KINEMATIC FEATURES OF THE PROCESS OF FORMATION OF ELEMENTAL CHIPS IN METAL CUTTING

V. I. Livshits

(Presented by the scientific seminar of the departments of machine tools and metal cutting and of mechanical-engineering technology)

Many difficult-to-machine steels, when machined by cutting, produce elemental chips. The cutting process during the formation of elemental chips has a sharply pronounced dynamic character, whose effects are experienced by the entire MTFT system. Therefore, the study of the complex of questions concerning the kinematic, dynamic, and stress–strain states in the cutting zone during the formation of elemental chips is of not only theoretical but also practical interest.

The investigations were performed on chip roots obtained in free planing of steel 45G17Yu3Kh at a speed \(V_{\text{cut}} = 17.5\ \text{m/min}\). The dimensions of the cut were: \(a = 0.85 \div 1.1\ \text{mm}\); \(b = 3.0 \div 3.7\ \text{mm}\). The tool was a plate of VK8 hard alloy with the following geometry: \(\gamma = 8^\circ\), \(\alpha = 7^\circ\), land on the blade: \(\gamma_{\phi} = -10^\circ\), \(f = 0.25 \div 0.30\ \text{mm}\). The experiments were carried out on a transverse-planing machine, model 7M37. The cutting process was stopped in order to obtain the chip root by means of a special device ensuring high quality of the chip root of difficult-to-machine materials.

Specimens of steel 45G17Yu3Kh were made in the form of bars, on the upper plane of which rectangular ribs of width \(b\) were cut. On the lateral sides of the bars a square grid with a base of \(0.25\ \text{mm}\) was applied. In all, about 20 roots were obtained, recording various stages of formation of a chip element. Then the lateral surface of the roots with the deformed grid was photographed under a “BIM” microscope with a “Start” camera, and the negatives obtained were processed on a BP projector. As a result, the total magnification of the root image was \(44^*\).

From all the roots obtained, 10 specimens were selected that most clearly represented the various stages of formation of a chip element and were arranged in sequential order. The arrangement by stages was carried out as follows. One of the vertical grid lines (the 24th, if counted from the front face of the cutter to the left) was taken as the origin for the horizontal coordinates. The machined surface was taken as the origin for the vertical coordinates. The point \(O\) of intersection of these origins was taken as the coordinate origin, from which two coordinate axes \(X\) and \(Y\), associated with the specimen fixed immovably on the machine table, were drawn. The chip roots

were arranged in order of decreasing distance from the origin of coordinates to the tool tip. To check the obtained arrangement of the roots by stages, other features were also considered (the length of the contact area of the chip with the tool, the height of the element, the shape of the upper boundary of the element, etc.), confirming the correctness of the adopted sequence of stages in the formation of the chip element.

Then the time \(t\) was calculated during which the tool traveled the path from the initial stage to each of the intermediate ones. To determine the displacements, velocities, and accelerations of points in the chip-formation zone, Lagrangian and Eulerian coordinates were used. The origins of both coordinate systems were combined at point \(O\) of the grid. For all grid nodes at each stage of formation of the element, the Eulerian coordinates \(x\) and \(y\) were found from the distorted-grid pattern. From these data, graphical laws of motion of the grid nodes were obtained—the functions \(x=f(t)\) and \(y=f(t)\). By graphical differentiation of these functions, their first and second derivatives were found—the functions \(V_x=f(t)\), \(a_x=f(t)\) for the coordinate \(x\), and \(V_y=f(t)\), \(a_y=f(t)\) for the coordinate \(y\). An assessment of the accuracy of differentiation showed satisfactory agreement between the velocity values obtained graphically and the initial experimental data.

Fig. 1

Analysis of the obtained functions showed that the closer the points of the chip-formation zone are located to the tool tip, the more intense is the decrease in the function \(x=f(t)\) as \(t\) increases (Fig. 1, a). The maximum values of the velocity \(V_x\) are close to the velocity \(V_{\text{cut}}\). The maximum absolute value of the accelerations \(a_x\) reaches \(200\ \text{m}/\text{s}^2\). The most intense increase in the function \(y=f(t)\) as \(t\) increases (Fig. 1, b) is observed for points located near the upper boundary of the chip element. About half of all 25 obtained functions \(y=f(t)\) have a minimum in the first stages of formation of the chip element (Fig. 1, b). Some functions \(y=f(t)\) have a maximum before the last stage of formation of the chip element (Fig. 1, c). The maximum values of the velocity \(V_y\) reach \(0.75 V_{\text{cut}}\) in the positive and negative directions. The maximum absolute value of the accelerations \(a_y\) reaches \(350\ \text{m}/\text{s}^2\).

