A new method for durability dependance of a cutting tool on a cutting speed

20 K O M U N I K Á C I E / C O M M U N I C A T I O N S 3 / 2 0 0 0 V celej histórii rozvoja teórie obrábania sa na opis závislosti medzi trvanlivosťou rezného nástroja a reznou rýchlosťou používa Taylorov vzťah, ktorý vznikol r. 1905. Predložená práca analyzuje doterajšie pokusy o vylepšenie tohto vzťahu. Návrh vyúsťuje do metodiky zostrojenia T-v závislosti, ktorá zabezpečuje výrazne lepšiu zhodu s experimentom. V druhej časti práce je metodika verifikovaná experimentálne na významnom počte typických príkladov.

Za úspešný pokus možno označiť prístup TEMČINA, ktorý v r. 1957 vylepšíl Taylorov vzťah tým, že mu v menovateli pridal člen: In the entire history of the development of the metal cutting theory Taylor's whhich appeared in 1905, has been used to describe the relation between a cutting tool durability and a cutting speed. This relation was established in 1905. This work presents the analysis of the up to now attempts carried out to improve the mentioned relation. The submitted proposal results in the method of creation of the TϪv relation, which provides a much better identity with the experiment. In the second part of the work the method is verified experimentally on a series of experimental results.

The current state of the T-v relation and its use
The most important principle of cutting -a relation between the durability of a cutting tool and a cutting speed has been the subject of interest of research workers in the whole history of the process of a cutting acquisition as a technological method.
As early as in 1905, the American scientist TAYLOR defined the course of this relation and creatid it as a double logaritmic set; its mathematical formula was as follows: The formula has been used up to now [2,3,5].
Since that time, there were many, more or less successful, attempts to provide a more precise definition and mathematical description of this function. In 1933 SAFONOV [4] defined the relation: The relation describes TϪv relation more precisely, however, it is more complicated for practical use and it does not comprise a declining curve.
The whole relation is then as follows: Compared to the classical Taylor's relation, the difference lies in the fact that with small values of cutting speeds, the second in the denominator prevails and the relation converts to a straight line which is parallel to the axis of the cutting speeds. On the contrary, if the cutting speed is sufficient, the first term in the denominator is considerably bigger than the second term and the relation converts to the Taylor's one.
Leaving out of the account the mentionded solutions, the topicality of the Taylor' relation can be explained by the fact that it is simple for practical applications in spite of fact that the latest computing technique is able to work with relation of any difficulty.
The basis postulate of the definition of the classical Taylor's relation is correct choise of the blunting through which it is defined. This criterion is based on the use of a tool working at a cutting speed, which is close to an optimal one for a used cutting material. It is obvious that which such a choice the other cutting tools will not be utilized until blunting appears, i.e. their cutting properties will not be utilized. The application of NC cutting tools, which leads to the applications of intensive cutting conditions as well as a defined frequency of tool change, requires a new approach to blunt criterion of blunting. Each cutting tool should be utilized until it is blunt. The realization of this aim is shown in the following.

T-v relation with constant blunt criterion
As it is known, the classical approach to a creation of the TϪv relation is based on obtaining an experimental curve VB ϭ f() with various cutting speeds.
From the set of curves the tools durability with a constant criterion of blunting is substracted. In Fig. 1 there is a set of such experimental curves obtained under the following conditions: -cutting material: P 20 -worked material: steel 12 060.1 -tool orthogonal race angle: Fig. 2 shows a corresponding TϪv relation. The curve is substituted by Taylor's relation so that it is valid within in the range of cutting speeds over 200 m.min -1 . Obr. 1 Experimentálne krivky VB ϭ f( s ) Fig. 1 Experimental curves VB ϭ f( s ) Odtiaľ: C T ϭ C m v ϭ 4,6.10 13 .
As it can be seen, the exponent m ϭ 5,7, C v ϭ 250.
The experiment shows that outside the areas where the curve is substituted by a straight line, we make a serious mistake in the applications of the Taylor's relation. This is in fact the reason why many authors are interested in this problem.

T-v relation with a variable criterion of blunting
The possibility of creation of the TϪv relation with a variable criteria of blunting appears in the monograph by GRANOVSKICH, 1985 [3]. Howewer the method how to determine different criteria was not defined. Closer studies of a large number of the relation curves VB ϭ f() lead to the conclusion that there is a relatively precise definition of the criterion of blunting which is applied with the "optimal" cutting speed according to the methods of ZOREV and LARIN. It can be actually expected that those methods can also be used also for incomplete wear curves. The following approaches are based on the above mentioned conclusions.
For the experiment, let us choose the set of curves from Fig.1. With the cutting speed 80 m.min Ϫ1 the criterion the blunting is visually evident, and in this case it is VB k ϭ 0.4 mm. If we draw a straight line from this point towards a similar point on the curve for speed 60 m-min Ϫ1 and further on, we also bordered "intuitive" criterion of blunting for other cutting speeds. If we draw a TϪv curve according to this, it will be very different from Fig. 2. Its course is in Fig. 3 (triangles). At the identification of the slope angle of the TϪv relation and the exponent m, we find out that it is smaller.
The next difference is that with smaller cutting speeds (40 to 60 m.min Ϫ1 ), higher durability than during a classical process are recorded. Durability maximum is less significant. All the differences is an
Let us try to choose the criteria of blunting differently. In Fig. 4 the border of criteria is a circle. The corresponding TϪv relation can be seen in Fig. 3. A more fluent curve was created, while the exponent m has the same value. This approach indicates that we are approaching the correct criterion of blunting.

