On the Calculation of the Tool Blunting Criterion
Abstract Generated abstract
This paper addresses the problem of defining and calculating a tool blunting criterion in cases where conventional lifetime curve methods are unsuitable, especially in machining high manganese steels whose wear curves may lack a catastrophic wear region. The authors propose a calculation scheme based on the loss of the tool’s ability to cut into the chip, interpreting this event as a consequence of elastic deflection in the machine, tool, workpiece system under increasing forces caused by flank wear. For planing with specified tool geometry, they derive relations between wear, cutting forces, deflection, actual chip removal, and time, leading to a differential equation whose solution gives the critical time and corresponding flank wear. The method is presented as a limited but extensible framework for estimating critical tool wear under different tool materials and cutting conditions.
Full Text
PROCEEDINGS
OF THE TOMSK POLYTECHNIC INSTITUTE
OF THE ORDER OF THE OCTOBER REVOLUTION AND THE ORDER
OF THE RED BANNER OF LABOR
NAMED AFTER S. M. KIROV
ON THE CALCULATION OF THE TOOL WEAR CRITERION
G. L. Kufarev, V. I. Livshits
(Presented by the scientific seminar of the departments of machine tools and metal cutting
and mechanical-engineering technology)
The question of the tool wear criterion is perhaps the most urgent one for production and, at the same time, the least developed in machinability studies. There is no complete unanimity of views even on the question of what should be considered the tool wear criterion and whether there exists a wear criterion common to all machining cases. Most of the wear criteria cited in the literature are subjective in character. Methods for calculating the tool wear criterion are absent from the literature.
A fairly widely used method is that of choosing the wear criterion \((h_{\mathrm{opt}})\) on the basis of analysis of the curve of the tool’s total life. The wear corresponding to the maximum of the curve is taken as optimal. Unfortunately, this method is inapplicable in many cases because, as experiments show, the maximum of the curve \(kT=f(h_{\mathrm{zf}})\) appears only when the tool-wear curve has a second inflection—the transition to the region of catastrophic wear. If the second inflection is absent, then the curve \(kT=f(h_{\mathrm{zf}})\) increases monotonically. And in most cases of machining difficult-to-machine materials, the tool-wear curves do not have a second inflection. An increase in total life with increasing wear in the case of precisely such a wear curve is noted by N. N. Zorev [1] and S. S. Rudnik [2]. In such cases, a possibly larger wear criterion is economically advantageous (Brewer and Rueda [3]).
Naturally, in such cases, when assigning the wear criterion, technological requirements come to the fore—the fulfillment of specified dimensions and surface finish of the part. When machining high-manganese steels, the surface finish of parts remains high even with considerable tool wear. The change in part dimensions as the tool wears is relatively small and makes it possible to maintain tolerances for semifinish machining even with considerable cutter wear. Thus, the technological requirements are met for a long time with significant tool wear and therefore do not act as limiting ones.
The limiting sign in machining high-manganese steels was the loss by the cutter of the ability to cut into the chip in one spindle revolution or in one double stroke of the ram. Such a phenomenon was obser—
it was possible, in turning, when attempting to cut into the heavily work-hardened machined surface of steel G13L with a worn tool. In planing, similar cases of the tool emerging from under the chip onto the machined surface of the preceding pass occurred at the end of the overwhelming majority of experiments and were adopted as a stable criterion of tool blunting. In addition, the loss by the tool of the ability to cut under the chip was sometimes also observed in the middle of an experiment.
It is quite obvious that the degree of tool wear at which the ability to cut under the chip is lost is ultimately determined by the rigidity of the MTW system, since the very phenomenon of losing the ability to cut under the chip is nothing other than a deflection, i.e., an elastic deformation of one or several elements of the MTW system under the action of forces on the rake and flank faces of the tool. Therefore there arises the possibility of calculating the blunting criterion as that wear at which the increasing deflection of the MTW system makes impossible the process of the tool cutting under the chip.
