFa, dFt and dFr are, respectively, the force components in axial, tangential and radial directions. c(z) is the zenith angle and R is the nominal radius of the tool. The differential cutting force components can be calculated as: dF t; j ðu j ; cðzÞÞ ¼ K tc hðu j ; cðzÞÞdbðzÞ þ K te dSðzÞ dF r; j ðu j ; cðzÞÞ ¼ K rc hðu j ; cðzÞÞdbðzÞ þ K re dSðzÞ dF a; j ðu j ; cðzÞÞ ¼ K ac hðu j ; cðzÞÞdbðzÞ þ K ae dSðzÞ
(1)
where, uj, db(z), h and ds(z) are, respectively, the current angular position of cutting edge, the chip width, the instantaneous chip thickness and the length of cutting edge for a discrete disk j shown in Fig. 1b and c. Ktc, Krc and Kac are cutting constants and Kte, Kre and Kae are edge constants in tangential, radial and axial directions, respectively [6,7]. The differential cutting forces in tool coordinate frame (XtYtZt) are transformed to workpiece coordinate frames (XwYwZw) as shown in Fig. 2a to determine the normal cutting force along the normal axis (Zw) that cause deflection of the part due to
http://dx.doi.org/10.1016/j.cirp.2015.04.067 0007-8506/ß 2015 CIRP.
Please cite this article in press as: Layegh K SE, et al. Analysis of tool orientation for 5-axis ball-end milling of flexible parts. CIRP Annals Manufacturing Technology (2015), http://dx.doi.org/10.1016/j.cirp.2015.04.067
G Model
CIRP-1334; No. of Pages 4 S.E. Layegh K. et al. / CIRP Annals - Manufacturing Technology xxx (2015) xxx–xxx
2
3. Effects of tool orientation on the cutting force waveforms and on the forced vibration of a flexible part
Fig. 1. (a) Tool posture in 5-axis ball-end milling of a flexible part, (b) Instantaneous chip thickness, (c) Differential force components.
Changing tool orientation in 5-axis ball end milling directly affects the instantaneous tool-workpiece engagement region. Therefore, magnitudes and waveforms of cutting forces, as well as forced vibration amplitudes of flexible parts are affected by tool posture. In the cases when the tool tip is in contact with the workpiece, the cutting process would be less interrupted which in turn reduces the magnitude of the tool and workpiece oscillations because of the lower fluctuation of cutting forces. However, due to the fact that cutting speed at the tip of the tool is zero, having the tip in contact causes poor surface quality and significant ploughing forces [8]. In order to solve this problem, all the possible discrete lead and tilt angle pairs, which make the tool tip in contact with the workpiece are determined from engagement model. Then, the tool tip was adjusted marginally to be located outside of the toolworkpiece engagement domain. It is experimentally proved in Section 4.1 that this strategy leads to pseudo-constant cutting force magnitudes with lower fluctuations on the waveforms and therefore lower forced vibration on the flexible parts. In order to prevent the tool tip from contact with the workpiece, the critical positive and negative tilt angles (tcrp and tcrn) should be considered based on Fig. 2b and c as the following; a so t crp ¼ cos1 1 ; t crn ¼ tan1 R 2ðR aÞ
(5)
The critical lead angle lcr can be calculated as;
R sh for R cosðtÞ R a for lcr ¼ cos1 R cosðtÞ
lcr ¼ cos1
t crn t 0 (6) 0 t t crp
where a, sh and so are respectively depth of cut, scallop height and step over. 4. Simulation and experimental validation
Fig. 2. (a) 5-axis milling of flexible cantilever workpiece (airfoil blade) (b) Critical positive tilt angle, (c) Critical negative tilt angle.
