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The influence of cryogenic cooling on milling stability
Journal of Materials Processing Technology 214 (2014) 3169–3178
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Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec
The influence of cryogenic cooling on milling stability Xinda Huang, Xiaoming Zhang ∗ , Haikuo Mou, Xiaojian Zhang, Han Ding State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China
a r t i c l e
i n f o
Article history: Received 21 May 2014 Received in revised form 22 July 2014 Accepted 24 July 2014 Available online 30 July 2014 Keywords: Chatter Cryogenic cooling End milling Stability lobe diagram (SLD)
a b s t r a c t Cryogenic cooling is emerging as an effective process for high performance machining. However, the influence of cryogenic cooling on milling stability is seldom reported. This paper involves experimental study on the effect of cryogenic cooling on milling stability, using a dedicated cryogenic cooling system to applying liquid nitrogen (LN2) jet to the cutting zone. We observe that cryogenic cooling leads to higher stability limit compared with conventional milling operations, which indicates that the cutting efficiency can be improved greatly in LN2 environment as opposed to the conventional one. The stability improvement is explained from the perspective of machining dynamics parameters variation between the two conditions. Cutting force coefficients and modal parameters of spindle-tool system are identified during cryogenic machining, then milling stability lobe diagrams are predicted by time domain and frequency domain methods. On the basis of milling stability analysis, the enhancement of stability boundary is attributed to the significant reduction of cutting force coefficients during cryogenic cooling. Additionally, the experiment result indicates that cryogenic cooling decreases the dominant modal frequency of the spindle-tool system, which shifts the milling stability boundary slightly to lower spindle speed range. The explanations are verified by a plenty of cutting tests. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Cooling plays a significant role in metal cutting process for its main functions in transferring excessive heat and reducing tool wear. Increased application of difficult-to-machine materials, such as nickel based high-temperature alloy, titanium alloy in aerospace and energy industry promotes the development of new cooling methods to get higher machining performance, better surface integrity economically and environmental-friendly. In the past decades, various methods have been proposed, including high-pressure coolant (HPC), minimum quantity lubrication (MQL), compressed air cooling, and cryogenic cooling etc., which has been summarized in detail by Sharma et al. (2009). As one of these methods, cryogenic cooling is emerging as a promising approach for application in industry and LN2 is the most widely used cryogenic coolant for its non-toxic and sufficient resource (Yildiz and Nalbant, 2008). Much research has been done to explore and confirm the improvement of cryogenic cooling on machinability. Hong et al. (2001b) proposed an economical approach to transfer LN2 to flank and rake face near the cutting edge and five times enhancement of tool life was achieved when turning Ti6Al4V at cutting speed of 150 m/min. Moreover, they found that LN2 can act as an effective
∗ Corresponding author. Tel.: +86 2787559842; fax: +86 2787559416. E-mail address: [email protected] (X. Zhang). http://dx.doi.org/10.1016/j.jmatprotec.2014.07.023 0924-0136/© 2014 Elsevier B.V. All rights reserved.
lubricant (Hong et al., 2001a), which was validated by the reduction of feed force and thickness of secondary deformation zone. Wang and Rajurkar (2000) investigated the cryogenic machining of hard-to-cut materials, and their result showed that cryogenic cooling can enhance tool life and surface roughness significantly but has no remarkable influence on the cutting force. Venugopal et al. (2007) investigated the tool wear in cryogenic turning of Ti6Al4V alloy and found that cryogenic cooling enhances tool life substantially at moderate cutting speed of 70 m/min. Khan and Ahmed (2008) found that the tool life increases more than four times when machining AISI304 stainless steel with modified tool, in which the insert is cooled by LN2 through an internal chamber. While most of publications about cryogenic cooling focused on turning operation and its influence on machinability, there is almost no report about the stability in cryogenic milling. Puˇsavec et al. (2011) conducted an experimental study on the influence of cryogenic cooling on process stability in turning operations, in which coarse-grained entropy rate (CER) method was used for detection of chatter in cutting tests. It is observed that a higher machining stability limit is achieved during cryogenic machining due to the reduction of specific cutting force components. In fact, Chatter in milling operation is always gaining significant attention in order to achieve higher productivity and better surface finish, which is very important in high speed machining (HSM) of aluminum alloy and low speed milling of thermal resistant alloy. With cryogenic cooling being applied to aerospace industry, where
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Fig. 1. Experiment setup for end milling with varying cutting depth and cryogenic cooling system.
Table 1 Tool parameters.
Table 2 Cutting parameters for end milling with varying axial depth.
Tool
Diameter (mm)
Flutes num
Helix angle (deg)
Overhang (mm)
Material
Tool
Short cutter Long cutter
8 8
2 2
30 30
40 64
Carbide Carbide
Short cutter Long cutter
milling occupied most of material removal process, it is necessary to analyze its influence on milling stability so as to optimize the process. The remainder of this paper offers the followings: - We report the experiments of great milling stability limit improvement under LN2 condition. End milling tests with varying axial depth are carried out to show the difference of stability limit under dry and cryogenic conditions. In order to explain the difference, cutting force coefficients and modal parameters of a two-degree-of-freedom (2-DOF) end milling system are identified before and after cryogenic cooling. The SLDs are predicted using time domain and frequency domain methods. - To confirm the stability limit differences shown in predicted SLDs, a series of experiments are conducted to catch the variation of stability boundary after cryogenic cooling. 2. Experimental conditions and procedure The experiments are performed on a machining center VMC-50 with maximum spindle speed 14,000 rpm. In the first experiment, to achieve continuously varying axial depth, a specific workpiece made of 7075-T6 aluminum alloy is prepared (Fig. 1). There is a slope on the workpiece and axial depth ap varies from 2 mm (side B) to 8 mm (side A) linearly after machining a path of 74 mm long. In the case of cryogenic milling, a copper nozzle is mounted on a fixture moving along with the spindle housing, through which LN2 jet is sprayed into cutting zone. Both short stiffer cutter and long slender cutter are adopted in order to reveal the influence of cryogenic cooling on the onset of chatter as well as the vibration during post-chatter stage. The tool parameters are listed in Table 1. Cutting forces are measured by a Kistler9257B multicomponent dynamometer mounted on worktable and are recorded by a Labview-based PC data acquisition system. The cutting parameters are listed in Table 2, and sampling rate is set as 40 kHz so that the dynamic cutting force can be measured precisely during high speed (s > 10,000 rpm). In the case for experimental verification of SLDs, end milling tests with constant axial depth are performed using the long slender end mill mentioned in Table 1 (L/D = 8), which is mounted in a HSK-A63 tool holder by collet chuck. As reported in several
Spindle speed (rpm) 12,240 12,240
Axial depth (mm)
Radial depth (mm)
Feed rate (mm/tooth)
2–8 2–8
4 1.2
0.05 0.05
studies on milling dynamics, cylindrical end mill with large length-diameter ratio is prone to have a single dominant vibration mode, which will make it more convenient for the following milling stability analysis (Gradiˇsek et al., 2005). The workpiece is a 7075-T6 aluminum alloy block fixed on dynamometer, which can be regarded as rigid for its much higher stiffness. A number of cutting tests are conducted to catch the variation of SLD for half-immersion down-milling under cryogenic cooling, in which a straight path about 80 mm long is machined repeatedly at different points in the cutting parameter space of spindle speed and axial depth. The feed rate is set as ft = 0.05 mm/tooth. In order to detect the occurrence of chatter during milling process, cutting forces and sound pressure signals are recorded simultaneously by Kister9257B dynamometer and B&K 4189 freefield microphone at sampling rate 40 kHz. A small label is pasted on the tool holder and periodic 1/revolution-sampled impulse signal synchronized with the tool rotation is generated by a laser displacement sensor fixed with spindle, which is then interpolated to achieve 1/tooth-sampled signals. The experiment setup for Case 2 is shown in Fig. 2. The cutting forces and sound pressure signals are processed offline in time domain and frequency domain for chatter detection.
