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Analysis of mechanical wear during grinding by empirical-stochastic models
Wear, 29 (1974) 247-257 (cl Elsevier Sequoia S.A., Lausanne
247 - Printed
in The Netherlands
ANALYSIS OF MECHANICAL WEAR DURING EMPIRICAL-STOCHASTIC MODELS
GRINDING
BY
S. J. DEUTSCH Georgia Institute of Technology, School of Industrial and Systems Engineering, Atlanta, Georgia 30332 (U.S.A.) S. M. WU Unioersity of Wisconsin, Department of Mechanical Engineering, Madison, Wisconsin 53705 (U.S.A.) (Received
March
19, 1974)
SUMMARY
The wear process caused by the grinding wheel-workpiece interaction is analyzed. An empirical-stochastic model is used to .characterize sequential profile measurements obtained during two different grinding cycles. The type and rate of mechanical wear which altered the wheel configuration are identified and quantified from the resulting model parameters. Relationships between the wear process and the corresponding three stages of the observed wheel wear curves are discussed.
INTRODUCTION
The decipherment of the wheel wear phenomena caused by the interaction between the wheel and workpiece is a crucial step in the eventual optimization of grinding performance. Visual observation of this process from either the viewpoint of the actual contact between tool and workpiece or the type of chip produced (which has proven useful for other metal cutting operations) is difficult due to the high wheel speeds and small magnitude of the chips. Furthermore due to the intricate configuration of the wheel, the nature of the metal removal and tool wear phenomena is more complex than any other metal cutting process. Much experimental work has been conducted to analyze both the chemical and mechanical wear during grinding14. Although chemical wear can comprise a significant part of the total wear in a grinding process, for a high purity aluminum oxide wheel and steel workpiece combination, chemical wear is small’. In this case, the effects of the machining variables on grinding wheel wear may be adequately described in terms of the two principal components of mechanical wear: attrition and fracture. Due to the complexity of the tool cutting space, investigators in order to analyze mechanical wear, have abstracted from the total cutting configuration of the wheel, a single grain mounted in a holder to simulate the whee13. This enabled visual or analytical analysis of the intricate phenomena to be made, however such simplification constrained the analysis to solely attritious wear.
S. J. DEUTSCH.
248
S. M. WU
Empirical-stochastic models of grinding wheel cross-sectional configurations have proved noteworthy in describing their topographies5-‘. A recent analysis has shown the cutting space of the wheel to consist of a pseudo-period, formed by aggregates of grits above and below a mean profile height value’. Therefore, all three types of metal removal processes (rubbing, ploughing and cutting) would be expected to occur simultaneously in actual grinding. In turn depending upon these relative occurrences and their duration, the nature of the ongoing mechanical wear process would be determined. This paper presents a preliminary investigation in which the entire wheel configuration was employed in analyzing the nature of the wheellworkpiece interaction. The objectives of this study were to identify the components of mechanical wear while quantifying the corresponding rates of wear occurring during actual cutting in a grinding cycle. The experimental procedures. equipment and data collection effort are first delineated. Four measurements of the wheel configuration were taken for each of two different grinding cycles at corresponding locations in their respective wheel wear curves. The wheel conligurations were then described via an empirical-stochastic model. The resulting estimated parameters which completely describe the information contained in the wheel profiles are employed to delineate and compare the type and rate of the wear phenomena occurring during each grinding cycle. Photographs of the wheel topography are presented to complement the statistical analysis. EXPERIMENTAL
PROCEDURES
A DoAll precision surface grinder, model D824-10 was used during the course of this investigation. All tests were conducted using plunge grinding on workpieces cut from high speed tool steel, M-2, through hardened to 62---63 Rockwell C. The experiment consisted of grinding a single face of the prepared specimens using a high purity aluminum oxide 4658 wheel at a preselected combination of wheel speed, table speed and depth of cut. Two different grinding cycles were run. Both cycles employed a single depth of cut and wheel speed combination (0.002 in. and 4500 ft/min) but each differed in the selection of their table speeds. Cycle I had a table speed of 10 ft/min while that for cycle II was 20 ft/min. Each grinding cycle was terminated when the wheel noise indicated the tool cutting space to have sufficiently degraded. Measurements of both the ground specimens and the grinding wheel were made simultaneously during each cycle. For each of the block specimens the height dimension before and after grinding was recorded. From this dimensional change, the amount of metal removal was determined. The corresponding wheel wear volume was obtained by concurrently measuring the decrease in the wheel diameter. The wheel wear volume and metal removal volume were used to construct the corresponding wheel wear curves for the experiment. This on line construction enabled quick detection of the transition points separating the three stages of the wheel wear curve. Thus after each stage, the wheel’s cross-sectional configuration was measured. For each cycle, then a total of the four essential measurements of the changing wheel profile was obtained; the freshly dressed condition, the end of stage one and two and lastly the end of stage three or cycle termination. To
.O
I
200.0
configuration
NUMBER OF OBSERVATIONS
100.0
NO. 3
NO.
Fig. 1. Digitized cross-sectional after stage three.