the bending as given below: 2 3 2 3 dF xw dF r 4 dF yw 5 ¼ ½T1 ½A4 dF c 5 dF zw2 dF t 3 sinðcÞsinðuÞ cosðcÞsinðu Þ cosðu Þ 4 ½A ¼ sinðcÞsinðuÞ sinðcÞsinðu Þ sinðuÞ 5 cosð c Þ sinð c Þ 0 2 3 cosðlÞ 0 sinðlÞ ½T ¼ 4 sinðtÞsinðlÞ cosðtÞ sinðtÞcosðlÞ 5 cosðtÞsinðlÞ sinðtÞ cosðtÞcosðlÞ
(2)
Differential cutting torque can be determined by local radius r(z) and differential tangential force (Fig. 1c) as the following; dt ¼ rðzÞ dF t
(3)
The differential cutting force and torque in Eqs. (2) and (3) are integrated along cutter-workpiece engagement domain defined by a solid modeler kernel to find the total cutting force and torque [7]. The flexible workpiece shown in Figs. 1a and 2a is modeled as a cantilever beam. The maximum static deflection of flexible part along Zw at point 1 can be determined from; 2
d¼
F zw l ð3L lÞ 6EI
(4)
L and l are the length of the flexible part and the distance of the tool from the fixture as shown in Fig. 1a. E and I are the elastic modulus and the area moment of inertia determined numerically.
The effects of tool posture on the magnitudes and waveforms of cutting force, torque as well as on the forced vibration of the flexible part and the quality of machined surface are investigated. The experimental setup is shown in Fig. 2a. The cutting force and torque were measured using a Kistler 9123C rotary dynamometer. Deflection of the workpiece was measured at point 1, which is located at the tip of the workpiece, using a Keyence LK-H052 laser displacement sensor with 0.025 [mm] repeatability and 0.02% linearity. All of the simulation and experimental cases were designed for Al 7050 blocks with 98 38 10 [mm3] dimension. A two fluted ballend mill with the diameter of 12 [mm] was used in all cases. Other cutting parameters are indicated in Table 1. Experiments were designed and conducted in Mori Seiki NMV 5000 DCG 5-axis vertical machine. Table 1 Cutting parameters in ball-end milling of the flexible airfoil parts. Operation Depth of cut [mm] Step over [mm] Spindle speed [rpm] Feedrate [mm/min]
Roughing
Semi-finishing
Finishing
1 5.8 2500 250
0.6 1.4 3500 350
0.15 0.35 4500 500
4.1. Effect of tool posture on cutting force waveforms The effects of the tool posture on the engagement domain and on the cutting force waveforms and magnitudes are investigated. Feasibility of the proposed strategy presented in Section 3 is illustrated with an example in Fig. 3. The cutting forces were acquired while 5-axis milling of the airfoil blade shown in Fig. 2a. Spindle speed, feedrate and depth of cut were respectively 2500 [rpm], 250 [mm/min] and 1 [mm].
Please cite this article in press as: Layegh K SE, et al. Analysis of tool orientation for 5-axis ball-end milling of flexible parts. CIRP Annals Manufacturing Technology (2015), http://dx.doi.org/10.1016/j.cirp.2015.04.067
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CIRP-1334; No. of Pages 4 S.E. Layegh K. et al. / CIRP Annals - Manufacturing Technology xxx (2015) xxx–xxx
3
4.3. Mechanics-based reference maps for tool orientation selection in 5-axis ball end milling of flexible parts
Fig. 3. (a) Engagement domain for lead angle of 258 and tilt angle of 58, (b) engagement domain for lead angle of 28 and tilt angle of 108, (c) normal and resultant cutting force measured by a rotary dynamometer.
In order to illustrate the effects tool orientation in roughing, semi-finishing and finishing processes, mechanics-based reference maps are generated by considering cutting forces, torque and the deflection of flexible part, as shown in Fig. 5. Roughing, semifinishing and finishing zones are depicted based on Eqs. (5) and (6). It is experimentally proven in Section 4.1 that inside of those zones, the amplitude of cutting force vibration is lower than other possible tool postures. Moreover, the hatched rectangular zone in Fig. 5 is where the tip of the tool is marginally avoided from cutting and for less than 2% of the tool rotation period there is no toolworkpiece engagement. This region is highly recommended, especially for the finishing processes to achieve better surface quality. The contours of average cutting torque and average workpiece deflection are extracted from the simulation shown in Fig. 4a and b. The average deflection of the workpiece is simulated based on the analytical deflection model given in Eq. (4). The red dots in Fig. 5, named from A to M, are the test points for the experimental validations of the proposed approach.