Fig. 2. Experiment Setup for cutting tests to verify the predicted SLDs.
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Fig. 3. Chatter mark and cutting forces for short cutter at cutting parameters: ft = 0.05 mm/tooth, S = 12,240 rpm, ae = 4 mm. (a) Dry milling; (b) cryogenic milling.
3. Results and discussion This section describes the experimental results of two cases. In the experiment for Case 1, the difference of stability limit for end milling under two cooling conditions is demonstrated conveniently and visually while varying axial depth continuously with the designated workpiece adopted. In the experiment for Case 2, the impacts of cryogenic cooling on cutting forces and modal parameters of spindle-tool system are explored, so as to get quantitative interpretation in the perspective of milling dynamics. Based on these, milling stability analysis is conducted to predict SLDs using time domain and frequency domain methods, considering the influence of cryogenic cooling. A plenty of cutting tests are performed to verify the predicted SLDs.
3.1. Case 1: End milling with varying axial depth In the case of short cutter, cutting forces and chatter mark under dry and cryogenic conditions are shown in Fig. 3, respectively. In comparison to cryogenic milling, the chatter mark appears earlier and looks more severe with axial depth increasing during dry milling. At the location about 20 mm away from side A, the cutting forces with LN2 cooling are more steady and regular. In contrast, the cutting forces in dry milling have shown unsynchronized vibrations coursed by chatter. In the case of long cutter, although severe chatter mark appears in both situations for the weak stiffness of tool system, it is obvious
that the chatter mark in cryogenic milling is slighter (Fig. 4(b)). The spectrum of cutting force in dry milling shows that strong chatter occurs at 1561 Hz, 1969 Hz, 2378 Hz, the difference equals to tooth passing frequency T = 12, 240/60 × 2 =408 Hz. In comparison, the frequency components of chatter (1555 Hz, 1963 Hz, 2372 Hz) during cryogenic milling are much smaller. The phenomenon in Case 1 demonstrates that chatter in milling can be relieved at some extent when cryogenic cooling is adopted. Since chatter is mainly caused by self-excited vibration motivated by dynamic cutting forces near the most flexible system mode, the improvement of milling stability under cryogenic cooling is likely to be related to the variations of cutting forces and modal parameters of the machining system. 3.2. Case 2: Prediction and verification of SLDs under dry and cryogenic conditions The stability during machining is mainly determined by the dynamic characteristics of system and the dynamic cutting forces caused by regenerative effect. Thus it is reasonable to find out the mechanism of cryogenic cooling’s effect on stability by exploring its influence on these two aspects. 3.2.1. The influence of cryogenic cooling on the dynamics of milling system In order to predict SLD for end milling, frequency response function (FRF) at the tool tip is needed. FRFs of the slender tool are
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Fig. 4. Chatter mark, cutting forces and spectrums for long cutter at cutting parameters: ft = 0.05 mm/tooth, S = 12,240 rpm, ae = 1.2 mm. (a) Dry milling; (b) cryogenic milling.
obtained by impact tests, in which the tip of cutter is adhered to a tiny small accelerometer of only 0.2 g (Endevco 25A) and is excited by an impulse hammer (B&K 8206). The impact tests are conducted in X and Y direction 10 times, respectively, so as to reduce the disturbance of noise. Signals are acquired and processed on a LabView-based PC data acquisition systems using software ModalView. The FRFs of tool at tip are measured under dry and cryogenic conditions, respectively (Fig. 5). Considering that LN2 jet
may cause damage to the accelerometer for low temperature, the nozzle is directed at the point about 20 mm above the tool tip, which is adhered to the accelerometer. The modal parameters are fitted by rational fraction polynomial method (Richardson and Formenti, 1982) ranging from 500 Hz to 6000 Hz and results are listed in Table 3. As Fig. 6 shows, the fitted FRFs meet well with the measured ones and there is only a single dominant modal in both X and Y direction, whose resonance peak is
Fig. 5. Impact testing of the slender tool under dry and cryogenic conditions.
X. Huang et al. / Journal of Materials Processing Technology 214 (2014) 3169–3178 Table 3 Modal parameters of slender tool.
x 10
Direction
Mode
Frequency ωn (Hz)
Damping ratio
Stiffness k (N/m)
X Y X (LN2) Y (LN2)
1st mode 1st mode 1st mode 1st mode
1785.7 1782.5 1761.1 1758.5
0.01546 0.01538 0.01617 0.01621
1522,334 1553,675 1748,103 1663,012
Amplitude [m/N]
2.5
3173
-5
X: 1762 Y: 1.914e-005
2
Dry LN2
X: 1783 Y: 2.23e-005
1.5 1 0.5 0 1500
-5
x 10
Real [m/N]
1
500
1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000
Frequency [Hz] -5
x 10
Imag [m/N]
1
Exp Fitting
0 -1 -2 500
1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000
Frequency [Hz]
(a) FRF in x direction -5
x 10
Real [m/N]
1
Exp Fitting
0 -1 500
1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 -5
Imag [m/N]
1
Frequency [Hz]
0 -1
500
1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000
Frequency [Hz]
(b) FRF in y direction Fig. 6. FRFs of tool under dry condition in X and Y direction.
1700
1750
1800
1850
1900
1950
2000
3.2.2. The influence of cryogenic cooling on cutting force coefficients The cutting force coefficients for end milling cutter with 7075T6 aluminum alloy can be calibrated by the quick mechanistic approach proposed by Budak et al. (1996). According to this approach, cutting tests are conducted with constant axial depth at different feed rates. The spindle speed is set as 1800 rpm, the axial depth is 2 mm, and the feed rates are {0.06, 0.09, 0.12, 0.15} mm/tooth. In order to enhance the cooling effect of LN2 jet, half-immersion down-milling is adopted, instead of slotting (Fig. 8). As a result, both the cutting edge and workpiece can be accessed by LN2 jet. For half-immersion down- milling in which st = /2, ex = , the formula of average milling forces on the tool becomes: Fx = Fy = Fz =
-2
1650
around 1785 Hz at room temperature. It is noteworthy that when LN2 jet is sprayed onto the tool, the dominant modal frequency decreases by nearly 24 Hz (Fig. 7). This may be explained by the cold shrinkage of tool, which decreases the contact stiffness between the tool and collet chuck. The change of cutter’s elastic modulus during cryogenic cooling also contributes to the slight shift of dominant modal.
x 10
Exp Fitting
1600
Fig. 7. The shift of tool’s resonance peak under cryogenic cooling.
0 -1
1550
Frequency [Hz]
Exp Fitting
Na
p
8
Krc −
Na p −
4
Nap Ktc 4
Krc −
Nap Ktc 8
ft +
Nap (Kre − Kte ), 2
ft +
Nap (−Kre − Kte ), 2
Nap Nap Kac ft + Kae 2 4
(1)
which can be deduced from the general expression proposed by Altintas (2012), shown in Appendix A. The average milling forces in the cutting tests are plotted in Fig. 9 and the cutting force coefficients are listed in Table 4. Significant decreases of the cutting force coefficients Ktc and Krc are observed, while the edge force coefficients Kte and Kre increase. The decreases
Fig. 8. (a) Identification of cutting force coefficients under LN2 cooling (b) diagram for mechanic analysis of down milling.
