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Theoretical and experimental investigation of the frictional behavior of the tool–chip interface in ultrasonic-vibration assisted turning
International Journal of Machine Tools & Manufacture 65 (2013) 1–7
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International Journal of Machine Tools & Manufacture journal homepage: www.elsevier.com/locate/ijmactool
Theoretical and experimental investigation of the frictional behavior of the tool–chip interface in ultrasonic-vibration assisted turning H. Jamshidi, M.J. Nategh n Tarbiat Modares University, Mechanical Engineering Department, Tehran, Iran
a r t i c l e i n f o
abstract
Article history: Received 10 May 2012 Received in revised form 9 September 2012 Accepted 13 September 2012 Available online 25 September 2012
The frictional behavior of the tool–chip interface has a significant role in the cutting mechanics. The frictional and normal forces, the contact length between the cutting tool and chip, the coefficient of friction and the stress distribution are the influential parameters. The behavior of the tool–chip interface in ultrasonic-vibration assisted cutting is different from conventional cutting and needs to be investigated. The ultrasonic-vibration assisted cutting has several advantages compared with conventional process. In the present study a frictional model has been developed for studying the above mentioned parameters and predicting the tool–chip behavior in ultrasonic-vibration assisted turning at different cutting speeds and vibration amplitudes. The results have been verified by experiments. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Ultrasonic vibration Turning Friction Cutting tool
1. Introduction The frictional forces are among the most influential parameters in the cutting processes. Astakhov [1] has shown on the basis of an energy model that only 30–50 percent of the energy is useful in cutting of metals and the rest will be spent to overcome the frictional forces at the tool–chip and workpiece-chip interfaces. The heat produced due to this frictional effect can also cause rapid tool wear. High frictional forces can also lead to formation of built up edge resulting in reduction of the workpiece surface integrity [2]. The frictional behavior of the tool–chip interface has thus a significant role in the cutting mechanics. The frictional and normal forces, the contact length between the cutting tool and chip, the coefficient of friction and the stress distribution are the relevant influential parameters. The ultrasonic-vibration assisted turning (UAT) is an efficient machining process resulting in the improvement of workpiece’s surface integrity and tool life and the decrease of machining forces compared with conventional turning (CT) [3–6]. It is especially suitable for cutting brittle and hard-to-cut materials such as super alloys, ceramics and glass. Some researchers [7] have simply attributed the reduction of machining forces in UAT to the reduction in frictional and normal forces. However, further work is needed for a better understanding of the condition at the tool–chip interface.
n Correspondence to: Tarbiat Modares University, Mechanical Engineering Department, Jalal-e Al-e Ahmad Boulevard, P.O. Box 14115-143, Tehran, Iran. Tel./fax: þ98 21 82884396. E-mail address: [email protected] (M.J. Nategh).
0890-6955/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijmachtools.2012.09.004
The behavior of the tool–chip interface in UAT is different from conventional cutting and needs to be investigated. In the present study, various parameters concerned at the tool–chip interface in UAT have been investigated and an analytical model has been developed for this purpose. The results have been verified by experiments.
2. Frictional model in UAT 2.1. Tool–chip interface in CT The length of interaction between the cutting tool and chip is generally divided into two parts [2,8–10]; the first one is sticking part (lst), which starts from the tool edge and continues up to the middle of interface length [1,11]. In this part the normal stress on the rake face is high so that welding can occur between the two surfaces and the frictional stress reaches to the yield stress of the workpiece. Therefore, the inner layers of the chip will undergo plastic deformation. In the second part the chip slides over tool surface (lsl). The latter extends from the middle of the interface length to the point that chip separates from tool rake face. Zorev modeled the contact stress distribution over these two distinct parts as follows [9]: y x s ¼ smax ð1Þ lc
t¼
8 < ms :
y
x max lc
0 rx r lc lst
tst
lc lst r x r lc
ð2Þ
2
H. Jamshidi, M.J. Nategh / International Journal of Machine Tools & Manufacture 65 (2013) 1–7
where smax is the maximum compression stress; lc is the tool– chip contact length; tst, is the yield stress of the workpiece; y is a constant value which depends on the tool and workpiece properties and x is the distance from the separation point of chip on the rake face. 2.2. Tool–chip interface in UAT In UAT, the cutting tool vibrates along the direction of cutting velocity at an ultrasonic frequency with a few microns of amplitude. The vibration is superimposed on the cutting motion of the tool. The cutting tool thus periodically looses contact with the workpiece. The vibration of the cutting tool can be expressed as [3,4,12]: xtool ¼ asinðotÞ ¼ asinð2pf tÞ
ð3Þ
where xtool is the position at time t, a is amplitude of vibration, o is the angular frequency and f is the frequency of vibration. The tool velocity relative to the workpiece (Vt w) can be written as: V tw ¼ 2paf cosð2pf tÞ þV c
ð4Þ
where V c is the cutting speed in CT. This equation implies that cutting is carried out at a varying speed when the cutting tool and the workpiece are in contact. The relative cutting speed varies continuously from zero to a maximum value of (2paf þVc). The variation of cutting speed causes variation of forces, temperature, tool–chip contact length, coefficient of friction and other machining parameters. Much research has been done to study the effect of cutting speed based on experimental results [2,13–15]. The variation of cutting speed influences the chip formation process in two ways. First, it changes the strain rate and temperature in the cutting zone and consequently changes the flow stress of the workpiece’s material. Second, it changes the tool–chip relative speed and thus influences the tool–chip contact length [1]. The stress distribution and the tool– chip contact length in UAT will be a function of the cutting speed. According to Eq. (4), the relative cutting speed between the workpiece and the cutting tool in UAT depends on the amplitude and frequency of vibration, cutting speed and time. The relative cutting speed would thus be a time function as the amplitude, frequency and cutting speed are constant. Therefore, the distribution of normal stress can be expressed as a function of distance and time:
sUAT ðx,tÞ ¼ qxy f ðtÞ
ð5Þ
where q and y are constants; x is the distance from the separation point of chip on the rake face and f(t) is a function indicating the effect of cutting speed variation on the normal stress equation. The tool–chip contact length in UAT when the contact is maintained can also be expressed as a function of time, as follows: lc ðtÞ ¼ lc gðtÞ
Also at t ¼T/4 when x ¼ lc , the normal stress has its maximum magnitude (smax) and according to Eqs. (5) and (6): T T T y y ¼ qlc f ¼ smax -q ¼ smax lc t ¼ -lUAT ¼ lCT -sUAT lc , 4 4 4 where smax and y are the same as in Eq. (1). Substituting the above value of q in Eq. (5): y x sUAT ðx,tÞ ¼ smax f ðtÞ ð8Þ lc A stress distribution similar to Fig. 1 is obtained by Eq. (8) for UAT where the stress changes not only along the tool–chip contact length but also changes with time. The average shear stress remains almost constant at different cutting speeds provided that the temperature rise is not high [1,9,11]. By considering this assumption and that the ultrasonic vibration does not change the property of the workpiece, the yield shear stress in UAT and CT are assumed to be equal. Therefore, by considering Eq. (2), the distribution of shear or frictional stress in UAT can be written as follows: 8 y < msmax x f ðtÞ 0 r x rlc ðtÞlst ðtÞ lc tUAT ¼ ð9Þ : t l ðtÞl ðtÞ r x rl ðtÞ st
c
st
c
The distribution of the normal stress is a two-variable function. Therefore, the mean normal force, NUATðave,t1 t2 Þ , during the machining time i.e. during the portion of each cycle that tool is in contact with the workpiece, can be calculated with double integration from Eq. (8): ZZ 1 NUATðave,t1 t2 Þ ¼ sUAT ðx,tÞdAdt ðt 2 t 1 Þ y Z lc ðtÞ Z t2 1 x ¼ bsmax f ðtÞdxdt ðt 2 t 1 Þ 0 lc t1 where limits of t1 and t2 are the duration of contact and separation between the tool and workpiece, respectively, and b is the depth of cut. After integrating and some mathematical manipulation, the above equation can be written as follows: Z t2 bsmax lc NUATðave,t1 t2 Þ ¼ gðtÞy þ 1 f ðtÞdt ð10Þ ðyþ 1Þðt 2 t 1 Þ t1 Based on Zorev model, the normal force in CT is equal to: NCT ¼
bsmax lc ðy þ1Þ
As a result, Eq. (10) can be written as: Z t2 N CT NUATðave,t1 t2 Þ ¼ gðtÞy þ 1 f ðtÞdt ðt 2 t 1 Þ t1
ð6Þ
where lc is tool–chip contact length in CT and g(t) indicates the effect of variation of cutting speed on the length of contact. According to Eq. (4), the relative cutting speed (Vt w) in UAT is equal to the cutting speed in CT (V c ) when t ¼T/4 (T is the period of the tool vibration cycle equal to 1/f). As a result, the length of contact and distribution of stresses in CT and UAT are equal at this moment; so according to Eq. (5): T T T T t ¼ -sUAT ¼ sCT -sUAT x, ¼ qxy f ¼ qxy -f ¼ 1 ð7Þ 4 4 4 4 It should be noted that in the above equation it has been assumed that (sCT ¼qxy). This is the basic stress distribution over the tool–chip contact surface. It can be shown that Eq. (1) is obtained from this relation by applying the boundary conditions, i.e. sCT ¼ smax at x ¼lc and sCT ¼0 at x ¼0.
Fig. 1. Distribution of normal and shear stresses in UAT.
ð11Þ
H. Jamshidi, M.J. Nategh / International Journal of Machine Tools & Manufacture 65 (2013) 1–7
3
Fig. 2. Experimental setup.
Fig. 3. The coated tool insert after conventional turning; the contact length measured 1.43 mm (right side), depth of cut 2.25 mm, feed rate 10 mm/min, cutting speed 15.198 m/min; the contact length measured 1.33 mm (left side) and cutting speed 21.277 m/min.
Similarly, the friction force in UAT can be calculated by double integration from Eq. (9): ZZ 1 F UATðave,t1 t2 Þ ¼ tUAT ðx,tÞdAdt ðt 2 t 1 Þ Z lc ðtÞ Z t2 1 btUAT ðx,tÞdxdt ¼ ðt 2 t 1 Þ 0 t1 After integration and some mathematical manipulation: Z t2 Z t2 F sl F st gðtÞy þ 1 f ðtÞdt þ gðtÞdt ð12Þ F UATðave,t1 t2 Þ ¼ ðt 2 t 1 Þ t1 ðt 2 t 1 Þ t1 where Fsl and Fst are friction forces in the sliding and sticking zone, respectively. The sliding and sticking forces can be obtained from Zorev model, as follows: F sl ¼
btst ðlc lst Þ ðyþ 1Þ
F st ¼ btst lst The mean forces in UAT in one cycle can be obtained from: NUATðave,TÞ ¼
t 2 t 1 N UATðave,t1 t2 Þ T
t 2 t 1 F UATðave,t1 t2 Þ F UATðave,TÞ ¼ T
ð13Þ
ð14Þ
Finally, the mean coefficient of friction in UAT can be obtained from the two above equations, as follows:
mUAT ¼
F UATðave,TÞ NUATðave,TÞ
ð15Þ
The proposed model will be completed when the functions f(t) and g(t) are specified. As mentioned earlier, these functions indicate the relation of the normal stress and the contact length with the variation of relative cutting speed, respectively.
Fig. 4. Correlation between the cutting speed and the tool–chip contact length in conventional turning; Al 6061 workpiece, rake angle¼ 01 and feed rate 10 mm/ min.
The functions f(t)and g(t) can be experimentally obtained for specific materials of the workpiece. It should be noted that the function f (t) does not change the profile of the normal stress distribution, as depicted in Fig. 1, in UAT compared with CT, but just changes the magnitudes. It should be noted that the duration of contact between the cutting tool and chip in each ultrasonic vibration cycle is too short for a direct UAT experiment and the instantaneous changes of the contact length and normal stress cannot be traced in a UAT process. On the other hand, it is expected the changes of the contact length and normal stress in UAT during the machining interval to follow a similar trend with respect to the cutting speed as in CT. Therefore, it is justifiable to find empirical relations for the contact length and normal stress in CT and employ them to find f(t) and g(t), as follows. For a workpiece of Al6061, the following relations have been found experimentally for the changes of normal stress and contact length with respect to cutting speed in CT:
s ¼ 161:4935 e0:0088 V
ð16Þ
lc ¼ 1:791 e0:01V
ð17Þ
The way of obtaining these experimental equations are elaborated in the next section (Figs. 4 and 5). From Eq. (16), the variation of normal stress with respect to cutting speed can be considered as an exponential function, as follows: f ðtÞ ¼ n1 en2 ðV tw Þ or f ðtÞ ¼ n1 en2 ð2paf cosð2pf tÞ þ V c Þ
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H. Jamshidi, M.J. Nategh / International Journal of Machine Tools & Manufacture 65 (2013) 1–7
Table 1 Results of CT experiments; depth of cut 2.25 mm, feed rate 10 mm/min, rake angle¼01, material Al 6061.
Fig. 5. Correlation between the cutting speed and the normal stress in conventional turning; Al 6061 workpiece, rake angle ¼01 and feed rate 10 mm/min.
