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  • 标题:Theoretical model of the surface roughness at the end milling with circular tips.
  • 作者:Slatineanu, Laurentiu ; Toca, Alexei ; Mazuru, Sergiu
  • 期刊名称:Annals of DAAAM & Proceedings
  • 印刷版ISSN:1726-9679
  • 出版年度:2008
  • 期号:January
  • 语种:English
  • 出版社:DAAAM International Vienna
  • 摘要:The milling is the cutting process which uses rotating tools having many cutting teeth placed on the revolution or plane surface; there is a feed motion achieved usually in a plan perpendicular on the tool axis. There are milling techniques which use cylindrical mills, end mills, conical mils etc. If in the case of the rough milling the interest is focused on the material removal rate, on the tool wear, on the sizes of the cutting forces, at the finish milling the main aspects are the surface roughness and the machining accuracy. To obtain a diminished surface roughness, there are used cutting teeth with secondary approach angle k1=0 or teeth with circular inserts; the main advantage of the last solution is the possibility to re-establish the cutting properties of the worn tool by the rotation of the circular inserts.

Theoretical model of the surface roughness at the end milling with circular tips.


Slatineanu, Laurentiu ; Toca, Alexei ; Mazuru, Sergiu 等


1. INTRODUCTION

The milling is the cutting process which uses rotating tools having many cutting teeth placed on the revolution or plane surface; there is a feed motion achieved usually in a plan perpendicular on the tool axis. There are milling techniques which use cylindrical mills, end mills, conical mils etc. If in the case of the rough milling the interest is focused on the material removal rate, on the tool wear, on the sizes of the cutting forces, at the finish milling the main aspects are the surface roughness and the machining accuracy. To obtain a diminished surface roughness, there are used cutting teeth with secondary approach angle k1=0 or teeth with circular inserts; the main advantage of the last solution is the possibility to re-establish the cutting properties of the worn tool by the rotation of the circular inserts.

[FIGURE 1 OMITTED]

At the plane surfaces milling by the using of the end mills with circular inserts, there are (fig. 1) two situations: a) when the tool axis is perpendicular on the plane of the feed motion, the asperities generated by each tool tooth are intersected (fig. 1, a); b) if the tool axis is a little inclined (practically, it is difficult to ensure the absolute perpendicularity of the tool axis on the machined surface), the asperities generated by each tooth do not intersect (fig. 1, b). In the last case, the machined surface roughness is usually appreciated only along the direction corresponding to the tool axis motion. The problem is to establish if the surface roughness parameter [R.sub.a] is constant or variable along other directions existing on the machined surface.

As above mentioned, different researchers measured the surface roughness especially along the direction defined by the tool axis motion.

Thus, Lu et al. (Lu et al., 1998) established a multiple regression equation corresponding to the CNC end milling; they considered that the model predicts the size of the surface roughness parameter [R.sub.a] with about 90% accuracy. In the case of the theoretical profile of the machined surface consisting of elliptical or circular arcs,

Jun Qu and Albert J. Shih developed (Qu and Shih, 2003) some dimensionless form expressions for three surface roughness parameters ([R.sub.t], [R.sub.a], and [R.sub.q]). Amin et al. (Amin et al., 2007) studied the influence exerted by the preheating on the surface roughness, in the case of the end milling of carbon steel by the using of the circular carbide inserts. There is not clear information concerning the variation of the surface roughness parameters in different directions included in the plan of the machined surface.

2. THEORETICAL MODELLING

A theoretical model could emphasize the eventual variation of surface roughness parameters along the surface machined by the using of the end mills with circular inserts. To establish such a model, the information included in the figure 2 can be taken into consideration. One can notice that if the rake angle has the value [gamma]=0[degrees] and the face of the circular insert is placed in the axial plan, the profile of the machined surface includes a concatenation of arcs of circle along the direction corresponding to the tool axis motion (fig. 3). For any other direction, the surface profile includes arcs of curves different of the arcs of circles.

[FIGURE 2 OMITTED]

The machining scheme is presented in the figure 1; the end mill achieves the rotating motion and the feed motion. The radius of the circular inserts is symbolized by R; the cutting edges of the circular inserts are placed at the radius a.

