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Investigation of the direction of chip motion in diamond turning
Precision Engineering Journal of the International Societies for Precision Engineering and Nanotechnology 25 (2001) 155–164
Investigation of the direction of chip motion in diamond turning Bradley H. Jareda,*, Thomas A. Dowb a
Corning, Inc., Corning, NY, USA Precision Engineering Center, North Carolina State University, Raleigh, NC, USA
b
Abstract Management of the chips generated in diamond turning is often critical since contact between chips and the workpiece can result in superficial damage to the finished surface. Controlling chip motion is not a trivial process as the proper positioning of an oil or an air stream requires an understanding of the dynamics of a diamond turned chip and the machining parameters that affect it. Previous work [1] introduced the chip curvature parameter, , which is useful in predicting chip radius of curvature over a wide range of cutting speeds, depths of cut, tool geometries and workpiece material properties. To control chip motion, however, an understanding of the direction chips leave the tool/workpiece interface must also be obtained. Cutting experiments were performed investigating the influence of cutting speed, depth of cut, feed rate, tool path angle, tool geometry and tool orientation on the directional characteristics of the motion of diamond turned chips. Flow angle measurements obtained during cutting were found to remain within ⫾ 10° of predictions from a simple geometrical model originally proposed for conventional machining. © 2001 Elsevier Science Inc. All rights reserved. Keywords: Diamond turning; Chip geometry; Chip dynamics; Chip control
1. Introduction Modeling and predicting the motion of chips generated in a machining process is not a trivial task. Chip formation involves a complicated interaction of plastic and elastic deformations within a small region known as the shear zone [2,3]. It is the interactions in this small area that ultimately define both the geometry and motion of the chips that are generated. Due to the complexity of chip formation, very few models exist for predicting the direction of chip motion. The simplest model was developed for conventional machining by Colwell [4] and involves drawing a chord between the two extreme points of contact between the tool and the workpiece. The flow angle, , is then predicted using the normal to the chord and a parallel to the uncut workpiece surface, as demonstrated in Figure 1. Colwell performed conventional cutting tests using both round and sharp nose tools with rake angles of 0° and 30°, finding that the model predicted the flow angle within 1–2° of the measured value for depth of cut to crossfeed ratios up to 8. Later work by van Luttervelt demonstrated that Colwell’s
* Corresponding author. Fax: ⫹1-607-974-2925. E-mail address: [email protected] (B.H. Jared).
model performs as well as other, more complex chip flow angle models [5]. Although Colwell’s model is very simple and forms the basis for other flow angle research [6,7], other flow angle models do exist. Stabler [8] developed a model for tools with both a major and a minor cutting edge as the chip flow angle is calculated by summing the vectors of the velocities of the chip across the two cutting edges. In a similar manner, Okushima and Minato [9] generated a model where chip flow angle is obtained by summing the flow angle of small elements along the length of the cutting edge. The flow angle of each element corresponds to the perpendicular to the cutting edge in contact with the element. Other, more complicated models have also been developed [10 –14], but each of these consider oblique cutting geometries and are not necessary for use in the orthogonal machining typically performed in diamond turning. It is important to note that the flow angle of a chip only defines its initial direction of motion. External forces such as gravity, contact with the tool or the workpiece, and/or the presence of an oil or an air stream will alter the trajectory of the chip as it moves away from the tool/workpiece interface. This change in motion is not described by the flow angle. In controlling the motion of diamond turned chips, however, an understanding of initial chip motion is valuable as it can
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Fig. 1. Colwell flow angle model (top view of the tool).
be used to improve the position and direction of oil and/or air streams.
2. Cutting experiments To begin understanding the flow angle of diamond turned chips, cutting experiments were performed on a 292 mm diameter, plated copper workpiece using a Nanoform 600 diamond turning machine. Thread and plunge cut experiments were performed using v-nose tools with included angles of 45° and 90° as the effects of depth of cut, feed rate, cutting speed, tool geometry and orientation, workpiece hardness and tool path angle were all investigated. Video of each of the thread and plunge cuts was obtained using a Costar CV-755 CCD color video camera with an adjustable electronic shutter speed of up to 1/10,000 sec. An Edmund Scientific VZM Model 300 microscopic lens was mounted to the CV-755 camera producing magnifications from 0.75x to 3x with a corresponding field of view from 8 to 2 mm. Lighting was provided by a 150 W fiber optic illuminator aimed at the tool/workpiece interface. Once tests were completed, flow angle measurements were made from digitized images of the chips generated during each cut. All of the images presented in this paper have a magnification on the order of 1–3x as the camera is oriented above the tool, looking down onto the tool face. Crossfeeding of the tool occurs from right to left in each image. Flow angle values in the figures provide the value measured for the chip in that image only. Flow angle data presented in plots, however, represent an average value from up to ten measurements during a single cut.
3. Thread cutting experiments 3.1. Description of a thread cut Thread cutting experiments involved infeeding the tool to the desired depth of cut and then crossfeeding the tool parallel to the workpiece surface at a constant depth of cut.
Fig. 2. Machining parameters for a thread cut (top view of the tool).
Figure 2 illustrates a thread cut by a tool with included angle, , that is oriented to the workpiece surface with the major cutting edge angle, . The feed of the cut is f, while the depth of cut is represented by dc. Excluding the start and finish of the cut when the slides are accelerating and decelerating, the geometry of a chip produced during a thread cut is constant. Thus, in theory, the flow angle of the chips generated in a thread cut should remain constant. 3.2. Prediction of the chip flow angle Initial predictions of the flow angle of chips generated by an overlapping thread cut were made using Colwell’s model. From the geometry of Figure 2,  can be described by the relationship
冢
 ⫽ 90⬚ ⫺ tan⫺1
dc ⫺
冣
f
1 tan f 䡠 tan ␥ dc ⫹ tan 1 tan ␥ ⫹ tan tan ␥ ⫹
(1)
where ␥, the angle between the minor cutting edge of the tool and a perpendicular with the uncut workpiece surface, is given by
␥ ⫽ ⫹ ⫺ 90⬚
(2)
Eq. (1) applies for any feed smaller than the width of the tool at the point where it contacts the uncut surface of the workpiece. If the feed becomes larger than the width of the tool at the uncut surface, a non-overlapping cut occurs and the flow angle should be 90°. Using Eq. (1), a prediction of the variation of chip flow angle with different cutting parameters can be easily established. Increases in either the feed rate or the major cutting edge angle should increase the flow angle of the chips, while increasing either the depth of cut or the included angle of the tool should result in a decrease in the flow angle of the chips.
