CALCULATION OF THE DEGREE OF CHIP DEFORMATION IN FACE MILLING

G. L. Kufarev, A. A. Kozlov, V. V. Ovcharenko

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

One of the most important tasks in the theory of metal cutting is the study of the stress–strain state of the chip-formation zone.

This question has been studied most fully in turning and planing, i.e., for the simplest chip-formation schemes.

In milling, when the thickness of the cut changes continuously as the tooth moves along the contact arc, there is as yet no sufficiently convincing method for determining the degree of deformation of the layer being cut. This conclusion follows from an analysis of the very few works devoted to this question.

Thus, in the work of Yu. P. Keloglu [1], results are presented for determining chip shrinkage in cylindrical milling of three grades of steel. The extensive experimental material presented by the author raises doubts, since in a whole series of experiments he obtained chip shrinkage in thickness $\zeta_a$ greater than shrinkage in length $\zeta_l$. The latter is impossible, since shrinkage in width $\zeta_b$ is always greater than or equal to unity and, proceeding from the generally known relation between shrinkages in different directions,

\[ \zeta_l=\zeta_a \cdot \zeta_b, \]

when $\zeta_b \geq 1$, $\zeta_l$ cannot be less than $\zeta_a$.

As applied to cylindrical milling, A. N. Reznikov and Yu. P. Novoselov proposed a method for determining shrinkage [2], consisting in the following: by changing the milling depth stepwise and measuring the chip length in each case, a curve is constructed in the coordinates: length of the contact arc—chip length. With equal scales along the coordinate axes, the cotangent of the angle of inclination of the tangent to the constructed curve determines the instantaneous value of chip shrinkage.

\[ \zeta_l=\frac{dl}{dl_1}=\operatorname{ctg}\alpha. \]

As an example, Fig. 1 gives one of such graphs, obtained by S. I. Takhman [3] in cylindrical milling.

The disadvantages of this method include the following: first, changing the cutting depth in each experiment distorts the character of the chip-formation process; second, there is a nonconstancy of the state of the tool cutting edge when conducting a series of experiments with

with variable depth, and, moreover, in graphical differentiation it is impossible to take into account precisely a small change in shrinkage.

Determining chip shrinkage from the texture angle $\delta$ [3] gives insufficient accuracy as a result of errors in determining $\delta$ and possible nonuniformity of the structure of the metal being machined.

Fig. 1. Distribution of chip shrinkage along the contact arc in cylindrical milling. (According to S. I. Takhman.)

This observation is confirmed by the large scatter of the experimental points in Fig. 2.

In the metal-cutting laboratory of TPI, a method was also used for determining the degree of deformation from chip roots [4]. In this

Fig. 2. Distribution of chip shrinkage, cutting temperature, and texture angle along the contact arc in face milling

case, chip shrinkage was calculated from the rake angle measured at the root and the angle of inclination of the plane of maximum tangential stresses. The laboriousness of obtaining the results and the presence of shortcomings inherent in method [2] make this method of little practical use.

The analysis carried out enabled us to propose a new method for determining chip shrinkage in milling. Its essence is as follows: before the experiments, marks were applied to the workpiece every \(10^\circ\) along the length of the arc of contact of the tool with the workpiece. On the chip, from the trace left by the marks, the length of each segment was measured and, accordingly, the chip shrinkage was determined by the formula:

\[ \xi_l=\frac{l_i}{l_{i1}}, \]

where

\(l_i\) is the length of the arc corresponding to a \(10^\circ\) contact angle of the milling-cutter tooth with the workpiece,

\(l_{i1}\) is the chip length between the marks on the same contact segment.

The advantage of the proposed method is the possibility of calculating shrinkage over the entire contact length in a single pass.

Using this method, the degree of chip deformation in face milling of steel 45 with a single-tooth milling cutter was determined. The cutting conditions and tool geometry were as follows: \(V=50\text{–}200\ \text{m/min}\), \(S_z=0.03\text{–}0.2\ \text{mm/tooth}\), \(\gamma=10^\circ\), \(\varphi=90^\circ\), \(\lambda=0^\circ\), \(\alpha=10^\circ\), \(\varphi_1=5^\circ\). The results of these experiments are shown in Fig. 2 and Fig. 3. It follows from Fig. 2 that at very small chip thicknesses, chip shrinkage along the length and thickness reaches large values. As the chip thickness increases,

Fig. 3. Dependence of chip shrinkage on cutting speed at different feeds per tooth

the chip shrinkage \(\xi_{a,l}\) initially drops sharply, and then changes into a smooth curve, reaching its lowest value at a chip thickness equal to the feed per tooth.

The instantaneous temperature values, like shrinkage along the length and thickness, do not remain constant along the length of the contact arc. In the experiments of S. I. Takhman [3], an analogous relationship between \(\xi_{a,l}\) and temperature in the thickness range \(a>0.03\ \text{mm}\) is not observed.

Chip shrinkage across the width, under the cutting conditions and tool geometry selected by us, remains practically constant over the entire length of the contact arc and is equal to 1.

Figure 3 presents the dependence of chip shrinkage on cutting speed for different feeds per tooth. Chip shrinkage values are taken for the contact angle \(\psi=90^\circ\).

At large feeds per tooth, as the cutting speed increases, a decrease in chip contraction is observed. At smaller feeds per tooth, the contraction remains constant within the selected range of speeds.

The proposed method gives a more accurate representation of the distribution of chip contraction along the length of the arc of contact between the tool and the workpiece and, consequently, makes it possible to investigate more accurately the force relationships in face milling.

REFERENCES

1. Yu. P. Keloglu. Some questions concerning the deformation of the layer being removed during milling. Scientific Notes of Kishinev University, vol. 29, 1957.

2. A. N. Reznikov, Yu. A. Novoselov. A method for determining chip contraction in cylindrical milling. Proceedings of Higher Educational Institutions, Mechanical Engineering, No. 10, 1966.

3. S. I. Takhman. Investigation of questions of the mechanics of the cutting process in milling steels with carbide cylindrical cutters. Dissertation. Kurgan Machine-Building Institute, 1966.

4. G. L. Kufarev, A. A. Kozlov, V. V. Ovcharenko, D. E. Zaitsev. A device for instantaneous stopping of the cutting process in face milling. Proceedings of TPI, vol. 183, 1968.