0.0
,
40.07
of 4658 wheel during
300.0
0
.O
L
L
100.0
200.0
200.0
.
.
I
1
300.0
300.0
(2) after stage one. (3) after stage two, (4)
100.0
No. 4
NO.2
cycle I. (1) freshly dressed,
00
25.0
5ao
“._
5ao
I----
200.0
Fig. 2. Digitized after stage three.
cross-sectional
configuration
300-o
of 4658 during
NUMBER OF OBSERVATIONS
100.0
.O
3
NO.1
p “““F NO. c
r
50.0 c
cycle II. (1) freshly
.O
dressed,
.o
(2) after
100.0
100.0
stage
one, (3) after
200.0
zoo.0
stage
two. (4)
330.0
300.0
251
WEAR DURING GRINDING
-_____-__
Fig. 3. Sample correlations and partial correlation functions for cycle I. Fig. 4. Sample correlations and partial correlation functions for cycle II.
complement these profile measurements visually, photographs of the same section of the wheel topography were taken using a camera equipped with a high axial resolution objective lens”. STOCHASTIC MODELING
OF THE GRINDING
CYCLE
Figures 1 and 2 each contain computer drawings of the four digitized peak to valley profiles recorded sequentially during cycles I and II respectively. The pseudo-sinusoidal decay exhibited in the sample correlation functions and the truncation of the sample partial correlation functions after two lags, led to the tentative identification of an autoregressive model of order two for all eight profiles (Figs. 3 and 4)“*“. The parameters of each model were estimated and from each fitted model the residuals calculated. The correlation functions of these residual sets did not exibit any additional discernible structure. In addition, since the histograms of the residuals for each series appeared reasonably normal’ O,the models were accepted as adequate. Therefore, during each of the two cycles the same model form,
where a, N NID (0, a:), y. = Variance (Z,), and dr, C#I~are autoregressive parameters, appears adequate in describing the changing physical configuration of the wheel due to wear.
S.J. DEUTSCH, S. M. WU
252 TABLE I STATISTICAL
SUMMARY
OF CYCLES I AND 11
Model no.
Metal removed (in’)
c$,
CYCLE I 1 2 3 4
0.000 0.088 0.367 0.468
0.95228 0.98190 0.93143 0.96603
CYCLE II 1 2 3 4
0.000 0.067 0.174 0.241
0.99540 1.01322 0.82717 0.98983
YO
Pseudoperiod (in. x 103)
-0.18126 - 0.20280 -0.17123 - 0.28740
28.2560 26.5029 26.0165 26.2282
49.2 49.0 48.4 55.4
-0.23579 - 0.24599 - 0.22670 -0.12988
30.8407 28.9432 26.0360 25.8217
44.0 44.8 48.9 84.0
0.050 cl
c
I
W 0.040 H E E L
0.030
W
.k
R 0.020 (lN3,
-
/ /
/ /,X0 ,X’
.x
_NX
/-
/” XI’
WHEEL
: 32A.46
WORK
MATERIAL,
HARDNESS
I I 0.010
d
I 0.10
SPEED
DEPTH
OF CUT : 0.002
METAL
REMOVED
CM21
3 19.0 I 0.50
I 0.40
INCHES F/M
1 0.60
(lN3)
x I
b
; I
i 0.020 -
:
I’
: E 0.015 -
W : R
’ 4500
RATIO
0.025
L
STEEL
3 IO F/M
SPEED
I 0.30
0.20
TOOL
TABLE WHEEL
0.00
JBVBE
2 62 RC
GRINDING
W
/x
x’
x’ x
0.010 -
(IN’)
/’
/’
P’ x-WHEEL: 32A46 J8VBE WORK MATERIAL~TOOL
/’
DEPTH
1”
OF CUT iO.002
WHEEL
0.005
STEEL
(M2)
HARDNESS j 62 RC TA6LE SPEED: 20 F/M
I’
SPEED:
GRINDING
RATIO-
4500
INCHES F/M
27.6
,’ t
L
0.00
,
I
0.10 METAL
0.20 REMOVED
/
0.30
(IN3)
Fig. 5. Wheel wear curves for (a) grinding cycle I, (b) grinding cycle II.
WEAR
DURING
253
GRINDING
It should be noted, that since the model forms are the same, any change in the wheel configurations due to wear will be directly reflected by the changes in the estimates of the parameters of the second order autoregressive process, 41, 42 and ye. Table I lists the eight sets of estimated model parameters and the corresponding pseudo-periods which are functions of the estimates 4,) 42’os ‘I. ANALYSIS
OF EXPERIMENTAL
RESULTS
The wheel wear curves, relating volume of wheel wear versus volume of metal removed are shown for each cycle in Fig. 5. Each curve displays the three characteristic stages: the rapid initial wear stage, the constant wear stage and the rapid wear-out stage. Figures 6 and 7 display the pseudo-periods and profile variances (obtained from the modeling sequences) versus the metal removed during the cycle. Similarly, the profile peak to valley distance obtained during the modeling sequence is plotted uersus metal removed in Fig. 8. By comparing these figures, which use the amount of metal removed as a common basis, the transitions in the wheel’s pseudo-period and variance are seen to readily correspond to the three stages of the wheel wear curve. 29.0
r CYCLE
0.15
32.0
I
0.30
0.45
0.60
r CYCLE
<
II
A
r,26.0
40.0
’
0.10
0.20 METAL
Fig. 6. Profile pseudo-periods
I 0.30 REMOVED
0.40
0.50
24.0L
( IN3)
OS. metal removed
Fig. 7. Profile variances
us. metal removed
(a)
ofthe wheel wear
The first stage
, 0.60
-
I 0.10 METAL
I
, 0.20
REMOVED
I 0.30 IIN31
for cycles I and II.
for cycles I and II.
