PARAMETERS ON CHIP FORMATION PROCESS
4. NUMERICAL RESULTS AND DISCUSSION
4.1. General Characteristics of the Results
First, the general characteristics of the chip formation process in this set of cutting simulations are described. The results presented in this section pertain mainly to the case of cutting with 0 °rake angle tool and feed rate of 0.125 mm/rev. The results of other cases are similar in nature, though different in quantities.
ON THE EFFECTS OF CUTTING PARAMETERS ON CHIP FORMATION 95
- ___ ..., _____ __.. -
Figure 1. Velocity fields in the chip and the workpiece
96 M.R. MOVAHHEDY ET Al.
4.1.1. Material Flow
Figure (I) depicts the distribution of nodal velocity vectors in the cutting region. The streamlines clearly show the flow of material around the tool tip to form the chip and the machined surface. On the lower portion of the tool rake face, the material has relatively small velocity, because the chip sticks to the tool at this area due to existence of very high pressure between the chip and the tool. With reducing pressure further up on the tool, the chip velocity gradually increases in the sliding friction zone, until the chip is separated from the tool surface.
4.1.2. Strain and Strain Rate
Typical distributions of equivalent plastic strain and strain rate in the cutting zone are shown in figures (2a) and (2b). For a sharp edge tool, the tip of the tool is a singular point at which the strain is theoretically infinite, similar to a crack tip. For a tool with a finite edge radius, the strain is expected to reach very high values at the tip, which may be captured in numerical simulation if a sufficiently fine mesh isused in this area. It can be seen in Fig. (2a) that a very large value of strain is attained in the immediate neighborhood of the tip, which rapidly reduces to much smaller values at the back of the chip. The average equivalent plastic strain on the shear plane is around 2.5, whereas the average strain predicted by shear plane theory for a sharp tool gives a value of 1.75 based on experimentally obtained shear angle. The strain is also very high on the rake face where the highly pressurized friction between the tool and the chip, assisted by thermal softening of the material, causes further straining in the secondary deformation zone. Also evident in the figure is the high magnitude of strain on the machined surface, which is the result of the interaction between the edge of the tool and the workpiece at the tertiary deformation zone. The edge radius of tool on the flank side acts as a tool with a large negative rake angle, ploughing the material before it leaves the tool surface.
Similar pattern is seen in the distribution of equivalent plastic strain rate in Fig. (2b). As expected, high values of strain rate are found in the primary and secondary deformation zones. The strain rate reaches its peak in the immediate neighborhood of the tool tip, where it has a magnitude of order 1 OS sec-1 for the cutting speed of 150 m/min. Such high rate at this point is due to the combination of cutting action of the tool and ploughing action of the tool flank. The strain rate is also high on the rake face suggesting substantial plastic straining of material in the area of sticking friction on the rake. The strain rate contour provides an indication of the size of the two deformation zones. On the other hand, there exists a high gradient of strain rate across the thickness of chip, as the strain rate decreases substantially toward the back of the chip. The profile of equivalent plastic strain rate on the primary shear plane is plotted in Fig. (3a) for two cutting speeds. As expected, the magnitude of strain rate is a strong function of the cutting speed, such that doubling the speed almost doubles the strain rate.
ON THE EFFECTS OF CUTTING PARAMETERS ON CHIP FORMATION 97
(c) Temperature distribution (d) Effective stress contour
Figure 2. Contours of distribution of solution variables in the cutting zones .
98 M.R. MOV AHHEDY ET AL.
2.0E+-05 800
-+-V=150 rnlrnin ii'
1.5E+05 0. 700
u -a-V =300 rnlrnin !.
GI tll
!!? tll
~ GI ...
.!! 1.0E-+-05 .... 600
"'
/}. ...
l'G
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en 5. OE+-04 ,( 500
~ l'G -+--V=150 m/mln
-a-V=300 m/mln
O.OE+OO 400
0 0.25 0.5 0.75
(b) 0 0.25 0.5 0.75 (a) Normalized llstance, x/Ls Normalized llstance, x/Ls
Figure 3. Distribution of(a) equivalent plastic strain rate, and (b) maximum shear stress on the shear plane.