From Eq. (7) and (16), n1 and n2 can be obtained as follows:
Cutting speed Vc (m/min)
Tool–chip contact length lc (mm)
Normal force in CT, NCT (N)
Friction force in CT, FCT (N)
sCT ¼ NCT =lc b (MPa)
15.198 21.277 27.356 33.435 39.514 48.632 57.751 66.869 72.948 82.067
1.430 1.330 1.132 1.125 1.041 0.787 0.700 0.684 0.591 0.529
515 385 375 255 244 190 135 136 132 95
112 100 109 93 82 65 66 53 52 42
160 129 147 101 104 107 86 88 99 80
f ðT=4Þ ¼ n1 en2 ðV c Þ ¼ 1-n1 ¼ en2 ðV c Þ -f ðtÞ ¼ en2 ð2pafcosð2pf tÞÞ f ðtÞ ¼ en2 ð2paf cosð2pf tÞÞ ¼ e0:0088ð2paf cosð2pf tÞÞ At a ¼6 mm and f¼20 KHz and considering the unit of cutting speed (m/min): 6
f ðtÞ ¼ e0:0088ð2p 610
2000060cosð2pf tÞÞ
¼ e0:3979cosð2p 20000 tÞ
And similarly from Eq. (17) for g(t): 0:4521cosð2p 20000tÞ
gðtÞ ¼ e
:
The proposed model predicts the normal force, the frictional force and the coefficient of friction in UAT on the basis of their magnitudes in CT. According to this mechanistic model, any change in the forces occurs via two mechanisms. First, as the vibration of the cutting tool causes connection and separation between the workpiece and the cutting tool, the normal and friction forces vanish in a portion of each cycle, i.e. during the period of separation. The average forces in a cycle are thus expected to reduce in proportion of t2 t1/T (Eqs. (13) and (14)). This reduction is independent of the workpiece’s and tool’s material. It only depends on vibration of UAT parameters including the vibration amplitude and frequency, and the cutting speed. Second, the normal and friction forces change due to the variation of the relative cutting speed in the period of the contact between the cutting tool and the workpiece. The average forces are calculated from Eqs. (11) and (12); theoretically, the forces may decrease, increase or remain unchanged. By choosing the material of the workpiece and machining condition, the normal and friction forces can be obtained from Eqs. (13) and (14), as mentioned earlier.
3. Experiments Two groups of experiments were carried out using Al 6061 workpieces. In the first group the behavior of the tool–chip contact length and the normal stress were obtained at different cutting speeds (15–82 m/min) in CT, which were subsequently used for developing the time functions. In the second group, the cutting forces and coefficient of friction were measured in UAT at amplitude of 6 mm and frequency of 20 KHz, in order to verify the theoretical results at different cutting speeds (15–40 m/min). It should be noted that the cutting speed in UAT experiments could not exceed its critical value 2paf 45 m=min. The critical speed would be explained later in this paper in Section 4. Tube turning was carried out in order to approximately achieve orthogonal cutting condition. A CNC-TME40 lathe was used for the experiments. A Kistler dynamometer was used to measure the cutting forces. An ultrasonic frequency generator and an ultrasonic transducer (fE20 KHz) were used to generate the vibration. The experiments were carried out at amplitude of 6 mm
Table 2 Results of UAT experiments; depth of cut 2.25 mm, feed rate 10 mm/min, amplitude 6 mm, frequency 20 KHz, material Al 6061. Cutting speed (m/min)
Normal force in UAT (N)
Friction force in UAT (N)
mUAT ¼ F UATðavr,TÞ
15.198 21.277 27.356 33.435 39.514
102 109 128 117 203
31 35 39 44 70
0.304 0.321 0.305 0.376 0.345
=N UATðavr,TÞ
and frequency of 20 KHz. A horn was designed and manufactured to transmit the vibration at a resonance frequency of 20 70.5 KHz to the carbide tool (VBMW160404). The experimental setup is shown in Fig. 2. There are different ways to measure the tool–chip contact length such as painting, coating and microscopic examination of the wear traces. The painting technique was not successful at the common cutting speeds. Instead, a thin layer of aluminum–zinc spray (Galva brite CRC) coating was applied to the cutting tool’s rake face. The coated layer was more stable than the painting so the curled chip could not affect the coating. The coating remained on the tool tip in conventional turning is illustrated in Fig. 3. The results of the first group of experiments are presented in Table 1. The cutting forces were measured by dynamometer in the directions of cutting speed and feed motion. These forces were actually the same as the normal and friction forces as the tool rake angle was zero. From these data, the correlation between the tool–chip contact length and the cutting speed and also the correlation between the normal stress and the cutting speed are illustrated in Figs. 4 and 5, respectively. An exponential curve can best fit the experimental points in each case leading to order of errors considerably lower than other functions. The exponential functions are indicated on the figures. The equations mentioned in Figs.4 and 5 were used for obtaining time functions as described in Section 2. The values of cutting forces measured in UAT (second group of experiments) and their ratio (mUAT ¼ F UATðavr,TÞ =NUATðavr,TÞ ) are presented in Table 2.
4. Results and discussion Based on Eqs. (11)–(15) and the functions obtained for f(t) and g(t), the theoretical correlation between the ratio of the normal and friction forces in UAT to CT, i.e. NUAT(ave,T)/NCT and FUAT(ave,T)/ FCT, versus the vibration amplitude and frequency are obtained as shown in Figs. 6 and 7, respectively. These figures indicate that an
H. Jamshidi, M.J. Nategh / International Journal of Machine Tools & Manufacture 65 (2013) 1–7
increase in the amplitude or frequency leads to the decrease of the force ratio. In other words, with an increase in the vibration amplitude or frequency, the normal and friction forces in UAT decrease compared with CT. The decrease of forces as a result of increase in the amplitude and frequency has also been reported by others [3–6,12]. The coefficient of friction can be calculated from the normal and friction forces. The variation of the ratio of friction coefficient, i.e. mUAT/mCT, versus the vibration amplitude has been shown in Fig. 8. It is evident from this figure that the friction coefficient in UAT is higher than CT. In addition, with an increase in the amplitude, the ratio of the friction coefficients, mUAT/mCT, also increases. In other words, the increase of friction coefficient in UAT compared with CT is more obvious at larger vibration amplitudes.
5
The maximum difference between the coefficient of friction in UAT and CT was about 39 percent; in other words, the ratio of friction coefficient in UAT to CT, mUAT/mCT, was about 1.39 when the amplitude of vibration increased from 4 to 10 mm. In Figs. 9 and 10, the friction and normal forces at different cutting speeds obtained by experiments (Table 2) have been compared with the theoretical results, respectively. It can be seen from these figures that there is good agreement between the theoretical and experimental results. It is noteworthy that in UAT the forces increase with an increase in the cutting speed, as is evident from Figs. 9 and 10. This increasing trend of forces is obviously contrary to the commonly decreasing trend in conventional turning. The reason is that the UAT characteristic is dominant here. In fact, the advantages of UAT compared with CT including the lower cutting
Fig. 6. Variation of the ratio of normal and friction forces in UAT to CT vs. amplitude; cutting speed 27.36 m/min, feed rate 10 mm/min, depth of cut 2.25 mm and frequency 20 KHz.
Fig. 9. Comparison between the theoretical and experimental normal forces at different cutting speeds; amplitude 6 mm, feed rate 10 mm/min, depth of cut 2.25 mm.
Fig. 7. Variation of the ratio of normal and friction force in UAT to CT vs. frequency; cutting speed 27.36 m/min, feed rate 10 mm/min, depth of cut 2.25 mm and amplitude 10 mm.