Through the first two stages of wheel wear, the profile pseudo-periods for each cycle are seen from Fig. 6 to remain essentially constant. In addition, the rate of wheel wear, as seen from the slopes of the individual stages of the wheel
254
S. J. DEUTSCH, S. M. WU
wear curves (Fig. 5) or of the profile plot (Fig. 8) is many times larger during stage one than stage two. Lastly, there is for stage one a sharp drop in the profile variance of each cycle. Since the 4658 wheel has approximately two grains per pseudo-period*, these three simultaneous occurrences suggest the dominance of some type of a fracture mechanism during stage one. This information by itself, however, cannot be used to distinguish clearly whether this fracturing is due to a whole grain rupturing from its supporting bond matrix or is due to the subdividing of single grains into parts or some combination of the two. The identification of the proper mechanism from these alternatives is aided by viewing the differences in the initial or freshly dressed wheel topographies observed for each cycle. For each cycle, two passes at a depth of penetration of 0.002 in. were made with the diamond tool. The traverse rate in both cases was 0.15 in./s. In cycle I a third pass, identical to the first two, was made. In cycle II, however, multiple passes at these same conditions were made until sparkout. Thus all grains which protruded into the cutting tool space are either cut or fractured until no further interferences between tool and wheel exists. Under identical dressing conditions, empirical-stochastic models and their associated parameters developed for cross-sectional measurement anywhere on the cutting face have been shown to be statistically identical tx7. Therefore real differences in the profile characteristics as indicated by the significant differences in the model parameters noted for model one of cycle I and II can be attributed to the differences in the dressing methods employed. One effect of the different dressing procedures appears to be the different initial peak to valley distance within the cutting profile (Fig. 8). The profile depth height of cycle I is seen to be larger than that of cycle II (23.6 x 10m3 versu.s 23.0 x lop3 in.). In addition from the initial dressed condition, until the onset of the second stage of constant wear, the wheel used in cycle I wore twice the amount of the wheel prepared for cycle II (1.0 x 1O-3 uersus 0.5 x 10e3 in.). At the onset of the second stage of wheel wear however, wheels for both cycles exhibit nearly equivalent peak to valley heights. Since the pseudo-periods have been constant while the peak to valley depth of each cycle is adjusted at different rates until reaching a nearly identical configuration, there appears to be a dominance of fracture within the grains due to the stabilization of the wheel structure. Further, the rate of fracture appears to depend upon the degree of occurrence of nonobliquely oriented or nonstable grits imminent within the wheel profile due to the configuration imposed by the dressing conditions. (b)
The second stage of wheel wear During the course of the second state, the pseudo-periods do not exhibit any pronounced changes but remain essentially constant while the profile variance decreases (Figs. 6 and 7 respectively). In addition, as seen from the wheel wear curves, Fig. 5 or the profile depth plot, Fig. 8, the rate of wheel wear during the second stage is small compared to the first stage in which fracture wear dominates. This coalition of events is indicative of the dominance of an attritious wear process. When comparing the rates of change of the variance with respect to the
WEAR
DURING
3.00 W
255
GRINDING
CYCLE
I
x----x
CYCLE
I[
v
r
: E L
,x
2.00
1.00
..
,x’
::
r
(X IOt31N)
I” 0.00
24.00
P R 0 F
1. \
II E D E P T H
--x
(X lot3 IN)
21.00-
8
’ 0.15 METAL
Fig. 8. Vertical
. .
’ 0.30
a
REMOVED
.X ’ 0.45
profile dimensions
Fig. 9. Wheel photographs removed.
’ 0.60
(IN31
vs. metal removed.