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Dry LN
140 120 100 80 60 0.04
0.06
0.08
0.1
0.12
0.14
30
Cutting force Fy [N]
Cutting force Fx [N]
160
Dry LN
25 20 15 10 5 0.04
0.16
0.06
0.08
0.1
0.12
0.14
0.16
feed rate [mm/tooth]
feed rate [mm/tooth]
Fig. 9. The average milling forces on workpiece in X and Y direction at different feed rates. -3
x 10
1 NIM ZOA
0.8 0.6 0.4 0.2 0 0.8
0.9
(a)
1 1.1 1.2 Spindle speed [rpm]
1.3
Axial depth [m]
Axial depth [m]
1
x 10
-3
0.8 0.6 0.4 0.2
NIM ZOA
0 0.8
1.4 4 x 10
SLD for dry milling
0.9
1 1.1 1.2 Spindle speed [rpm]
1.3
(b)
SLD for cryogenic milling
1.4 4 x 10
Fig. 10. Prediction of SLDs for half-immersion down-milling.
3.2.3. Milling stability lobe diagram prediction Based on the 2-DOF milling dynamics model briefly described in Appendix B (Altintas, 2012), SLD for half-immersion down-milling (ae = 0.5D) is calculated by NIM method proposed by Ding et al. (2011) for its high accuracy and computation efficiency. To construct the SLD in Fig. 10, a 300 × 100 grid is taken in parameter space of spindle speed and axial depth, and the discretized number n is set as 50. Similar results can also be achieved by several other methods, such as ZOA method proposed by Altintas and Budak (1995). It is noted that, as for half-immersion down-milling in which higher order Fourier coefficients of directional dynamic milling force coefficients matrix can be neglected for the low-pass filtering effect of the dynamics of the system, the difference between stability boundaries predicted by ZOA and NIM is very small. Table 4 Cutting force coefficients of Al7075-T6 for the end mill used in experiment. Condition
Ktc (N/mm2 )
Krc (N/mm2 )
Kte (N/mm)
Kre (N/mm)
Dry LN2
1384.03 834.83
695.70 100.48
10.50 24.27
9.24 29.66
x 10
-3
Axial depth [m]
1 0.8 0.6 0.4 0.2 0 0.8 x 10
0.9
1
0.9
1
-3
1.1 1.2 Spindle speed [rpm]
1.3
1.4 4 x 10
1.3
1.4 4 x 10
1
Axial depth [m]
in Kte and Kre , which characterize the resistance of workpiece material to the shearing effect of cutting edge, might be attributed to the reduction of friction between the chip and cutting edge for the lubrication effect of LN2 (Hong et al., 2002). Additionally, LN2 jet is beneficial to chip breaking when it is delivered in suitable direction so that chips are swept away from the cutter, thus the chip contact length might be shortened. As for the edge forces generated by ploughing or rubbing effect, their increases can be explained by the reinforcement of 7075 aluminum alloy while cryogenic machining. It has been reported that the mechanical properties of 7000 series alloys, including yield strength, tensile strength, plasticity and toughness etc., will improve while temperature drops (Das et al., 2011), thus increasing its resistance to plastic deformation. This might help to strengthen the process damping effect in milling, which can enhance the stability due to the interaction between the cutting edge and wavy surface finish of workpiece.
0.8 0.6 0.4 0.2 0 0.8
1.1
1.2
Spindle speed [rpm]
Fig. 11. Predicted SLDs and measured chatter stability results in half-immersion down-milling: (a) dry milling; (b) cryogenic milling. Symbols: clearly stable; ♦ not clearly stable or unstable; × clearly unstable; stable during cryogenic milling, unstable during dry milling; red line denotes the SLD of dry milling while blue line denotes the SLD of cryogenic milling. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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The predicted SLDs show that the most stable regions are around the cutting speeds, where the tooth pass frequency equals to integer fractions of the natural frequency of the dominant modal j = 60fn /jN , j = 1, 2, 3· · ·, N is the number of flutes. Thus when the dominant modal frequency of tool decreases slightly along with cryogenic cooling, the most stable regions will also shift a little to lower speed range. What is more, significant reductions in cutting forces while cryogenic milling can enhance stability boundary. 3.2.4. Experimental stability lobe diagram verification Chatter caused by regenerative vibration always occurs at chatter frequency ωc that is close to the natural frequency of dominant modal and at frequencies which are tooth passing harmonics away from the chatter frequency ωc + iωT (i = ±1, 2, . . .). Both the cutting forces and sound pressure spectrums, calculated by the fast Fourier transform (FFT) of time domain signals, are used to detect these characteristic frequencies. Additionally, the 1/tooth-sampled cutting forces are adopted for analysis of
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the quasi-periodic behavior of the slender tool during chatter, inspired by the Poincaré sectioning techniques applied to nonlinear dynamics. Similar experimental method has been applied to the research on milling stability, where displacement of flexible workpiece (Mann et al., 2003) or tool shaft deflection (Gradiˇsek et al., 2005) was 1/tooth-sampled to construct experimental Poincaré sections. Compared with the vibration of tool shaft, cutting forces are more convenient to measure in the present study. When the process is stable which corresponds to a periodic solution, the 1/tooth-sampled displacements of tool converge to a fixed point in Poincaré section. If regenerative chatter occurs, which corresponds to a quasi-periodic solution, the 1/tooth-sampled displacements no longer converge to a single point, but distribute on a loop or several points. According to mechanistic model, cutting forces are determined by uncut chip thickness h, which depends on dynamic displacement of cutting edge and instantaneous angle of immersion . As for 1/tooth-sampled cutting force, the instantaneous angle of immersion is constant. As
Fig. 12. Comparison of experiment results for dry milling and cryogenic milling. (1) Cutting force and 1/tooth-sampled signal; (2) sound pressure signal; (3) force spectrum; (4) sound pressure spectrum; (5) Poincaré section for Fx; (6) Poincaré section for Fy.
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Fig. 13. Stability change before and after cryogenic cooling. (a) Cutting force and 1/tooth-sampled signal; (b) force spectrum; (c) sound pressure; (d) sound pressure spectrum.
X. Huang et al. / Journal of Materials Processing Technology 214 (2014) 3169–3178
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Fig. 14. Dynamic model of 2-DOF end milling considering regenerative effect.
a result, it will show similar pattern demonstrated by 1/toothsampled displacements. In conclusion, dynamic cutting force is both the cause and result of tool’s vibration and 1/tooth-sampled cutting force can also help to detect the behavior of chatter. In the present study, cutting forces in X and Y direction are 1/toothsampled for the construction of Poincaré sections in delayed coordinates. The experiment results are compared with predicted SLDs under dry and cryogenic conditions, respectively, in Fig. 11(a) and (b). For both dry and cryogenic cases, the experimental results agreed with prediction and several typical points are emphasized as follow. Points A (9610 rpm, 0.5 mm, dry) and C (11,250 rpm, 0.5 mm, LN2) are obviously unstable and are related to Hopf instability. Cutting forces, sound pressure and their spectrums are shown in Fig. 12. For point A, strong chatter occurrs at frequencies (1829 Hz, 2149 Hz, 2469 Hz) and their difference equals to tooth passing frequency about 320 Hz. The spectrum of sound pressure also confirms these chatter frequencies. The circular trajectory in Poincaré section demonstrates quasi-periodic behavior during unstable machining. Similar results are achieved at point C. Points B (13,350 rpm, 0.5 mm, dry) and D (13,030 rpm, 0.5 mm, LN2) are related to stable machining. In the spectrums of forces and sound pressure, the main frequency components are tooth pass harmonics. Apart from these, there are some weak spindle rotate harmonics caused by slight runout. The 1/tooth-sampled signals locate around the same value, which corresponds to concentrated point sets in Poincaré sections. Several unstable points in dry milling turn to be stable points in cryogenic cooling, including points E (10,280 rpm, 0.4 mm), F (10,480 rpm, 0.5 mm), G (13,030 rpm, 0.6 mm) and H (8900 rpm, 1 mm) etc. Cutting forces and sound spectrums of these points are listed in Fig. 13. Point E is obviously unstable in dry cutting test. It is noteworthy that it belongs to periodic instability, in which odd harmonics of half tooth passing frequency (2k + 1) ωT /2 become the dominant components near the natural frequency of structure. As shown in Fig. 13(1), strong chatter occurrs at frequencies (1884 Hz, 2226 Hz, 2569 Hz) which equal to 5.5ωT , 6.5ωT , 7.5ωT , respectively, with ωT = 342.67 Hz. However, this point is stable in cryogenic machining. Cutting force is much smaller and the chatter frequency components almost disappear in the spectrums of cutting force and sound pressure (Fig. 13(2)). This is the case for points H, shown in Fig. 13(7)–(8). Points F and G are unstable points of Hopf type in dry cutting test, in which slight chatter frequencies components appear (Fig. 13(3)–(6)). After cryogenic cooling, vibrations at these chatter frequencies vanish.
