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On-line identification of thermally-induced convex deformationof the workpiece in surface grinding
H.H. Tsaia,*, H. Hochengb
aU-CONN Technology, Inc., 9 First Innovation Rd., Science Based Industrial Park, Hsinchu, Taiwan, ROCbDepartment of Power Mechanical Engineering, National Tsing Hua University, Hsinchu, Taiwan, ROC
Received 10 February 2000
Abstract
In this paper, the time-series modeling techniques of grinding forces is used to identify over-grinding induced by thermal convex
deformation within one pass. It is shown that the earlier the over-grinding is detected the better are the opportunities to avoid the detrimental
features of this phenomenon, therefore, prediction is an important feature of monitoring strategy. # 2002 Published by Elsevier Science
B.V.
Keywords: Convex deformation; Workpiece; Grinding
1. Introduction
In mould manufacturing, steels of low coefficient of heat
conduction are commonly used. The poor heat-conductivity
of the workpiece induces a high gradient of temperature
within the workpiece in surface grinding, and the high
temperature-gradient gives a large thermal bending moment.
On account of the thermal moment, a transient convex
profile of workpiece is ground during the grinding process,
the workpiece profile, therefore, being concave after having
cooled. When the workpiece is convex-deformed, the grind-
ing depth varies within one pass, the increased grinding
depth during the pass being called over-grinding.
Since over-grinding induces poor accuracy of the work-
piece, a monitoring function is, therefore, applied to identify
and prevent grinding damage. The monitoring function can
be configured in various degrees of complexity. The simplest
and most common configuration is that one sensor produces
one feature. In other cases, several different features might
be evaluated from a single sensor (multi-model monitoring).
Several sensors can be integrated into a system to generate a
number of symptoms of over-grinding, which is referred to
as sensor fusion [1]. Monitoring is thus quite clearly defined
as a function that generates symptoms of the state of the
machining process.
Feature extraction is the most important step in monitor-
ing due to need for accurate indication of catastrophic failure
in the process, for example, tool breakage and grinding burn.
Adequate proper sensor and signal processing are the basic
requirements for successful feature selection in monitoring.
A good monitoring function offers a successful control
function in the machining process based on the selected
feature and signal processing scheme.
Surface grinding with stroke passes differs from the
continuous machining process, the feature extraction in
monitoring being intended to be carried out based on a
three-stage strategy.
Stage 1: within-pass monitoring. The symptoms can
clearly indicate the state of the grinding process, namely,
the feature gives a strong signal once the failure has
occurred. Further, the time for signal processing should
be decreased as much as possible.
Stage 2: between-passes monitoring. Limited to the pro-
cessing of signal and feature selection, the symptoms of
grinding between passes should be a suitable monitoring
strategy because of the sufficient time for signal processing.
Stage 3: between-parts monitoring. Similar to human
monitoring, between-parts monitoring gives poor results
by the monitoring function. The strategy of between-parts
monitoring is the poorest situation in machining process,
since it produces a non-rescuable part once the damage is
monitored, where the machining cost has already been added
onto the part. This strategy is not been considered in the
current investigation, where stage 3 is used as merely a
Journal of Materials Processing Technology 121 (2002) 189–201
* Corresponding author. Present address: 84 Gungjuan Road, 243 Taishan,
Taipei County, Taiwan. Fax: þ886-2-29063269.
E-mail address: [email protected]
0924-0136/02/$ – see front matter # 2002 Published by Elsevier Science B.V.
PII: S 0 9 2 4 - 0 1 3 6 ( 0 1 ) 0 1 0 5 8 - 5
preparatory level due to the delay in rescuing the workpiece.
The best way to monitor the damage during grinding is within
one pass, since the problem can be identified as early as
possible. A proper monitoring index (feature) and processing
scheme should be set for within-pass monitoring, otherwise
the processing time cannot catch the grinding time within one
pass. The transverse time between passes equals the actual
grinding time. Therefore, between-passes monitoring would
be a reliable approach due to the time for signal processing
being double that of within-pass monitoring.
2. Sensing techniques
Since over-grinding often occurs in grinding for mould
steels, the over-grinding gives a defective workpiece
because of the poor geometrical and dimensional accuracies.
Hence a reliable sensing technique is needed to advise the
controller or the technician for preventing over-grinding.
Sensing techniques for the grinding process have been one
of the focuses of research on process automation. The
effectiveness of sensing techniques depends on the depen-
dency of the measured signal on the machining conditions.
A strong correlation is a prerequisite to obtaining useful
information from the measured signal. Furthermore, a good
sensor should be easy to use without disturbing the machin-
ing process, and it should also have a high resolution and a
fast dynamic response [2].