In Fig. 3, simulated engagement zones for the same cutting conditions, but two different tool orientations are shown. The solid line (position A) represents the cutter flute after leaving the engagement area and the dashed line (position B) shows the cutter flute which is about to engage. In the case of lead angle of 258 and tilt angle of 58, the engagement zone is far from the tool tip (Fig. 3a), and this causes the oscillatory waveform in the cutting forces. However, in the case of lead angle of 28 and tilt angle of 108, the tool tip is marginally avoided from the cutting. As experimentally shown in Fig. 3c, this tool posture results in lower oscillation in the cutting force waveforms. 4.2. Effect of tool posture on normal cutting force and torque In order to investigate the effects of tool orientation on normal cutting force and torque, simulations and experimental validation were conducted on thirty different combinations of lead and tilt angles. In the tests, tilt angle changed from 258 to +258 and lead angle changed from 158 to +258 at every 58. Fig. 4 illustrates variations of the average cutting force normal to the machined surface and average cutting torque. For all of the cases, spindle speed, feedrate and depth of cut was respectively 2500 [rev/min], 250 [mm/min] and 1 [mm].
Fig. 5. Mechanics-based tool posture reference maps of part deflection (a) and cutting torque values (b) for the selection of lead-tilt angle combinations in the ballend milling of the flexible airfoil blade.
Fig. 5a clearly indicates that the part deflections significantly changes by varying tool posture. According to the Fig. 5b, the measured cutting torque does not change significantly inside the roughing, semi-finishing and finishing boundaries. However, it is possible to decrease the average of cutting torque and power up to 15% in the roughing process by selecting the appropriate tool orientation using Fig. 5b. 4.4. Validation and discussion
Fig. 4. Average normal force (a) and average torque (b) for different lead and tilt angles in the 5-axis ball-end milling of flexible airfoil.
In order to validate the reference maps given in Fig. 5, experimental tests were conducted using the setup shown in Fig. 2a. As shown in Table 2, the average surface roughness (Sa) of the finished surfaces were measured using a White Light Interferometer (WLI) with the cut-off value of 0.25 mm. According to Table 2, the best surface roughness of all the cases is achieved in case A (lead = 28 and tilt = 108). All the cases located in the red and red-hatched area of Fig. 5 perform well with
Please cite this article in press as: Layegh K SE, et al. Analysis of tool orientation for 5-axis ball-end milling of flexible parts. CIRP Annals Manufacturing Technology (2015), http://dx.doi.org/10.1016/j.cirp.2015.04.067
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CIRP-1334; No. of Pages 4 S.E. Layegh K. et al. / CIRP Annals - Manufacturing Technology xxx (2015) xxx–xxx
4
Table 2 Average surface roughness measured with the WLI. Case (Fig. 5)
A
B
C
D
E
F
G
H
I
J
L
M
Lead [8] Tilt [8] Sa [mm]
2 10 2.0
2 0 2.1
2 5 2.8
5 10 2.8
20 10 3.0
0 25 3.3
5 5 3.9
20 10 4.2
2 25 5.2
10 10 5.8
25 5 9.0
30 30 9.0
relatively lower Sa values. In the cases located outside of the red and green boundaries, up to four times increase in the Sa value was observed. Consequently, the experimental results prove that by selecting lead and tilt angles in the red finishing zone and redhatched area in Fig. 5, the best surface roughness can be obtained. In order to show the effectiveness of the proposed approach, the details of test results for the cases of A, D and H are demonstrated thoroughly in Fig. 6.