for cycle II. (a) as dressed,
(b) 0.07 in3 metal
removed,
(c) 0.18 in3 metal
256
S. J. DEUTSCH,
S. M. WU
amount of metal removed for each cycle (Fig. 7) the rate for cycle II is seen to be approximately eighteen times that of cycle I (29.0 versus 1.6) although both cycles exhibit an identical rate of change in peak to valley depth. This high rate of change for cycle II is of the same order of magnitude, as the rate of change of the variance exhibited in both cycles during the lirst stage of wear. Thus only in cycle II, which is run at twice the table speed of cycle I, does there appear to be any appreciable quantity of wear due to fracture. The performance of any wheel during stage two of the grinding cycle is dependent upon the relative occurrences of attritious and fracture wear. A proper “balance” guaranteeing the rejuvenation of fresh cutting edges. A measure of the wheel’s ability to “balance” these mechanisms observed would be the consistency of the pseudo-period and profile variance during the cycle. Model number two and three of each cycle (Table I) correspond to the stochastic model representations of the wheel configuration at the beginning and end of the second wear stage. From the numerical changes in the value of the pseudo-periods and profile variances, it is seen that neither of the two cycles has undergone total selfdressing during the constant wear stage. Although for each cycle the period remains essentially constant, the variance does significantly decrease for both cycles. The latter phenomenon being indicative of either a smoothing of the cutting edges of the grains or wheel loading or a combination of the two. (c)
7he third stage of wheel wear
Both experiments exhibit a dominant increase in the pseudo-periods of the wheel profile near the third stage of the cutting cycle (Fig. 6). This increase in the average profile periods (which is synonymous with an increase in the intergrain spacing since the 46 grit wheel contains two grains per pseudo-period) would result from an increased propensity for the grits to be either pulled out of the bond matrix in entirety or partially fractured. It should be noted that the third stage of the wheel wear curve is more pronounced for cycle II than it is for cycle I. The change in the wheel periods is likewise more pronounced for cycle II than cycle I. The transition point in the wear curves between stages I and II is seen to correspond to the point for which there is a noticeable increase in the profile periods. For example, in Fig. 5 the transition point is seen to be approximately 0.40 in3 of metal removed. From Fig. 6, the period of the profile tends to increase likewise, at 0.40 in3 of metal removed. A similar comparison for cycle II indicates a more pronounced common transition point at about 0.18 in3 of metal removed. Thus the rapid wear out stage appears to be initiated by the increased proliferation of the whole or nearly whole grains fracturing from the bond matrix. Figure 9 illustrates an example of this phenomenon. Three photographs were taken of the same section of the wheel periphery during cycle II. The photographs show the freshly dressed wheel and the wheel after 0.07 and 0.18 in3 of metal removed. In addition to showing a gradual increase in number as well as size of the flats caused by attrition during stage II, a dislodging of a grain is seen for the lirst time in the lower right quarter of the photographs which correspond to the onset of stage III at 0.18 in3 of metal removed.
WEAR
DURING
GRINDING
257
CONCLUSIONS
Employing the total grinding wheel topography a preliminary experimental study was conducted to analyze the nature of the ongoing mechanical wear phenomena occurring during the grinding cycle. From the parameters of empiricalstochastic models built to describe sequentially measured wheel configurations during two different grinding cycles, the type of mechanical wear was segregated, quantified and associated to a particular stage of the wheel wear curve. For the two different grinding cycles analyzed, the following observations were made regarding wheel wear during the three stages of the wheel wear curve. (a) During the first stage, fracture accounted for a major part of the wheel wear. The dressing conditions were seen to determine the nature of this fracturing. When a wheel was not dressed until sparkout there was a greater occurrence of fracture within a single grit than dislodging of whole grains from the bond matrix. (b) Attritious wear is the dominant wear mechanism occurring during the second stage. The ability of the wheel to self-dress by balancing fracture and attritious wear was quantified by using the empirical stochastic model parameters. (c) The fracture of whole grains from the wheel due to the rupturing of bond posts appears to correspond to the onset of the third stage as well as being the predominant wear mechanism during this stage. ACKNOWLEDGEMENTS
The authors are indebted and the University of Wisconsin project, as well as to the Norton
to the Wisconsin Alumni Research Foundation Computer Center for financial support of this Company for supplying the grinding wheels.
REFERENCES 1 J. Peklenik, Untersuchungen iiber das Verschleisskriterium beim Schleifer, Ind.-Am., 80 (27) (1958) 397. 2 H. Tsuwa, Evaluation of grinding by behavior of cutting edges, Sci. Much., Japan, 13 (1961) 237. 3 N. Takenaka, A study of the grinding action by single grit, Ann. C.I.R.P., XIII (1966) 183-190. 4 N. S. Eiss, Jr., Fracture of abrasive grain in grinding, J. Eng. hd., B89 (1967) 463470. 5 J. Peklenik, Contribution to the correlation theory for the grinding process, J. Eng. Znd., B86 (1964) 85-94. 6 C. M. Stralkowski, S. M. Wu and R. E. DeVor, Characterization of grinding wheel profiles by autoregressive-moving average models, Znt. J. Mach. Tool Des. Res., 9 (1969) 145-163. 7 S. J. Deutsch and S. M. Wu, Selection of sampling parameters for modeling grinding wheels, J. Eng. Znd., B92 (1970) 667-677. 8 S. J. Deutsch and S. M. Wu, Relationship between the parameters of an autoregressive model and grinding wheel constituents, J. Eng. Znd., B95 (1973). 9 S. J. Deutsch, S. M. Wu and C. M. Stralkowski. A new irregular surface measuring system, Znt. J. Mach. Tool Des. Res., 13 (1973) 24442. 10 S. J. Deutsch, An analysis of the structure and wear of grinding wheels by autoregressive-moving average models, Ph. D. Thesis. University of Wisconsin. 1970. 11 G. E. P. Box and G. M. Jenkins, Time Series Analysis Forecasting and Control, Holden-Day, San Francisco, 1970.