Let us consider the process of planing with a tool having angles \(\gamma=0^\circ\), \(\varphi=90^\circ\). We are interested in the deflection \(y\) in the feed direction.
\[ y = C P_x = \frac{1}{j} P_x, \tag{1} \]
where \(j\) is the rigidity of the MTW system, and \(C\) is the proportionality coefficient. From cutting theory it is known that for a tool with angle \(\varphi=90^\circ\)
\[ P_x = N_1 + F \cdot \cos \gamma - N \cdot \sin \gamma, \tag{2} \]
where \(N_1\) is the normal force acting on the flank face of the tool;
\(N\) is the normal force acting on the rake face of the tool;
\(F\) is the tangential force acting on the rake face of the tool.
For the purpose of simplifying the calculation under consideration, we assume that the normal force on the rake face \(N\) is proportional to the chip thickness \(S\):
\[ N = C_2 S, \]
and that the coefficient of friction is a constant quantity.
\[ \mu = \frac{F}{N} = \text{const}. \]
Hence
\[ F = \mu N = \mu C_2 S = C_1 S, \]
\[ y = C\left(N_1 + C_1 S \cdot \cos \gamma - C_2 S \cdot \sin \gamma\right). \]
For \(\gamma=0\),
\[ y = C(N_1 + C_1 S). \tag{3} \]
In what follows we analyze the case of tool wear only on the flank face. This type of wear is often encountered in the planing of high-manganese steels. The deflection \(y\), as flank wear increases, grows as a result of the increase in the force \(N_1\). The chip thickness, or actual depth of cut \(S\), decreases as wear increases, and, finally, the tool loses the ability to remove a chip \((S=0)\). The instant of time corresponding to this should be taken as critical, and the tool wear as the blunting criterion. According to A. M. Danielyan [4], flank wear may be expressed by the relation
\[ \delta = p t^q, \tag{4} \]
where \(\delta\) is wear in mm, \(t\) is time in minutes, and \(p\) and \(q\) are constants. Thus, the problem reduces to finding the critical instant of time,
which can be found in the following way: an equation relating the actual removal \(S\) and the operating time \(t\) is found; then this equation is solved with respect to \(t\) for the case \(S=0\).
The relation between \(S\) and \(t\) can be obtained from formula (3)
\[ S=\frac{y-CN_1}{CC_1}. \tag{5} \]
In the expression obtained, \(y=f_1(t)\) and \(N_1=f_2(t)\).
On the basis of the data of N. N. Zorev [5], one may take
\[ N_1=N_1^0+k\delta, \tag{6} \]
where \(N_1^0\) is the normal force on the flank face on a sharp cutter;
\(\delta\) is wear on the flank face.
Taking (4) into account,
\[ N_1=N_1^0+kpt^q. \tag{7} \]
Thus, in order to solve the problem it remains to find the relation between \(y\) and \(t\).
The expression for the amount of deflection as a function of time can be established on the basis of the following reasoning. The actual removal \(S\) on each double stroke of the slide is equal to the metal fed under the tool minus the deflection on the given double stroke \(y_n\). The metal fed under the tool is the table feed per double stroke \(S_0\) plus the deflection on the preceding double stroke \(y_{n-1}\). During the operating period when the actual removal is equal to the feed, the difference between the deflections on the given \((y_n)\) and preceding double strokes \((y_{n-1})\) is equal to zero; in other words, on each double stroke the tool receives a constant deflection \(y_k\). If, however, wear increases, then the deflection also increases, and in such a way that the difference \(y_n-y_{n-1}\) grows and tends to \(S_0\). Hence it follows that the actual removal decreases. Table 1 is constructed on the basis of the above reasoning. The expressions for the deflection on each double stroke were obtained on the basis of formula (3).