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157
Fig. 3. Variation of chip flow angle with depth of cut.
3.3. Experimental results The validity of Eq. (1) was examined through a number of experiments involving thread cuts. Both 45° and 90° included angle tools were utilized as tests were performed with major cutting edge angles of 54° and 67.5° for the 45° tool, and 31.5° and 45° for the 90° tool. Feed rates varied from 0.25 to 50 m/rev. A depth of cut of 30.2 m was used for the 45° tool, while depths of 12.5 and 25 m were used for the 90° tool. Thread cuts were performed at cutting speeds of 0.77 and 7.7 m/sec. 3.3.1. Depth of cut. The predicted decrease in chip flow angle with increasing depth of cut is demonstrated in Figure 3 which compares chips from 12.5 and 25 m depths of cut using a 90° tool, a 2.5 m/rev crossfeed and a 45° major cutting edge angle. Figure 3(a) shows the 12.5 m depth of cut chip with a measured flow angle of 69°, while Figure 3(b) shows that the flow angle of the 25 m depth of cut resulted in a chip with a 44° flow angle. In addition to changes in the chip flow angle, Figure 3 also demonstrates changes in the motion of the chips away from the tool/workpiece interface. The 12.5 m depth of cut chip curled towards the workpiece, and can be seen tangled above and below the tool face. The 25 m depth of cut chip, however, moved farther away from the tool/workpiece interface and did not wrap itself around the tool. Doubling the depth of cut from 12.5 to 25 m doubles the area moment of the chip (from 7.7 ⫻ 10⫺12 mm4 to 15.9 ⫻ 10⫺12 mm4), subsequently doubling its stiffness. As a result, the 25 m chip was not as strongly influenced by external forces and followed its initial trajectory farther away from the tool/ workpiece interface. Previous work [1] has shown that increasing the area moment of inertia of the chip produced a
chip with a larger radius of curvature, further inducing its tendency to move away from the tool/workpiece interface. 3.3.2. Feed rate. Opposite to the trend observed with depth of cut, an increase in flow angle was expected for an increase in the feed rate. Figure 4 compares 0.25 and 50 m/rev feeds using a 90° tool, a 25 m depth of cut and a 45° major cutting edge angle. As expected from Eq. (1), the flow angle increased from 60° for the 0.25 m/rev feed to 90° for the 50 m/rev feed. Similar to increasing the depth of cut, Figure 4 shows that increasing the feed rate produced a chip that moved away from the tool/workpiece interface and did not become entangled around the tool. Increasing the feed rate from 0.25 to 50 m/rev produces a large increase in the area moment of inertia (1.6 ⫻ 10⫺14 mm4 to 4.3 ⫻ 10⫺8 mm4). Again, the chip becomes stiffer and develops a larger radius of curvature, leading to the desirable motion away from the workpiece. 3.3.3. Tool included angle. Figure 5 demonstrates the decrease in flow angle observed with increases in the tool included angle as it compares chips generated with a 25 m/rev crossfeed using 45° and 90° v-nose tools. The chip generated with the 45° tool involved a 67.5° major cutting edge angle and a 30.2 m depth of cut, while the cut with the 90° tool used a 45° major cutting edge angle and a 25 m depth of cut. Although the depth of cut differs for the two tools, the width of the tool at the uncut workpiece surface is the same for both tests. As expected from Eq. (1), the flow angle decreased from 71° for the 45° tool (Figure 5(a)) to 61° for the 90° tool (Figure 5(b)). The area moment of inertias of the chips produced by the 45° and the 90° tool are almost identical (1.1 ⫻ 10⫺8 mm4
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Fig. 4. Variation of chip flow angle with feed rate.
and 1.2 ⫻ 10⫺8 mm4 respectively). Therefore, the motion of the chip off of the 45° tool in Figure 5(a) is a result of the smaller surface area of the tool face rather than a change in the stiffness of the chip. 3.3.4. Tool major cutting edge angle. The influence of tool orientation on chip flow is demonstrated in Figure 6 which shows chips generated with a 90° tool, a 25 m depth of cut and a 37.5 m/rev crossfeed rate. The major cutting edge angle is increased from 31.5° to 45° resulting in an increase in the flow angle from 66° to 84°. The similar motion of the two chips away from the tool/workpiece interface is re-
flected in the relatively small change in the area moment of inertia of the two chips (1.8 ⫻ 10⫺8 mm4 to 3.0 ⫻ 10⫺8 mm4). 3.3.5. Cutting speed. Since Eq. (1) describes a purely geometrical relationship for chip flow angle, cutting experiments were also performed to examine how a non-geometrical machining parameter such as cutting speed influences the flow angle of diamond turned chips. Cutting tests were performed using a 90° tool, a major cutting edge angle of 45° and cutting speeds of 0.77 and 7.7 m/sec. The feed rates varied from 0.25 to 50 m/rev with 12.5 and 25 m depths
Fig. 5. Variation of chip flow angle with tool included angle.
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Fig. 6. Variation of chip flow angle with major cutting edge angle.
of cut. Figure 7 compares average measured flow angles with the predictions from Eq. (1) for both cutting speeds and both depths of cut. The predicted values are equal to the measured values along the solid line and the dashed lines
Fig. 7. Measured verses predicted chip flow angle.
provide the boundaries ⫾10° of the predicted values. Error bars represent ⫾ one standard deviation in the measurements. With only two exceptions, flow angle values from the tests fell within ⫾10° of the predicted values. Despite an order of magnitude increase in the cutting speed, no significant variation is observed between the flow angle of the chips generated at 0.77 m/sec and 7.7 m/sec. Thus, it is concluded that the flow angle of chips generated in diamond turning is independent of the cutting speed. Figure 8 compares chip motion at cutting speeds of 0.77 and 7.7 m/sec for a 25 m depth of cut and a feed rate of 2.5 m/rev. In corroboration with the data in Figure 7, the initial direction of motion of the chips does not vary with cutting speed. Differences in the motion of the chips away from the
Fig. 8. Variation of chip flow angle with cutting speed.