Measured resultant cutting forces in Fig. 6a, e and i are given to illustrate how the amplitude of force vibration is affected by the tool orientation. The instantaneous deflection of the flexible airfoil blade at the tip of the workpiece (Point 1 in Fig. 2a), was measured using the laser displacement sensor and presented in Fig. 6c, g and k. For same cutting conditions, but different tool postures, in case D compared with case H, the peak to peak amplitude of cutting force vibration is 2.7, 2 and 1.7 times less for roughing, semi-finishing and finishing operations respectively. Because of this, as is seen in Fig. 6g and k, lower peak to peak amplitude of part vibration was detected in case D. Moreover, as is presented in Table 2, the average of surface roughness (Sa) in case D is 33% better than case H. Significant improvement can be achieved by avoiding the tool tip from contact. As shown in Fig. 6f for case D, tool leaves tip marks on the final finished surface due to the engagement with the workpiece. However, in cases of A, B and C the tool tip is not in contact with the workpiece. WLI measurement presented in Fig. 6b shows that the tip marks on the generated surface are removed after finishing operation of case A. Due to this reason, the surface roughness is improved more than twice compared to case H. Generally, it is possible to decrease Sa value from 9.0 [mm] in case M to 2.0 [mm] in case A which is 4.5 times improvement. The roughing, semifinishing and finishing surface images are shown in Fig. 6d, h and l. The measured deflection of the workpiece, which is shown in Fig. 6c, g and k, are in good agreement with the deflection contours in Fig. 5a. The results clearly show that tool posture in 5-axis milling of flexible parts is critical. As a complementary solution to the current geometry-based CAM technology, the effectiveness of the mechanics-based modeling approach for the selection of lead and tilt angles is shown and validated. 5. Conclusion A mechanics-based novel approach is introduced to select the lead and tilt angles for high-performance 5-axis ball-end milling of flexible parts commonly used in the Aerospace industry. The presented strategy is developed as a complementary approach to the current geometry-based CAM technology. This approach considers cutting force, torque, part deflection, forced vibration and surface quality of flexible parts. Effectiveness of the strategy is validated by conducting experiments on 5-axis ball-end milling of flexible freeform structures. Acknowledgements The authors thank the Turkish Aerospace Industries, Inc. and Sandvik Coromant and KUYTAM for their kind supports for the research and also would like to acknowledge the Scientific and Technological Research Council of Turkey (TUBITAK) for providing International Research Fellowship for Ismail Lazoglu’s academic research.
References
Fig. 6. Comparison of cutting forces (a, e, i), WLI surface roughness measurements (b, f, j), measured and simulated part deflections (c, g, k) and part surface images (R – Roughed, S – Semifinished, F – Finished) (d, h, l) for the cases of A (lead = 28, tilt = 108), D (lead = 58, tilt = 108) and H (lead = 208, tilt = 108).
[1] Altintas Y, Kersting P, Biermann E, Denkena B, Lazoglu I (2014) Virtual Process Systems for Part Machining Operations. CIRP Annals – Manufacturing Technology 63(2):585–605. [2] Lauwers B, Plakhotnik D (2012) Five-Axis Milling Tool Path Generation With Dynamic Step-Over Calculation Based on Integrated Material Removal Simulation. CIRP Annals – Manufacturing Technology 61(1):139–142. [3] Schulz H, Hock S (1995) High-Speed Milling of Dies and Molds — Cutting Conditions and Technology. CIRP Annals – Manufacturing Technology 44(1):35–38. [4] Kruth J-P, Klewais P (1994) Optimization and Dynamic Adaptation of the Cutter Inclination During Five-Axis Milling of Sculptured Surfaces. CIRP Annals – Manufacturing Technology 43(1):443–448. [5] Budak E, Ozturk E, Tunc LT (2009) Modeling and Simulation of 5-Axis Milling Processes. CIRP Annals – Manufacturing Technology 58(1):347–350. [6] Lazoglu I, Liang SY (2000) Modeling of Ball-End Milling Forces With Cutter Axis Inclination. The ASME Journal of Manufacturing Science and Engineering 122(1):3–11. [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] Tuysuz O, Altintas Y, Feng H-Y (2013) Prediction of Cutting Forces in Three and Five-Axis Ball-End Milling With Tool Indentation Effect. International Journal of Machine Tools and Manufacture 66:66–81.
Please cite this article in press as: Layegh K SE, et al. Analysis of tool orientation for 5-axis ball-end milling of flexible parts. CIRP Annals Manufacturing Technology (2015), http://dx.doi.org/10.1016/j.cirp.2015.04.067
CIRP-1334; No. of Pages 4 CIRP Annals - Manufacturing Technology xxx (2015) 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
Analysis of tool orientation for 5-axis ball-end milling of flexible parts S. Ehsan Layegh K., I. Enes Yigit, 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: Milling Modeling Tool posture
This article investigates the effects of lead and tilt angles in 5-axis ball-end milling of flexible freeform aerospace parts by considering process mechanics. In current CAM technology, tool posture is determined by geometrical analysis only. However, in high-performance 5-axis milling, not only the geometry, but also the mechanics of the process is critical. Therefore, a new and comprehensive mechanics-based strategy is proposed for selection of tool postures considering process parameters such as cutting force, torque, part vibration, and surface quality. Effectiveness of the proposed strategy is validated by conducting experiments on 5-axis ball-end milling of flexible freeform structures. ß 2015 CIRP.
