MEASUREMENT OF CUTTING FORCES WITH AN ELASTIC STRAIN GAUGE

G. L. KUFAREV

(Presented by Prof. A. M. Rozenberg, Doctor of Technical Sciences)

The study of many questions in the theory of metal cutting is connected with the need to measure the magnitude of the forces acting on the cutter during the cutting process.

The basic operating principle of the apparatus currently used for this purpose is the recording of the elastic deflection of the cutter, or of another element rigidly connected with it, under the action of the forces being measured. In this case it is desirable that the deflection of the elastic element be as small as possible. This ensures high rigidity of the dynamometer, thereby bringing the cutting process with the cutter mounted in the dynamometer closer to the process that we have under production conditions.

The use of a dynamometer of low rigidity leads to a whole series of difficulties: over a wide range of cutting speeds vibrations arise, distorting the process of chip deformation; the actual geometry of the cutter changes, as do the shear section, and so on.

From this point of view, the most successful are dynamometers having micron-scale displacements of the elastic element; however, in many cases this displacement may be allowed to reach a value, at maximum load on the cutter, of 0.1 mm.

For reliable recording of small displacements, electrical transducers operating on a variety of principles are currently used. The pulses from the latter are amplified and fed to galvanometers or to an oscillograph. Without dwelling on the existing types of electrical transducers, it should be noted that their use is associated with considerable difficulties, owing to the complexity of the electrical part of the apparatus. In addition, the electrical circuit inevitably introduces its own errors into the readings of the instruments, and these errors are sometimes extremely difficult to take into account.

For this reason, work on improving mechanical recording has continued up to the present time, since it is usually incomparably simpler in operation and more reliable in use.

In recent years, at the Department of Machine Tools and Metal Cutting of the Tomsk Polytechnic Institute, so-called elastic strain gauges have been manufactured, investigated, and applied for recording cutting forces; these gauges record, on an enlarged scale, the elastic displacements caused by the action of cutting forces.

The main element of an elastic strain gauge is a flat metal spring, one half of which is wound in one direction and the other in the opposite direction (Fig. 1). When such a spring is stretched, its middle part rotates; attached to this part is a pointer ending in a pen.

The principle underlying the elastic strain gauge is widely used both in foreign and domestic instrument-making industry. Spring micrometers [1] operate on this principle, having...

…mechanical springs that are strongly twisted (through a plastic angle of the order of \(10\pi\)) and have a very small cross section (from \(0.3 \times 0.004\) mm to \(0.25 \times 0.01\) mm). G. A. Aparin and I. E. Gorodetskii [1] indicate that the ratio of the angle of rotation of such a spring to the magnitude of its elongation varies depending on the cross section and the degree of initial twisting.

Fig. 1

To record with a pen the magnitude of the force being measured, a very stiff spring, i.e., one of considerably larger cross section, was required; however, the sensitivity of such a spring proved to be extremely small. Investigations of the operation of springs of different cross sections, having different lengths and degrees of initial twisting, showed that the required sensitivity, with sufficient stiffness, can be obtained by placing several springs of comparatively small cross section in a single measuring element.

The proposed elastic strain gauge consists of 2–4 flat hardened springs, assembled into a packet and twisted through a definite angle, made of U10A steel. The cross section of each spring is from \(0.2 \times 2.15\) mm to \(0.16 \times 1.5\) mm; the length of the twisted part of the spring is 40–120 mm. For manufacturing the elastic strain gauge, a ready-made clock spring of the appropriate section may be used.

Even before twisting (the twisting is carried out in the hardened state), the ends of the springs are pressed into heads by means of a split cone. These heads serve as supports during twisting and during operation. Such a design of the elastic strain gauge makes it possible to fasten it securely in the dynamometer and to replace it easily if necessary.

The twisting of the springs is carried out in a special device, the schematic diagram of which is shown in Fig. 2.

A weight \(P\) is suspended from the lower clamp 1; its magnitude produces stresses in the springs 2 approximately 20% below the yield point. This constant weight ensures uniformity of the plastic twisting of the spring. By means of the flat wedge 3, the disk 4 is fastened to the middle of the springs; by rotating this disk, the spring is twisted.

Fig. 2

For uniform plastic deformation along the entire length and to avoid breakage of the springs, twisting is performed gradually, by slowly increasing the magnitude of the plastic angle of twisting. After the required angle of plastic twisting (from \(2\) to \(4\pi\)) has been reached, the spring remains under load for one or two days.

The study of the sensitivity and comparison of various elastic strain gauges was carried out on the device shown in Fig. 2. The axial displacement produced by a nut screwed onto clamp 1 was measured with an indicator. An indicator needle was attached to the middle cross-section of the springs, and its rotation was read on a dial fixed immovably to the body of the device. Before each test, an initial tension was produced in the system; its magnitude was determined by rotating the needle through 60–90°.

Fig. 3

The tests performed showed that the sensitivity of elastic strain gauges increases with an increase in the working length (Fig. 3) and decreases with an increase in the number of springs of the measuring element (Fig. 4).

Fig. 4

As for the degree of plastic twisting, increasing it leads to an increase in sensitivity only up to a certain value characteristic of a spring of the given size. An example of the influence of the angle of plastic twisting on the sensitivity of a strain gauge is given in Fig. 5¹.