If the circle corresponding to the insert active edge is placed in the plan yOz, its defining relations are the following:

[(x - a).sup.2] + [z.sup.2] - [R.sup.2] = 0

y = 0 (1)

At the distance b from the plan zOy (this plan is defined by the mill axis and by the direction of the feed motion), the profile of the surface is given (Slatineanu, 2004) by the relation:

z = [[square root of [R.sup.2] - [square root of [y.sup.2] + [b.sup.2]] - a).sup.2]] (2)

On the other hand, the surface roughness parameter [R.sub.a] is generally given by the relation:

[R.sub.a] = 1/n [n.summation over (l)] [absolute value of [y.sub.i]], (3)

where [y.sub.i] is the distance from a point of the profile to the mean line and n is the number of the points on the segment of the abscissa semiaxis where the roughness parameter [R.sub.a] must be calculated. Because the surface roughness parameter is defined by taking into consideration the position of the so-called mean line, defined by the parameter m (the distance from the mean line to the axis Ox), in the presented case the surface roughness parameter [R.sub.a] corresponds to the relation:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

A numerical method was used to determine the position of the mean line. It is known (Surface, 2003) that the mean line must have such a position that the sum of the squares of the deviation [z.sub.i] of the profile from the mean line be minim:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

Adequate software (Crefu, 1992) was used to determine the size of the parameter m. This software is based on the following considerations (Slatineanu et al., 2004); one can consider the initial position of the mean line just near the axis O[y.sub.1]. By taking into consideration an increment [DELTA]y, the first sum S1 of the squares of the profile deviations [(z-m).sup.2] (for a pre established number n of the points of the profile) can be determined.

[FIGURE 3 OMITTED]

Within the next step, a new line placed at the distance from the axis Oy increased with the increment [DELTA]m can be taken into consideration and a new sum [S.sub.2] is calculated. The process is retaken; initially, to series of the sum [S.sub.1], [S.sub.2], [S.sub.3] etc. decreases; when the series begins to increase, the penultimate size of m can be appreciated as offering information about the position of the mean line. The limits of the interval used for the calculus (fig. 3) are

[square root of [(a - f/2).sup.2] - [b.sup.2]], [[square root of (a - f/2).sup.2] - [b.sup.2]].

Knowing the size of the parameter m, the size of the surface roughness parameter [R.sub.a] can be determined, by the using of the relation (4). This relation was used to calculate the size of the parameter [R.sub.a], by taking into consideration two levels of the radius a, the feed /, the distance b and the radius R of the circular insert. The mathematical processing of the results thus obtained (by means of software based essentially on the method of the smallest squares) led to the relation:

[R.sub.a] = 20.51[R.sup.-1068] [a.sup.0.1214] [f.sup.1.977] [b.sup.-0.0001579]. (6)

The analysis of this relation (based on a simplified geometrical model) shown that the size of the surface roughness parameter [R.sub.a] does not depend on the size of the distance b On the other hand, the main influence on the size of the parameter [R.sub.a] is exerted by de feed f, the absolute size of the exponent attached to this size having the biggest value.

The established model offers an image concerning the influence exerted by different factors on the surface roughness at the end milling. In the future, one will try to use other methods to study the surface roughness within a surface obtained by end milling with circular inserts and practically verify the validity of such mathematical models.

3. CONCLUSION

A theoretical model able to emphasize the influence exerted by the feed f, the radius R of the circular inserts, the radius where the cutting edges are placed and by the position of the plane where the surface roughness parameter [R.sub.a] is measured was proposed.

4. REFERENCES

Amin, K.M.N.; Abraham, I.; Khairusshima, N. & Mirghani I. Ahmed, M.I. (2007). Influence of preheating on performance of circular carbide inserts in end milling of carbon steel. Journal o/Materials Processing Technology Vol. 185, No. 1-3, 2007-04-30, 97-105, ISSN 0924-0136

Cretu, G. (1992). Fundamentals of experimental research. Laboratory handbook (in Romanian). Technical University "Gh. Asachi" of Iasi, Romania

Lou, M.S.; Chen, J.C. & Li, C.M. (1998). Surface Roughness Prediction Technique for CNC End-Milling. Journal o/ Industrial Technology. Vol. 15, No. 1, November 1998-January 1999. Available /rom: www.nait.org/jit/Articles/ lou1198.pdf. Accessed: 2008-06-23

Qu, J. & Shih, A.J. (2003) Analytical Surface Roughness Parameters of a Theoretical Profile Consisting of Elliptical Arcs. Machining science and technology, Vol. 7, No. 2, 281-294, ISSN 1091-0344

Slatineanu, L.; Dodun, O.; Coteata, M. & Santo, L. (2004). Study of the surface roughness at the machining of the plane surfaces with end mills. Progressivnye technologhii i sistemy machinostroenia. Mejdunarodnyi sbornik nauchinyh trudov. ISBN 966-7907-16-3, Donetskii Natsionalnyi Tekhnicheskii Universitet, Ukraine, 28, 265-270

*** (2003). Surfaces and Profiles (2003). Available from: http://www.predev.com/smg/intro.htm. Accessed: 2005-03-02
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