Fig. 8. Correlation between ratio of coefficients of friction vs. amplitude; cutting speed 27.36 m/min, feed rate 10 mm/min, depth of cut 2.25 mm and frequency 20 KHz.
Fig. 10. Comparison between the theoretical and experimental friction forces at different cutting speeds; amplitude 6 mm; feed rate 10 mm/min, and depth of cut 2.25 mm.
6
H. Jamshidi, M.J. Nategh / International Journal of Machine Tools & Manufacture 65 (2013) 1–7
of tool in ultrasonic-vibration assisted turning (UAT). The following conclusions can be drawn from this study:
Fig. 11. Comparison between the friction coefficient in UAT and CT at different cutting speeds; amplitude 6 mm, feed rate 10 mm/min, and depth of cut 2.25 mm.
forces continuously diminish when the cutting speed increases. The values of the cutting forces in UAT approach their CT counterparts with an increasing cutting speed. There is an upper limit to the cutting speed in UAT known as critical speed beyond which the advantages of UAT are lost and the same machining regime would dominate as in CT. The upper limit of the cutting speed in UAT is 2paf. At cutting speeds smaller than the critical value, the increasing trend of the cutting forces is attributable to the increase in the duration of contact time between the cutting tool and the workpiece occurring when the cutting speed increases. The increase of contact time continues into a permanent contact beginning from critical speed and the UAT process virtually changes to CT. At cutting speeds smaller than the critical value, the increase of cutting force due to the increase in contact time overweighs the decrease of the cutting force with increasing cutting speed. The increasing trend of cutting forces in UAT has also been reported in several other works such as [5,6]. The theoretical and experimental results for the coefficients of friction in UAT and CT have been compared in Fig. 11. As is clear from this figure, higher coefficients of friction are encountered in UAT relative to CT. The reduction being witnessed in the cutting forces in UAT relative to CT cannot thus be attributed to a lower friction coefficient as traditionally perceived by some researchers without any theoretical or experimental basis. At the best situation, the coefficient of friction in UAT and CT were taken equal, for example in [16]. This reduction can, however, be attributed to a higher decrease in the normal force compared with the decrease of the frictional force both acting on the tool–chip interface. The higher coefficient of friction in UAT compared with CT would be more evidenced with an increase in the amplitude of the vibration. It is noteworthy that the normal stress, s, decreases with an increase in the cutting speed [1,9,11] whereas the average shear stress, t, does not decrease so much due to its constant sticking friction constituent, and thus the ratio m ¼ t=s shows a noticeable increase in CT in Fig. 11.
5. Conclusion In the present study, a mechanistic model was derived for predicting the normal and frictional forces acting on the rake face
1. The experiments showed that both the tool–chip contact length and the normal stress acting on the tool–chip interface exponentially reduced when the cutting speed increased. Based on these experiments, functions were derived for modeling the variation of the contact length and the normal stress in each cycle of vibration in UAT. 2. According to the proposed model, any change in forces in UAT occurs via the periodic separation of the cutting tool and the workpiece and also variation in the relative cutting speed during the contact time. 3. The proposed model predicts that with an increase in the amplitude and frequency of the vibration, the normal and friction forces reduce. This reduction in UAT was about 19–82 percent for the normal force and 24–76 percent for the friction force acting on the tool–chip interface when the cutting speed and the frequency were 27 m/min and 20 KHz, respectively, and the amplitude increased from 4 to 10 mm. 4. Unlike the conventional turning, both the normal and friction forces acting on the tool–chip interface increase with an increase in the cutting speed in UAT. 5. The proposed model predicts a higher coefficient of friction on the tool–chip interface in UAT compared with CT. The reduction being witnessed in the cutting forces in UAT relative to CT cannot thus be attributed to a lower friction coefficient as traditionally perceived by some researchers without any theoretical or experimental basis. This reduction can, however, be attributed to a higher decrease in the normal force compared with the decrease of the frictional force both acting on the tool–chip interface. The higher coefficient of friction in UAT compared with CT would be more evidenced with an increase in the amplitude of the vibration. The maximum difference between the coefficient of friction in UAT and CT was about 39 percent; in other words, the ratio of friction coefficient in UAT to CT,mUAT =mCT , was about 1.39 when the amplitude of vibration increased from 4 to 10 mm. 6. The results of the proposed model were verified by the experiments. The discrepancies between the mechanistic models and the experimental results were about 9 percent for the normal force and 11 percent for the friction force in UAT. The trends of changes in the parameters were similar both predicted by the model and evidenced in the experiments.
Acknowledgment The authors would like to thank Mr. H. Soleimanimehr and Mr. B. Gholamzadeh for their assistance. References [1] V.P. Astakhov, Tribology of Metal Cutting, first edition, Elsevier, London, 2006. [2] E.M. Trent, P.K. Wright, Metal Cutting, fourth edition, Butterworth-Heinemann, Boston, 2000. [3] D.E. Brehl, T.A. Dow, Review of vibration-assisted machining, Precision Engineering 32 (2008) 153–172. [4] M.J. Nategh, S. Amini, H. Soleimanimehr, Modeling the force, surface roughness and cutting temperature in ultrasonic vibration-assisted turning of Al7075, Advanced Material Research 83–86 (2010) 315–325. [5] N. Ahmed, A.V. Mittofanov, V.I. Babitsky, V.V. Silberchmidt, Analysis of forces in ultrasonically assisted turning, Journal of Sound and Vibration 308 (2007) 845–854. [6] C. Nath, M. Rahman, Effect of machining parameters in ultrasonic vibration cutting, International Journal of Machine Tools and Manufacture 48 (2008) 965–974. [7] C.L. Chou, Wave effects of ultrasonic vibration on machining, Ph.D. Thesis, The Pennsylvania State University, 1994. [8] E.M. Trent, Metal cutting and the tribology of seizure. I. Seizure in metal cutting, Wear 128 (1988) 29–45.
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[9] N.N. Zorev, Interrelationship between shear processes occurring along tool face on shear plane in metal cutting, International Research in Production Engineering, ASME, New York, 1963, pp. 42–49. [10] J.A. Bailey, G. Boothroyd, Critical review of some previous work on the mechanics of the metal cutting process, Production Engineering Conference, ASME, Ohio, 1968, pp. 54–62. [11] P.W. Wallace, G. boothroyd, Tool forces and tool–chip friction in orthogonal machining, Journal of Mechanical Engineering Science 6 (1964) 74–87. [12] S. Amini, H. Soleimanimehr, M.J. Nategh, A. Abudollah, M.H. Sadeghi, FEM analysis of ultrasonic-vibration-assisted turning and the vibratory tool, Journal of Material Processing Technology 201 (2008) 43–47.