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Fig. 9. Variation of chip flow angle with workpiece hardness.
tool/workpiece interface, however, were observed. At a cutting speed of 0.77 m/sec, the chips exhibit side curvature and move off the tool face within the field of view of the camera. At 7.7 m/sec, however, the chip exhibits no side curvature and maintains its initial direction of motion across the entire field of view of the camera. One explanation for such behavior is that the order of magnitude increase in the cutting speed significantly increases the inertia of the chip. Consequently, it is not as strongly influenced by external forces near the cutting zone and moves in a straight path away from the tool/workpiece interface. Previous work demonstrating the increase in chip radius of curvature with increasing cutting speed [1] may also contribute to this behavior. 3.3.6. Hardness. Tests investigating the dependence of flow angle on material hardness were also conducted. Cuts were performed in plated copper with a 90° tool, a major cutting edge angle of 45°, a 25 m depth of cut, a 7.7 m/sec cutting speed and a 50 m/rev crossfeed. Figure 9 shows the chips generated with hardnesses of 125 HV and 238 HV. Despite a 2x difference in hardness, the flow angle is not affected as the chip moves perpendicular to the workpiece surface in both tests. These result and the observed independence of flow angle with cutting speed confirm the usefulness of a geometrical model to estimate the flow angle of chips generated in diamond turning. 3.3.7. Comparison with Colwell’s model. Figure 10 summarizes the flow angle data obtained from all of the tests performed with a cutting speed of 7.7 m/sec. As in Figure 7, the measured flow angle data equal the predicted values along the solid line, while the dashed lines provide the boundaries for data falling within ⫾10° of predicted values. The error bars show ⫾ one standard deviation in the mea-
surements. Although large deviations were observed in some of the tests, a majority of the measured values fall within ⫾10° of the predicted values from Eq. (1). 3.3.8. Flow angle variation during a thread cut. Assuming constant machining conditions, Eq. (1) predicts that the flow angle of a chip will remain constant throughout a thread cut. Cutting experiments, however, demonstrate that the flow angle of a chip will change throughout each cut. For chips with larger area moments of inertia, variations in the flow angle were observed to be small because the stiffness of the chip prevents it from being easily influenced by external forces. Figure 11 provides an example of a stiff chip where the flow angle of chips generated with a 90° tool, a major cutting edge angle of 45°, a 25 m depth of cut, a cutting speed of 7.65 m/sec and a 50 m/rev crossfeed rate varied by only 1° during the cut. Figure 12 shows a less stiff chip generated with a 90° tool and a major cutting edge angle of 45°, but with a smaller 12.5 m depth of cut, a lower cutting speed of 0.77 m/sec and a smaller 12.5 m/rev crossfeed rate. The smaller area moment of inertia (from 4.3 ⫻ 10⫺8 mm4 to 7.4 ⫻ 10⫺10 mm4) means it is significantly less stiff than the chip in Figure 11. As a result, the flow angle varies
Fig. 10. Measured verses predicted chip flow angle.
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161
Fig. 11. Variation of chip flow angle during a thread cut generating a stiff chip.
throughout the cut ⫾10° from its predicted value of 72°. The motion away from the tool/workpiece interface is also considerably different for the less stiff chip as Figure 12 shows the chip falling off different sides of the tool at different times during the cut. Such motion often results in tangling of the chip around the tool, potentially leading to damage to the finished workpiece surface.
Fig. 14. Chip geometries for a plunge cut.
ing and crossfeeding the tool with the tool path angle, , to a final depth of cut, dc, using an infeed of f. 4.2. Prediction of the chip flow angle
4. Plunge cutting experiments 4.1. Description of a plunge cut Plunge cut experiments involved feeding the tool into the workpiece surface, as shown in Figure 13. As with the thread cuts, the tool has an included angle, , and is oriented to the workpiece surface with the major cutting edge angle, . Unlike the thread cuts, plunge cuts involved both infeed-
The prediction of the flow angle of the chip generated during a plunge cut is more complicated than that for a thread cut. Since the geometry of the contact between the tool and the workpiece changes throughout the cut, the flow angle of the chip will also change during the cut. Depending on the orientation and motion of the tool with respect to the workpiece surface, different chip cross-sectional geometries may also be generated, as illustrated in Figure 14. The geometry of the chip generated by a plunge cut will depend on the relationship of the minor cutting edge angle, , to the tool path angle, . For less than , a v-shaped chip is generated (Figure 14(a)) as a flow angle of 90° is predicted throughout the cut. When is equal to (Figure 14(b)), the minor cutting edge of the tool follows the path of the tool into the workpiece surface and the chip flow angle, , is predicted by
 ⫽ 90⬚ ⫺ Fig. 12. Variation of chip flow angle during a thread cut generating a soft chip.
For greater than , Figure 14(c) illustrates the resulting cross-sectional geometry of the chip and the workpiece surface. Using the geometry of Figure 13,  is predicted as
 ⫽ tan⫺1
Fig. 13. Machining parameters for a plunge cut (top view of the tool).
