Mathematical models of flank wear curve during the turning of steel C60E4.

Qehaja, Nexhat ; Bunjaku, Avdyl ; Kacani, Jorgaq 等

1. INTRODUCTION

Mathematical models represent the highest degree of approximation, they use certain mathematical symbols to be marked or changing the original parameters. Relationship between variable parameters and the original introduced through mathematical logic relations. Mathematical models offer the possibility to realize highly experiments (Zelinski, 2005).

With experimental research has proved that the function of the instrument tool flank wear VB = f (t) according to the site held back by the curves shown in fig.1.

[FIGURE 1 OMITTED]

Determination of mathematical models of the flank wear curve VB = f (t) based on experimental data is implemented in two stages: defining the structure of regressive curve and finding the numerical values of their parameters, which forms the curve parameters and their should be defined so that in the best way to describe the group of experimental points.

With the analysis of curve obtained in order to reach the conclusion that the experimental curve empirical type: VB= a [t.sup.b], VB= [ab.sup.t], VB=c+[at.sup.b], dhe VB=c+[ab.sup.t] does not accurately represent the experimental curve, so, passed on a combination of these curve, where the gain curve of form, fig.1 (Qehaja, 2006).

VB = [at.sup.b] [v.sup.ct.sub.c] (1)

provided that: c> 0; 0 <b <1, which best represents the experimental curve.

Due to the complexity of this function presents the problem of calculating the parameters a, b, c. However, the use of the method of "cutting" established linear dependence t--[DELTA]1log VB and overcome this problem. To determine the constant a, b and c linear dependence; t--[DELTA]1log VB method based on average values collected by the conditional equations:

[[DELTA].sub.1] logVB = b log2 + c t log [v.sub.c] (2)

[summation] logVB = [summation]loga + [summation]b logt + [summation] c t [logv.sub.c] (3)

Calculation of the constant a, b and c be under way in showing tab.1

Taken the first three values [[DELTA].sub.1] logVB, placed in equation 2 and thus gain an equation, then taken again three other values [[DELTA].sub.1] logVB which again placed in the formula 2 where the second win equation. Of these two win, the equations b and c. With the replacement of values b and c in equation 3 are gain value obtained with this form of concluding function VB = f (t).

2. EXPERIMENTAL CONDITIONS

The reference material for work piece is rolled steel C60E4 (according to ISO). The initial work piece diameter is 20,2 mm and the length is 360 mm.

The experiments have been performed by using the similar processing parameters in volume productions of the piston of shock absorber at the shock Absorber Factory in Pristina, Kosovo.

During the experiment there have been used the hard metal plates TNMGS04 10 FR according the ISO standard No.1832 the product from "Sintal"-Zagreb, of the quality SCM-105 (covered by three layers TiC-Al2O3-TiN on the hard metal base P25) (Fig.1).

The plate is attached mechanically to the holder PSBNR2020K12 with the fastening system PROMAX-C. The testing has been realized on automatic 6 axis machine Wickman .

3. EXPERIMENTAL RESULTS

On the basis of experimental data on flank wear (Tab. 1), by applying mathematical model (1) is calculated and drawn gradient consumer VB = [at.sup.b] [v.sup.ct.sub.c] (fig.2).

[FIGURE 2 OMITTED]

4. CONCLUSION

From the experimental result of flank wear of the cutting tool VB = f (t) are obtained in the mathematical models depending of time work t and cutting speed that [v.sub.c] VB= [at.sup.b][V.sup.ct.sub.c], where is the relative influence of these factors in the flank wear of the cutting tool VB

By comparing the obtained curve of flank wear so experimental VB = f (t) curve and so earned empirical Figure 2, there is a consistent high their which means that the mathematical model of acquiring formal VB = [at.sup.b][V.sup.ct.sub.c] describes so accurate experimental curve to avoid an average of 0.03-0.05 mm in the zone of initial flank wear, which then goes with being reduced from 0002-0008 mm in the area of uniform flank wear, which also determines the moment of flank wear of the tool shearing

5. REFERENCE

Aleksander, B. (1976). Mechanical technology, Volume 2, Faculty of Mechanical Engineering, Tirane

Bunjaku, A., Bodinaku, A., Osmani, H. & Zeqiri, H. (2002). The influence of cutting process on consuming of cutting plates during turning process of steel Ck 60, Scientific Journal for the Theory and Application in Mechanical Engineering "Makineria" nr.1, p.15-19, Faculty of Mechanical Engineering, Prishtine

Elbestebawi, M. (2002). Course notes for Mashine Tool Analisis, McMaster University

Milton C.Shaw (2005). Metal cutting principles, second edition, New York Oxford, Oxford University Press

Qehaja N. (2006). Research of the reliability of the metal cutting tools during processing with turning of the shock absorber piston rod. doctoral dissertation, Faculty of Mechanical Engineering, Prishtina

Qehaja, N. (1989). Dependence of cutting tools and productivity in the process of exploitation, master, FSB Zagreb

Salihu, A. (2001), Research of machinability of cutting material with increased speed, doctoral dissertation, Faculty of Mechanical Engineering, Prishtina

Zeqiri, H. (2005). Research of machinability by turning of 42CrMo4 steel, doctoral dissertation, Faculty of Mechanical Engineering, Prishtina

Zelinski, P. (2005). How to Succeed At Failure, Gardner Publications Inc., Cincinati

Tab.1. Conditions for experiment realization

n T [min] VBexp logt

 0 0

1 1 0.06 0.000
2 5 0.10 0.699
3 9 0.12 0.954
4 13 0.13 1.114
5 17 0.15 1.230
6 21 0.16 1.322
7 36 0.22 1.556
8 56 0.27 1.748
9 63 0.28 1.799
10 68 0.31 1.833
11 74 0.36 1.869
12 85 0.39 1.929
[SIGMA] 448 2.538 16.055

n logVB [DELTA]logt

1 -1.222 0.699
2 -1.000 0.255
3 -0.921 0.160
4 -0.886 0.117
5 -0.824 0.092
6 -0.796 0.234
7 -0.666 0.192
8 -0.577 0.051
9 -0.553 0.033
10 -0.509 0.037
11 -0.445 0.060
12 -0.411 0.000
[SIGMA] -8.808 1.929

n [DELTA]log [DELTA]1lo [VB.sub.llo]
 VB VB
 0

1 0.222 0.222 0.075
2 0.079 0.114 0.116
3 0.035 0.125 0.138
4 0.062 0.309 0.155
5 0.028 0.315 0.170
6 0.130 0.385 0.183
7 0.089 0.000 0.228
8 0.024 0.000 0.284
9 0.044 0.000 0.304
10 0.064 0.000 0.319
11 0.034 0.000 0.336
12 0.000 0.000 0.370
[SIGMA] 0.811

n DIF [%] t [s]

 0 0

1 -0.015 -20.4 60
2 -0.016 -14.2 300
3 -0.018 -13.3 300
4 -0.025 -16.4 780
5 -0.020 -11.8 1020
6 -0.023 -12.8 1260
7 -0.012 -5.4 2160
8 -0.019 -6.8 3360
9 -0.024 -8.0 3780
10 -0.009 -2.8 4080
11 0.023 6.7 4440
12 0.018 5.0 5100
[SIGMA]