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[13] M.Y. Friedman, E. Lenz, Investigation of the tool–chip contact length in metal cutting, International Journal of Machine Tool Design Research 10 (1970) 401–416. [14] J.A. Bailey, Friction in metal machining-mechanical aspects, Wear 31 (1975) 243–275. [15] J.P. Davim, Machining Fundamentals and Recent Advances, Springer, London, 2008. [16] A.V. Mitrofanov, N. Ahmed, V.I. Babitsky, V.V. Silberschmidt, Effect of lubrication and cutting parameters on ultrasonically assisted turning of Inconel 718, Journal of Material Processing Technology 162–163 (2005) 649–654.
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International Journal of Machine Tools & Manufacture journal homepage: www.elsevier.com/locate/ijmactool
Theoretical and experimental investigation of the frictional behavior of the tool–chip interface in ultrasonic-vibration assisted turning H. Jamshidi, M.J. Nategh n Tarbiat Modares University, Mechanical Engineering Department, Tehran, Iran
a r t i c l e i n f o
abstract
Article history: Received 10 May 2012 Received in revised form 9 September 2012 Accepted 13 September 2012 Available online 25 September 2012
The frictional behavior of the tool–chip interface has a significant role in the cutting mechanics. The frictional and normal forces, the contact length between the cutting tool and chip, the coefficient of friction and the stress distribution are the influential parameters. The behavior of the tool–chip interface in ultrasonic-vibration assisted cutting is different from conventional cutting and needs to be investigated. The ultrasonic-vibration assisted cutting has several advantages compared with conventional process. In the present study a frictional model has been developed for studying the above mentioned parameters and predicting the tool–chip behavior in ultrasonic-vibration assisted turning at different cutting speeds and vibration amplitudes. The results have been verified by experiments. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Ultrasonic vibration Turning Friction Cutting tool
1. Introduction The frictional forces are among the most influential parameters in the cutting processes. Astakhov [1] has shown on the basis of an energy model that only 30–50 percent of the energy is useful in cutting of metals and the rest will be spent to overcome the frictional forces at the tool–chip and workpiece-chip interfaces. The heat produced due to this frictional effect can also cause rapid tool wear. High frictional forces can also lead to formation of built up edge resulting in reduction of the workpiece surface integrity [2]. The frictional behavior of the tool–chip interface has thus a significant role in the cutting mechanics. The frictional and normal forces, the contact length between the cutting tool and chip, the coefficient of friction and the stress distribution are the relevant influential parameters. The ultrasonic-vibration assisted turning (UAT) is an efficient machining process resulting in the improvement of workpiece’s surface integrity and tool life and the decrease of machining forces compared with conventional turning (CT) [3–6]. It is especially suitable for cutting brittle and hard-to-cut materials such as super alloys, ceramics and glass. Some researchers [7] have simply attributed the reduction of machining forces in UAT to the reduction in frictional and normal forces. However, further work is needed for a better understanding of the condition at the tool–chip interface.
n Correspondence to: Tarbiat Modares University, Mechanical Engineering Department, Jalal-e Al-e Ahmad Boulevard, P.O. Box 14115-143, Tehran, Iran. Tel./fax: þ98 21 82884396. E-mail address: [email protected] (M.J. Nategh).
0890-6955/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijmachtools.2012.09.004
The behavior of the tool–chip interface in UAT is different from conventional cutting and needs to be investigated. In the present study, various parameters concerned at the tool–chip interface in UAT have been investigated and an analytical model has been developed for this purpose. The results have been verified by experiments.
2. Frictional model in UAT 2.1. Tool–chip interface in CT The length of interaction between the cutting tool and chip is generally divided into two parts [2,8–10]; the first one is sticking part (lst), which starts from the tool edge and continues up to the middle of interface length [1,11]. In this part the normal stress on the rake face is high so that welding can occur between the two surfaces and the frictional stress reaches to the yield stress of the workpiece. Therefore, the inner layers of the chip will undergo plastic deformation. In the second part the chip slides over tool surface (lsl). The latter extends from the middle of the interface length to the point that chip separates from tool rake face. Zorev modeled the contact stress distribution over these two distinct parts as follows [9]: y x s ¼ smax ð1Þ lc
t¼
8 < ms :
y
x max lc
0 rx r lc lst
tst
lc lst r x r lc
ð2Þ
2
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where smax is the maximum compression stress; lc is the tool– chip contact length; tst, is the yield stress of the workpiece; y is a constant value which depends on the tool and workpiece properties and x is the distance from the separation point of chip on the rake face. 2.2. Tool–chip interface in UAT In UAT, the cutting tool vibrates along the direction of cutting velocity at an ultrasonic frequency with a few microns of amplitude. The vibration is superimposed on the cutting motion of the tool. The cutting tool thus periodically looses contact with the workpiece. The vibration of the cutting tool can be expressed as [3,4,12]: xtool ¼ asinðotÞ ¼ asinð2pf tÞ
ð3Þ
where xtool is the position at time t, a is amplitude of vibration, o is the angular frequency and f is the frequency of vibration. The tool velocity relative to the workpiece (Vt w) can be written as: V tw ¼ 2paf cosð2pf tÞ þV c
ð4Þ
where V c is the cutting speed in CT. This equation implies that cutting is carried out at a varying speed when the cutting tool and the workpiece are in contact. The relative cutting speed varies continuously from zero to a maximum value of (2paf þVc). The variation of cutting speed causes variation of forces, temperature, tool–chip contact length, coefficient of friction and other machining parameters. Much research has been done to study the effect of cutting speed based on experimental results [2,13–15]. The variation of cutting speed influences the chip formation process in two ways. First, it changes the strain rate and temperature in the cutting zone and consequently changes the flow stress of the workpiece’s material. Second, it changes the tool–chip relative speed and thus influences the tool–chip contact length [1]. The stress distribution and the tool– chip contact length in UAT will be a function of the cutting speed. According to Eq. (4), the relative cutting speed between the workpiece and the cutting tool in UAT depends on the amplitude and frequency of vibration, cutting speed and time. The relative cutting speed would thus be a time function as the amplitude, frequency and cutting speed are constant. Therefore, the distribution of normal stress can be expressed as a function of distance and time:
sUAT ðx,tÞ ¼ qxy f ðtÞ
ð5Þ
where q and y are constants; x is the distance from the separation point of chip on the rake face and f(t) is a function indicating the effect of cutting speed variation on the normal stress equation. The tool–chip contact length in UAT when the contact is maintained can also be expressed as a function of time, as follows: lc ðtÞ ¼ lc gðtÞ
Also at t ¼T/4 when x ¼ lc , the normal stress has its maximum magnitude (smax) and according to Eqs. (5) and (6): T T T y y ¼ qlc f ¼ smax -q ¼ smax lc t ¼ -lUAT ¼ lCT -sUAT lc , 4 4 4 where smax and y are the same as in Eq. (1). Substituting the above value of q in Eq. (5): y x sUAT ðx,tÞ ¼ smax f ðtÞ ð8Þ lc A stress distribution similar to Fig. 1 is obtained by Eq. (8) for UAT where the stress changes not only along the tool–chip contact length but also changes with time. The average shear stress remains almost constant at different cutting speeds provided that the temperature rise is not high [1,9,11]. By considering this assumption and that the ultrasonic vibration does not change the property of the workpiece, the yield shear stress in UAT and CT are assumed to be equal. Therefore, by considering Eq. (2), the distribution of shear or frictional stress in UAT can be written as follows: 8 y < msmax x f ðtÞ 0 r x rlc ðtÞlst ðtÞ lc tUAT ¼ ð9Þ : t l ðtÞl ðtÞ r x rl ðtÞ st
c
st
c
The distribution of the normal stress is a two-variable function. Therefore, the mean normal force, NUATðave,t1 t2 Þ , during the machining time i.e. during the portion of each cycle that tool is in contact with the workpiece, can be calculated with double integration from Eq. (8): ZZ 1 NUATðave,t1 t2 Þ ¼ sUAT ðx,tÞdAdt ðt 2 t 1 Þ y Z lc ðtÞ Z t2 1 x ¼ bsmax f ðtÞdxdt ðt 2 t 1 Þ 0 lc t1 where limits of t1 and t2 are the duration of contact and separation between the tool and workpiece, respectively, and b is the depth of cut. After integrating and some mathematical manipulation, the above equation can be written as follows: Z t2 bsmax lc NUATðave,t1 t2 Þ ¼ gðtÞy þ 1 f ðtÞdt ð10Þ ðyþ 1Þðt 2 t 1 Þ t1 Based on Zorev model, the normal force in CT is equal to: NCT ¼
bsmax lc ðy þ1Þ
As a result, Eq. (10) can be written as: Z t2 N CT NUATðave,t1 t2 Þ ¼ gðtÞy þ 1 f ðtÞdt ðt 2 t 1 Þ t1
ð6Þ
where lc is tool–chip contact length in CT and g(t) indicates the effect of variation of cutting speed on the length of contact. According to Eq. (4), the relative cutting speed (Vt w) in UAT is equal to the cutting speed in CT (V c ) when t ¼T/4 (T is the period of the tool vibration cycle equal to 1/f). As a result, the length of contact and distribution of stresses in CT and UAT are equal at this moment; so according to Eq. (5): T T T T t ¼ -sUAT ¼ sCT -sUAT x, ¼ qxy f ¼ qxy -f ¼ 1 ð7Þ 4 4 4 4 It should be noted that in the above equation it has been assumed that (sCT ¼qxy). This is the basic stress distribution over the tool–chip contact surface. It can be shown that Eq. (1) is obtained from this relation by applying the boundary conditions, i.e. sCT ¼ smax at x ¼lc and sCT ¼0 at x ¼0.
Fig. 1. Distribution of normal and shear stresses in UAT.
ð11Þ
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Fig. 2. Experimental setup.
Fig. 3. The coated tool insert after conventional turning; the contact length measured 1.43 mm (right side), depth of cut 2.25 mm, feed rate 10 mm/min, cutting speed 15.198 m/min; the contact length measured 1.33 mm (left side) and cutting speed 21.277 m/min.
Similarly, the friction force in UAT can be calculated by double integration from Eq. (9): ZZ 1 F UATðave,t1 t2 Þ ¼ tUAT ðx,tÞdAdt ðt 2 t 1 Þ Z lc ðtÞ Z t2 1 btUAT ðx,tÞdxdt ¼ ðt 2 t 1 Þ 0 t1 After integration and some mathematical manipulation: Z t2 Z t2 F sl F st gðtÞy þ 1 f ðtÞdt þ gðtÞdt ð12Þ F UATðave,t1 t2 Þ ¼ ðt 2 t 1 Þ t1 ðt 2 t 1 Þ t1 where Fsl and Fst are friction forces in the sliding and sticking zone, respectively. The sliding and sticking forces can be obtained from Zorev model, as follows: F sl ¼
btst ðlc lst Þ ðyþ 1Þ
F st ¼ btst lst The mean forces in UAT in one cycle can be obtained from: NUATðave,TÞ ¼
t 2 t 1 N UATðave,t1 t2 Þ T
t 2 t 1 F UATðave,t1 t2 Þ F UATðave,TÞ ¼ T
ð13Þ
ð14Þ
Finally, the mean coefficient of friction in UAT can be obtained from the two above equations, as follows:
mUAT ¼
F UATðave,TÞ NUATðave,TÞ
ð15Þ
The proposed model will be completed when the functions f(t) and g(t) are specified. As mentioned earlier, these functions indicate the relation of the normal stress and the contact length with the variation of relative cutting speed, respectively.
Fig. 4. Correlation between the cutting speed and the tool–chip contact length in conventional turning; Al 6061 workpiece, rake angle¼ 01 and feed rate 10 mm/ min.
The functions f(t)and g(t) can be experimentally obtained for specific materials of the workpiece. It should be noted that the function f (t) does not change the profile of the normal stress distribution, as depicted in Fig. 1, in UAT compared with CT, but just changes the magnitudes. It should be noted that the duration of contact between the cutting tool and chip in each ultrasonic vibration cycle is too short for a direct UAT experiment and the instantaneous changes of the contact length and normal stress cannot be traced in a UAT process. On the other hand, it is expected the changes of the contact length and normal stress in UAT during the machining interval to follow a similar trend with respect to the cutting speed as in CT. Therefore, it is justifiable to find empirical relations for the contact length and normal stress in CT and employ them to find f(t) and g(t), as follows. For a workpiece of Al6061, the following relations have been found experimentally for the changes of normal stress and contact length with respect to cutting speed in CT:
s ¼ 161:4935 e0:0088 V
ð16Þ
lc ¼ 1:791 e0:01V
ð17Þ
The way of obtaining these experimental equations are elaborated in the next section (Figs. 4 and 5). From Eq. (16), the variation of normal stress with respect to cutting speed can be considered as an exponential function, as follows: f ðtÞ ¼ n1 en2 ðV tw Þ or f ðtÞ ¼ n1 en2 ð2paf cosð2pf tÞ þ V c Þ
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Table 1 Results of CT experiments; depth of cut 2.25 mm, feed rate 10 mm/min, rake angle¼01, material Al 6061.
Fig. 5. Correlation between the cutting speed and the normal stress in conventional turning; Al 6061 workpiece, rake angle ¼01 and feed rate 10 mm/min.