(3)
冤
dc ⫺
f 䡠 cos ␥
冉
冊
1 tan f 䡠 sin ␥ dc ⫹ tan 1 sin 䡠 tan ⫹ tan sin 䡠 tan ⫹
冉
冊
冥
(4)
As with the thread cuts, ␥ is the angle between the minor cutting edge of the tool and a perpendicular to the uncut
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Fig. 15. Decrease in chip flow angle for a 5° tool path angle.
workpiece surface, given by Eq. (2). and are angles not shown in Figure 13, but are represented by the relationships
⫽ 90⬚ ⫺ ␥ ⫺
(5)
⫽ 90⬚ ⫺ ⫺
(6)
4.3. Experimental results As with the thread cutting experiments, a number of plunge cuts were performed to examine the usefulness of a geometric model in the prediction of chip flow angle. The cutting tests were also utilized to examine the dynamic behavior of the chips during a plunge cut as well as the influence of tool path angle on chip motion. Tests involved
plunging the tool to a depth of 80 m using a cutting speed of 7.65 m/sec. As with the thread cuts, 45° and 90° included angle tools were utilized at major cutting edge angles of 54° and 67.5° for the 45° tool and 31.5° and 45° for the 90° tool. Tool path angles were varied from 5 to 90° with feed rates of 0.25 and 5 m/rev. 4.3.1. Tool path angle. From Eq. (4), increases in the tool path angle will increase the flow angle of the chips produced during a plunge cut. A decrease in the variation of the flow angle during the cut will also occur as the tool path angle increases. A comparison of the chips in Figures 15 and 16 demonstrate both of these trends. Both cuts involved the 90° tool, a major cutting edge angle of 45° and a feed rate of 5 m/rev. Figure 15 shows that flow angle of the chips generated with the 5° tool path angle varied by 42°, decreasing
Fig. 16. Approximately constant chip flow angle for a 90° tool path angle.
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163
Fig. 17. Decrease in chip flow angle during a plunge cut.
from 90° to 48°. In contrast, Figure 16 shows the larger flow angles and small variation in the chips generated at the start and finish of a plunge with a 90° tool path angle. 4.3.2. Flow angle variation during a plunge cut. An important distinction between a thread cut and a plunge cut is the variation of the chip geometry throughout the cut. Consequently, in plunge cuts, the flow angle of the chip will be a more dynamic quantity than in a thread cut. Theoretically, the flow angle at the start of a plunge cut will always begin at 90°. As the tool feeds into the workpiece, the flow angle will then decrease, reaching some minimum, min, when the final depth of cut is achieved. Figure 17 shows the chips generated during a plunge cut with a 90° tool, a 45° major cutting edge angle, a 5° tool path angle and a 5 m/rev infeed. When the tool first enters the workpiece surface (Figure 17(a)), the chip is created by a small depth of cut and is not very stiff, piling up around the tool/workpiece interface. As the tool feeds into the workpiece, the flow angle decreases while the cross-section of the chip becomes larger, producing a chip with a greater stiffness. Subsequently, the chip moves away from the tool/workpiece interface at the end of the cut (Figure 17(b)) and does not tangle upon itself or the tool. Changes in flow angle were observed to occur most rapidly near the beginning of the cut. As the tool is fed deeper into the workpiece, the flow angle changes very little. Such behavior is expected from Eq. (4) as an incremental infeed will have a greater impact on the flow angle at small depths of cut than at large depths. 4.3.3. Comparison with Colwell’s model. Figure 18 summarizes flow angle data from the plunge cutting experiments. Again, the solid line illustrates where measured flow angle data would equal its predicted values, while the dashed lines provide the boundaries for data falling within ⫾10° of predicted values. Most of the data values recorded in Figure 18 are within ⫾10° of the predicted values. It is seen in
several of the cuts involving predicted flow angles of 90°, measured values were significantly smaller. Analysis of these cuts reveals that the minor cutting edge angle is less than the tool path angle in all of them. Thus, each of these cuts generated chips with the more complex chip geometry of Figure 14(a) whose motion is not estimated accurately using Colwell’s simple geometric model.
5. Conclusions Experiments were conducted to examine the direction of motion of the thin, lightweight chips generated in diamond turning. Chip flow angle data has shown that use of Colwell’s simple geometrical model is accurate to within ⫾10° for thread cuts and many plunge cuts with a v-nose tool cutting plated copper. Based on this model, diamond turned chips are expected to initially move in a direction opposite the feed direction of the tool. Such behavior was observed in the majority of the cutting tests, even for predicted flow angles of 90° where the chip would seemingly have as good a “chance” in moving one direction as in another. The positive aspect of this behavior is that it is very repeatable and can be expected to occur for a wide range of machining conditions. Unfortunately, the predicted direction of motion is opposite the feed direction, resulting in chips that move
Fig. 18. Measured verses predicted chip flow angle.
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towards the machined surface, the area where contact with the chips is least desired for the surface finish applications typically involved in diamond turning. Another important phenomenon that has been observed in cutting experiments is the correlation between chip stiffness and the tendency of the chip to tangle, either on or around the tool. Chips with a low stiffness become easily entangled near the tool/workpiece interface, while chips with a greater stiffness follow their initial trajectories away from the cutting zone, reducing the chance of workpiece damage. While the geometry of the desired diamond turned surface may often mandate the geometry of the chips generated during the cutting process, it was observed throughout the tests that the greatest problems occurred with small radius, small cross-section chips. This work has demonstrated that to aid in the removal of chips from the tool/ workpiece interface, cutting speed, depth of cut, feed rate, included tool angle and tool path angle should all be maximized, while the cutting edge angle should be minimized.
References [1] Jared B, Dow T. Investigation and prediction of chip geometry in diamond turning. Prec Eng 2000;24:88 –96.
