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Thermoelectric wear in tools
Wear, 26 (1973) 3944 0 Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands
THERMOELECTRIC
39
WEAR IN TOOLS
H. BAGCHI and S. K. BASU Mechanical Engineering Research and Development Organisation, Poona-8 (India)
(Received November 3, 1972; in revised form March 26, 1973)
SUMMARY
Thermoelectric tool wear was measured by the thermocurrent generated in Machine-Tool-Workpiec-Machine (MTWM) circuit. The relationship between thermocurrent and the cutting parameters in the machining of EN 24 steel with a carbide tool and the significance of the influencing parameters are assessed statistically.
NOMENCLATURE
Speed, m/min feed, mm/rev t depth of cut, mm r time of cut, min r nose radius of tool, mm Z thermocurrent, A b,, b, coefficient of regression equation. correlation coefficient between Y and Xi rOi r.. correlation coefficient between ith and jth variable (Xi or Xj) ? logarithmic value of thermocurrent logarithmic value of cutting parameters Xi average value of Xi xi Y average value of Y (T standard deviation chi-square value x2 INTRODUCTION
Thermoelectric wear of a cutting tool caused by the thermoelectric current generated in MTWM circuit is a complex phenomenon dependent on variables other than the normal cutting parameters. The magnitude of thermoelectric tool wear can be controlled by the cutting variables. Experimental results of the machining of EN 24 stee1 with carbide tools were analysed to establish generalised equations connecting thermoelectric current wit.h significant parameters.
40
H. BAGCHI,
DESIGN
S. K. BASU
OF EXPERIMENTS
Experiments were designed on live factors factorial regression constructing 25 blocks under two levels of experimentation as shown in Table I. Thermocurrent was measured by a milliammeter using a current pick up as shown in Fig. 1; 32 sets of readings were taken, Table II. It is customary to employ high order interactions as an estimate of error variance. Bartlett’s criterion as reported by Davies’ was applied to determine if high order interactions were relevant (see appendix A). At the 1% significance level, the high order interactions could be compiled to form an error variance. Table III gives the variance analysis of the results given in Table II. It is noted that the main variables, speed, feed, depth of cut, time of cut and nose radius of the tool all have a significant effect on the thermocurrent as the F-value corresponding to error variance was 8.5. The interaction of (speed x depth of cut) and (feed x depth of cut) are just significant at the 1% significance level. Thus the effect of speed may be dependent on the depth of cut. Experiments carried out to investigate the effect of interaction showed little interaction. Thus controlling factors may be graded: (1) speed, (2) feed, (3) depth of cut, (4) time of cut, (5) nose radius of tool. TABLE
I
TWO LEVELS
High Low
OF EXPERIMENTATION
FOR
FIVE FACTORS
V (factor A) (mjmin)
f (factor B) (mm/rev)
T (factor D) (min)
r (factor E)
(mm)
126 56
0.20 0.05
1.5 0.25
10 2
1.2 0.8
Fig. 1. Experimental
set up for measuring
t (factor C)
(25 BLOCK)
thermocurrent;
(1) current
pick-up,
(mm)
(2) milliammeter,
(3) job.
THERMOELECTRIC
41
WEAR IN TOOLS
TABLE II OBSERVATIONAL
DATA FOR THERMOCURRENT
Speed (m/min)
Feed (mmlrev)
Depth of cut (mm)
Time of cut (min)
Nose radius
no.
