ISSN 20673604, Vol. III, No. 1 / 2011

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CALCULUS RELATIONS OF THE AXIAL CUTTING FORCE AND CUTTING MOMENT AT WIDENING OF THE STEEL X6CrNiTi18-10 Ovidiu Bljin1, Bogdan Vlase1 & Aurelian Vlase1 1University POLITEHNICA of Bucharest-Romania, Production Engineering Department 313 Splaiul Independenei Street, 060032, Bucharest, Romania Corresponding author: Ovidiu Bljin, [email protected]

Abstract: This paper presents a series of experimentally establish data at widening of the stainless steel X6CrNiTi18-10 and the means for the determination of the axial cutting force and cutting moment with respect to the specific Working Conditions. The experimental data and their following processing represent the original contribution of the authors to determination of the calculus relations of the axial cutting force and cutting moment for widening of the studied steel. These were modified with respect to the relations available in the technical literature for common steels. The presented results can be taken into consideration in the Educational Studies and in the theoretiCal Technical research. They can be implemented in the manufacturing activity. Key words: widening, force, moment, steel, polytropic. 1. INTRODUCTION The stainless steels are used more and more in various key domains of the technique. The processing of these steels is determined by their specific physical-chemical characteristics and by their technological properties (Roukema & Alintas, 2006), (Vlase, 1977). The great difficulties for the cutting of the stainless steels involved intense studies to create New Materials for tools and sensible choice for the tools geometric parameters and cutting regime (Tnase, 2009), (Trent & Wright, 2000). On the other hand, due to the high costs of these steels their machinability should be studied using rapid cutting methods capable of assuming minimum tool and material requirements (Barlier & Girardin, 1999), (Vlase et al., 2007). With this object in view, this paper expounds a series of experimentally found data concerning the widening of the stainless steel X6CrNiTi18-10 and the ways and means to determine the cutting forces and the cutting moments. The axial cutting force function and the cutting moment function will be determined in the terms of four inDependent variables (the diameter D, the feed f, the depth ap, the tool speed v) for widening of the analyzed stainless steel, with respect to the specific

working conditions. 2. MEANS AND CONDITIONS USED FOR EXPERIMENTS The tests were performed using a stand of determinations for recording the values of the force variations and the values of the moment variations at different splintering parameters, consisting of the following (Figure 1): a build dynamometer with resistive tensometer transducers for measuring the forces; a MGC amplifier, produced by Hottinger Baldwin Messtechnic; a data acquisition board type DAQ Pad 6020E; PC; LabWIEW software. The build dynamometer is a rotating one being fixed by a taper shank in the tapered bore of the drilling shaft. A spring collet type force and moment detecting element was adapted for the dynamometer construction. On the perimeter of the elastic detecting element four equidistant resistive transducers were placed, inclined at 450 with respect to generatrix, in opposite, alternative successively. By using this placement of the transducers, and by connecting them to a bridge, highest measurement sensitivity has been achieved. In order to calibrate the dynamometer, the following were used: a standard dynamometer; a taper rod (TC-01-03), axial and tangential loading device. The means and the cutting conditions during the experiments are given below: the machine tool: a GC0 32 DM3 drilling device, the dimensions of the mass are 480420 and a Morse cone 4 was used; the cutting equipment: Rp5 high-speed steel spiral drill with the Rockwell Hardness Number = 62; the geometric features of the drill have met the requirements of the R1370/2-69 standard, A1 type cutting, with diameters within the range 10 through 30 mm; the cooling and lubricating fluid: P 20% emulsion. The Table 1 shows the chemical characteristics of the stainless steel X6CrNiTi18-10. The Table 2 contains

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Fig.1. The experimental stand of determinations

Table 1. Percentage chemical composition [%]

C

Cr

Ni

Ti

Si Mn

S

P

0.08 18 10.5 0.6 1.0 2.0 0.018 0.027

Density (at 200 C) [kg/dm3] 7.86

Table 2. physical characteristics

Elasticity modulus (at 200 C) [GPa]

Heat conductivity [W/m 0K]

specific heat [J/kg 0K]

208

16

500

Electric resistivity [ mm2/m] 0.74

Stainless steel type X6CrNiTi18-10

Table 3. Mechanical characteristics (at 200 C)

Tensile strength Rm [MPa]

Flowing limit R02 [MPa]

Elongation A [%]

620

200

40

Hardness [HB] 260

the physical characteristics of this steel. In the Table 3 are presented the mechanical characteristics of the studied steel.

