Chip Formation in the Process of Non-Free Cutting of Ductile Metals
Abstract Generated abstract
This paper examines chip formation in non-free cutting of ductile metals when two cutting edges act and the tool tip included angle is 90 degrees or less, a case not adequately described by earlier schemes based on independent action of the main and auxiliary edges. Experiments on Armco iron using rapid tool withdrawal, chip-root photography, transverse chip sections, and polished sections show that chip thickness, shear direction, and chip shrinkage vary along the main cutting edge. The authors propose that the shear surface in this case is a closed helical surface and relate transverse chip shape to the local shear angle, offering a less laborious way to infer shear-surface geometry. The resulting scheme explains chip flow and curling on the rake face and suggests implications for controlling machined-surface quality.
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Chip Formation in the Process of Non-Free Cutting of Ductile Metals
G. L. Kufarev, K. B. Okenov
(Presented by the scientific seminar of the Department of Machine Tools and Metal Cutting)
All the main types of machining of metals by cutting reproduce, in most cases, the process of non-free cutting, i.e., a process in which two or several cutting edges take part.
The scheme of chip formation and the regularities of the process of free cutting have by now been developed in sufficient detail [7]. As for the features of the process of non-free cutting, few have investigated them [1, 2, 3, 4, 5, 6], and especially in the period when the theory of force cutting was being developed, characterized by a small ratio of the width of the removed layer to its thickness. At the same time, experience shows that a correct conception of the scheme of chip formation in the process of non-free cutting makes it possible actively to regulate the process of chip curling and, to a considerable extent, to determine not only the roughness of the machined surface, but also the degree and depth of its plastic deformation arising in the process of chip removal.
The existing schemes of the chip-formation process have been created on the basis of the law of independence of the action of forces on the main and auxiliary cutting edges and assume the existence of a metal-shear surface, complex in form, which copies in a section parallel to the principal plane the contour line of the cutting edges of the tool. Investigations carried out in recent years in the metal-cutting laboratory of the Tomsk Polytechnic Institute make it possible to say that these schemes are valid, to a greater or lesser degree, when working with a tool whose included angle at the tip is \(\varepsilon > 90^\circ\). The process of chip formation proceeds quite differently if the included angle of the tool tip is \(\varepsilon \leq 90^\circ\). It is precisely this case, which is also widespread in machine-building practice, that is analyzed in the present work.
The investigations were carried out in machining various materials, but their results are illustrated by the example of cutting Armco iron with a tool fitted with a T15K6 hard-alloy insert and having the following geometrical parameters: rake angle \(\gamma = 10^\circ\), inclination angle of the main cutting edge \(\lambda = 0\), principal plan angle \(\varphi = 90^\circ\), auxiliary plan angle \(\varphi_1 = 6^\circ\), the main and auxiliary clearance angles equal, respectively, to \(\alpha = 8^\circ\) and \(\alpha_1 = 6^\circ\), and the tool-tip radius \(r = 0\).
Cutting in the series of experiments described was carried out at a speed of \(V = 80\ \text{m/min}\), which ensured the absence of a built-up edge for the various combinations of thickness and width of the removed layer given in Table 1.
Thus, in this series of experiments, cutting was carried out while removing forward \((b/a > 1)\), reverse \((b/a < 1)\), and equal-sided \((b/a = 1)\) chips.
During the experiments the cutter was mounted in a special fixture that made it possible to withdraw it instantaneously from under the chip, thereby obtaining an undistorted zone of chip formation (the chip root). After each experiment:
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The average chip shrinkage along the length was measured by the weighing method;
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The chip root was photographed from the side of the rake face of the cutter;
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A polished section of the chip cross section was prepared in a plane perpendicular to the direction of its flow;
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Several polished sections of the chip root were prepared in sections parallel to the main cutting plane;
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A polished section of the chip root was prepared in a section parallel to the auxiliary cutting plane.
Table 1
| Experiment no. | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| \(S = a\) | 0.36 | 0.73 | 1.5 | 1.5 | 1.5 |
| \(t = b\) | 1.5 | 1.5 | 1.5 | 0.73 | 0.36 |
| \(\dfrac{b}{a}\) | 4.17 | 2.06 | 1.00 | 0.486 | 0.240 |
Fig. 1
As an illustration, Fig. 1 shows the results of processing the chip root from experiment no. 2. In Fig. 1, a, b, and c show microsections of the chip root in sections parallel to the main cutting plane and located at distances from the free surface of the chip equal, respectively, to 0.15, 0.45, and 0.75 mm. Figure 1, d presents an image of the chip root in a section parallel to the auxiliary cutting plane.