(mm)
Thermocurrent (Ix IO5 A)
1 2 3 4 5 6 I 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
52 126 52 126 52 126 52 126 52 126 52 126 52 126 52 126 52 126 52 126 52 126 52 126 52 126 52 126 52 126 52 126
0.05 0.05 0.2 0.2 0.05 0.05 0.2 0.2 0.05 0.05 0.2 0.2 0.05 0.05 0.2 0.2 0.05 0.05 0.2 0.2 0.05 0.05 0.2 0.2 0.05 0.05 0.2 0.2 0.05 0.05 0.2 0.2
0.25 0.25 0.25 0.25 1.5 1.5 1.5 1.5 0.25 0.25 0.25 0.25 1.5 1.5 1.5 1.5 0.25 0.25 0.25 0.25 1.5 1.5 1.5 1.5 0.25 0.25 0.25 0.25 1.5 1.5 1.5 1.5
2 2 2 2 2 2 2 2 10 10 10 10 10 10 10 10 2 2 2 2 2 2 2 2 10 10 10 10 10 10 10 10
0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2
I 13 12 19 11.5 16.5 15.5 20.5 9.5 15.5 14.5 20.5 14.5 18.5 16.5 22.5 8 16 14 20 13.5 17.5 16.5 22.5 8.5 16.5 16 22 15 19 19 25
Sl.
MULTIPLE
REGRESSION
TECHNIQUE
In the multiple regression technique2, only the first four significant parameters have been considered as the nose radius is the least significant and difficult to control. If all other factors remain constant, it is assumed that Z=Z%f,~,r) Approximating
a response surface Y =log,,Z
and it is exponential in nature.
Y=b,x,+b,x,+b,x,+b,x,+c where x is the logarithmic transformed values of parameters, b the regression coefficients and c the logarithmic transformed value of the constant relating the function.
42
H. BAGCHI,
TABLE
III
ANALYSIS
OF VARIANCE
BASED
Sources
Sum of
Degrees
of
square
of
variation
ON RESULTS
SHOWN
Mean square
F
210 180 85 28 15.2 0.28 5.3 4.5 0.03 0.125 0.125 0.28 1.13 0.125 0.5 0.5
54O* 36O* 160* 56* 30.4* 0.56 10.6* 9.0* 0.06 0.25 0.25 0.56 2.26 0.25 1.0
IN TABLE
II
freedom
A B C D E AB AC BC AD BD CD AE BE CE DE Error (high order interaction) Total:
l
S. K. BASU
Significant
270 180 85 28 15.2 0.28 5.3 4.5 0.03 0.125 0.125 0.28 1.13 0.125 0.5 8.1
16
598.695
31
1 1 1 1 1 1 1 1 1 1
1 1 1
I I
at 1% level.
100 observational readings were taken during the experimentation. Standard deviations and mean of the 100 experimental readings are given below: Y = 1.3083 x, = 1.9713 ;I;; = 1.8330 zs = 2.6682 x, = 0.7037 Correlation rol =
coefficients are given below
0.810 0.146 rc,s= 0.392 Yo4= 0.344 r12 = 0.062 r13= 0.172 r14= -0.038 r2s = - 0.605 r24 = 0.602 rJ4 = 0.023 r 02=
co= 11.5 x 1o-2 fll = 17.71 x lo- 2 0,=19.42x 1O-2 03 = 30.41 x lo- 2 0,=26.40x 1O-2
THERMOELECTRIC
WEAR IN TOOLS
43
Regression coefficients were calculated as b, = b, =
0.462 0.265 b,= 0.177 b,= 0.148 c = -0.663 Hence the final equation attains the form 1 = 0.2178 v0.462f0.265~0.177T0.148 where u in m/min, f in pm/rev, t in pm and r in min. Using a multiple regression coefficient of 0.9872 a nomogram to calculate I is given in Fig. 2.
I55 150
_ ..
IS0
140
..
140
130
.
120
‘.
110
.-
130
1100
-
1400
.-
1300
*.
1200
.-
II00
..
45
II IO
40
9 8
35
7
120
b
110
5 100 100
25
.
4 22 90
boo--
.-
70 .-
LO.-
56, V c MlMlN.)
CMICRON/T(EY.>
CMICRON
)CAMPX
lo’,
C MIN.)
Fig. 2. Nomogram for thermocurrent.