The most interesting result of the experiment is the extremal character of the function \(y=f(t)\) in the first stages of formation of the chip element, indicating that at the beginning of formation of the chip element the deformation along the \(y\)-axis of the material in the chip-formation zone is directed “into the workpiece,” toward the cutting plane, and only after some time does the deformation change sign and proceed upward from the cutting plane.

The presumed reason for the detected feature of the process of formation of the chip element is the following. The rake face

of the cutter just before the very fracture of the element, when a crack has already formed along some part of the length of the slip line, acts on the material behind the slip surface not directly, but through the half-separated chip element. This action leads to a certain deformation of the material behind the slip surface “into the workpiece.” Thus arise the maxima of the functions \(y=f(t)\) (Fig. 1, c). Such functions are characteristic of the points first involved in the process of formation of the next element.

Further, after separation of the element, the action on the material is exerted directly by the growing contact area of the front face of the tool. In this case the material in front of the cutter tip, already having some deformation “into the workpiece,” continues to deform in the same direction, like a rod having low longitudinal stability and having initially received a small downward deflection (Fig. 1 b).

Then, as the chip element is formed, separation of the layers of material in the cutting zone occurs: some of the layers go under the rear face of the tool, while the remaining layers enter the front face of the cutter. Here, under the influence of the advance of the cutter and of the considerable friction of the chip against the cutter, material accumulates, which leads to the appearance of deformation of the material of the cutting zone upward from the cutting plane. This deformation first leads to a decrease and disappearance of the downward deflection of the horizontal grid lines, and then to the appearance in them of an upward deflection. This also explains the minima of the functions \(y=f(t)\).

The nodes of the grid that first found themselves inside the volume of the future chip element are the first to be involved in the described process. Those nodes which, at the end of element formation, turn out to be near the slip line and near the outer boundary of the element are the last to be involved in this process, or are not involved at all.

Of considerable interest is the question of whether the future slip plane of the chip element is characterized by any kinematic features during the process of element formation. With respect to continuous chips, V. I. Sadchikov [1] showed that the function \(V'_x=f(t)\), where \(V'_x\) is the component of the velocity of points in the cutting zone directed along the shear plane, undergoes a discontinuity when passing through the shear plane, while the perpendicular component \(V'_y\) preserves everywhere in the velocity field the constant value \(V_{xy}=V_0\cdot\sin\beta_1\), where \(V_0\) is the cutting speed and \(\beta_1\) is the angle of the shear plane. With respect to segmented chips, this question has not been treated in the literature.

From the data of the kinematic investigation, the velocity fields \(V_x\) and \(V_y\) and the acceleration fields \(a_x\) and \(a_y\) were obtained at each stage of formation of the chip element. Analysis of the velocity fields showed that neither the functions \(V_x=f(t)\) nor the functions \(V'_x=f(t)\) undergo a discontinuity when passing through the slip plane. The function \(V'_y=f(t)\) does not have a constant value at all points of the cutting zone even at one stage of element formation, not to mention at different stages. Apparently, the features of the functions \(V'_x\) and \(V'_y\) noted by V. I. Sadchikov are characteristic only of the formation of continuous chips in the case of a scheme with a shear zone degenerated into a plane.

Analysis of the acceleration fields \(a_x\) showed that the drop of the acceleration \(a_x\) from maximum values to zero occurs in a rather narrow region located relative to the cutting plane at an angle approximately equal to the angle \(\beta_1\). The line of maximum accelerations \(a_x\) directly

before the onset of shear of the element coincides with the future shear plane.

Thus, during the formation of chip elements in the shear plane of the future element, accelerations \(a_x\) of maximum magnitude are observed. A number of additional data make it possible to conclude that the acceleration \(a_x\) is directly associated with the localization of deformation leading to the appearance of the shear plane and then to the separation of the chip element.

REFERENCES

1. V. I. Sadchikov. On the theory of formation of continuous chips, dissertation, Tomsk, 1962.