While stability of these cutting tests meets well with the tendency shown by the predicted SLDs, it is discerned that the prediction seems to be a little conservative, which become obvious gradually with spindle speed decreasing, such as the lobe around 8900 rpm. This can be explained by the process damping effect, which becomes crucial when the ratio of spindle period to regenerative vibration period is high, i.e. at the lobes which are higher than five (j > 5) (Altintas and Weck, 2004). In our experiments, the dominant frequency of spindle-tool system is fn = 1785 Hz, and the critical spindle speed is around j = 60fn / (5 × 2) = 10, 710 rpm. Thus, the actual stability lobes are higher than the predicted ones in the speed range lower than 10,710 rpm, just as experiments show. Nevertheless, the influence of cryogenic cooling on SLD is still obvious in the cutting tests. 4. Conclusions The influence of cryogenic cooling on the stability limit of milling operation is investigated intensively for the first time in this research. A series of experiments are conducted to achieve the effects of LN2 jet cooling on cutting forces and dynamic characteristics of tool system in end milling 7075-T6 aluminum alloy. Using NIM method and ZOA method, SLDs under dry and cryogenic conditions are predicted, which reveal the enhancement of stability boundary. The predictions agree well with the experimental results of a large number of cutting tests, in which the spectrums of cutting forces, sound pressure and Poincaré sections constructed by 1/tooth-sampled force are used to detect regenerative vibrations during half-immersion down-milling. Here are some important conclusions: (1) Cryogenic cooling can enhance stability limits in end milling. For most cases in the present study, the stability limits could be improved by 50–100%. (2) When applying LN2 jet to cutting zone in the direction that helps to take away the chips, cutting forces can be significantly reduced, meanwhile the edge forces increase. This is the main reason for the enhancement of stability boundary. (3) The dominant modal frequency of tool system decreases a little while cryogenic cooling, which will shift the stability boundary slightly to lower spindle speed range. With cryogenic machining developing into a practical technique in industry, understanding how the stability boundary changes is helpful to achieve higher productivity, thus reduce the cost of cryogenic coolant, which is beneficial to its widely application in the shop floor. To understand the influence of cryogenic cooling on milling dynamics better, the model for the variation of cutting forces and modal parameters of the tool system, which are
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caused by cryogenic cooling, need to be built in the future so as to guide the tuning of cooling parameters for optimal stability limits.
When the axial depth is much smaller than the helical pitch of spiral mill, the immersion angle can be simplified as: j (t, z) =
Acknowledgements
This work is partially supported by the National Natural Science Foundation of China (51375005, 51121002), the National Basic Research Program of China (2014CB046704), and the National Science & Technology Pillar Program (2012BAF08B01). Appendix A. Cutting force coefficients The general expression of average milling forces: Fx =
N 2
ex
st
+ap
Fy =
N 2
ex
st
ex
st
sin2 Ktc d
st
ex
cos Kre d −
(A.1)
ex
sin cos Krc d −
+ap
N Fz = 2
cos Kte d st
ap ft
sin Kte d
(A.2)
st
ex
ap ft
ex
sin Kac d + ap st
Kae d
(A.3)
st
Appendix B. Dynamic model for 2-DOF milling Considering the regenerative effect, milling dynamic equation for 2-DOF milling system in Fig. 14 can be represented as: ¨ ˙ M q(t) + C q(t) + Kq(t) = ap Kc (t)[q(t) − q(t − T )]
Kc (t) =
axx (t)
axy (t)
ayx (t)
ayy (t)
(B.1) (B.2)
1 axx (t) = − g j (t, z) Ktc sin 2j (t, z) + Krc 1 − cos 2j (t, z) , 2 ayx (t) =
1 g j (t, z) Ktc 1 − cos 2j (t, z) − Krc sin 2j (t, z) , 2
1 axy (t) = − g j (t, z) Ktc 1 + cos 2j (t, z) + Krc sin 2j (t, z) , 2 ayy (t) =
j = (1, 2, . . ., N)
1
if j (t, z) ∈ (st , ex )
0
otherwise
(B.4)
(B.5)
Taking the influence of cryogenic cooling on cutting forces and dynamics of machine-tool system into consideration, dynamic parameters in the left side of equation (B.1) can be rewritten as variables M(, P, Q, . . .), C(, P, Q, . . .), K(, P, Q, . . .) changing with cooling conditions such as temperature , pressure P, and coolant flow rate Q etc. So does the time varying milling force in the right side Kc (t, , P, Q, . . .). References
ex
sin Kre d + st
g j (t, z) =
sin cos Ktc d st
ex
ex
sin2 Krc d +
ap ft
2˝ 2 t + (j − 1) 60 N
1 g j (t, z) Ktc sin 2j (t, z) − Krc 1 + cos 2j (t, z) 2
(B.3)
Altintas, Y., 2012. Manufacturing Automation: Metal Cutting Mechanics, Machine Tool Vibrations, and CNC Design. Cambridge University Press, Cambridge. Altintas, Y., Budak, E., 1995. Analytical prediction of stability lobes in milling. Ann. CIRP 44, 357–362. Altintas, Y., Weck, M., 2004. Chatter stability of metal cutting and grinding. Ann. CIRP 53, 619–642. Budak, E., Armarego, E.J.A., Altintas¸, Y., 1996. Prediction of milling force coefficients from orthogonal cutting data. J. Manuf. Sci. Eng. Trans. ASME 118, 216–224. Das, P., Jayaganthan, R., Singh, I.V., 2011. Tensile and impact-toughness behaviour of cryorolled Al 7075 alloy. Mater. Des. 32, 1298–1305. Ding, Y., Zhu, L.M., Zhang, X.J., Ding, H., 2011. Numerical integration method for prediction of milling stability. J. Manuf. Sci. Eng. Trans. ASME 133, 31005. Gradiˇsek, J., Kalveram, M., Insperger, T., Weinert, K., Stépán, G., Govekar, E., Grabec, I., 2005. On stability prediction for milling. Int. J. Mach. Tool Manuf. 45, 769–781. Hong, S.Y., Ding, Y.H., Jeong, W., 2001a. Friction and cutting forces in cryogenic machining of Ti–6Al–4V. Int. J. Mach. Tool Manuf. 41, 2271–2285. Hong, S.Y., Markus, I., Jeong, W., 2001b. New cooling approach and tool life improvement in cryogenic machining of titanium alloy Ti–6Al–4V. Int. J. Mach. Tool Manuf. 41, 2245–2260. Hong, S.Y., Ding, Y.C., Jeong, J., 2002. Experimental evaluation of friction coefficient and liquid nitrogen lubrication effect in cryogenic machining. Mach. Sci. Technol. 6, 235–250. Khan, A.A., Ahmed, M.I., 2008. Improving tool life using cryogenic cooling. J. Mater. Process. Technol. 196, 149–154. Mann, B.P., Insperger, T., Bayly, P.V., Stepan, G., 2003. Stability of up-milling and down-milling, Part 2: Experimental verification. Int. J. Mach. Tool Manuf. 43, 35–40. Puˇsavec, F., Govekar, E., Kopaˇc, J., Jawahir, I.S., 2011. The influence of cryogenic cooling on process stability in turning operations. Ann. CIRP 60, 101–104. Richardson, M.H., Formenti, D.L., 1982. Parameter estimation from frequency response measurements using rational fraction polynomials. In: Proceedings of the First International Modal Analysis Conference, vol. 1, pp. 167–186. Sharma, V.S., Dogra, M., Suri, N.M., 2009. Cooling techniques for improved productivity in turning. Int. J. Mach. Tool Manuf. 49, 435–453. Venugopal, K.A., Paul, S., Chattopadhyay, A.B., 2007. Growth of tool wear in turning of Ti–6Al–4V alloy under cryogenic cooling. Wear 262, 1071–1078. Wang, Z.Y., Rajurkar, K.P., 2000. Cryogenic machining of hard-to-cut materials. Wear 239, 168–175. Yildiz, Y., Nalbant, M., 2008. A review of cryogenic cooling in machining processes. Int. J. Mach. Tool Manuf. 48, 947–964.