Testing the goodness of fit for the regression equation by Chi-Square (x2) test’ showed that calculated value of x2 is much less than the tabulated value of 1’. Hence the regression equation is correct.
44
H. BAGCHI,
S. K. BASU
CONCLUSION
(i) Thermoelectric tool wear and thermocurrent are related and wear can be assessed by the thermocurrent in the MTWM circuit. (ii) Speed, feed, depth of cut, time of cut and nose radius of the tool have a significant effect on thermocurrent and hence on thermoelectric tool wear. (iii) The thermoelectric current can be determined from the nomogram constructed. ACKNOWLEDGEMENTS
The authors thank Dr. A. K. De, Director, CMERI, Durgapur-9, for allowing them to carry out the work at MERADO, Poona, and Mr. Krishna and Mr. Shinde for their help and co-operation. REFERENCES 1 0. L. Davies, Design and Analysis of Industrial Experiments, Imperial Chemical Industries Ltd., London, 1954. 2 G. U. Yule and M. G. Kendall, An Introduction to the Theory of Statistics, Griffin, London, 1916.
APPENDIX
A
Bartlett’s criterion to determine high order interactions Referring to Davies’ for Bartlett’s criterion, total mean squares of high order interactions (starting from 3-order) x lo2 = 810. Since there are 16 high order interactions T/= 810 = 50.6 ~i=l, ~=16 In Vy2.3 x 1.704 = 3.92 16 In V= 62.8 Z log (MS x 102) = 16.902 = X log v X In y = 38.8 M=161n V-Xln v=62.8-38.8=24 To apply F test A
=
@+I) 3
P+l) = 0.354 = ___ 3x 16
fr=K-1=15 f2 = (K + l)/A2 = 17/(0.354)2 = 133 b = [l+k2,f2,
= [1-0,3:::2,133,
= 204
b-M=204-24=180 f2.M
F =f,(b-M)
133 x 24 ___ = 1.18 = 15 x 180
From the F-table the F value is not significant at the 1% level. Hence high order interactions can be compiled to form error variance.
THERMOELECTRIC
39
WEAR IN TOOLS
H. BAGCHI and S. K. BASU Mechanical Engineering Research and Development Organisation, Poona-8 (India)
(Received November 3, 1972; in revised form March 26, 1973)
SUMMARY
Thermoelectric tool wear was measured by the thermocurrent generated in Machine-Tool-Workpiec-Machine (MTWM) circuit. The relationship between thermocurrent and the cutting parameters in the machining of EN 24 steel with a carbide tool and the significance of the influencing parameters are assessed statistically.
NOMENCLATURE
Speed, m/min feed, mm/rev t depth of cut, mm r time of cut, min r nose radius of tool, mm Z thermocurrent, A b,, b, coefficient of regression equation. correlation coefficient between Y and Xi rOi r.. correlation coefficient between ith and jth variable (Xi or Xj) ? logarithmic value of thermocurrent logarithmic value of cutting parameters Xi average value of Xi xi Y average value of Y (T standard deviation chi-square value x2 INTRODUCTION
Thermoelectric wear of a cutting tool caused by the thermoelectric current generated in MTWM circuit is a complex phenomenon dependent on variables other than the normal cutting parameters. The magnitude of thermoelectric tool wear can be controlled by the cutting variables. Experimental results of the machining of EN 24 stee1 with carbide tools were analysed to establish generalised equations connecting thermoelectric current wit.h significant parameters.