3. experimental results AND data processing FOR THE AXIAL CUTTING FORCE

The technical literature (Schnadt, 1991), (Vlase, 1977) provided the equation (1), which has been the starting point in the analysis of the axial cutting forces for widening:

Fz

CF

DxF

f

yF

a

zF p

[N]

(1)

where: D is the final diameter; f is the feed; ap is the depth; CF is a constant; xF, yF, zF are polytropic exponents. This equation has proved to be inappropriate since after the practical estimation of the exponents and constants, several tests determinations have been performed and have showed a wide result scattering noted under the same cutting conditions. The problem

is that during the steel machining at various speeds, different parameter values were recorded even if all the other machining conditions are kept constant. Therefore, it has led to introduce a speed factor:

Fz

CF

D xF

f

yF

a

zF p

v wF

[N]

(2)

In order to the CF constant and the xF, yF, zF, wF polytropic exponents were estimated, the equation (2) has been linearized by using the logarithm. It obtained the equation:

lg Fz lg CF xF lg D yF lg f zF lg a p wF lg v

(3)

The Table 4 shows a selection of the most conclusive experimental results obtained for the studied stainless steel. If the data of the first five experiments from the Table 4 are substituted in the equation (3), then a linear inhomogeneous system of five equations with five unknowns (xF, yF, zF, wF, lgCF) is obtained:

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Table 4. Experimental results

Exp. No

Initial diameter Di [mm]

Final diameter D [mm]

Feed f [mm/rot]

Depth ap [mm]

Rotation n [rot/min]

Speed v [m/min]

Cutting force Fz [N]

Cutting moment M [Nm]

1

16

2

12

24

0.12

4

224

16.88

1929

26.90

16

0.20

2

355

17.83

874

13.78

3

16

24

0.32

4

224

16.88

2490

40.61

4

18

5

16

6

14

24

0.12

3

224

16.88

1366

23.16

24

0.12

4

355

26.75

2225

27.78

20

0.20

3

355

22.30

1630

23.26

7

14

24

0.12

5

224

16.88

2540

30.40

lg CF xF lg 24 yF lg 0.12 zF lg 4

lg

wF lg16.88 lg1929 CF xF lg 16 yF lg 0.20 wF lg17.83 lg 874

zF

lg

2

lg lg

CF xF lg 24 yF lg 0.32 wF lg16.88 lg 2490 CF xF lg 24 yF lg 0.12

zF zF

lg lg

4 3

(4)

wF lg16.88 lg1366

lg

CF xF lg 24 yF lg 0.12 wF lg 26.75 lg 2225

zF

lg

4

force depending on the tool speed, for different feeds; the force increases with the tool speed. 4. EXPERIMENTAL RESULTS AND DATA PROCESSING FOR THE CUTTING MOMENTS The technical literature (Sarawut & Wirote, 2005), (Vlase, 1977) provided the equation (6), which has been the starting point in the analysis of the cutting moments for widening:

The system (4) has the following solution: CF = 112; xF = 0.27; yF = 0.26; zF = 1.2; wF = 0.31. The formula of the axial cutting force for the widening of the stainless steel X6CrNiTi18-10 is obtained by inserting the above solution in the equation (2):

Fz 112 D0.27 f 0.26 a1p.2 v0.31 [N]

(5)