247 - Printed
in The Netherlands
ANALYSIS OF MECHANICAL WEAR DURING EMPIRICAL-STOCHASTIC MODELS
GRINDING
BY
S. J. DEUTSCH Georgia Institute of Technology, School of Industrial and Systems Engineering, Atlanta, Georgia 30332 (U.S.A.) S. M. WU Unioersity of Wisconsin, Department of Mechanical Engineering, Madison, Wisconsin 53705 (U.S.A.) (Received
March
19, 1974)
SUMMARY
The wear process caused by the grinding wheel-workpiece interaction is analyzed. An empirical-stochastic model is used to .characterize sequential profile measurements obtained during two different grinding cycles. The type and rate of mechanical wear which altered the wheel configuration are identified and quantified from the resulting model parameters. Relationships between the wear process and the corresponding three stages of the observed wheel wear curves are discussed.
INTRODUCTION
The decipherment of the wheel wear phenomena caused by the interaction between the wheel and workpiece is a crucial step in the eventual optimization of grinding performance. Visual observation of this process from either the viewpoint of the actual contact between tool and workpiece or the type of chip produced (which has proven useful for other metal cutting operations) is difficult due to the high wheel speeds and small magnitude of the chips. Furthermore due to the intricate configuration of the wheel, the nature of the metal removal and tool wear phenomena is more complex than any other metal cutting process. Much experimental work has been conducted to analyze both the chemical and mechanical wear during grinding14. Although chemical wear can comprise a significant part of the total wear in a grinding process, for a high purity aluminum oxide wheel and steel workpiece combination, chemical wear is small’. In this case, the effects of the machining variables on grinding wheel wear may be adequately described in terms of the two principal components of mechanical wear: attrition and fracture. Due to the complexity of the tool cutting space, investigators in order to analyze mechanical wear, have abstracted from the total cutting configuration of the wheel, a single grain mounted in a holder to simulate the whee13. This enabled visual or analytical analysis of the intricate phenomena to be made, however such simplification constrained the analysis to solely attritious wear.
S. J. DEUTSCH.
248
S. M. WU
Empirical-stochastic models of grinding wheel cross-sectional configurations have proved noteworthy in describing their topographies5-‘. A recent analysis has shown the cutting space of the wheel to consist of a pseudo-period, formed by aggregates of grits above and below a mean profile height value’. Therefore, all three types of metal removal processes (rubbing, ploughing and cutting) would be expected to occur simultaneously in actual grinding. In turn depending upon these relative occurrences and their duration, the nature of the ongoing mechanical wear process would be determined. This paper presents a preliminary investigation in which the entire wheel configuration was employed in analyzing the nature of the wheellworkpiece interaction. The objectives of this study were to identify the components of mechanical wear while quantifying the corresponding rates of wear occurring during actual cutting in a grinding cycle. The experimental procedures. equipment and data collection effort are first delineated. Four measurements of the wheel configuration were taken for each of two different grinding cycles at corresponding locations in their respective wheel wear curves. The wheel conligurations were then described via an empirical-stochastic model. The resulting estimated parameters which completely describe the information contained in the wheel profiles are employed to delineate and compare the type and rate of the wear phenomena occurring during each grinding cycle. Photographs of the wheel topography are presented to complement the statistical analysis. EXPERIMENTAL
PROCEDURES
A DoAll precision surface grinder, model D824-10 was used during the course of this investigation. All tests were conducted using plunge grinding on workpieces cut from high speed tool steel, M-2, through hardened to 62---63 Rockwell C. The experiment consisted of grinding a single face of the prepared specimens using a high purity aluminum oxide 4658 wheel at a preselected combination of wheel speed, table speed and depth of cut. Two different grinding cycles were run. Both cycles employed a single depth of cut and wheel speed combination (0.002 in. and 4500 ft/min) but each differed in the selection of their table speeds. Cycle I had a table speed of 10 ft/min while that for cycle II was 20 ft/min. Each grinding cycle was terminated when the wheel noise indicated the tool cutting space to have sufficiently degraded. Measurements of both the ground specimens and the grinding wheel were made simultaneously during each cycle. For each of the block specimens the height dimension before and after grinding was recorded. From this dimensional change, the amount of metal removal was determined. The corresponding wheel wear volume was obtained by concurrently measuring the decrease in the wheel diameter. The wheel wear volume and metal removal volume were used to construct the corresponding wheel wear curves for the experiment. This on line construction enabled quick detection of the transition points separating the three stages of the wheel wear curve. Thus after each stage, the wheel’s cross-sectional configuration was measured. For each cycle, then a total of the four essential measurements of the changing wheel profile was obtained; the freshly dressed condition, the end of stage one and two and lastly the end of stage three or cycle termination. To
.O
I
200.0
configuration
NUMBER OF OBSERVATIONS
100.0
NO. 3
NO.
Fig. 1. Digitized cross-sectional after stage three.
0.0
,
40.07
of 4658 wheel during
300.0
0
.O
L
L
100.0
200.0
200.0
.
.