1. Introduction In today’s competitive world, there is a significant demand for high-performance 5-axis milling of flexible parts in the aerospace industry. In the current state of the art of CAM technology, tool postures (lead and tilt angles) in 5-axis milling are determined only by geometrical concerns and the mechanics of the process has not been included yet. Ignoring the mechanics of the process may lead to the risks of suboptimal performance, such as undesired forces, tool/workpiece deflection, excessive vibration, poor surface quality, longer machining cycle time and relatively higher machining costs especially for freeform parts such as turbine blades, blisks and impellers. Nowadays, only geometry-based analysis for the selection of tool postures is not sufficient for competitive machining industries. In order to explore the full potential of 5axis machining for higher performance, current selection strategy of tool orientation must be enhanced by considering mechanical constraints of the process. Significant amount of research has been dedicated to gouge-free and geometry-based tool posture identification [1,2]. On the other hand, little research has been conducted to illustrate the effects of tool posture on mechanical parameters. Some studies considered the effects of tool orientation on wear [3], scallop height, workpiece accuracy, surface roughness [4] and the chatter stability [5]. The effects of tool orientation on multi-axis ball-end milling cutting forces were modeled in the frequency domain analytically using the convolution integration technique in rigid part machining [6]. Cutting forces for multi axis ball-end milling were modeled numerically in the time domain for rigid parts and did not focus on the effects of tool posture [7]. As indicated in all above-mentioned studies, 5-axis ball-end milling of freeform parts is challenging due to the fact that there are nonlinear relations between tool orientation and mechanical parameters of the process.
* Corresponding author. E-mail address: [email protected] (I. Lazoglu).
Despite all the research work have been carried out in this field, up to today, there is still a lack of mechanics-based strategy that is able to predict the ideal tool posture in 5-axis milling of flexible workpieces. Therefore, the aim of this article is to investigate the effects of lead and tilt angles on cutting force, torque, deflection and surface quality in 5-axis ball-end milling of flexible parts such as turbine blades. The novelty of the proposed strategy lies in presenting a mechanics-based reference map that suggests the appropriate tool orientation considering above-mentioned parameters. The effectiveness of the approach is demonstrated experimentally.
2. Effects of tool orientation on ball-end milling mechanics A cutting force model for 5-axis ball-end milling developed already [7] is utilized here to estimate the cutting force and torque at each cutter location (CL) point. Fig. 1 depicts 5-axis ball-end milling of a flexible freeform part. In this figure, l and t represent lead and tilt angles respectively. dFa, dFt and dFr are, respectively, the force components in axial, tangential and radial directions. c(z) is the zenith angle and R is the nominal radius of the tool. The differential cutting force components can be calculated as: dF t; j ðu j ; cðzÞÞ ¼ K tc hðu j ; cðzÞÞdbðzÞ þ K te dSðzÞ dF r; j ðu j ; cðzÞÞ ¼ K rc hðu j ; cðzÞÞdbðzÞ þ K re dSðzÞ dF a; j ðu j ; cðzÞÞ ¼ K ac hðu j ; cðzÞÞdbðzÞ þ K ae dSðzÞ
(1)
where, uj, db(z), h and ds(z) are, respectively, the current angular position of cutting edge, the chip width, the instantaneous chip thickness and the length of cutting edge for a discrete disk j shown in Fig. 1b and c. Ktc, Krc and Kac are cutting constants and Kte, Kre and Kae are edge constants in tangential, radial and axial directions, respectively [6,7]. The differential cutting forces in tool coordinate frame (XtYtZt) are transformed to workpiece coordinate frames (XwYwZw) as shown in Fig. 2a to determine the normal cutting force along the normal axis (Zw) that cause deflection of the part due to
http://dx.doi.org/10.1016/j.cirp.2015.04.067 0007-8506/ß 2015 CIRP.
Please cite this article in press as: Layegh K SE, et al. Analysis of tool orientation for 5-axis ball-end milling of flexible parts. CIRP Annals Manufacturing Technology (2015), http://dx.doi.org/10.1016/j.cirp.2015.04.067
G Model
CIRP-1334; No. of Pages 4 S.E. Layegh K. et al. / CIRP Annals - Manufacturing Technology xxx (2015) xxx–xxx
2
3. Effects of tool orientation on the cutting force waveforms and on the forced vibration of a flexible part
Fig. 1. (a) Tool posture in 5-axis ball-end milling of a flexible part, (b) Instantaneous chip thickness, (c) Differential force components.