[2] Ernst H, Merchant M. Chip formation, friction, and high quality machined surfaces. Surface treatment of metals. ASM 1941;29:299 – 335. [3] Lee E, Shaffer B. The theory of plasticity applied to a problem of machining. J App Mech 1951;18:405–13. [4] Colwell L. Predicting the angle of chip flow for single-point cutting tools. Trans ASME 1954;76:199 –204. [5] van Luttervelt C. Chip formation in machining operation at small diameter. Ann CIRP 1976;25:71– 6. [6] Jawahir I, van Luttervelt C. Recent developments in chip control research, and applications. Ann CIRP 1993;42(2):659 – 85. [7] Jiang C, Zhang Y, Chi Z. Experimental research of the chip flow direction, and its application to the chip control. Ann CIRP 1984;33: 81– 4. [8] Stabler G. The chip flow law, and its consequences. Proc 5th MTDR 1964:243–51. [9] Okushima K, Minato L. On the behavior of chip in steel cutting. Bull Jap Soc Mech Eng 1959;2(5):58 – 64. [10] Stabler G. The fundamental geometry of cutting tools. Proc Inst Mech Eng 1951:14 –21. [11] Luk W. The direction of chip flow in oblique cutting. Int J Prod Res 1972;10(1):67–76. [12] Usui E, Hirota A, Masuko M. Analytical prediction of 3D cutting process. J Eng Ind 1978:222– 43. [13] Young H, Mathew P, Oxley P. Allowing for nose radius effects in predicting the chip flow direction, and cutting forces in bar turning. Proc Inst Mech Eng 1987;201(C3):213–26. [14] Arsecularatne J, Mathew P, Oxley P. Prediction of chip flow direction, and cutting forces in oblique machining with nose radius tools. Proc Inst Mech Eng 1995;209:305–15.
Investigation of the direction of chip motion in diamond turning Bradley H. Jareda,*, Thomas A. Dowb a
Corning, Inc., Corning, NY, USA Precision Engineering Center, North Carolina State University, Raleigh, NC, USA
b
Abstract Management of the chips generated in diamond turning is often critical since contact between chips and the workpiece can result in superficial damage to the finished surface. Controlling chip motion is not a trivial process as the proper positioning of an oil or an air stream requires an understanding of the dynamics of a diamond turned chip and the machining parameters that affect it. Previous work [1] introduced the chip curvature parameter, , which is useful in predicting chip radius of curvature over a wide range of cutting speeds, depths of cut, tool geometries and workpiece material properties. To control chip motion, however, an understanding of the direction chips leave the tool/workpiece interface must also be obtained. Cutting experiments were performed investigating the influence of cutting speed, depth of cut, feed rate, tool path angle, tool geometry and tool orientation on the directional characteristics of the motion of diamond turned chips. Flow angle measurements obtained during cutting were found to remain within ⫾ 10° of predictions from a simple geometrical model originally proposed for conventional machining. © 2001 Elsevier Science Inc. All rights reserved. Keywords: Diamond turning; Chip geometry; Chip dynamics; Chip control
1. Introduction Modeling and predicting the motion of chips generated in a machining process is not a trivial task. Chip formation involves a complicated interaction of plastic and elastic deformations within a small region known as the shear zone [2,3]. It is the interactions in this small area that ultimately define both the geometry and motion of the chips that are generated. Due to the complexity of chip formation, very few models exist for predicting the direction of chip motion. The simplest model was developed for conventional machining by Colwell [4] and involves drawing a chord between the two extreme points of contact between the tool and the workpiece. The flow angle, , is then predicted using the normal to the chord and a parallel to the uncut workpiece surface, as demonstrated in Figure 1. Colwell performed conventional cutting tests using both round and sharp nose tools with rake angles of 0° and 30°, finding that the model predicted the flow angle within 1–2° of the measured value for depth of cut to crossfeed ratios up to 8. Later work by van Luttervelt demonstrated that Colwell’s
* Corresponding author. Fax: ⫹1-607-974-2925. E-mail address: [email protected] (B.H. Jared).
model performs as well as other, more complex chip flow angle models [5]. Although Colwell’s model is very simple and forms the basis for other flow angle research [6,7], other flow angle models do exist. Stabler [8] developed a model for tools with both a major and a minor cutting edge as the chip flow angle is calculated by summing the vectors of the velocities of the chip across the two cutting edges. In a similar manner, Okushima and Minato [9] generated a model where chip flow angle is obtained by summing the flow angle of small elements along the length of the cutting edge. The flow angle of each element corresponds to the perpendicular to the cutting edge in contact with the element. Other, more complicated models have also been developed [10 –14], but each of these consider oblique cutting geometries and are not necessary for use in the orthogonal machining typically performed in diamond turning. It is important to note that the flow angle of a chip only defines its initial direction of motion. External forces such as gravity, contact with the tool or the workpiece, and/or the presence of an oil or an air stream will alter the trajectory of the chip as it moves away from the tool/workpiece interface. This change in motion is not described by the flow angle. In controlling the motion of diamond turned chips, however, an understanding of initial chip motion is valuable as it can
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Fig. 1. Colwell flow angle model (top view of the tool).
be used to improve the position and direction of oil and/or air streams.
2. Cutting experiments To begin understanding the flow angle of diamond turned chips, cutting experiments were performed on a 292 mm diameter, plated copper workpiece using a Nanoform 600 diamond turning machine. Thread and plunge cut experiments were performed using v-nose tools with included angles of 45° and 90° as the effects of depth of cut, feed rate, cutting speed, tool geometry and orientation, workpiece hardness and tool path angle were all investigated. Video of each of the thread and plunge cuts was obtained using a Costar CV-755 CCD color video camera with an adjustable electronic shutter speed of up to 1/10,000 sec. An Edmund Scientific VZM Model 300 microscopic lens was mounted to the CV-755 camera producing magnifications from 0.75x to 3x with a corresponding field of view from 8 to 2 mm. Lighting was provided by a 150 W fiber optic illuminator aimed at the tool/workpiece interface. Once tests were completed, flow angle measurements were made from digitized images of the chips generated during each cut. All of the images presented in this paper have a magnification on the order of 1–3x as the camera is oriented above the tool, looking down onto the tool face. Crossfeeding of the tool occurs from right to left in each image. Flow angle values in the figures provide the value measured for the chip in that image only. Flow angle data presented in plots, however, represent an average value from up to ten measurements during a single cut.
3. Thread cutting experiments 3.1. Description of a thread cut Thread cutting experiments involved infeeding the tool to the desired depth of cut and then crossfeeding the tool parallel to the workpiece surface at a constant depth of cut.
Fig. 2. Machining parameters for a thread cut (top view of the tool).