I
1
300.0
300.0
(2) after stage one. (3) after stage two, (4)
100.0
No. 4
NO.2
cycle I. (1) freshly dressed,
00
25.0
5ao
“._
5ao
I----
200.0
Fig. 2. Digitized after stage three.
cross-sectional
configuration
300-o
of 4658 during
NUMBER OF OBSERVATIONS
100.0
.O
3
NO.1
p “““F NO. c
r
50.0 c
cycle II. (1) freshly
.O
dressed,
.o
(2) after
100.0
100.0
stage
one, (3) after
200.0
zoo.0
stage
two. (4)
330.0
300.0
251
WEAR DURING GRINDING
-_____-__
Fig. 3. Sample correlations and partial correlation functions for cycle I. Fig. 4. Sample correlations and partial correlation functions for cycle II.
complement these profile measurements visually, photographs of the same section of the wheel topography were taken using a camera equipped with a high axial resolution objective lens”. STOCHASTIC MODELING
OF THE GRINDING
CYCLE
Figures 1 and 2 each contain computer drawings of the four digitized peak to valley profiles recorded sequentially during cycles I and II respectively. The pseudo-sinusoidal decay exhibited in the sample correlation functions and the truncation of the sample partial correlation functions after two lags, led to the tentative identification of an autoregressive model of order two for all eight profiles (Figs. 3 and 4)“*“. The parameters of each model were estimated and from each fitted model the residuals calculated. The correlation functions of these residual sets did not exibit any additional discernible structure. In addition, since the histograms of the residuals for each series appeared reasonably normal’ O,the models were accepted as adequate. Therefore, during each of the two cycles the same model form,
where a, N NID (0, a:), y. = Variance (Z,), and dr, C#I~are autoregressive parameters, appears adequate in describing the changing physical configuration of the wheel due to wear.
S.J. DEUTSCH, S. M. WU
252 TABLE I STATISTICAL
SUMMARY
OF CYCLES I AND 11
Model no.
Metal removed (in’)
c$,
CYCLE I 1 2 3 4
0.000 0.088 0.367 0.468
0.95228 0.98190 0.93143 0.96603
CYCLE II 1 2 3 4
0.000 0.067 0.174 0.241
0.99540 1.01322 0.82717 0.98983
YO
Pseudoperiod (in. x 103)
-0.18126 - 0.20280 -0.17123 - 0.28740
28.2560 26.5029 26.0165 26.2282
49.2 49.0 48.4 55.4
-0.23579 - 0.24599 - 0.22670 -0.12988
30.8407 28.9432 26.0360 25.8217
44.0 44.8 48.9 84.0
0.050 cl
c
I
W 0.040 H E E L
0.030
W
.k
R 0.020 (lN3,
-
/ /
/ /,X0 ,X’
.x
_NX
/-
/” XI’
WHEEL
: 32A.46
WORK
MATERIAL,
HARDNESS
I I 0.010
d
I 0.10
SPEED
DEPTH
OF CUT : 0.002
METAL
REMOVED
CM21
3 19.0 I 0.50
I 0.40
INCHES F/M
1 0.60
(lN3)
x I
b
; I
i 0.020 -
:
I’
: E 0.015 -
W : R
’ 4500
RATIO
0.025
L
STEEL
3 IO F/M
SPEED
I 0.30
0.20
TOOL
TABLE WHEEL
0.00
JBVBE
2 62 RC
GRINDING
W
/x
x’
x’ x
0.010 -
(IN’)
/’
/’
P’ x-WHEEL: 32A46 J8VBE WORK MATERIAL~TOOL
/’
DEPTH
1”
OF CUT iO.002
WHEEL
0.005
STEEL
(M2)
HARDNESS j 62 RC TA6LE SPEED: 20 F/M
I’
SPEED:
GRINDING
RATIO-
4500
INCHES F/M
27.6
,’ t
L
0.00
,
I
0.10 METAL
0.20 REMOVED
/
0.30
(IN3)
Fig. 5. Wheel wear curves for (a) grinding cycle I, (b) grinding cycle II.
WEAR
DURING
253
GRINDING
It should be noted, that since the model forms are the same, any change in the wheel configurations due to wear will be directly reflected by the changes in the estimates of the parameters of the second order autoregressive process, 41, 42 and ye. Table I lists the eight sets of estimated model parameters and the corresponding pseudo-periods which are functions of the estimates 4,) 42’os ‘I. ANALYSIS
OF EXPERIMENTAL
RESULTS
The wheel wear curves, relating volume of wheel wear versus volume of metal removed are shown for each cycle in Fig. 5. Each curve displays the three characteristic stages: the rapid initial wear stage, the constant wear stage and the rapid wear-out stage. Figures 6 and 7 display the pseudo-periods and profile variances (obtained from the modeling sequences) versus the metal removed during the cycle. Similarly, the profile peak to valley distance obtained during the modeling sequence is plotted uersus metal removed in Fig. 8. By comparing these figures, which use the amount of metal removed as a common basis, the transitions in the wheel’s pseudo-period and variance are seen to readily correspond to the three stages of the wheel wear curve. 29.0
r CYCLE
0.15
32.0
I
0.30
0.45
0.60
r CYCLE
<
II
A
r,26.0
40.0
’
0.10
0.20 METAL
Fig. 6. Profile pseudo-periods
I 0.30 REMOVED
0.40
0.50
24.0L
( IN3)
OS. metal removed
Fig. 7. Profile variances
us. metal removed
(a)
ofthe wheel wear
The first stage
, 0.60
-
I 0.10 METAL
I
, 0.20
REMOVED
I 0.30 IIN31
for cycles I and II.
for cycles I and II.