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Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec
The influence of cryogenic cooling on milling stability Xinda Huang, Xiaoming Zhang ∗ , Haikuo Mou, Xiaojian Zhang, Han Ding State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China
a r t i c l e
i n f o
Article history: Received 21 May 2014 Received in revised form 22 July 2014 Accepted 24 July 2014 Available online 30 July 2014 Keywords: Chatter Cryogenic cooling End milling Stability lobe diagram (SLD)
a b s t r a c t Cryogenic cooling is emerging as an effective process for high performance machining. However, the influence of cryogenic cooling on milling stability is seldom reported. This paper involves experimental study on the effect of cryogenic cooling on milling stability, using a dedicated cryogenic cooling system to applying liquid nitrogen (LN2) jet to the cutting zone. We observe that cryogenic cooling leads to higher stability limit compared with conventional milling operations, which indicates that the cutting efficiency can be improved greatly in LN2 environment as opposed to the conventional one. The stability improvement is explained from the perspective of machining dynamics parameters variation between the two conditions. Cutting force coefficients and modal parameters of spindle-tool system are identified during cryogenic machining, then milling stability lobe diagrams are predicted by time domain and frequency domain methods. On the basis of milling stability analysis, the enhancement of stability boundary is attributed to the significant reduction of cutting force coefficients during cryogenic cooling. Additionally, the experiment result indicates that cryogenic cooling decreases the dominant modal frequency of the spindle-tool system, which shifts the milling stability boundary slightly to lower spindle speed range. The explanations are verified by a plenty of cutting tests. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Cooling plays a significant role in metal cutting process for its main functions in transferring excessive heat and reducing tool wear. Increased application of difficult-to-machine materials, such as nickel based high-temperature alloy, titanium alloy in aerospace and energy industry promotes the development of new cooling methods to get higher machining performance, better surface integrity economically and environmental-friendly. In the past decades, various methods have been proposed, including high-pressure coolant (HPC), minimum quantity lubrication (MQL), compressed air cooling, and cryogenic cooling etc., which has been summarized in detail by Sharma et al. (2009). As one of these methods, cryogenic cooling is emerging as a promising approach for application in industry and LN2 is the most widely used cryogenic coolant for its non-toxic and sufficient resource (Yildiz and Nalbant, 2008). Much research has been done to explore and confirm the improvement of cryogenic cooling on machinability. Hong et al. (2001b) proposed an economical approach to transfer LN2 to flank and rake face near the cutting edge and five times enhancement of tool life was achieved when turning Ti6Al4V at cutting speed of 150 m/min. Moreover, they found that LN2 can act as an effective
∗ Corresponding author. Tel.: +86 2787559842; fax: +86 2787559416. E-mail address: [email protected] (X. Zhang). http://dx.doi.org/10.1016/j.jmatprotec.2014.07.023 0924-0136/© 2014 Elsevier B.V. All rights reserved.
lubricant (Hong et al., 2001a), which was validated by the reduction of feed force and thickness of secondary deformation zone. Wang and Rajurkar (2000) investigated the cryogenic machining of hard-to-cut materials, and their result showed that cryogenic cooling can enhance tool life and surface roughness significantly but has no remarkable influence on the cutting force. Venugopal et al. (2007) investigated the tool wear in cryogenic turning of Ti6Al4V alloy and found that cryogenic cooling enhances tool life substantially at moderate cutting speed of 70 m/min. Khan and Ahmed (2008) found that the tool life increases more than four times when machining AISI304 stainless steel with modified tool, in which the insert is cooled by LN2 through an internal chamber. While most of publications about cryogenic cooling focused on turning operation and its influence on machinability, there is almost no report about the stability in cryogenic milling. Puˇsavec et al. (2011) conducted an experimental study on the influence of cryogenic cooling on process stability in turning operations, in which coarse-grained entropy rate (CER) method was used for detection of chatter in cutting tests. It is observed that a higher machining stability limit is achieved during cryogenic machining due to the reduction of specific cutting force components. In fact, Chatter in milling operation is always gaining significant attention in order to achieve higher productivity and better surface finish, which is very important in high speed machining (HSM) of aluminum alloy and low speed milling of thermal resistant alloy. With cryogenic cooling being applied to aerospace industry, where
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Fig. 1. Experiment setup for end milling with varying cutting depth and cryogenic cooling system.
Table 1 Tool parameters.
Table 2 Cutting parameters for end milling with varying axial depth.