Figure 2 presents photographs of transverse sections of chips and of chip roots from the side of the rake face of the cutter, obtained in this series of experiments. Processing and analysis of information obtained from several similar series of experiments, performed on different materials and at different cutting speeds, made it possible to establish a number of features of the chip-formation process in non-free cutting with a cutter with \(\varepsilon \leq 90^\circ\):
- The chip thickness along the main cutting edge is variable. Its variability is the greater, the smaller the ratio \(b/a\) for forward chips and the larger this ratio for reverse chips. The greatest—
the chip has the greatest thickness at the free surface and the least at the tool tip. The chip thickness at the tool tip is different from zero and has the greater value, the greater the thickness of the layer being cut.
- The angle \(\Phi\), which determines the direction of shear in different sections of the chip-formation zone, is different (Fig. 1, a, b, c). It increases from the free surface of the chip toward the tool tip. Thus,
Fig. 2
the shear surface is represented as a closed helical surface whose axis is the cutting edge \(AO\) (Fig. 3), and whose generating line is the straight line \(AB\).
- The chip shrinkage along the largest (main) cutting edge is variable and can be determined either from the corresponding section of the chip root, or as the ratio of the thickness measured on the transverse section of the chip itself (Fig. 2) to the thickness of the layer being cut, as illustrated by the data in Table 2.
Table 2
| Parameter determined | Section I—I | Section II—II | Section III—III |
|---|---|---|---|
| Distance from the free surface of the chip, in mm | 0.15 | 0.45 | 0.75 |
| Angle \(\Phi\) in the section, determined from Fig. 1, a, b, c | \(24^\circ\) | \(33^\circ\) | \(45^\circ\) |
| Chip thickness, determined from Fig. 2 (item 2), in mm | 1.82 | 1.70 | 0.88 |
| Chip shrinkage \(\xi = \dfrac{a_1}{a}\) | 2.43 | 1.6 | 1.2 |
| Chip shrinkage \(\xi = \dfrac{\cos \Phi - \gamma}{\sin \Phi}\) | 2.35 | 1.67 | 1.11 |
This circumstance makes it possible, subsequently, from the shape of the transverse section of the chip, to determine the shape of the shear surface (the angle \(\Phi\) in any section) without resorting to analysis of polished sections of the chip root in different sections, the preparation of which is a laborious operation.
Fig. 3.
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As follows from Fig. 1, e, the angle determining the direction of shear in a section parallel to the auxiliary cutting plane is equal to zero. This means that here the shear occurs in a plane perpendicular to the main cutting edge and passing through the auxiliary cutting edge.
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In the region of contact between the chip and the tool, within the feed, the direction of chip flow is perpendicular to the main cutting edge. Confirmation of this is provided by the depiction of the chip root in Fig. 1, d, as well as by the fact that the angle between the free lateral surface of the chip and its near-tool surface is equal to 90° (see angle BAF in Fig. 3 and the chip sections in Fig. 2).
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During subsequent motion of the chip, the variability of its upsetting along the cutting edge and, as a consequence of this, the different velocities of motion of different points of the chip along its width \((V_E > V_A)\), lead to curling of the chip in the plane of the rake face of the tool. In this case, the velocity of motion of different chip sections along the cutting edge is determined by the known relation [8]
\[ V_i = V \frac{\sin \Phi_i}{\cos(\Phi - \gamma)}, \]
where \(V_i\) is the cutting speed,
\(\Phi_i\) is the angle determining the position of the conditional shear plane in the chip section of interest.
- The radius of chip curling in the plane of the rake face of the tool is determined not only by the variability of the angle \(\Phi\) along the cutting edge, but also depends on the coefficient of friction of the chip on the tool and the axial moment of resistance of the chip.
The conclusions drawn on the basis of the investigation carried out made it possible to create a fundamentally new scheme of chip formation in non-free cutting both with straight chips (Fig. 3, a) and with reverse chips (Fig. 3, b). The proposed scheme makes it possible to approach the problem of the quality of the machined surface in a new way.
The small size of the article does not allow a detailed description of the process of transition of a straight chip into a reverse chip, which turns out to be very complex, since it depends above all on the combination of rake angles on the main and auxiliary cutting edges.
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