Through the first two stages of wheel wear, the profile pseudo-periods for each cycle are seen from Fig. 6 to remain essentially constant. In addition, the rate of wheel wear, as seen from the slopes of the individual stages of the wheel
254
S. J. DEUTSCH, S. M. WU
wear curves (Fig. 5) or of the profile plot (Fig. 8) is many times larger during stage one than stage two. Lastly, there is for stage one a sharp drop in the profile variance of each cycle. Since the 4658 wheel has approximately two grains per pseudo-period*, these three simultaneous occurrences suggest the dominance of some type of a fracture mechanism during stage one. This information by itself, however, cannot be used to distinguish clearly whether this fracturing is due to a whole grain rupturing from its supporting bond matrix or is due to the subdividing of single grains into parts or some combination of the two. The identification of the proper mechanism from these alternatives is aided by viewing the differences in the initial or freshly dressed wheel topographies observed for each cycle. For each cycle, two passes at a depth of penetration of 0.002 in. were made with the diamond tool. The traverse rate in both cases was 0.15 in./s. In cycle I a third pass, identical to the first two, was made. In cycle II, however, multiple passes at these same conditions were made until sparkout. Thus all grains which protruded into the cutting tool space are either cut or fractured until no further interferences between tool and wheel exists. Under identical dressing conditions, empirical-stochastic models and their associated parameters developed for cross-sectional measurement anywhere on the cutting face have been shown to be statistically identical tx7. Therefore real differences in the profile characteristics as indicated by the significant differences in the model parameters noted for model one of cycle I and II can be attributed to the differences in the dressing methods employed. One effect of the different dressing procedures appears to be the different initial peak to valley distance within the cutting profile (Fig. 8). The profile depth height of cycle I is seen to be larger than that of cycle II (23.6 x 10m3 versu.s 23.0 x lop3 in.). In addition from the initial dressed condition, until the onset of the second stage of constant wear, the wheel used in cycle I wore twice the amount of the wheel prepared for cycle II (1.0 x 1O-3 uersus 0.5 x 10e3 in.). At the onset of the second stage of wheel wear however, wheels for both cycles exhibit nearly equivalent peak to valley heights. Since the pseudo-periods have been constant while the peak to valley depth of each cycle is adjusted at different rates until reaching a nearly identical configuration, there appears to be a dominance of fracture within the grains due to the stabilization of the wheel structure. Further, the rate of fracture appears to depend upon the degree of occurrence of nonobliquely oriented or nonstable grits imminent within the wheel profile due to the configuration imposed by the dressing conditions. (b)
The second stage of wheel wear During the course of the second state, the pseudo-periods do not exhibit any pronounced changes but remain essentially constant while the profile variance decreases (Figs. 6 and 7 respectively). In addition, as seen from the wheel wear curves, Fig. 5 or the profile depth plot, Fig. 8, the rate of wheel wear during the second stage is small compared to the first stage in which fracture wear dominates. This coalition of events is indicative of the dominance of an attritious wear process. When comparing the rates of change of the variance with respect to the
WEAR
DURING
3.00 W
255
GRINDING
CYCLE
I
x----x
CYCLE
I[
v
r
: E L
,x
2.00
1.00
..
,x’
::
r
(X IOt31N)
I” 0.00
24.00
P R 0 F
1. \
II E D E P T H
--x
(X lot3 IN)
21.00-
8
’ 0.15 METAL
Fig. 8. Vertical
. .
’ 0.30
a
REMOVED
.X ’ 0.45
profile dimensions
Fig. 9. Wheel photographs removed.
’ 0.60
(IN31
vs. metal removed.