Tool
Diameter (mm)
Flutes num
Helix angle (deg)
Overhang (mm)
Material
Tool
Short cutter Long cutter
8 8
2 2
30 30
40 64
Carbide Carbide
Short cutter Long cutter
milling occupied most of material removal process, it is necessary to analyze its influence on milling stability so as to optimize the process. The remainder of this paper offers the followings: - We report the experiments of great milling stability limit improvement under LN2 condition. End milling tests with varying axial depth are carried out to show the difference of stability limit under dry and cryogenic conditions. In order to explain the difference, cutting force coefficients and modal parameters of a two-degree-of-freedom (2-DOF) end milling system are identified before and after cryogenic cooling. The SLDs are predicted using time domain and frequency domain methods. - To confirm the stability limit differences shown in predicted SLDs, a series of experiments are conducted to catch the variation of stability boundary after cryogenic cooling. 2. Experimental conditions and procedure The experiments are performed on a machining center VMC-50 with maximum spindle speed 14,000 rpm. In the first experiment, to achieve continuously varying axial depth, a specific workpiece made of 7075-T6 aluminum alloy is prepared (Fig. 1). There is a slope on the workpiece and axial depth ap varies from 2 mm (side B) to 8 mm (side A) linearly after machining a path of 74 mm long. In the case of cryogenic milling, a copper nozzle is mounted on a fixture moving along with the spindle housing, through which LN2 jet is sprayed into cutting zone. Both short stiffer cutter and long slender cutter are adopted in order to reveal the influence of cryogenic cooling on the onset of chatter as well as the vibration during post-chatter stage. The tool parameters are listed in Table 1. Cutting forces are measured by a Kistler9257B multicomponent dynamometer mounted on worktable and are recorded by a Labview-based PC data acquisition system. The cutting parameters are listed in Table 2, and sampling rate is set as 40 kHz so that the dynamic cutting force can be measured precisely during high speed (s > 10,000 rpm). In the case for experimental verification of SLDs, end milling tests with constant axial depth are performed using the long slender end mill mentioned in Table 1 (L/D = 8), which is mounted in a HSK-A63 tool holder by collet chuck. As reported in several
Spindle speed (rpm) 12,240 12,240
Axial depth (mm)
Radial depth (mm)
Feed rate (mm/tooth)
2–8 2–8
4 1.2
0.05 0.05
studies on milling dynamics, cylindrical end mill with large length-diameter ratio is prone to have a single dominant vibration mode, which will make it more convenient for the following milling stability analysis (Gradiˇsek et al., 2005). The workpiece is a 7075-T6 aluminum alloy block fixed on dynamometer, which can be regarded as rigid for its much higher stiffness. A number of cutting tests are conducted to catch the variation of SLD for half-immersion down-milling under cryogenic cooling, in which a straight path about 80 mm long is machined repeatedly at different points in the cutting parameter space of spindle speed and axial depth. The feed rate is set as ft = 0.05 mm/tooth. In order to detect the occurrence of chatter during milling process, cutting forces and sound pressure signals are recorded simultaneously by Kister9257B dynamometer and B&K 4189 freefield microphone at sampling rate 40 kHz. A small label is pasted on the tool holder and periodic 1/revolution-sampled impulse signal synchronized with the tool rotation is generated by a laser displacement sensor fixed with spindle, which is then interpolated to achieve 1/tooth-sampled signals. The experiment setup for Case 2 is shown in Fig. 2. The cutting forces and sound pressure signals are processed offline in time domain and frequency domain for chatter detection.
Fig. 2. Experiment Setup for cutting tests to verify the predicted SLDs.
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Fig. 3. Chatter mark and cutting forces for short cutter at cutting parameters: ft = 0.05 mm/tooth, S = 12,240 rpm, ae = 4 mm. (a) Dry milling; (b) cryogenic milling.
3. Results and discussion This section describes the experimental results of two cases. In the experiment for Case 1, the difference of stability limit for end milling under two cooling conditions is demonstrated conveniently and visually while varying axial depth continuously with the designated workpiece adopted. In the experiment for Case 2, the impacts of cryogenic cooling on cutting forces and modal parameters of spindle-tool system are explored, so as to get quantitative interpretation in the perspective of milling dynamics. Based on these, milling stability analysis is conducted to predict SLDs using time domain and frequency domain methods, considering the influence of cryogenic cooling. A plenty of cutting tests are performed to verify the predicted SLDs.
3.1. Case 1: End milling with varying axial depth In the case of short cutter, cutting forces and chatter mark under dry and cryogenic conditions are shown in Fig. 3, respectively. In comparison to cryogenic milling, the chatter mark appears earlier and looks more severe with axial depth increasing during dry milling. At the location about 20 mm away from side A, the cutting forces with LN2 cooling are more steady and regular. In contrast, the cutting forces in dry milling have shown unsynchronized vibrations coursed by chatter. In the case of long cutter, although severe chatter mark appears in both situations for the weak stiffness of tool system, it is obvious
that the chatter mark in cryogenic milling is slighter (Fig. 4(b)). The spectrum of cutting force in dry milling shows that strong chatter occurs at 1561 Hz, 1969 Hz, 2378 Hz, the difference equals to tooth passing frequency T = 12, 240/60 × 2 =408 Hz. In comparison, the frequency components of chatter (1555 Hz, 1963 Hz, 2372 Hz) during cryogenic milling are much smaller. The phenomenon in Case 1 demonstrates that chatter in milling can be relieved at some extent when cryogenic cooling is adopted. Since chatter is mainly caused by self-excited vibration motivated by dynamic cutting forces near the most flexible system mode, the improvement of milling stability under cryogenic cooling is likely to be related to the variations of cutting forces and modal parameters of the machining system. 3.2. Case 2: Prediction and verification of SLDs under dry and cryogenic conditions The stability during machining is mainly determined by the dynamic characteristics of system and the dynamic cutting forces caused by regenerative effect. Thus it is reasonable to find out the mechanism of cryogenic cooling’s effect on stability by exploring its influence on these two aspects. 3.2.1. The influence of cryogenic cooling on the dynamics of milling system In order to predict SLD for end milling, frequency response function (FRF) at the tool tip is needed. FRFs of the slender tool are
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Fig. 4. Chatter mark, cutting forces and spectrums for long cutter at cutting parameters: ft = 0.05 mm/tooth, S = 12,240 rpm, ae = 1.2 mm. (a) Dry milling; (b) cryogenic milling.
obtained by impact tests, in which the tip of cutter is adhered to a tiny small accelerometer of only 0.2 g (Endevco 25A) and is excited by an impulse hammer (B&K 8206). The impact tests are conducted in X and Y direction 10 times, respectively, so as to reduce the disturbance of noise. Signals are acquired and processed on a LabView-based PC data acquisition systems using software ModalView. The FRFs of tool at tip are measured under dry and cryogenic conditions, respectively (Fig. 5). Considering that LN2 jet
may cause damage to the accelerometer for low temperature, the nozzle is directed at the point about 20 mm above the tool tip, which is adhered to the accelerometer. The modal parameters are fitted by rational fraction polynomial method (Richardson and Formenti, 1982) ranging from 500 Hz to 6000 Hz and results are listed in Table 3. As Fig. 6 shows, the fitted FRFs meet well with the measured ones and there is only a single dominant modal in both X and Y direction, whose resonance peak is
Fig. 5. Impact testing of the slender tool under dry and cryogenic conditions.
X. Huang et al. / Journal of Materials Processing Technology 214 (2014) 3169–3178 Table 3 Modal parameters of slender tool.
x 10
Direction
Mode
Frequency ωn (Hz)
Damping ratio
Stiffness k (N/m)
X Y X (LN2) Y (LN2)
1st mode 1st mode 1st mode 1st mode
1785.7 1782.5 1761.1 1758.5
0.01546 0.01538 0.01617 0.01621
1522,334 1553,675 1748,103 1663,012
Amplitude [m/N]
2.5
3173
-5
X: 1762 Y: 1.914e-005
2
Dry LN2
X: 1783 Y: 2.23e-005
1.5 1 0.5 0 1500
-5
x 10
Real [m/N]
1
500
1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000
Frequency [Hz] -5
x 10
Imag [m/N]
1
Exp Fitting
0 -1 -2 500
1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000
Frequency [Hz]
(a) FRF in x direction -5
x 10
Real [m/N]
1
Exp Fitting
0 -1 500
1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 -5
Imag [m/N]
1
Frequency [Hz]
0 -1
500
1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000
Frequency [Hz]
(b) FRF in y direction Fig. 6. FRFs of tool under dry condition in X and Y direction.