Figure 2 illustrates a thread cut by a tool with included angle, , that is oriented to the workpiece surface with the major cutting edge angle, . The feed of the cut is f, while the depth of cut is represented by dc. Excluding the start and finish of the cut when the slides are accelerating and decelerating, the geometry of a chip produced during a thread cut is constant. Thus, in theory, the flow angle of the chips generated in a thread cut should remain constant. 3.2. Prediction of the chip flow angle Initial predictions of the flow angle of chips generated by an overlapping thread cut were made using Colwell’s model. From the geometry of Figure 2,  can be described by the relationship
冢
 ⫽ 90⬚ ⫺ tan⫺1
dc ⫺
冣
f
1 tan f 䡠 tan ␥ dc ⫹ tan 1 tan ␥ ⫹ tan tan ␥ ⫹
(1)
where ␥, the angle between the minor cutting edge of the tool and a perpendicular with the uncut workpiece surface, is given by
␥ ⫽ ⫹ ⫺ 90⬚
(2)
Eq. (1) applies for any feed smaller than the width of the tool at the point where it contacts the uncut surface of the workpiece. If the feed becomes larger than the width of the tool at the uncut surface, a non-overlapping cut occurs and the flow angle should be 90°. Using Eq. (1), a prediction of the variation of chip flow angle with different cutting parameters can be easily established. Increases in either the feed rate or the major cutting edge angle should increase the flow angle of the chips, while increasing either the depth of cut or the included angle of the tool should result in a decrease in the flow angle of the chips.
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157
Fig. 3. Variation of chip flow angle with depth of cut.
3.3. Experimental results The validity of Eq. (1) was examined through a number of experiments involving thread cuts. Both 45° and 90° included angle tools were utilized as tests were performed with major cutting edge angles of 54° and 67.5° for the 45° tool, and 31.5° and 45° for the 90° tool. Feed rates varied from 0.25 to 50 m/rev. A depth of cut of 30.2 m was used for the 45° tool, while depths of 12.5 and 25 m were used for the 90° tool. Thread cuts were performed at cutting speeds of 0.77 and 7.7 m/sec. 3.3.1. Depth of cut. The predicted decrease in chip flow angle with increasing depth of cut is demonstrated in Figure 3 which compares chips from 12.5 and 25 m depths of cut using a 90° tool, a 2.5 m/rev crossfeed and a 45° major cutting edge angle. Figure 3(a) shows the 12.5 m depth of cut chip with a measured flow angle of 69°, while Figure 3(b) shows that the flow angle of the 25 m depth of cut resulted in a chip with a 44° flow angle. In addition to changes in the chip flow angle, Figure 3 also demonstrates changes in the motion of the chips away from the tool/workpiece interface. The 12.5 m depth of cut chip curled towards the workpiece, and can be seen tangled above and below the tool face. The 25 m depth of cut chip, however, moved farther away from the tool/workpiece interface and did not wrap itself around the tool. Doubling the depth of cut from 12.5 to 25 m doubles the area moment of the chip (from 7.7 ⫻ 10⫺12 mm4 to 15.9 ⫻ 10⫺12 mm4), subsequently doubling its stiffness. As a result, the 25 m chip was not as strongly influenced by external forces and followed its initial trajectory farther away from the tool/ workpiece interface. Previous work [1] has shown that increasing the area moment of inertia of the chip produced a
chip with a larger radius of curvature, further inducing its tendency to move away from the tool/workpiece interface. 3.3.2. Feed rate. Opposite to the trend observed with depth of cut, an increase in flow angle was expected for an increase in the feed rate. Figure 4 compares 0.25 and 50 m/rev feeds using a 90° tool, a 25 m depth of cut and a 45° major cutting edge angle. As expected from Eq. (1), the flow angle increased from 60° for the 0.25 m/rev feed to 90° for the 50 m/rev feed. Similar to increasing the depth of cut, Figure 4 shows that increasing the feed rate produced a chip that moved away from the tool/workpiece interface and did not become entangled around the tool. Increasing the feed rate from 0.25 to 50 m/rev produces a large increase in the area moment of inertia (1.6 ⫻ 10⫺14 mm4 to 4.3 ⫻ 10⫺8 mm4). Again, the chip becomes stiffer and develops a larger radius of curvature, leading to the desirable motion away from the workpiece. 3.3.3. Tool included angle. Figure 5 demonstrates the decrease in flow angle observed with increases in the tool included angle as it compares chips generated with a 25 m/rev crossfeed using 45° and 90° v-nose tools. The chip generated with the 45° tool involved a 67.5° major cutting edge angle and a 30.2 m depth of cut, while the cut with the 90° tool used a 45° major cutting edge angle and a 25 m depth of cut. Although the depth of cut differs for the two tools, the width of the tool at the uncut workpiece surface is the same for both tests. As expected from Eq. (1), the flow angle decreased from 71° for the 45° tool (Figure 5(a)) to 61° for the 90° tool (Figure 5(b)). The area moment of inertias of the chips produced by the 45° and the 90° tool are almost identical (1.1 ⫻ 10⫺8 mm4
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Fig. 4. Variation of chip flow angle with feed rate.
and 1.2 ⫻ 10⫺8 mm4 respectively). Therefore, the motion of the chip off of the 45° tool in Figure 5(a) is a result of the smaller surface area of the tool face rather than a change in the stiffness of the chip. 3.3.4. Tool major cutting edge angle. The influence of tool orientation on chip flow is demonstrated in Figure 6 which shows chips generated with a 90° tool, a 25 m depth of cut and a 37.5 m/rev crossfeed rate. The major cutting edge angle is increased from 31.5° to 45° resulting in an increase in the flow angle from 66° to 84°. The similar motion of the two chips away from the tool/workpiece interface is re-
flected in the relatively small change in the area moment of inertia of the two chips (1.8 ⫻ 10⫺8 mm4 to 3.0 ⫻ 10⫺8 mm4). 3.3.5. Cutting speed. Since Eq. (1) describes a purely geometrical relationship for chip flow angle, cutting experiments were also performed to examine how a non-geometrical machining parameter such as cutting speed influences the flow angle of diamond turned chips. Cutting tests were performed using a 90° tool, a major cutting edge angle of 45° and cutting speeds of 0.77 and 7.7 m/sec. The feed rates varied from 0.25 to 50 m/rev with 12.5 and 25 m depths
Fig. 5. Variation of chip flow angle with tool included angle.