From Eq. (7) and (16), n1 and n2 can be obtained as follows:
Cutting speed Vc (m/min)
Tool–chip contact length lc (mm)
Normal force in CT, NCT (N)
Friction force in CT, FCT (N)
sCT ¼ NCT =lc b (MPa)
15.198 21.277 27.356 33.435 39.514 48.632 57.751 66.869 72.948 82.067
1.430 1.330 1.132 1.125 1.041 0.787 0.700 0.684 0.591 0.529
515 385 375 255 244 190 135 136 132 95
112 100 109 93 82 65 66 53 52 42
160 129 147 101 104 107 86 88 99 80
f ðT=4Þ ¼ n1 en2 ðV c Þ ¼ 1-n1 ¼ en2 ðV c Þ -f ðtÞ ¼ en2 ð2pafcosð2pf tÞÞ f ðtÞ ¼ en2 ð2paf cosð2pf tÞÞ ¼ e0:0088ð2paf cosð2pf tÞÞ At a ¼6 mm and f¼20 KHz and considering the unit of cutting speed (m/min): 6
f ðtÞ ¼ e0:0088ð2p 610
2000060cosð2pf tÞÞ
¼ e0:3979cosð2p 20000 tÞ
And similarly from Eq. (17) for g(t): 0:4521cosð2p 20000tÞ
gðtÞ ¼ e
:
The proposed model predicts the normal force, the frictional force and the coefficient of friction in UAT on the basis of their magnitudes in CT. According to this mechanistic model, any change in the forces occurs via two mechanisms. First, as the vibration of the cutting tool causes connection and separation between the workpiece and the cutting tool, the normal and friction forces vanish in a portion of each cycle, i.e. during the period of separation. The average forces in a cycle are thus expected to reduce in proportion of t2 t1/T (Eqs. (13) and (14)). This reduction is independent of the workpiece’s and tool’s material. It only depends on vibration of UAT parameters including the vibration amplitude and frequency, and the cutting speed. Second, the normal and friction forces change due to the variation of the relative cutting speed in the period of the contact between the cutting tool and the workpiece. The average forces are calculated from Eqs. (11) and (12); theoretically, the forces may decrease, increase or remain unchanged. By choosing the material of the workpiece and machining condition, the normal and friction forces can be obtained from Eqs. (13) and (14), as mentioned earlier.
3. Experiments Two groups of experiments were carried out using Al 6061 workpieces. In the first group the behavior of the tool–chip contact length and the normal stress were obtained at different cutting speeds (15–82 m/min) in CT, which were subsequently used for developing the time functions. In the second group, the cutting forces and coefficient of friction were measured in UAT at amplitude of 6 mm and frequency of 20 KHz, in order to verify the theoretical results at different cutting speeds (15–40 m/min). It should be noted that the cutting speed in UAT experiments could not exceed its critical value 2paf 45 m=min. The critical speed would be explained later in this paper in Section 4. Tube turning was carried out in order to approximately achieve orthogonal cutting condition. A CNC-TME40 lathe was used for the experiments. A Kistler dynamometer was used to measure the cutting forces. An ultrasonic frequency generator and an ultrasonic transducer (fE20 KHz) were used to generate the vibration. The experiments were carried out at amplitude of 6 mm
Table 2 Results of UAT experiments; depth of cut 2.25 mm, feed rate 10 mm/min, amplitude 6 mm, frequency 20 KHz, material Al 6061. Cutting speed (m/min)
Normal force in UAT (N)
Friction force in UAT (N)
mUAT ¼ F UATðavr,TÞ
15.198 21.277 27.356 33.435 39.514
102 109 128 117 203
31 35 39 44 70
0.304 0.321 0.305 0.376 0.345
=N UATðavr,TÞ
and frequency of 20 KHz. A horn was designed and manufactured to transmit the vibration at a resonance frequency of 20 70.5 KHz to the carbide tool (VBMW160404). The experimental setup is shown in Fig. 2. There are different ways to measure the tool–chip contact length such as painting, coating and microscopic examination of the wear traces. The painting technique was not successful at the common cutting speeds. Instead, a thin layer of aluminum–zinc spray (Galva brite CRC) coating was applied to the cutting tool’s rake face. The coated layer was more stable than the painting so the curled chip could not affect the coating. The coating remained on the tool tip in conventional turning is illustrated in Fig. 3. The results of the first group of experiments are presented in Table 1. The cutting forces were measured by dynamometer in the directions of cutting speed and feed motion. These forces were actually the same as the normal and friction forces as the tool rake angle was zero. From these data, the correlation between the tool–chip contact length and the cutting speed and also the correlation between the normal stress and the cutting speed are illustrated in Figs. 4 and 5, respectively. An exponential curve can best fit the experimental points in each case leading to order of errors considerably lower than other functions. The exponential functions are indicated on the figures. The equations mentioned in Figs.4 and 5 were used for obtaining time functions as described in Section 2. The values of cutting forces measured in UAT (second group of experiments) and their ratio (mUAT ¼ F UATðavr,TÞ =NUATðavr,TÞ ) are presented in Table 2.
4. Results and discussion Based on Eqs. (11)–(15) and the functions obtained for f(t) and g(t), the theoretical correlation between the ratio of the normal and friction forces in UAT to CT, i.e. NUAT(ave,T)/NCT and FUAT(ave,T)/ FCT, versus the vibration amplitude and frequency are obtained as shown in Figs. 6 and 7, respectively. These figures indicate that an
H. Jamshidi, M.J. Nategh / International Journal of Machine Tools & Manufacture 65 (2013) 1–7
increase in the amplitude or frequency leads to the decrease of the force ratio. In other words, with an increase in the vibration amplitude or frequency, the normal and friction forces in UAT decrease compared with CT. The decrease of forces as a result of increase in the amplitude and frequency has also been reported by others [3–6,12]. The coefficient of friction can be calculated from the normal and friction forces. The variation of the ratio of friction coefficient, i.e. mUAT/mCT, versus the vibration amplitude has been shown in Fig. 8. It is evident from this figure that the friction coefficient in UAT is higher than CT. In addition, with an increase in the amplitude, the ratio of the friction coefficients, mUAT/mCT, also increases. In other words, the increase of friction coefficient in UAT compared with CT is more obvious at larger vibration amplitudes.
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The maximum difference between the coefficient of friction in UAT and CT was about 39 percent; in other words, the ratio of friction coefficient in UAT to CT, mUAT/mCT, was about 1.39 when the amplitude of vibration increased from 4 to 10 mm. In Figs. 9 and 10, the friction and normal forces at different cutting speeds obtained by experiments (Table 2) have been compared with the theoretical results, respectively. It can be seen from these figures that there is good agreement between the theoretical and experimental results. It is noteworthy that in UAT the forces increase with an increase in the cutting speed, as is evident from Figs. 9 and 10. This increasing trend of forces is obviously contrary to the commonly decreasing trend in conventional turning. The reason is that the UAT characteristic is dominant here. In fact, the advantages of UAT compared with CT including the lower cutting
Fig. 6. Variation of the ratio of normal and friction forces in UAT to CT vs. amplitude; cutting speed 27.36 m/min, feed rate 10 mm/min, depth of cut 2.25 mm and frequency 20 KHz.
Fig. 9. Comparison between the theoretical and experimental normal forces at different cutting speeds; amplitude 6 mm, feed rate 10 mm/min, depth of cut 2.25 mm.
Fig. 7. Variation of the ratio of normal and friction force in UAT to CT vs. frequency; cutting speed 27.36 m/min, feed rate 10 mm/min, depth of cut 2.25 mm and amplitude 10 mm.
Fig. 8. Correlation between ratio of coefficients of friction vs. amplitude; cutting speed 27.36 m/min, feed rate 10 mm/min, depth of cut 2.25 mm and frequency 20 KHz.