Changing tool orientation in 5-axis ball end milling directly affects the instantaneous tool-workpiece engagement region. Therefore, magnitudes and waveforms of cutting forces, as well as forced vibration amplitudes of flexible parts are affected by tool posture. In the cases when the tool tip is in contact with the workpiece, the cutting process would be less interrupted which in turn reduces the magnitude of the tool and workpiece oscillations because of the lower fluctuation of cutting forces. However, due to the fact that cutting speed at the tip of the tool is zero, having the tip in contact causes poor surface quality and significant ploughing forces [8]. In order to solve this problem, all the possible discrete lead and tilt angle pairs, which make the tool tip in contact with the workpiece are determined from engagement model. Then, the tool tip was adjusted marginally to be located outside of the toolworkpiece engagement domain. It is experimentally proved in Section 4.1 that this strategy leads to pseudo-constant cutting force magnitudes with lower fluctuations on the waveforms and therefore lower forced vibration on the flexible parts. In order to prevent the tool tip from contact with the workpiece, the critical positive and negative tilt angles (tcrp and tcrn) should be considered based on Fig. 2b and c as the following; a so t crp ¼ cos1 1 ; t crn ¼ tan1 R 2ðR aÞ
(5)
The critical lead angle lcr can be calculated as;
R sh for R cosðtÞ R a for lcr ¼ cos1 R cosðtÞ
lcr ¼ cos1
t crn t 0 (6) 0 t t crp
where a, sh and so are respectively depth of cut, scallop height and step over. 4. Simulation and experimental validation
Fig. 2. (a) 5-axis milling of flexible cantilever workpiece (airfoil blade) (b) Critical positive tilt angle, (c) Critical negative tilt angle.
the bending as given below: 2 3 2 3 dF xw dF r 4 dF yw 5 ¼ ½T1 ½A4 dF c 5 dF zw2 dF t 3 sinðcÞsinðuÞ cosðcÞsinðu Þ cosðu Þ 4 ½A ¼ sinðcÞsinðuÞ sinðcÞsinðu Þ sinðuÞ 5 cosð c Þ sinð c Þ 0 2 3 cosðlÞ 0 sinðlÞ ½T ¼ 4 sinðtÞsinðlÞ cosðtÞ sinðtÞcosðlÞ 5 cosðtÞsinðlÞ sinðtÞ cosðtÞcosðlÞ
(2)
Differential cutting torque can be determined by local radius r(z) and differential tangential force (Fig. 1c) as the following; dt ¼ rðzÞ dF t
(3)
The differential cutting force and torque in Eqs. (2) and (3) are integrated along cutter-workpiece engagement domain defined by a solid modeler kernel to find the total cutting force and torque [7]. The flexible workpiece shown in Figs. 1a and 2a is modeled as a cantilever beam. The maximum static deflection of flexible part along Zw at point 1 can be determined from; 2
d¼
F zw l ð3L lÞ 6EI
(4)
L and l are the length of the flexible part and the distance of the tool from the fixture as shown in Fig. 1a. E and I are the elastic modulus and the area moment of inertia determined numerically.
The effects of tool posture on the magnitudes and waveforms of cutting force, torque as well as on the forced vibration of the flexible part and the quality of machined surface are investigated. The experimental setup is shown in Fig. 2a. The cutting force and torque were measured using a Kistler 9123C rotary dynamometer. Deflection of the workpiece was measured at point 1, which is located at the tip of the workpiece, using a Keyence LK-H052 laser displacement sensor with 0.025 [mm] repeatability and 0.02% linearity. All of the simulation and experimental cases were designed for Al 7050 blocks with 98 38 10 [mm3] dimension. A two fluted ballend mill with the diameter of 12 [mm] was used in all cases. Other cutting parameters are indicated in Table 1. Experiments were designed and conducted in Mori Seiki NMV 5000 DCG 5-axis vertical machine. Table 1 Cutting parameters in ball-end milling of the flexible airfoil parts. Operation Depth of cut [mm] Step over [mm] Spindle speed [rpm] Feedrate [mm/min]
Roughing
Semi-finishing
Finishing
1 5.8 2500 250
0.6 1.4 3500 350
0.15 0.35 4500 500
4.1. Effect of tool posture on cutting force waveforms The effects of the tool posture on the engagement domain and on the cutting force waveforms and magnitudes are investigated. Feasibility of the proposed strategy presented in Section 3 is illustrated with an example in Fig. 3. The cutting forces were acquired while 5-axis milling of the airfoil blade shown in Fig. 2a. Spindle speed, feedrate and depth of cut were respectively 2500 [rpm], 250 [mm/min] and 1 [mm].