The data of the last two experiments, included in the Table 4, allow the verification of the formula from the relation (5). By tracing the diagrams of the cutting axial force variation with respect to the work parameters, using Maple software (Bljin, 2001), the resulted diagrams are shown in Figures 2 to 7 valid only for widening of the stainless steel X6CrNiTi18-10 with a Rp5 highspeed steel spiral. Figure 2 shows the variation of the axial cutting force depending on the feed, for different tool diameters; the force increases with the feed. Figure 3 shows the variation of the cutting force depending on the tool diameter, for different depths; the force increases with the diameter. Figure 4 shows the variation of the axial cutting force depending on the feed, for different tool speeds; the force increases with the feed. Figure 5 shows the variation of the axial cutting force depending on the depth, for different tool speeds; the force increases exponentialy with the depth. Figure 6 shows the variation of the axial cutting force depending on the tool speed, for different diameters; the force increases with the tool speed. Figure 7 shows the variation of the cutting

M

CM

D xM

f

yM

a

zM p

[Nm]

(6)

where: D is the final diameter; f is the feed; ap is the depth; CM is a constant; xM, yM, zM are polytropic exponents. This equation has proved to be inappropriate since after the practical estimation of the polytropic exponents and the constants, several tests determinations have been performed and have showed a wide result scattering under the same cutting conditions (Vlase et al., 2009). The problem is that during the steel machining at various speeds, different parameter values were recorded even if all the other machining conditions were kept constant. It has led to introduce a speed factor thus:

M

CM

D xM

f

yM

a

zM p

v wM

[Nm]

(7)

In order to the CM constant and the xM, yM, zM, wM polytropic exponents were estimated, the equation (7) has been linearized by using the logarithm. It obtained the equation:

lg M lg CM xM lg D yM lg f zM lg a p wM lg v

(8)

If the data of the first five experiments from the Table 4 are substituted in the equation (8), then the following linear inhomogeneous system of five equations with five unknowns (xM, yM, zM, wM, lgCM) is obtained:

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Fig.2. The force variation depending on the feed for different tool diameters

Fig.5. The force variation depending on the depth for different tool speeds

Fig.3. The force variation depending on the tool diameter for different depths

Fig.6. The force variation depending on the tool speed for different diameters

Fig.4. The force variation depending on the feed for different tool speeds

Fig.7. The force variation depending on the tool speed for different feeds

lg CM xM lg 24 yM lg 0.12 zM lg 4

lg CM

wM lg16.88 lg 26.90 xM lg16 yM lg 0.20 wM lg17.83 lg13.78

zM

lg

2

lg lg

CM CM

xM lg 24 yM lg 0.32 wM lg16.88 lg 40.61 xM lg 24 yM lg 0.12

zM zM

lg 4 lg 3

(9)

lg

CM

wM lg16.88 lg 23.16 xM lg 24 yM lg 0.12 wM lg 26.75 lg 27.78

zM

lg 4

The system (4) has the following solution: CM = 0.42; xM = 1.3; yM = 0.42; zM = 0.52; wM = 0.07. The formula of the cutting moment for the widening of the steel X6CrNiTi18-10 is obtained by inserting this solution in the equation (8):

M

0.42 D1.3

f

0.42

a

0.52 p

v0.07

[Nm]

(10)

31 The data of the last two experiments, included in the Table 4, allow the verification of the formula from the relation (10). By tracing the diagrams of the cutting moment variation with respect to the work parameters, using Maple software, the resulted diagrams are shown in Figures 8 to 13 valid only for widening of the steel X6CrNiTi1810 with a Rp5 high-speed steel spiral. Figure 8 shows the variation of the cutting moment depending on the feed, for different diameters; the moment increases with the feed. Figure 9 shows the variation of the cutting moment depending on the diameter, for different depths; the moment increases exponentialy with the diameter. Figure 10 shows the variation of the moment depending on the feed, for different speeds; the moment increases with the feed. Figure 11 shows the variation of the cutting moment depending on the depth, for different feeds; the moment increases with the depth. Figure 12 shows