The angle of elastic rotation of the pointer for the elastic strain gauges tested, per 0.1 mm of axial displacement, varied from \(14^\circ 10'\) to \(18^\circ 45'\), and it always remained directly proportional to the axial displacement. Such an angle of rotation, with a pointer length \(l = 100 \div 150\) mm, corresponds to a 250–500-fold magnification of displacements.

Fig. 5

A very important condition determining the reliability, or even the possibility, of using elastic strain gauges in the study of the cutting process is the stability of their readings, i.e., the constancy of their characteristic under prolonged alternating loading.

To test the stability of the readings, the elastic strain gauge was mounted in the device shown in Fig. 2, on the table of a horizontal milling machine.

An additional helical spring was placed on the end of clamp 1 and compressed by a nut, which provided an initial tension of the spring. A periodic displacement of the order of 0.1 mm was imparted to the movable end of the strain gauge by means of a rotating eccentric mounted on the machine spindle. During the test, 520,000 displacements were imparted to the strain gauge, after which a new investigation of its sensitivity was carried out; it coincided exactly with the initial sensitivity.

When designing a recorder that measures the magnitude of a force through the elastic displacements of some element arising under the action of the force being measured, attention must be paid to the limit of variation of the measuring force of the recorder in the working zone. If this variation is large, then, by creating additional stiffness in the elastic system, it can substantially reduce the readings of the recorder.

The characteristic of a recorder from this point of view is the ratio of the limiting increment of the measuring force of the recorder to the maximum value of the force being measured,

\[ b = \frac{Q}{P_{\max}}. \]

The larger this ratio, the smaller the fraction that the actual reading of the recorder will constitute of that which would have been obtained in the absence of an increment in the measuring force.

If we denote:

$l_\partial$ — the actual reading of the recorder under the load $P_{max}$;

$l_0$ — the reading of the recorder at $P_{max}$ in the case when $Q=0$,

then, taking into account the rectilinearity of the characteristics of the elastic element and of the strain gauge, one may write:

\[ k=\frac{l_\partial}{l_0}=\frac{P_{max}}{P_{max}+Q}=\frac{1}{1+b}. \]

In Fig. 6 this dependence is presented graphically.

The graph shown in Fig. 7 depicts the results of a force test of a strain gauge consisting of 4 springs, each with a cross section of $0.2 \times 2.15$ mm. From the graph it follows that, for an axial elongation of the strain gauge by 0.1 mm (with rotation of the pointer through an angle $\varphi_{0.1}=18^\circ 30'$), the measuring force increases by 42 kg. If this strain gauge is used to measure a force whose maximum value is $P_{max}=500—1000$ kg, then

Fig. 6

Fig. 7

\[ b=\frac{Q}{P_{max}}=\frac{42}{(500 \div 1000)}=0.084 \div 0.042, \]

which corresponds to a value of $k=0.93—0.96$. Thus, the increase in the measuring force in the working range will cause a decrease in the recorder reading of only 7–4%, which is quite permissible, since in this case as well the transmission ratio of the dynamometer will remain sufficiently large.

Elastic strain gauges were installed for measuring torque and feed force in the work of A. I. Promtov [2].

In this investigation, torque was recorded by means of a dynamometer of the A. M. Rozenberg system [3], in which the hydraulic part was replaced by an elastic strain gauge (Fig. 8).

Pulley 1, under the action of the torque, through lever 2 presses on bracket 3, the elastic deflection of which determines the magnitude of the axial elongation of spring 4 and the rotation of the recording pointer 5 corresponding to the characteristic of the elastic strain gauge.

The average circumferential cutting force during milling, recorded in this way by the author [2], was compared with the corresponding cutting forces recorded by L. A. Khvorostukhin by means of a hydraulic dynamometer during turning [4].

Figure 9 presents the experimental dependence of the specific work of chip deformation on the relative shear, obtained by L. A. Khvo-

with chips with the experimental points of Promitsov superimposed on it. The coincidence of the points on the graph with the curve plotted from the data obtained with the aid of a hydraulic dynamometer confirms the suitability

Fig. 8

of the elastic strain gauge for recording the forces acting on the cutting tool in the process of chip removal.

Fig. 9

Conclusions

1. The proposed elastic strain gauge makes it possible to record small elastic displacements with an increase of approximately 500 times, without any lever or similar transmissions, and therefore without any friction losses (not counting the friction of the pointer on the paper).

2. The elastic strain gauge has a rectilinear characteristic, which is extremely convenient in operation.

3. The elastic strain gauge can be used not only for measuring displacements, but also as a force meter (see the graph of force tests in Fig. 7).

4. The elastic strain gauge cannot be used for recording

rapidly varying processes, since it has a certain inertia.

1. The sensitivity of the elastic strain gauge can be increased considerably if the mechanical recording is replaced by optical recording (in this case the cross-section of the strain-gauge springs can be substantially reduced).

REFERENCES

1. Aparin G. A. and Gorodetskii I. E.—Tolerances and Technical Measurements. Mashgiz, 1953.

2. Promptov A. I.—Dynamics of High-Speed Milling of Steels with Face Mills. Author’s abstract, Tomsk, 1954.

3. Rozenberg A. M.—Dynamics of Milling. Sovetskaya Nauka Publishing House, 1945.

4. Khvorostukhin L. A.—Calculation of Forces in High-Speed Cutting on the Basis of the Physico-Mechanical Characteristics of Metals. Author’s abstract, Tomsk, 1954.

1. The graphs in Figs. 3, 4, and 5 were plotted from data of L. M. Sedokova. ↩