L~ is the len~h of shear plane.
4. 1. 3. Temperature Distribution
The distribution of temperature within the chip, workpiece, and cutting tool is shown in Fig.
(2c ). The temperature reaches its highest values on the rake face. The high temperature at the primary deformation zone is mainly attributed to severe plastic deformation there. At the tip of the tool, temperature reaches a very high value, around 630 'C in the case shown. As the chip moves higher on the rake face, the temperature is further increased due to the combined effects of friction and additional plastic straining in the secondary deformation zone, until it reaches its peak above the middle of the contact zone. It then decreases as the chip moves toward the point of separation. The location of the peak seems to be related to the point of transformation of sticking friction into sliding condition. The above trends appear to conform to the experimental observations.7 A large temperature difference of the order of a few hundred degrees is observed across the thickness of the chip, which seems to be the direct result of high strain gradient. Figure (4a) shows the profile of temperature on the shear plane for two different cutting speeds. It is seen that temperature drops very quickly on this plane toward the back of the chip. The strong dependence of temperature on the cutting speed is also evident in the figure. This is because as the speed increases, adiabatic thermal conditions prevail, resulting in a larger temperature gradient across the chip. The temperature profile on the rake face is plotted in Fig. (4b), which shows its peak on the rake face, depending on the cutting speed. In the contours of Fig. (2c), the distribution of temperature in the tool is also
ON THE EFFECTS OF CUTTING PARAMETERS ON CHIP FORMATION 99
shown. There is a large heat flow into the tool, which, in combination with friction, raises the temperature along its rake face to the same level as that of the chip.
-+--->---< -G-- V=300 m'min -e-V=150 m'min
0.25 0.5 0.75 x/Ls
900 - - - -
e--V=300 m'min -a-V=150 m'rrin 500-l---'==;::====;====::::;:::=----__;
(b) 0 0.25 0.5 0.75 x/Lc
Figure 4. Temperature distribution on (a) the shear plane, (b) chip-tool interface. Ls and Le are length of shear plane and contact length, respectively.
4.1. 4. Effective Stress
Figure (2d) shows the distribution of effective stress in the chip and the workpiece. Large stress values are found in the primary and secondary deformation zones. The highest stress values occur at the primary deformation zone, and the stresses on the rake face are substantially smaller. This is due to the fact that the stress is a function of combined effects of strain, strain rate and temperature, and hardening effects of strain and strain rate compete with softening effects of temperature rise in the deformation zone. Although both strain and strain rate are high on the rake face, the large temperature rise seems to dominate the other factors on the rake face, resulting in considerable softening of the material and thus, reduction of stress values. On the other hand, the temperature on the free surface of the chip is significantly lower, and the effects of relatively large strain and strain rate increase the effective stress of the material in that region. The distribution of maximum shear stress on the shear plane is shown in figure (3b) for two cutting speeds. The typical value of average shear stress at the primary shear zone for the given material is about 650 MPa from simulations, compared to a value of around 700 MPa predicted in Childs, et al.5 based on shear plane theory. As the chip moves toward separation from the tool rake face, it is gradually unloaded and the stress reduces until it vanishes at the point of separation.
100 M.R. MOV AHHEDY ET AL.
4.1. 5. Contact Stresses on the Rake Face
In reference 5 , the distribution of nonnal and frictional contact stresses on the rake face is measured by split tool tests for the case of cutting with 0° rake angle, feed rate of 0.2 mm and cutting speed of JOO m/min. For the purpose of comparison, similar cutting conditions are simulated and the distribution of stresses on the rake face are reported in Fig. (5) along with experimental results. It is seen that the measured and predicted trends of both nonnal and frictional stresses on the rake face are quite similar. However, there are some differences between the values of stresses, especially the normal stress, on the rake face. The differences may be partially attributed to the approximations involved in material and frictional models.