Please cite this article in press as: Layegh K SE, et al. Analysis of tool orientation for 5-axis ball-end milling of flexible parts. CIRP Annals Manufacturing Technology (2015), http://dx.doi.org/10.1016/j.cirp.2015.04.067
G Model
CIRP-1334; No. of Pages 4 S.E. Layegh K. et al. / CIRP Annals - Manufacturing Technology xxx (2015) xxx–xxx
3
4.3. Mechanics-based reference maps for tool orientation selection in 5-axis ball end milling of flexible parts
Fig. 3. (a) Engagement domain for lead angle of 258 and tilt angle of 58, (b) engagement domain for lead angle of 28 and tilt angle of 108, (c) normal and resultant cutting force measured by a rotary dynamometer.
In order to illustrate the effects tool orientation in roughing, semi-finishing and finishing processes, mechanics-based reference maps are generated by considering cutting forces, torque and the deflection of flexible part, as shown in Fig. 5. Roughing, semifinishing and finishing zones are depicted based on Eqs. (5) and (6). It is experimentally proven in Section 4.1 that inside of those zones, the amplitude of cutting force vibration is lower than other possible tool postures. Moreover, the hatched rectangular zone in Fig. 5 is where the tip of the tool is marginally avoided from cutting and for less than 2% of the tool rotation period there is no toolworkpiece engagement. This region is highly recommended, especially for the finishing processes to achieve better surface quality. The contours of average cutting torque and average workpiece deflection are extracted from the simulation shown in Fig. 4a and b. The average deflection of the workpiece is simulated based on the analytical deflection model given in Eq. (4). The red dots in Fig. 5, named from A to M, are the test points for the experimental validations of the proposed approach.
In Fig. 3, simulated engagement zones for the same cutting conditions, but two different tool orientations are shown. The solid line (position A) represents the cutter flute after leaving the engagement area and the dashed line (position B) shows the cutter flute which is about to engage. In the case of lead angle of 258 and tilt angle of 58, the engagement zone is far from the tool tip (Fig. 3a), and this causes the oscillatory waveform in the cutting forces. However, in the case of lead angle of 28 and tilt angle of 108, the tool tip is marginally avoided from the cutting. As experimentally shown in Fig. 3c, this tool posture results in lower oscillation in the cutting force waveforms. 4.2. Effect of tool posture on normal cutting force and torque In order to investigate the effects of tool orientation on normal cutting force and torque, simulations and experimental validation were conducted on thirty different combinations of lead and tilt angles. In the tests, tilt angle changed from 258 to +258 and lead angle changed from 158 to +258 at every 58. Fig. 4 illustrates variations of the average cutting force normal to the machined surface and average cutting torque. For all of the cases, spindle speed, feedrate and depth of cut was respectively 2500 [rev/min], 250 [mm/min] and 1 [mm].
Fig. 5. Mechanics-based tool posture reference maps of part deflection (a) and cutting torque values (b) for the selection of lead-tilt angle combinations in the ballend milling of the flexible airfoil blade.
Fig. 5a clearly indicates that the part deflections significantly changes by varying tool posture. According to the Fig. 5b, the measured cutting torque does not change significantly inside the roughing, semi-finishing and finishing boundaries. However, it is possible to decrease the average of cutting torque and power up to 15% in the roughing process by selecting the appropriate tool orientation using Fig. 5b. 4.4. Validation and discussion
Fig. 4. Average normal force (a) and average torque (b) for different lead and tilt angles in the 5-axis ball-end milling of flexible airfoil.