Fig. 10. Comparison between the theoretical and experimental friction forces at different cutting speeds; amplitude 6 mm; feed rate 10 mm/min, and depth of cut 2.25 mm.
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of tool in ultrasonic-vibration assisted turning (UAT). The following conclusions can be drawn from this study:
Fig. 11. Comparison between the friction coefficient in UAT and CT at different cutting speeds; amplitude 6 mm, feed rate 10 mm/min, and depth of cut 2.25 mm.
forces continuously diminish when the cutting speed increases. The values of the cutting forces in UAT approach their CT counterparts with an increasing cutting speed. There is an upper limit to the cutting speed in UAT known as critical speed beyond which the advantages of UAT are lost and the same machining regime would dominate as in CT. The upper limit of the cutting speed in UAT is 2paf. At cutting speeds smaller than the critical value, the increasing trend of the cutting forces is attributable to the increase in the duration of contact time between the cutting tool and the workpiece occurring when the cutting speed increases. The increase of contact time continues into a permanent contact beginning from critical speed and the UAT process virtually changes to CT. At cutting speeds smaller than the critical value, the increase of cutting force due to the increase in contact time overweighs the decrease of the cutting force with increasing cutting speed. The increasing trend of cutting forces in UAT has also been reported in several other works such as [5,6]. The theoretical and experimental results for the coefficients of friction in UAT and CT have been compared in Fig. 11. As is clear from this figure, higher coefficients of friction are encountered in UAT relative to CT. The reduction being witnessed in the cutting forces in UAT relative to CT cannot thus be attributed to a lower friction coefficient as traditionally perceived by some researchers without any theoretical or experimental basis. At the best situation, the coefficient of friction in UAT and CT were taken equal, for example in [16]. This reduction can, however, be attributed to a higher decrease in the normal force compared with the decrease of the frictional force both acting on the tool–chip interface. The higher coefficient of friction in UAT compared with CT would be more evidenced with an increase in the amplitude of the vibration. It is noteworthy that the normal stress, s, decreases with an increase in the cutting speed [1,9,11] whereas the average shear stress, t, does not decrease so much due to its constant sticking friction constituent, and thus the ratio m ¼ t=s shows a noticeable increase in CT in Fig. 11.
5. Conclusion In the present study, a mechanistic model was derived for predicting the normal and frictional forces acting on the rake face
1. The experiments showed that both the tool–chip contact length and the normal stress acting on the tool–chip interface exponentially reduced when the cutting speed increased. Based on these experiments, functions were derived for modeling the variation of the contact length and the normal stress in each cycle of vibration in UAT. 2. According to the proposed model, any change in forces in UAT occurs via the periodic separation of the cutting tool and the workpiece and also variation in the relative cutting speed during the contact time. 3. The proposed model predicts that with an increase in the amplitude and frequency of the vibration, the normal and friction forces reduce. This reduction in UAT was about 19–82 percent for the normal force and 24–76 percent for the friction force acting on the tool–chip interface when the cutting speed and the frequency were 27 m/min and 20 KHz, respectively, and the amplitude increased from 4 to 10 mm. 4. Unlike the conventional turning, both the normal and friction forces acting on the tool–chip interface increase with an increase in the cutting speed in UAT. 5. The proposed model predicts a higher coefficient of friction on the tool–chip interface in UAT compared with CT. The reduction being witnessed in the cutting forces in UAT relative to CT cannot thus be attributed to a lower friction coefficient as traditionally perceived by some researchers without any theoretical or experimental basis. This reduction can, however, be attributed to a higher decrease in the normal force compared with the decrease of the frictional force both acting on the tool–chip interface. The higher coefficient of friction in UAT compared with CT would be more evidenced with an increase in the amplitude of the vibration. The maximum difference between the coefficient of friction in UAT and CT was about 39 percent; in other words, the ratio of friction coefficient in UAT to CT,mUAT =mCT , was about 1.39 when the amplitude of vibration increased from 4 to 10 mm. 6. The results of the proposed model were verified by the experiments. The discrepancies between the mechanistic models and the experimental results were about 9 percent for the normal force and 11 percent for the friction force in UAT. The trends of changes in the parameters were similar both predicted by the model and evidenced in the experiments.
Acknowledgment The authors would like to thank Mr. H. Soleimanimehr and Mr. B. Gholamzadeh for their assistance. References [1] V.P. Astakhov, Tribology of Metal Cutting, first edition, Elsevier, London, 2006. [2] E.M. Trent, P.K. Wright, Metal Cutting, fourth edition, Butterworth-Heinemann, Boston, 2000. [3] D.E. Brehl, T.A. Dow, Review of vibration-assisted machining, Precision Engineering 32 (2008) 153–172. [4] M.J. Nategh, S. Amini, H. Soleimanimehr, Modeling the force, surface roughness and cutting temperature in ultrasonic vibration-assisted turning of Al7075, Advanced Material Research 83–86 (2010) 315–325. [5] N. Ahmed, A.V. Mittofanov, V.I. Babitsky, V.V. Silberchmidt, Analysis of forces in ultrasonically assisted turning, Journal of Sound and Vibration 308 (2007) 845–854. [6] C. Nath, M. Rahman, Effect of machining parameters in ultrasonic vibration cutting, International Journal of Machine Tools and Manufacture 48 (2008) 965–974. [7] C.L. Chou, Wave effects of ultrasonic vibration on machining, Ph.D. Thesis, The Pennsylvania State University, 1994. [8] E.M. Trent, Metal cutting and the tribology of seizure. I. Seizure in metal cutting, Wear 128 (1988) 29–45.
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[9] N.N. Zorev, Interrelationship between shear processes occurring along tool face on shear plane in metal cutting, International Research in Production Engineering, ASME, New York, 1963, pp. 42–49. [10] J.A. Bailey, G. Boothroyd, Critical review of some previous work on the mechanics of the metal cutting process, Production Engineering Conference, ASME, Ohio, 1968, pp. 54–62. [11] P.W. Wallace, G. boothroyd, Tool forces and tool–chip friction in orthogonal machining, Journal of Mechanical Engineering Science 6 (1964) 74–87. [12] S. Amini, H. Soleimanimehr, M.J. Nategh, A. Abudollah, M.H. Sadeghi, FEM analysis of ultrasonic-vibration-assisted turning and the vibratory tool, Journal of Material Processing Technology 201 (2008) 43–47.
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[13] M.Y. Friedman, E. Lenz, Investigation of the tool–chip contact length in metal cutting, International Journal of Machine Tool Design Research 10 (1970) 401–416. [14] J.A. Bailey, Friction in metal machining-mechanical aspects, Wear 31 (1975) 243–275. [15] J.P. Davim, Machining Fundamentals and Recent Advances, Springer, London, 2008. [16] A.V. Mitrofanov, N. Ahmed, V.I. Babitsky, V.V. Silberschmidt, Effect of lubrication and cutting parameters on ultrasonically assisted turning of Inconel 718, Journal of Material Processing Technology 162–163 (2005) 649–654.