The predicted normal stresses reduce at a more monotonic pace than the measured values.
The predicted normal and friction stress distributions are somewhat similar to the distribution suggested by Barrow, et al.8 Temperature distribution on the rake face is also shown in figure (5).
-1600 .. ll.
~1200 .. -+-El<perirrent
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• 800
ii I§ 400 z 0 0
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~:~~• 600 I + - - - = - == . - - - t
I ~E +-- IF"" - ~ ---=--.=-.... ====~---- --~-~---1
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L/Lc
Figure 5. Distribution of normal and frictional stresses and temperature on the shear plane for cutting conditions given in the text in comparison with experimental data'.
ON mE EFFECTS OF CUTTING PARAMETERS ON CHIP FORMATION 101 4. 1.6. Cutting and Thrust Forces
The predicted cuttin§ and thrust forces under various cutting conditions are compared with experimental results in figures (6), (8) and (9). In general, good agreement between simulated and measured forces is observed, considering the many simplifying assumptions which have to be made in numerical analysis (frictional conditions, material model) as well as in extracting orthogonal cutting forces from turning operation in the above experiments. The predicted cutting forces are in general larger than the experimental values, while the predicted thrust forces are lower. One contributing factor might be the size of edge radius assumed in the simulation, since this parameter is not specified in reference 5. The magnitude of thrust force is also strongly affected by the coefficient of friction.
4.2. Influence of Cutting Conditions on Process Variables 4. 2. I. Effects of Rake Angle
Three different rake angles are used to study the effect of rake angle on the chip formation process. Figure (6a) depicts the trends of changes in cutting and thrust forces with change in rake angle. It can be seen that the forces on the rake face are slightly decreased at higher rake angles, which is similar to the trend for experimental cutting forces. The decrease in forces at higher rake angle can be attributed to the fact that as the rake angle increases, the chip remains on the rake of the tool for a shorter length, and the curling of the chip occurs faster and with a smaller curl radius.
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Figure 6. The effect of rake angle on cutting and thrust forces, shear angle temperature on the rake race.
102 M.R. MOV AHHEDY ET AL.
Figure (7) compares the configuration and contact length of the chip after same cutting length for different rake angles. The contact lengths are 0. 51, 0. 40, and 0. 36 mm for 0 ~ 6 ~ and 12 ° rake angles, respectively. The effects of rake angle on shear angle is demonstrated in figure (6b), which shows that the shear angle has a rising trend with the rising rake angle, similar to
Figure 7, Contact length and chip curling for 0°, 6°, and 12° rake angles, from left to right, respectively.
Temperature contours are also shown in the figure.
what is obtained from experiment. However, the predicted shear angles are higher than their experimental counterparts at low cutting speed, but they are closer in the case of higher cutting speed. Also shown in figure (6b) is the predicted change in maximum temperature on the rake fitce versus the rake angle.
4.2.2. Influence of Cutting Speed
Two different cutting speeds have been simulated for each combination of rake angle and feed rate. Figure (8a) shows the effect of cutting speed on the cutting and thrust forces in each case, in comparison to the experimentally obtained forces. It is seen that the forces slightly decrease with increasing the cutting speed. Same trend is also observed in experimental results, with some exceptions. Figure (8b) shows the predicted and experimental shear angles versus cutting speed. The experimental shear angles increase markedly when cutting speed is increased from 150 mlmin to 225 mlmin, but there is less change for the speed of 300 mlmin.
In contrast, the difference between predicted shear angles at different speeds are smaller, although they have the same rising trend. The cutting speed has a profound effect on the
ON THE EFFECTS OF CUTTING PARAMETERS ON CHIP FORMATION 103 maximwn temperatw-e in the chip, as shown in the figw-e. As explained earlier, prevailing of adiabatic thermal conditions at higher speed is responsible for increase in local temperatw-es and larger gradient of temperatw-e across the chip thickness. This, in tw-n, increases the softening of the material on the rake fuce, resulting in lower magnitudes of stress on the tool, which seems to be the reason for lower cutting forces at higher speed. Expectedly, the most profound effect of cutting speed is seen in the magnitude of strain rate in the cutting zone, such that it is essentially proportional to the cutting speed.