In order to validate the reference maps given in Fig. 5, experimental tests were conducted using the setup shown in Fig. 2a. As shown in Table 2, the average surface roughness (Sa) of the finished surfaces were measured using a White Light Interferometer (WLI) with the cut-off value of 0.25 mm. According to Table 2, the best surface roughness of all the cases is achieved in case A (lead = 28 and tilt = 108). All the cases located in the red and red-hatched area of Fig. 5 perform well with
Please cite this article in press as: Layegh K SE, et al. Analysis of tool orientation for 5-axis ball-end milling of flexible parts. CIRP Annals Manufacturing Technology (2015), http://dx.doi.org/10.1016/j.cirp.2015.04.067
G Model
CIRP-1334; No. of Pages 4 S.E. Layegh K. et al. / CIRP Annals - Manufacturing Technology xxx (2015) xxx–xxx
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Table 2 Average surface roughness measured with the WLI. Case (Fig. 5)
A
B
C
D
E
F
G
H
I
J
L
M
Lead [8] Tilt [8] Sa [mm]
2 10 2.0
2 0 2.1
2 5 2.8
5 10 2.8
20 10 3.0
0 25 3.3
5 5 3.9
20 10 4.2
2 25 5.2
10 10 5.8
25 5 9.0
30 30 9.0
relatively lower Sa values. In the cases located outside of the red and green boundaries, up to four times increase in the Sa value was observed. Consequently, the experimental results prove that by selecting lead and tilt angles in the red finishing zone and redhatched area in Fig. 5, the best surface roughness can be obtained. In order to show the effectiveness of the proposed approach, the details of test results for the cases of A, D and H are demonstrated thoroughly in Fig. 6.
Measured resultant cutting forces in Fig. 6a, e and i are given to illustrate how the amplitude of force vibration is affected by the tool orientation. The instantaneous deflection of the flexible airfoil blade at the tip of the workpiece (Point 1 in Fig. 2a), was measured using the laser displacement sensor and presented in Fig. 6c, g and k. For same cutting conditions, but different tool postures, in case D compared with case H, the peak to peak amplitude of cutting force vibration is 2.7, 2 and 1.7 times less for roughing, semi-finishing and finishing operations respectively. Because of this, as is seen in Fig. 6g and k, lower peak to peak amplitude of part vibration was detected in case D. Moreover, as is presented in Table 2, the average of surface roughness (Sa) in case D is 33% better than case H. Significant improvement can be achieved by avoiding the tool tip from contact. As shown in Fig. 6f for case D, tool leaves tip marks on the final finished surface due to the engagement with the workpiece. However, in cases of A, B and C the tool tip is not in contact with the workpiece. WLI measurement presented in Fig. 6b shows that the tip marks on the generated surface are removed after finishing operation of case A. Due to this reason, the surface roughness is improved more than twice compared to case H. Generally, it is possible to decrease Sa value from 9.0 [mm] in case M to 2.0 [mm] in case A which is 4.5 times improvement. The roughing, semifinishing and finishing surface images are shown in Fig. 6d, h and l. The measured deflection of the workpiece, which is shown in Fig. 6c, g and k, are in good agreement with the deflection contours in Fig. 5a. The results clearly show that tool posture in 5-axis milling of flexible parts is critical. As a complementary solution to the current geometry-based CAM technology, the effectiveness of the mechanics-based modeling approach for the selection of lead and tilt angles is shown and validated. 5. Conclusion A mechanics-based novel approach is introduced to select the lead and tilt angles for high-performance 5-axis ball-end milling of flexible parts commonly used in the Aerospace industry. The presented strategy is developed as a complementary approach to the current geometry-based CAM technology. This approach considers cutting force, torque, part deflection, forced vibration and surface quality of flexible parts. Effectiveness of the strategy is validated by conducting experiments on 5-axis ball-end milling of flexible freeform structures. Acknowledgements The authors thank the Turkish Aerospace Industries, Inc. and Sandvik Coromant and KUYTAM for their kind supports for the research and also would like to acknowledge the Scientific and Technological Research Council of Turkey (TUBITAK) for providing International Research Fellowship for Ismail Lazoglu’s academic research.
References
Fig. 6. Comparison of cutting forces (a, e, i), WLI surface roughness measurements (b, f, j), measured and simulated part deflections (c, g, k) and part surface images (R – Roughed, S – Semifinished, F – Finished) (d, h, l) for the cases of A (lead = 28, tilt = 108), D (lead = 58, tilt = 108) and H (lead = 208, tilt = 108).
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Please cite this article in press as: Layegh K SE, et al. Analysis of tool orientation for 5-axis ball-end milling of flexible parts. CIRP Annals Manufacturing Technology (2015), http://dx.doi.org/10.1016/j.cirp.2015.04.067