40
H. BAGCHI,
DESIGN
S. K. BASU
OF EXPERIMENTS
Experiments were designed on live factors factorial regression constructing 25 blocks under two levels of experimentation as shown in Table I. Thermocurrent was measured by a milliammeter using a current pick up as shown in Fig. 1; 32 sets of readings were taken, Table II. It is customary to employ high order interactions as an estimate of error variance. Bartlett’s criterion as reported by Davies’ was applied to determine if high order interactions were relevant (see appendix A). At the 1% significance level, the high order interactions could be compiled to form an error variance. Table III gives the variance analysis of the results given in Table II. It is noted that the main variables, speed, feed, depth of cut, time of cut and nose radius of the tool all have a significant effect on the thermocurrent as the F-value corresponding to error variance was 8.5. The interaction of (speed x depth of cut) and (feed x depth of cut) are just significant at the 1% significance level. Thus the effect of speed may be dependent on the depth of cut. Experiments carried out to investigate the effect of interaction showed little interaction. Thus controlling factors may be graded: (1) speed, (2) feed, (3) depth of cut, (4) time of cut, (5) nose radius of tool. TABLE
I
TWO LEVELS
High Low
OF EXPERIMENTATION
FOR
FIVE FACTORS
V (factor A) (mjmin)
f (factor B) (mm/rev)
T (factor D) (min)
r (factor E)
(mm)
126 56
0.20 0.05
1.5 0.25
10 2
1.2 0.8
Fig. 1. Experimental
set up for measuring
t (factor C)
(25 BLOCK)
thermocurrent;
(1) current
pick-up,
(mm)
(2) milliammeter,
(3) job.
THERMOELECTRIC
41
WEAR IN TOOLS
TABLE II OBSERVATIONAL
DATA FOR THERMOCURRENT
Speed (m/min)
Feed (mmlrev)
Depth of cut (mm)
Time of cut (min)
Nose radius
no.
(mm)
Thermocurrent (Ix IO5 A)
1 2 3 4 5 6 I 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
52 126 52 126 52 126 52 126 52 126 52 126 52 126 52 126 52 126 52 126 52 126 52 126 52 126 52 126 52 126 52 126
0.05 0.05 0.2 0.2 0.05 0.05 0.2 0.2 0.05 0.05 0.2 0.2 0.05 0.05 0.2 0.2 0.05 0.05 0.2 0.2 0.05 0.05 0.2 0.2 0.05 0.05 0.2 0.2 0.05 0.05 0.2 0.2
0.25 0.25 0.25 0.25 1.5 1.5 1.5 1.5 0.25 0.25 0.25 0.25 1.5 1.5 1.5 1.5 0.25 0.25 0.25 0.25 1.5 1.5 1.5 1.5 0.25 0.25 0.25 0.25 1.5 1.5 1.5 1.5
2 2 2 2 2 2 2 2 10 10 10 10 10 10 10 10 2 2 2 2 2 2 2 2 10 10 10 10 10 10 10 10
0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2
I 13 12 19 11.5 16.5 15.5 20.5 9.5 15.5 14.5 20.5 14.5 18.5 16.5 22.5 8 16 14 20 13.5 17.5 16.5 22.5 8.5 16.5 16 22 15 19 19 25
Sl.
MULTIPLE
REGRESSION
TECHNIQUE
In the multiple regression technique2, only the first four significant parameters have been considered as the nose radius is the least significant and difficult to control. If all other factors remain constant, it is assumed that Z=Z%f,~,r) Approximating
a response surface Y =log,,Z
and it is exponential in nature.
Y=b,x,+b,x,+b,x,+b,x,+c where x is the logarithmic transformed values of parameters, b the regression coefficients and c the logarithmic transformed value of the constant relating the function.
42
H. BAGCHI,
TABLE
III
ANALYSIS
OF VARIANCE
BASED
Sources
Sum of
Degrees
of
square
of
variation
ON RESULTS
SHOWN
Mean square
F
210 180 85 28 15.2 0.28 5.3 4.5 0.03 0.125 0.125 0.28 1.13 0.125 0.5 0.5
54O* 36O* 160* 56* 30.4* 0.56 10.6* 9.0* 0.06 0.25 0.25 0.56 2.26 0.25 1.0
IN TABLE
II
freedom
A B C D E AB AC BC AD BD CD AE BE CE DE Error (high order interaction) Total:
l
S. K. BASU
Significant
270 180 85 28 15.2 0.28 5.3 4.5 0.03 0.125 0.125 0.28 1.13 0.125 0.5 8.1
16
598.695
31
1 1 1 1 1 1 1 1 1 1
1 1 1
I I
at 1% level.