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(a) Cutting Speed (m/min) (b) Cutting Speed (m/mln) Figure 8: The effect of cutting speed on forces, shear angle and temperature.
4. 2. 3. Influence of Feed Rate
Two different feed rates of 0. I 25 and 0.254 mm are simulated. As expected, increasing the feed rate results in higher forces, simply because there is more material to remove.
Comparing the forces at different feed rates in Fig. (9a) shows that the forces are almost doubled with doubling the feed rate. The same trend is seen for the experimental forces. The predicted and experimental shear angles are plotted in Fig. (9b) as a function of feed rate.
The shear angle clearly increases at higher feed rates in both simulation and experiment.
However, the predicted shear angles are higher than the experimental ones. The predicted maximwn temperatw-e versus feed rate is also plotted in the above figure, which shows that the feed rate has little effect on the temperatw-e in the chip. The shape of the chip is also affected by the feed rate, because the contact length increases with the increase in feed rate, and the cw-I radius becomes larger.
104
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- Measured
~ ---Predicted . _ ã I
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M.R. MOV AHHEDY ET AL.
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500 E :I
ã;;: E 400 ra :::!:
300 + - - - + 200
0.1 0.2 0.3
Feed Rate (mm/rev)
Figure 9: The effect of feed rate on forces, shear angle and temperature
ON THE EFFECTS OF CUTTING PARAMETERS ON CHIP FORMATION 105
CONCLUSIONS
Arbitrary Lagrangian-Eulerian finite element formulation is used to study the effects of cutting condition; rake angle, cutting speed and feed rate, on the chip formation in orthogonal metal cutting process. The results of simulation are compared with experimental results obtained tmder similar cutting conditions, which show fairly good agreement in most cases.
This study confirms the applicability of the ALE formulation in providing a realistic representation of the cutting process and is hoped to pave the way for more comprehensive models that are of practical values for machining industries.
REFERENCES
l. Movahhedy, M.R., Gadala, M.S. and Altintas, Y., 2000, "Simulation of Orthogonal Metal Cutting Process Using Arbitrary Lagrangian-Eulerian Finite Element Method", Journal of Materials Processing Technology, 103, pp. 267-275.
2. Movahhedy, M.R., Gadala, M. S. and Altintas, Y., 2000, "'FE Modeling of Chip Formation in Orthogonal Metal Cutting Process: An ALE Approach'', Machining Science and Technology, 4, pp. 15-47.
3. Movahhedy, M.R., Altintas, Y. and Gadala, M. S., 2000, "'Numerical Analysis of Metal Cutting with Chamfered and Blunt Edge Tools", Submitted for publication in Journal of Mamifacturing Science and Engineering.
4. Movahhedy, M. , 2000, "ALE Simulation of Chip Formation in Orthogonal Metal Cutting Process'', PhD Dissertations, The University of British Columbia, Canada.
5. Childs, T.H.C. and Maekawa, K., 1990," Computer Aided Simulation and Experimental Studies of Chip Flow and Tool Wear in Turning Low Alloy Steels by Cemented Carbide Tools", Wear, 139, pp. 235-250.
6. Usui, E. and Shirakashi, T., 1982, "Mechanics of Machining - From Descriptive to Predictive Theory", On the art a/Cutting Metals, 75 Years Later, ASME-PED, 7, pp. 13-35.
7. Oxley, P.L.B., 1989, Mechanics of Machining- An Analytical Approach to Assessing Machinabillty, Ellis- Horwood Limited.
8. Barrow, G., Graham, W., Kurimoto, T., and Leong, Y.F., 1982, "Determination of Rake Face Stress Distribution in Orthogonal Cutting", Int. Journal of Machine Tool Design and Research, 22, pp. 75-85.
Jean Francois Molinari*
1. INTRODUCTION