1700
1750
1800
1850
1900
1950
2000
3.2.2. The influence of cryogenic cooling on cutting force coefficients The cutting force coefficients for end milling cutter with 7075T6 aluminum alloy can be calibrated by the quick mechanistic approach proposed by Budak et al. (1996). According to this approach, cutting tests are conducted with constant axial depth at different feed rates. The spindle speed is set as 1800 rpm, the axial depth is 2 mm, and the feed rates are {0.06, 0.09, 0.12, 0.15} mm/tooth. In order to enhance the cooling effect of LN2 jet, half-immersion down-milling is adopted, instead of slotting (Fig. 8). As a result, both the cutting edge and workpiece can be accessed by LN2 jet. For half-immersion down- milling in which st = /2, ex = , the formula of average milling forces on the tool becomes: Fx = Fy = Fz =
-2
1650
around 1785 Hz at room temperature. It is noteworthy that when LN2 jet is sprayed onto the tool, the dominant modal frequency decreases by nearly 24 Hz (Fig. 7). This may be explained by the cold shrinkage of tool, which decreases the contact stiffness between the tool and collet chuck. The change of cutter’s elastic modulus during cryogenic cooling also contributes to the slight shift of dominant modal.
x 10
Exp Fitting
1600
Fig. 7. The shift of tool’s resonance peak under cryogenic cooling.
0 -1
1550
Frequency [Hz]
Exp Fitting
Na
p
8
Krc −
Na p −
4
Nap Ktc 4
Krc −
Nap Ktc 8
ft +
Nap (Kre − Kte ), 2
ft +
Nap (−Kre − Kte ), 2
Nap Nap Kac ft + Kae 2 4
(1)
which can be deduced from the general expression proposed by Altintas (2012), shown in Appendix A. The average milling forces in the cutting tests are plotted in Fig. 9 and the cutting force coefficients are listed in Table 4. Significant decreases of the cutting force coefficients Ktc and Krc are observed, while the edge force coefficients Kte and Kre increase. The decreases
Fig. 8. (a) Identification of cutting force coefficients under LN2 cooling (b) diagram for mechanic analysis of down milling.
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Dry LN
140 120 100 80 60 0.04
0.06
0.08
0.1
0.12
0.14
30
Cutting force Fy [N]
Cutting force Fx [N]
160
Dry LN
25 20 15 10 5 0.04
0.16
0.06
0.08
0.1
0.12
0.14
0.16
feed rate [mm/tooth]
feed rate [mm/tooth]
Fig. 9. The average milling forces on workpiece in X and Y direction at different feed rates. -3
x 10
1 NIM ZOA
0.8 0.6 0.4 0.2 0 0.8
0.9
(a)
1 1.1 1.2 Spindle speed [rpm]
1.3
Axial depth [m]
Axial depth [m]
1
x 10
-3
0.8 0.6 0.4 0.2
NIM ZOA
0 0.8
1.4 4 x 10
SLD for dry milling
0.9
1 1.1 1.2 Spindle speed [rpm]
1.3
(b)
SLD for cryogenic milling
1.4 4 x 10
Fig. 10. Prediction of SLDs for half-immersion down-milling.
3.2.3. Milling stability lobe diagram prediction Based on the 2-DOF milling dynamics model briefly described in Appendix B (Altintas, 2012), SLD for half-immersion down-milling (ae = 0.5D) is calculated by NIM method proposed by Ding et al. (2011) for its high accuracy and computation efficiency. To construct the SLD in Fig. 10, a 300 × 100 grid is taken in parameter space of spindle speed and axial depth, and the discretized number n is set as 50. Similar results can also be achieved by several other methods, such as ZOA method proposed by Altintas and Budak (1995). It is noted that, as for half-immersion down-milling in which higher order Fourier coefficients of directional dynamic milling force coefficients matrix can be neglected for the low-pass filtering effect of the dynamics of the system, the difference between stability boundaries predicted by ZOA and NIM is very small. Table 4 Cutting force coefficients of Al7075-T6 for the end mill used in experiment. Condition
Ktc (N/mm2 )
Krc (N/mm2 )
Kte (N/mm)
Kre (N/mm)
Dry LN2
1384.03 834.83
695.70 100.48
10.50 24.27
9.24 29.66
x 10
-3
Axial depth [m]
1 0.8 0.6 0.4 0.2 0 0.8 x 10
0.9
1
0.9
1
-3
1.1 1.2 Spindle speed [rpm]
1.3
1.4 4 x 10
1.3
1.4 4 x 10
1
Axial depth [m]
in Kte and Kre , which characterize the resistance of workpiece material to the shearing effect of cutting edge, might be attributed to the reduction of friction between the chip and cutting edge for the lubrication effect of LN2 (Hong et al., 2002). Additionally, LN2 jet is beneficial to chip breaking when it is delivered in suitable direction so that chips are swept away from the cutter, thus the chip contact length might be shortened. As for the edge forces generated by ploughing or rubbing effect, their increases can be explained by the reinforcement of 7075 aluminum alloy while cryogenic machining. It has been reported that the mechanical properties of 7000 series alloys, including yield strength, tensile strength, plasticity and toughness etc., will improve while temperature drops (Das et al., 2011), thus increasing its resistance to plastic deformation. This might help to strengthen the process damping effect in milling, which can enhance the stability due to the interaction between the cutting edge and wavy surface finish of workpiece.
0.8 0.6 0.4 0.2 0 0.8
1.1
1.2
Spindle speed [rpm]
Fig. 11. Predicted SLDs and measured chatter stability results in half-immersion down-milling: (a) dry milling; (b) cryogenic milling. Symbols: clearly stable; ♦ not clearly stable or unstable; × clearly unstable; stable during cryogenic milling, unstable during dry milling; red line denotes the SLD of dry milling while blue line denotes the SLD of cryogenic milling. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
X. Huang et al. / Journal of Materials Processing Technology 214 (2014) 3169–3178
The predicted SLDs show that the most stable regions are around the cutting speeds, where the tooth pass frequency equals to integer fractions of the natural frequency of the dominant modal j = 60fn /jN , j = 1, 2, 3· · ·, N is the number of flutes. Thus when the dominant modal frequency of tool decreases slightly along with cryogenic cooling, the most stable regions will also shift a little to lower speed range. What is more, significant reductions in cutting forces while cryogenic milling can enhance stability boundary. 3.2.4. Experimental stability lobe diagram verification Chatter caused by regenerative vibration always occurs at chatter frequency ωc that is close to the natural frequency of dominant modal and at frequencies which are tooth passing harmonics away from the chatter frequency ωc + iωT (i = ±1, 2, . . .). Both the cutting forces and sound pressure spectrums, calculated by the fast Fourier transform (FFT) of time domain signals, are used to detect these characteristic frequencies. Additionally, the 1/tooth-sampled cutting forces are adopted for analysis of
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the quasi-periodic behavior of the slender tool during chatter, inspired by the Poincaré sectioning techniques applied to nonlinear dynamics. Similar experimental method has been applied to the research on milling stability, where displacement of flexible workpiece (Mann et al., 2003) or tool shaft deflection (Gradiˇsek et al., 2005) was 1/tooth-sampled to construct experimental Poincaré sections. Compared with the vibration of tool shaft, cutting forces are more convenient to measure in the present study. When the process is stable which corresponds to a periodic solution, the 1/tooth-sampled displacements of tool converge to a fixed point in Poincaré section. If regenerative chatter occurs, which corresponds to a quasi-periodic solution, the 1/tooth-sampled displacements no longer converge to a single point, but distribute on a loop or several points. According to mechanistic model, cutting forces are determined by uncut chip thickness h, which depends on dynamic displacement of cutting edge and instantaneous angle of immersion . As for 1/tooth-sampled cutting force, the instantaneous angle of immersion is constant. As
Fig. 12. Comparison of experiment results for dry milling and cryogenic milling. (1) Cutting force and 1/tooth-sampled signal; (2) sound pressure signal; (3) force spectrum; (4) sound pressure spectrum; (5) Poincaré section for Fx; (6) Poincaré section for Fy.
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Fig. 13. Stability change before and after cryogenic cooling. (a) Cutting force and 1/tooth-sampled signal; (b) force spectrum; (c) sound pressure; (d) sound pressure spectrum.