for cycle II. (a) as dressed,
(b) 0.07 in3 metal
removed,
(c) 0.18 in3 metal
256
S. J. DEUTSCH,
S. M. WU
amount of metal removed for each cycle (Fig. 7) the rate for cycle II is seen to be approximately eighteen times that of cycle I (29.0 versus 1.6) although both cycles exhibit an identical rate of change in peak to valley depth. This high rate of change for cycle II is of the same order of magnitude, as the rate of change of the variance exhibited in both cycles during the lirst stage of wear. Thus only in cycle II, which is run at twice the table speed of cycle I, does there appear to be any appreciable quantity of wear due to fracture. The performance of any wheel during stage two of the grinding cycle is dependent upon the relative occurrences of attritious and fracture wear. A proper “balance” guaranteeing the rejuvenation of fresh cutting edges. A measure of the wheel’s ability to “balance” these mechanisms observed would be the consistency of the pseudo-period and profile variance during the cycle. Model number two and three of each cycle (Table I) correspond to the stochastic model representations of the wheel configuration at the beginning and end of the second wear stage. From the numerical changes in the value of the pseudo-periods and profile variances, it is seen that neither of the two cycles has undergone total selfdressing during the constant wear stage. Although for each cycle the period remains essentially constant, the variance does significantly decrease for both cycles. The latter phenomenon being indicative of either a smoothing of the cutting edges of the grains or wheel loading or a combination of the two. (c)
7he third stage of wheel wear
Both experiments exhibit a dominant increase in the pseudo-periods of the wheel profile near the third stage of the cutting cycle (Fig. 6). This increase in the average profile periods (which is synonymous with an increase in the intergrain spacing since the 46 grit wheel contains two grains per pseudo-period) would result from an increased propensity for the grits to be either pulled out of the bond matrix in entirety or partially fractured. It should be noted that the third stage of the wheel wear curve is more pronounced for cycle II than it is for cycle I. The change in the wheel periods is likewise more pronounced for cycle II than cycle I. The transition point in the wear curves between stages I and II is seen to correspond to the point for which there is a noticeable increase in the profile periods. For example, in Fig. 5 the transition point is seen to be approximately 0.40 in3 of metal removed. From Fig. 6, the period of the profile tends to increase likewise, at 0.40 in3 of metal removed. A similar comparison for cycle II indicates a more pronounced common transition point at about 0.18 in3 of metal removed. Thus the rapid wear out stage appears to be initiated by the increased proliferation of the whole or nearly whole grains fracturing from the bond matrix. Figure 9 illustrates an example of this phenomenon. Three photographs were taken of the same section of the wheel periphery during cycle II. The photographs show the freshly dressed wheel and the wheel after 0.07 and 0.18 in3 of metal removed. In addition to showing a gradual increase in number as well as size of the flats caused by attrition during stage II, a dislodging of a grain is seen for the lirst time in the lower right quarter of the photographs which correspond to the onset of stage III at 0.18 in3 of metal removed.
WEAR
DURING
GRINDING
257
CONCLUSIONS
Employing the total grinding wheel topography a preliminary experimental study was conducted to analyze the nature of the ongoing mechanical wear phenomena occurring during the grinding cycle. From the parameters of empiricalstochastic models built to describe sequentially measured wheel configurations during two different grinding cycles, the type of mechanical wear was segregated, quantified and associated to a particular stage of the wheel wear curve. For the two different grinding cycles analyzed, the following observations were made regarding wheel wear during the three stages of the wheel wear curve. (a) During the first stage, fracture accounted for a major part of the wheel wear. The dressing conditions were seen to determine the nature of this fracturing. When a wheel was not dressed until sparkout there was a greater occurrence of fracture within a single grit than dislodging of whole grains from the bond matrix. (b) Attritious wear is the dominant wear mechanism occurring during the second stage. The ability of the wheel to self-dress by balancing fracture and attritious wear was quantified by using the empirical stochastic model parameters. (c) The fracture of whole grains from the wheel due to the rupturing of bond posts appears to correspond to the onset of the third stage as well as being the predominant wear mechanism during this stage. ACKNOWLEDGEMENTS
The authors are indebted and the University of Wisconsin project, as well as to the Norton
to the Wisconsin Alumni Research Foundation Computer Center for financial support of this Company for supplying the grinding wheels.
REFERENCES 1 J. Peklenik, Untersuchungen iiber das Verschleisskriterium beim Schleifer, Ind.-Am., 80 (27) (1958) 397. 2 H. Tsuwa, Evaluation of grinding by behavior of cutting edges, Sci. Much., Japan, 13 (1961) 237. 3 N. Takenaka, A study of the grinding action by single grit, Ann. C.I.R.P., XIII (1966) 183-190. 4 N. S. Eiss, Jr., Fracture of abrasive grain in grinding, J. Eng. hd., B89 (1967) 463470. 5 J. Peklenik, Contribution to the correlation theory for the grinding process, J. Eng. Znd., B86 (1964) 85-94. 6 C. M. Stralkowski, S. M. Wu and R. E. DeVor, Characterization of grinding wheel profiles by autoregressive-moving average models, Znt. J. Mach. Tool Des. Res., 9 (1969) 145-163. 7 S. J. Deutsch and S. M. Wu, Selection of sampling parameters for modeling grinding wheels, J. Eng. Znd., B92 (1970) 667-677. 8 S. J. Deutsch and S. M. Wu, Relationship between the parameters of an autoregressive model and grinding wheel constituents, J. Eng. Znd., B95 (1973). 9 S. J. Deutsch, S. M. Wu and C. M. Stralkowski. A new irregular surface measuring system, Znt. J. Mach. Tool Des. Res., 13 (1973) 24442. 10 S. J. Deutsch, An analysis of the structure and wear of grinding wheels by autoregressive-moving average models, Ph. D. Thesis. University of Wisconsin. 1970. 11 G. E. P. Box and G. M. Jenkins, Time Series Analysis Forecasting and Control, Holden-Day, San Francisco, 1970.