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159
Fig. 6. Variation of chip flow angle with major cutting edge angle.
of cut. Figure 7 compares average measured flow angles with the predictions from Eq. (1) for both cutting speeds and both depths of cut. The predicted values are equal to the measured values along the solid line and the dashed lines
Fig. 7. Measured verses predicted chip flow angle.
provide the boundaries ⫾10° of the predicted values. Error bars represent ⫾ one standard deviation in the measurements. With only two exceptions, flow angle values from the tests fell within ⫾10° of the predicted values. Despite an order of magnitude increase in the cutting speed, no significant variation is observed between the flow angle of the chips generated at 0.77 m/sec and 7.7 m/sec. Thus, it is concluded that the flow angle of chips generated in diamond turning is independent of the cutting speed. Figure 8 compares chip motion at cutting speeds of 0.77 and 7.7 m/sec for a 25 m depth of cut and a feed rate of 2.5 m/rev. In corroboration with the data in Figure 7, the initial direction of motion of the chips does not vary with cutting speed. Differences in the motion of the chips away from the
Fig. 8. Variation of chip flow angle with cutting speed.
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Fig. 9. Variation of chip flow angle with workpiece hardness.
tool/workpiece interface, however, were observed. At a cutting speed of 0.77 m/sec, the chips exhibit side curvature and move off the tool face within the field of view of the camera. At 7.7 m/sec, however, the chip exhibits no side curvature and maintains its initial direction of motion across the entire field of view of the camera. One explanation for such behavior is that the order of magnitude increase in the cutting speed significantly increases the inertia of the chip. Consequently, it is not as strongly influenced by external forces near the cutting zone and moves in a straight path away from the tool/workpiece interface. Previous work demonstrating the increase in chip radius of curvature with increasing cutting speed [1] may also contribute to this behavior. 3.3.6. Hardness. Tests investigating the dependence of flow angle on material hardness were also conducted. Cuts were performed in plated copper with a 90° tool, a major cutting edge angle of 45°, a 25 m depth of cut, a 7.7 m/sec cutting speed and a 50 m/rev crossfeed. Figure 9 shows the chips generated with hardnesses of 125 HV and 238 HV. Despite a 2x difference in hardness, the flow angle is not affected as the chip moves perpendicular to the workpiece surface in both tests. These result and the observed independence of flow angle with cutting speed confirm the usefulness of a geometrical model to estimate the flow angle of chips generated in diamond turning. 3.3.7. Comparison with Colwell’s model. Figure 10 summarizes the flow angle data obtained from all of the tests performed with a cutting speed of 7.7 m/sec. As in Figure 7, the measured flow angle data equal the predicted values along the solid line, while the dashed lines provide the boundaries for data falling within ⫾10° of predicted values. The error bars show ⫾ one standard deviation in the mea-
surements. Although large deviations were observed in some of the tests, a majority of the measured values fall within ⫾10° of the predicted values from Eq. (1). 3.3.8. Flow angle variation during a thread cut. Assuming constant machining conditions, Eq. (1) predicts that the flow angle of a chip will remain constant throughout a thread cut. Cutting experiments, however, demonstrate that the flow angle of a chip will change throughout each cut. For chips with larger area moments of inertia, variations in the flow angle were observed to be small because the stiffness of the chip prevents it from being easily influenced by external forces. Figure 11 provides an example of a stiff chip where the flow angle of chips generated with a 90° tool, a major cutting edge angle of 45°, a 25 m depth of cut, a cutting speed of 7.65 m/sec and a 50 m/rev crossfeed rate varied by only 1° during the cut. Figure 12 shows a less stiff chip generated with a 90° tool and a major cutting edge angle of 45°, but with a smaller 12.5 m depth of cut, a lower cutting speed of 0.77 m/sec and a smaller 12.5 m/rev crossfeed rate. The smaller area moment of inertia (from 4.3 ⫻ 10⫺8 mm4 to 7.4 ⫻ 10⫺10 mm4) means it is significantly less stiff than the chip in Figure 11. As a result, the flow angle varies
Fig. 10. Measured verses predicted chip flow angle.
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161
Fig. 11. Variation of chip flow angle during a thread cut generating a stiff chip.
throughout the cut ⫾10° from its predicted value of 72°. The motion away from the tool/workpiece interface is also considerably different for the less stiff chip as Figure 12 shows the chip falling off different sides of the tool at different times during the cut. Such motion often results in tangling of the chip around the tool, potentially leading to damage to the finished workpiece surface.
Fig. 14. Chip geometries for a plunge cut.
ing and crossfeeding the tool with the tool path angle, , to a final depth of cut, dc, using an infeed of f. 4.2. Prediction of the chip flow angle
4. Plunge cutting experiments 4.1. Description of a plunge cut Plunge cut experiments involved feeding the tool into the workpiece surface, as shown in Figure 13. As with the thread cuts, the tool has an included angle, , and is oriented to the workpiece surface with the major cutting edge angle, . Unlike the thread cuts, plunge cuts involved both infeed-
The prediction of the flow angle of the chip generated during a plunge cut is more complicated than that for a thread cut. Since the geometry of the contact between the tool and the workpiece changes throughout the cut, the flow angle of the chip will also change during the cut. Depending on the orientation and motion of the tool with respect to the workpiece surface, different chip cross-sectional geometries may also be generated, as illustrated in Figure 14. The geometry of the chip generated by a plunge cut will depend on the relationship of the minor cutting edge angle, , to the tool path angle, . For less than , a v-shaped chip is generated (Figure 14(a)) as a flow angle of 90° is predicted throughout the cut. When is equal to (Figure 14(b)), the minor cutting edge of the tool follows the path of the tool into the workpiece surface and the chip flow angle, , is predicted by
 ⫽ 90⬚ ⫺ Fig. 12. Variation of chip flow angle during a thread cut generating a soft chip.