Generalized description of T-v relation
From Fig. 3 it can seen that the application of the classical Taylor's relation would not lead to any progress when compared to the up to now approaches. Therefore, to describe TϪv relation the Temčin's relation was used (4). It was sucessfully applied also in other up to the present works [6,8,9,10]. The avantage of this relations the fact that it is based on the Taylor's relation and therefore it is well known to the users.
It is important to determine T m value as maximum durability which can be obtained within the entire range of cutting speeds. Its determination depends on the accuracy of the cutting speed estimate which correspondens with the maximum durability.The experiment is carried out under the mentioned conditions.
In previous experiment the value of the cutting speed for the cutting material P 10 was by a coincidence precisely estimated (80 m.min Ϫ1 ).
Another important parameters is the constant C T . It should be noted that in this case it has different meaning when compared to the classical Taylor's relation, i.e., this is not a section on durability axis. This fact requires that C T is determined analyticcaly. After the Temčin's relation is modified we obtain: T and v are particular values of both a durability and a cutting speed which are substracted from a declinning branch range of the curve in the section where the validity of the Taylor's relation is expected. In the observed case, there were thefollowing values used: v ϭ 300, T ϭ 25, T m ϭ 220, m ϭ 4, which after the substitution is C T ϭ 2,3.10 11 .
After substitution to the relation (4), it is possible to calculate T for any optional v. The result is as follows: In Fig. 3, the curve calculated this way is represented by a bold line. A very good coincidence of this curve with the experiment is evident, it is incomparably higher than with the applica-
Komplexný výsledok je na obr. 7, kde je krivka závislosti TϪv vytvorená na základe obr. 6 a jej vyhodnotenie podľa uvede-tion of the Taylor's relation. The analysis of several cases showed that the maximum error was only 8 percent. This fact leads to the conclusion that there is much hope of the application of used relation in the practice.

Exact criteria of blunting
The choice of the criteria of blunting according to the previous methlod is accompanied by inaccuracy and subjectivity. Therefore, the aim of further activities was to find more exact approach. It appeared that the forgotten Larin's approach could be the method of determination of the optimal blunting [7]. As we know, this approach is based on the following.
It is necessary to define tthikness of the cutting plate "b" which can be removed during the re-sharpening. For this purpose it can be chosen freely because we do not consider a concrete value of the re-shapening number, but the we searached local maximum.
For the chosen values of the criterion of blunting (e.g. 0.1; 0.2; 0.3 ... mm) a theoretical number of re-sharpenings of a tool "n" is determined according to the relation: For example: If the value which can be removed from the plate by grinding is 3 mm, the number of the re-sharpening for the individua VB k is as follows: Of course, n does not have to be a whole number. In the following the relation is determined for each cutting speed: nT ϭ f(VB k ) whereas T is always a corresponding durability of a concrete VB k and v.
This approach was applied to some curves from Fig. 1. The result is shown in Fig. 5. Bassicaly, it refers to the depen dence of the tool durability upon the chosen VB k criterion. Of each curve, the maximum and a corresponding optimal VB k is evaluated. The values of concrete VB k are given back on the curves of wear and we obtain a situation according to Fig. 6. It can be seen that previous tests were only approaching this situation. So far the aim is not to create the equation of this line. It is important that this approach can be considered as an exact one because into account the realistic principles of the cutting process.
A complex result can be found in Fig. 7, where the curve of TϪv is created on the base of Fig. 6 and its evaluation is done according to the
given method. The error is not more important then the dispersion of the measured durability values.
Referring to this results, the possibility of the application of this new TϪv relation with the common calculations of the cutting technology appears. Thus, is would be possible to specify the term "cutting" of the material as well as a "cutting tool efficiency".
The following series of tests deals with the verification of the outlined procedure with the various cases of cutting and the determination of the methdology of the creation of the exact TϪv relation. In Fig. 9 there is a final TϪv relation while the circles mark the experimental values. The result is, in fact, identical with the previous one. In spite of a lower number of cutting speeds, the TϪv relation is sufficiently precise. It shows the prossibility of decreasing range of experimental tests.

Verification of the creations procedure of the T-v relation and the methodology proposal
In Fig. 10 there is a set of four wear curves obtained by a detailed measuring (after 10 minutes of cutting).
In the lower part, there is a diagram nT ϭ f(VB) with 3 cutting speeds.
In Fig. 12 there is the TϪv relation. Tho following example presents a test which was carried out to verify the methodology with the use of three wear curves. In Fig. 13 there are wear curves at different cutting speeds 70, 100 and 130 m.min Ϫ1 . As a cutting material, research steel for bearing parts (NLO) was used. This steel has a higher strength and is approximately one class worse as regards worse workability by turning than the classical one (14209.3) - Fig. 9. From the point of view of the methodology of tests it follows that is was not necessary to observe the wear line over VB ϭ 0.4 mm. The tests with higher cutting speeds required relatively short time.
Curves for z ϭ f(VB) were created only for two cutting speeds which is sufficient for creation of the TϪv relation which is in Fig. 14.

Conclusion
The outlined procedure of obtaining the TϪv relation can be succesfully used instead of a classical test with a constant criterion of blunting. At the same time, the material and the time require-