Fig.8. The moment variation depending on the feed for different tool diameters

Fig.10. The moment variation depending on the feed for different tool speeds

Fig.9. The moment variation depending on the tool diameter for different depths

Fig.11. The moment variation depending on the depth for different feeds

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Fig.12. The moment variation depending on the tool speed for different diameters the variation of the cutting moment depending on the tool speed, for different diameters; the moment increases with the tool speed. Figure 13 shows the variation of the cutting moment depending on the tool speed, for different feeds; the moment increases with the tool speed. 5. CONCLUSIONS The experimental data and their processing represent the contribution of the authors to the estimation of the polytropic exponents and to the assessment in terms of structure of the calculus relations for the axial cutting force and for the cutting moment at the widening of the stainless steel X6CrNiTi18-10. For the determination of the force and the moment at the widening of the steel a special dynamometer was designed and manufactured. It was a rotative dynamometer fixed in the tapered bore of the drilling shaft foreseen with tensometer transducers attached to an elastic element. Measuring range of the forces and the moments permitted tests with diameters within the range 10 through 30mm. By many experimental tests, it was demonstrated the necessity of modifying the structure of the cutting force calculation relation and the structure of the cutting moment calculation relation, found in the technical literature, meaning that the tool speed has to be included with respect to equations (2) and (7). The experimental data and the diagrams prove the variation of the cutting axial force and the cutting moment values depending on the parameters of the cutting technology. The results presented in this study can be taken into consideration in the educational studies and in the theoretical technical research. Also, they can be readily implemented in the manufacturing activity. Our further studies aim these problems for another steels classes.

Fig.13. The moment variation depending on the tool speed for different feeds 6. REFERENCES 1. Barlier, C., Girardin, L. (1999). Memotech productique, materiaux et usinage, Ed. Casteilla, ISBN 2-7135.2051.7, pp. 215-218, Paris. 2. Bljin, O. (2001). Maple оn matematica asistat de calculator, Ed. Albastr, ISBN 973-650-007-1, pp.142144, Cluj-Napoca. 3. Roukema, C.J., Alintas, Y. (2006). Time domain simulation of torsional-vibrations in drilling, International Journal of Machine Tools and Manufacture, Vol. 46, Elsevier, ISSN 0890-6955, pp. 2073-2085. 4. Sarawut, S., Wirote, S. (2005). Combined slidingmode speed-torque observer, WSEAS International Conference on System Science and Simulation in Engineering, ICOSSSE'05, ISSN 1790-5117, pp.191196, Tenerife, Spain. 5. Schnadt, R. (1991). Austenitischen Stahlfrдsen, ZWF CIM, Vol.86, No.6, Verlag, ISSN 0932-0482, pp. 312315, Mьnchen. 6. Tnase, I. (2009). Scule aschietoare, Bren Publishing House, ISBN 978-973-648-849-8, pp.26-27, Bucharest. 7. Trent, E.M., Wright, P.K. (2000). Metal cutting, 4th Edition, Butterworth Heinemann, ISBN 0-7506-7069-X, pp.256-274, Boston. 8. Vlase, A. (1977). Contributions to the studies on the machinability of cutting romanian make stainless steels, PhD Thesis, Institute Polytechnic of Bucharest. 9. Vlase, A. et al. (2007). Tehnologii de prelucrare pe maini de gurit, Bren Publishing House, ISBN 978973-648-633-3, pp.136-141, Bucharest. 10. Vlase, A., Bljin, O., Sime, M. (2009). Determination of the regression relation of the cutting moments for widening of the stainless steel 4NiCr180, Proceedings of the 13-th International Conference "Modern Technologies, Quality and Innovation ModTech 2009", Politehnium Publishing House, ISSN 2066-3919, pp.691-694, Iasi. Received: February 05, 2011 / Accepted: May 30, 2011 / Paper published online: June 10, 2011 © International Journal of Modern Manufacturing Technologies

O Blăjină, B Vlase, A Vlase

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