For greater than , Figure 14(c) illustrates the resulting cross-sectional geometry of the chip and the workpiece surface. Using the geometry of Figure 13,  is predicted as
 ⫽ tan⫺1
Fig. 13. Machining parameters for a plunge cut (top view of the tool).
(3)
冤
dc ⫺
f 䡠 cos ␥
冉
冊
1 tan f 䡠 sin ␥ dc ⫹ tan 1 sin 䡠 tan ⫹ tan sin 䡠 tan ⫹
冉
冊
冥
(4)
As with the thread cuts, ␥ is the angle between the minor cutting edge of the tool and a perpendicular to the uncut
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Fig. 15. Decrease in chip flow angle for a 5° tool path angle.
workpiece surface, given by Eq. (2). and are angles not shown in Figure 13, but are represented by the relationships
⫽ 90⬚ ⫺ ␥ ⫺
(5)
⫽ 90⬚ ⫺ ⫺
(6)
4.3. Experimental results As with the thread cutting experiments, a number of plunge cuts were performed to examine the usefulness of a geometric model in the prediction of chip flow angle. The cutting tests were also utilized to examine the dynamic behavior of the chips during a plunge cut as well as the influence of tool path angle on chip motion. Tests involved
plunging the tool to a depth of 80 m using a cutting speed of 7.65 m/sec. As with the thread cuts, 45° and 90° included angle tools were utilized at major cutting edge angles of 54° and 67.5° for the 45° tool and 31.5° and 45° for the 90° tool. Tool path angles were varied from 5 to 90° with feed rates of 0.25 and 5 m/rev. 4.3.1. Tool path angle. From Eq. (4), increases in the tool path angle will increase the flow angle of the chips produced during a plunge cut. A decrease in the variation of the flow angle during the cut will also occur as the tool path angle increases. A comparison of the chips in Figures 15 and 16 demonstrate both of these trends. Both cuts involved the 90° tool, a major cutting edge angle of 45° and a feed rate of 5 m/rev. Figure 15 shows that flow angle of the chips generated with the 5° tool path angle varied by 42°, decreasing
Fig. 16. Approximately constant chip flow angle for a 90° tool path angle.
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163
Fig. 17. Decrease in chip flow angle during a plunge cut.
from 90° to 48°. In contrast, Figure 16 shows the larger flow angles and small variation in the chips generated at the start and finish of a plunge with a 90° tool path angle. 4.3.2. Flow angle variation during a plunge cut. An important distinction between a thread cut and a plunge cut is the variation of the chip geometry throughout the cut. Consequently, in plunge cuts, the flow angle of the chip will be a more dynamic quantity than in a thread cut. Theoretically, the flow angle at the start of a plunge cut will always begin at 90°. As the tool feeds into the workpiece, the flow angle will then decrease, reaching some minimum, min, when the final depth of cut is achieved. Figure 17 shows the chips generated during a plunge cut with a 90° tool, a 45° major cutting edge angle, a 5° tool path angle and a 5 m/rev infeed. When the tool first enters the workpiece surface (Figure 17(a)), the chip is created by a small depth of cut and is not very stiff, piling up around the tool/workpiece interface. As the tool feeds into the workpiece, the flow angle decreases while the cross-section of the chip becomes larger, producing a chip with a greater stiffness. Subsequently, the chip moves away from the tool/workpiece interface at the end of the cut (Figure 17(b)) and does not tangle upon itself or the tool. Changes in flow angle were observed to occur most rapidly near the beginning of the cut. As the tool is fed deeper into the workpiece, the flow angle changes very little. Such behavior is expected from Eq. (4) as an incremental infeed will have a greater impact on the flow angle at small depths of cut than at large depths. 4.3.3. Comparison with Colwell’s model. Figure 18 summarizes flow angle data from the plunge cutting experiments. Again, the solid line illustrates where measured flow angle data would equal its predicted values, while the dashed lines provide the boundaries for data falling within ⫾10° of predicted values. Most of the data values recorded in Figure 18 are within ⫾10° of the predicted values. It is seen in
several of the cuts involving predicted flow angles of 90°, measured values were significantly smaller. Analysis of these cuts reveals that the minor cutting edge angle is less than the tool path angle in all of them. Thus, each of these cuts generated chips with the more complex chip geometry of Figure 14(a) whose motion is not estimated accurately using Colwell’s simple geometric model.
5. Conclusions Experiments were conducted to examine the direction of motion of the thin, lightweight chips generated in diamond turning. Chip flow angle data has shown that use of Colwell’s simple geometrical model is accurate to within ⫾10° for thread cuts and many plunge cuts with a v-nose tool cutting plated copper. Based on this model, diamond turned chips are expected to initially move in a direction opposite the feed direction of the tool. Such behavior was observed in the majority of the cutting tests, even for predicted flow angles of 90° where the chip would seemingly have as good a “chance” in moving one direction as in another. The positive aspect of this behavior is that it is very repeatable and can be expected to occur for a wide range of machining conditions. Unfortunately, the predicted direction of motion is opposite the feed direction, resulting in chips that move
Fig. 18. Measured verses predicted chip flow angle.
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towards the machined surface, the area where contact with the chips is least desired for the surface finish applications typically involved in diamond turning. Another important phenomenon that has been observed in cutting experiments is the correlation between chip stiffness and the tendency of the chip to tangle, either on or around the tool. Chips with a low stiffness become easily entangled near the tool/workpiece interface, while chips with a greater stiffness follow their initial trajectories away from the cutting zone, reducing the chance of workpiece damage. While the geometry of the desired diamond turned surface may often mandate the geometry of the chips generated during the cutting process, it was observed throughout the tests that the greatest problems occurred with small radius, small cross-section chips. This work has demonstrated that to aid in the removal of chips from the tool/ workpiece interface, cutting speed, depth of cut, feed rate, included tool angle and tool path angle should all be maximized, while the cutting edge angle should be minimized.
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