Table 1
| Increasing deflection | Decreasing removal |
|---|---|
| \(y_1=C\{N_1+C_1(S_0+y_k-y_k)\}\) \(y_2=C\{N_1+C_1(S_0+y_1-y_2)\}\) \(y_3=C\{N_1+C_1(S_0+y_2-y_3)\}\) |
\(S_1=S_0+y_k-y_k\) \(S_2=S_0+y_1-y_2\) \(S_3=S_0+y_2-y_3\) |
| \(y_n=C\{N_1+C_1(S_0+y_{n-1}-y_n)\}\) | \(S_n=S_0+y_{n-1}-y_n\) |
Let us consider the expressions for \(y_n\).
\[ y_n=CN_1+CC_1S_0+CC_1y_{n-1}-CC_1y_n, \]
\[ y_n-y_{n-1}=\frac{1}{C_1}N_1+S_0-\frac{1}{CC_1}y_n. \]
Denote
\[ \frac{1}{C_1}=a;\qquad \frac{1}{CC_1}=b. \]
Then
\[ y_n-y_{n-1}=aN_1+S_0-by_n. \]
Passing from the discrete process to the continuous one and taking into account that previously the time interval was taken as unity, we have the right, on the basis of the data of works [6], to write the differential equation
\[ \frac{dy}{dt}=S_0+aN_1-by, \]
\[ \frac{dy}{dt}=S_0+aN_1^0+akpt^q-by, \tag{8} \]
\[ y'+by=S_0+aN_1^0+akpt^q. \tag{9} \]
The equation obtained is a nonhomogeneous linear differential equation. Its solution makes it possible to obtain the relation between the rebound \(y\) and the time \(t\) in the following form:
\[ y=\frac{S_0}{b}+\frac{a}{b}N_1^0+akpe^{-bt}\int_0^t t^q e^{bt}\,dt. \tag{10} \]
The integral in expression (10) can be found (in the case \(q<1\)) by methods of approximate integration, for example, by calculating the finite sum using Simpson’s formula. Substituting expressions (7) and (10) into (5) and solving the latter for the case \(S=0\), we obtain the value of the critical moment of time, knowing which we determine the critical wear (the blunting criterion) by the formula
\[ \delta=pt^q. \]
Thus, the possibility has been shown of calculating the tool-blunting criterion on the basis of the phenomenon of loss of the tool’s ability to cut into the chip. It should be noted that the scheme of the process considered above assumes that the decrease in removal occurs only due to an increase in the difference between the preceding and subsequent rebounds, and not due to destruction of the cutting blade itself. In other words, it is assumed that, as wear proceeds, a process of “self-sharpening” occurs, that is, maintenance of the cutting ability of the tool edge, or of the radius of its rounding, at a certain constant level. Such an assumption is justified, since experimental data confirming it are available in the literature.
The calculation scheme considered for the blunting criterion in no way claims to provide an exhaustive description of such a complex phenomenon as critical tool wear. In particular, it does not reflect such an important circumstance as the difference in critical wear for different cutting speeds, repeatedly noted in experiments. Apparently, to calculate the variation of the tool-blunting criterion under different cutting conditions, one can choose the same path as in the calculation scheme given above, with the addition of an analytical expression for the conditions of the tool cutting into the chip and for the change of these conditions with cutting speed.
A similar calculation method is applicable to a carbide tool. For a high-speed-steel tool and a tool made of cast compositions of the “Tantung” type, the critical condition will be the cutting temperature arising when the worn tool cuts into the chip.
Thus, the proposed scheme for calculating the tool-blunting criterion is capable of covering the entire range of phenomena observed in the wear of various tool materials.
References
-
P. P. Zorev. “Machine Tools and Tooling,” No. 8, 1949.
-
S. S. Rudnik. Production criteria for tool blunting. In: Problems of Metal Cutting, conference proceedings, pt. 1, Moscow, 1963.
-
K. Brewer, R. Ruda. “Werkstattstechnik,” 54, No. 6, 257–263, 1964.
-
A. M. Daniellan. Heat and wear of tools in the process of cutting metals. Moscow, Mashgiz, 1954.
-
P. P. Zorev. Problems in the mechanics of the metal-cutting process. Moscow, Mashgiz, 1956.
-
G. B. Lurie. “Bulletin of Mechanical Engineering,” No. 5, 1954.