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Fig. 14. Dynamic model of 2-DOF end milling considering regenerative effect.
a result, it will show similar pattern demonstrated by 1/toothsampled displacements. In conclusion, dynamic cutting force is both the cause and result of tool’s vibration and 1/tooth-sampled cutting force can also help to detect the behavior of chatter. In the present study, cutting forces in X and Y direction are 1/toothsampled for the construction of Poincaré sections in delayed coordinates. The experiment results are compared with predicted SLDs under dry and cryogenic conditions, respectively, in Fig. 11(a) and (b). For both dry and cryogenic cases, the experimental results agreed with prediction and several typical points are emphasized as follow. Points A (9610 rpm, 0.5 mm, dry) and C (11,250 rpm, 0.5 mm, LN2) are obviously unstable and are related to Hopf instability. Cutting forces, sound pressure and their spectrums are shown in Fig. 12. For point A, strong chatter occurrs at frequencies (1829 Hz, 2149 Hz, 2469 Hz) and their difference equals to tooth passing frequency about 320 Hz. The spectrum of sound pressure also confirms these chatter frequencies. The circular trajectory in Poincaré section demonstrates quasi-periodic behavior during unstable machining. Similar results are achieved at point C. Points B (13,350 rpm, 0.5 mm, dry) and D (13,030 rpm, 0.5 mm, LN2) are related to stable machining. In the spectrums of forces and sound pressure, the main frequency components are tooth pass harmonics. Apart from these, there are some weak spindle rotate harmonics caused by slight runout. The 1/tooth-sampled signals locate around the same value, which corresponds to concentrated point sets in Poincaré sections. Several unstable points in dry milling turn to be stable points in cryogenic cooling, including points E (10,280 rpm, 0.4 mm), F (10,480 rpm, 0.5 mm), G (13,030 rpm, 0.6 mm) and H (8900 rpm, 1 mm) etc. Cutting forces and sound spectrums of these points are listed in Fig. 13. Point E is obviously unstable in dry cutting test. It is noteworthy that it belongs to periodic instability, in which odd harmonics of half tooth passing frequency (2k + 1) ωT /2 become the dominant components near the natural frequency of structure. As shown in Fig. 13(1), strong chatter occurrs at frequencies (1884 Hz, 2226 Hz, 2569 Hz) which equal to 5.5ωT , 6.5ωT , 7.5ωT , respectively, with ωT = 342.67 Hz. However, this point is stable in cryogenic machining. Cutting force is much smaller and the chatter frequency components almost disappear in the spectrums of cutting force and sound pressure (Fig. 13(2)). This is the case for points H, shown in Fig. 13(7)–(8). Points F and G are unstable points of Hopf type in dry cutting test, in which slight chatter frequencies components appear (Fig. 13(3)–(6)). After cryogenic cooling, vibrations at these chatter frequencies vanish.
While stability of these cutting tests meets well with the tendency shown by the predicted SLDs, it is discerned that the prediction seems to be a little conservative, which become obvious gradually with spindle speed decreasing, such as the lobe around 8900 rpm. This can be explained by the process damping effect, which becomes crucial when the ratio of spindle period to regenerative vibration period is high, i.e. at the lobes which are higher than five (j > 5) (Altintas and Weck, 2004). In our experiments, the dominant frequency of spindle-tool system is fn = 1785 Hz, and the critical spindle speed is around j = 60fn / (5 × 2) = 10, 710 rpm. Thus, the actual stability lobes are higher than the predicted ones in the speed range lower than 10,710 rpm, just as experiments show. Nevertheless, the influence of cryogenic cooling on SLD is still obvious in the cutting tests. 4. Conclusions The influence of cryogenic cooling on the stability limit of milling operation is investigated intensively for the first time in this research. A series of experiments are conducted to achieve the effects of LN2 jet cooling on cutting forces and dynamic characteristics of tool system in end milling 7075-T6 aluminum alloy. Using NIM method and ZOA method, SLDs under dry and cryogenic conditions are predicted, which reveal the enhancement of stability boundary. The predictions agree well with the experimental results of a large number of cutting tests, in which the spectrums of cutting forces, sound pressure and Poincaré sections constructed by 1/tooth-sampled force are used to detect regenerative vibrations during half-immersion down-milling. Here are some important conclusions: (1) Cryogenic cooling can enhance stability limits in end milling. For most cases in the present study, the stability limits could be improved by 50–100%. (2) When applying LN2 jet to cutting zone in the direction that helps to take away the chips, cutting forces can be significantly reduced, meanwhile the edge forces increase. This is the main reason for the enhancement of stability boundary. (3) The dominant modal frequency of tool system decreases a little while cryogenic cooling, which will shift the stability boundary slightly to lower spindle speed range. With cryogenic machining developing into a practical technique in industry, understanding how the stability boundary changes is helpful to achieve higher productivity, thus reduce the cost of cryogenic coolant, which is beneficial to its widely application in the shop floor. To understand the influence of cryogenic cooling on milling dynamics better, the model for the variation of cutting forces and modal parameters of the tool system, which are
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caused by cryogenic cooling, need to be built in the future so as to guide the tuning of cooling parameters for optimal stability limits.
When the axial depth is much smaller than the helical pitch of spiral mill, the immersion angle can be simplified as: j (t, z) =
Acknowledgements
This work is partially supported by the National Natural Science Foundation of China (51375005, 51121002), the National Basic Research Program of China (2014CB046704), and the National Science & Technology Pillar Program (2012BAF08B01). Appendix A. Cutting force coefficients The general expression of average milling forces: Fx =
N 2
ex
st
+ap
Fy =
N 2
ex
st
ex
st
sin2 Ktc d
st
ex
cos Kre d −
(A.1)
ex
sin cos Krc d −
+ap
N Fz = 2
cos Kte d st
ap ft
sin Kte d
(A.2)
st
ex
ap ft
ex
sin Kac d + ap st
Kae d
(A.3)
st
Appendix B. Dynamic model for 2-DOF milling Considering the regenerative effect, milling dynamic equation for 2-DOF milling system in Fig. 14 can be represented as: ¨ ˙ M q(t) + C q(t) + Kq(t) = ap Kc (t)[q(t) − q(t − T )]
Kc (t) =
axx (t)
axy (t)
ayx (t)
ayy (t)
(B.1) (B.2)
1 axx (t) = − g j (t, z) Ktc sin 2j (t, z) + Krc 1 − cos 2j (t, z) , 2 ayx (t) =
1 g j (t, z) Ktc 1 − cos 2j (t, z) − Krc sin 2j (t, z) , 2
1 axy (t) = − g j (t, z) Ktc 1 + cos 2j (t, z) + Krc sin 2j (t, z) , 2 ayy (t) =
j = (1, 2, . . ., N)
1
if j (t, z) ∈ (st , ex )
0
otherwise
(B.4)
(B.5)
Taking the influence of cryogenic cooling on cutting forces and dynamics of machine-tool system into consideration, dynamic parameters in the left side of equation (B.1) can be rewritten as variables M(, P, Q, . . .), C(, P, Q, . . .), K(, P, Q, . . .) changing with cooling conditions such as temperature , pressure P, and coolant flow rate Q etc. So does the time varying milling force in the right side Kc (t, , P, Q, . . .). References
ex
sin Kre d + st
g j (t, z) =
sin cos Ktc d st
ex
ex
sin2 Krc d +
ap ft
2˝ 2 t + (j − 1) 60 N
1 g j (t, z) Ktc sin 2j (t, z) − Krc 1 + cos 2j (t, z) 2
(B.3)
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