100 observational readings were taken during the experimentation. Standard deviations and mean of the 100 experimental readings are given below: Y = 1.3083 x, = 1.9713 ;I;; = 1.8330 zs = 2.6682 x, = 0.7037 Correlation rol =
coefficients are given below
0.810 0.146 rc,s= 0.392 Yo4= 0.344 r12 = 0.062 r13= 0.172 r14= -0.038 r2s = - 0.605 r24 = 0.602 rJ4 = 0.023 r 02=
co= 11.5 x 1o-2 fll = 17.71 x lo- 2 0,=19.42x 1O-2 03 = 30.41 x lo- 2 0,=26.40x 1O-2
THERMOELECTRIC
WEAR IN TOOLS
43
Regression coefficients were calculated as b, = b, =
0.462 0.265 b,= 0.177 b,= 0.148 c = -0.663 Hence the final equation attains the form 1 = 0.2178 v0.462f0.265~0.177T0.148 where u in m/min, f in pm/rev, t in pm and r in min. Using a multiple regression coefficient of 0.9872 a nomogram to calculate I is given in Fig. 2.
I55 150
_ ..
IS0
140
..
140
130
.
120
‘.
110
.-
130
1100
-
1400
.-
1300
*.
1200
.-
II00
..
45
II IO
40
9 8
35
7
120
b
110
5 100 100
25
.
4 22 90
boo--
.-
70 .-
LO.-
56, V c MlMlN.)
CMICRON/T(EY.>
CMICRON
)CAMPX
lo’,
C MIN.)
Fig. 2. Nomogram for thermocurrent.
Testing the goodness of fit for the regression equation by Chi-Square (x2) test’ showed that calculated value of x2 is much less than the tabulated value of 1’. Hence the regression equation is correct.
44
H. BAGCHI,
S. K. BASU
CONCLUSION
(i) Thermoelectric tool wear and thermocurrent are related and wear can be assessed by the thermocurrent in the MTWM circuit. (ii) Speed, feed, depth of cut, time of cut and nose radius of the tool have a significant effect on thermocurrent and hence on thermoelectric tool wear. (iii) The thermoelectric current can be determined from the nomogram constructed. ACKNOWLEDGEMENTS
The authors thank Dr. A. K. De, Director, CMERI, Durgapur-9, for allowing them to carry out the work at MERADO, Poona, and Mr. Krishna and Mr. Shinde for their help and co-operation. REFERENCES 1 0. L. Davies, Design and Analysis of Industrial Experiments, Imperial Chemical Industries Ltd., London, 1954. 2 G. U. Yule and M. G. Kendall, An Introduction to the Theory of Statistics, Griffin, London, 1916.
APPENDIX
A
Bartlett’s criterion to determine high order interactions Referring to Davies’ for Bartlett’s criterion, total mean squares of high order interactions (starting from 3-order) x lo2 = 810. Since there are 16 high order interactions T/= 810 = 50.6 ~i=l, ~=16 In Vy2.3 x 1.704 = 3.92 16 In V= 62.8 Z log (MS x 102) = 16.902 = X log v X In y = 38.8 M=161n V-Xln v=62.8-38.8=24 To apply F test A
=
@+I) 3
P+l) = 0.354 = ___ 3x 16
fr=K-1=15 f2 = (K + l)/A2 = 17/(0.354)2 = 133 b = [l+k2,f2,
= [1-0,3:::2,133,
= 204
b-M=204-24=180 f2.M
F =f,(b-M)
133 x 24 ___ = 1.18 = 15 x 180
From the F-table the F value is not significant at the 1% level. Hence high order interactions can be compiled to form error variance.