Force measurement by a dynamometer is the most widely
used technique and is popular for process monitoring and
control in industry and research due to its sensitivity to
cutting conditions and reliability of measurement [3]. It is
well accepted that the force signal has a strong dependency
on the machining conditions. Most of the adaptive control
and feedback systems for grinding, milling and turning are
thus based on force measurement, although the force-sen-
sing technique suffers from the limitations and inconveni-
ence due to the competing effects on the machine tool
rigidity and the dynamic response [2]. For instance, when
the workpiece is mounted on the top of the dynamometer in
grinding, the rigidity of machine tool structure is reduced as
a result of the limited supporting surface provided by the
dynamometer, the consequent chatter and vibration being
detrimental to the machining quality [4].
There are numerous works on monitoring used force
measurement [5–8] to detect the occurrence of chatter
and estimate tool wear in cutting process. Li and Fu [9],
Matsui et al. [10], Younis et al. [11], Brach et al. [12] and Fu
et al. [13] constructed theoretical grinding force models,
finding that the grinding force is proportional to the grinding
depth, width and workpiece feedrate. The grinding force is
thus used to identify the occurrence of over-grinding arising
from the convex deformation of the workpiece in grinding
process.
Acoustic emission (AE) has been investigated as a sensing
alternative for tool condition monitoring since the late 1970s
[14–16]. The application of AE technique is based on the
strong dependency on the tool condition [17]. Dornfeld and
Kannatey-Asibu [18,19] have shown that the common AE
sources are: plastic deformation in the shear zone and the
tool/chip interface; rubbing of the tool on the tool/chip
interface and the machined workpiece surface; chip break-
age and entanglement; and chipping and breakage of the
cutting tool. The AE sensing technique has been used to
monitor the machining process due to its non-intrusiveness,
ease in operation and fast dynamic response. The AE sensor
is small and easy to be positioned, and the size and weight of
the workpiece or tool do not have a strong effect on the AE
sensor. The dependency of the AE signal on the cutting
conditions, therefore, becomes the key factor governing the
applicability of AE sensing to machining process monitoring.
The potential of AE in metal cutting process monitoring
has been demonstrated by various investigations, for exam-
ple, tool wear monitoring in turning and milling, tool fracture
detection, and grinding burn, where the sensing technique is
reliable and provides a rapid response. The averaged root
mean squared (RMS) energy of the signal shows good
sensitivity to cutting speed, workpiece hardness, depth of
cut and feedrate, hence the mean AE RMS are evaluated and
correlated to the length of flank wear in milling and turning
[20–22]. Asibu and Dornfeld [23] proposed a model for AE
generation in orthogonal metal cutting. The primary assump-
tion in the model is that the energy content of the AE signal
is proportional to the energy consumed in the plastic defor-
mation and friction in cutting zone.
In grinding research, AE has been used for detecting
malfunctions and dressing, wheel sharpness, chatter and
grinding burn. Kakino et al. [24,25] compared the AE
and accelerometer, and concluded that the AE signal is
17.5 ms faster. Inasaki and Omura [26] also found that
the AE is about 1 s earlier than the power of the spindle
motor. Tsai and Hocheng [27] monitored the creep-in depth
beyond the initial contact between the workpiece and the
wheel by means of AE and a dynamometer. They found that
AE gives an effective indication on the initial contact and
well predicts the creep-in depth. AE and a dynamometer are,
therefore, used to monitor the occurrence of wheel-bite in
this study.
3. Experimental set-up and data processing
Fig. 1 shows the experimental set-up. A series of experi-
ments was performed on a CNC grinder equipped with a
dynamometer (Kistler 9275A). The CNC controller is a
Fanuc 0M model. The force signal from the amplifier is
fed into a data acquisition system. The data acquisition is a
PCL-812PG card that has 30 kHz of the maximum A/D
sampling rate and 16 bits of digital output and 16 channels of
analog input. Once the system has monitored the occurrence
of wheel-bite in the grinding process, the corresponding
control signal from the PC is put through the electronic
190 H.H. Tsai, H. Hocheng / Journal of Materials Processing Technology 121 (2002) 189–201
control interface to the CNC controller to change the
grinding depth or stop the grinding operation. On-line
monitoring and control with feedback function is thus
realized in the grinding process.
The surface grinding experiments were conducted using
an aluminum oxide wheel (WA80K8V) on a CNC grinder.
The total grinding power at the wheel spindle is measured by
a dynamometer, and the tangential velocity of the wheel is
set by a converter. The force transducer has an interface with
a personal computer (PC) for data storage and analysis. The
materials are hardening mold steels of type SKD11, SKD61
and SKS3. Each workpiece has two 12 mm diameter holes
for being bolted onto the dynamometer.
The signal processing procedure is as follows: the
detected tangential grinding force signals are amplified
and sent to a common data acquisition system (PCL-
812PG). The force signals are sampled at 2 kHz and stored
in the PC. Once the sampled values are found to have
gradually increased based on a pre-determined criterion,
the grinding depth is changed or the grinder is stopped by a
control signal from the PC. This approach is reliable to
identify the occurrence of wheel-bite and reduces the discard
rate in grinding.
The data processing scheme used in the current study for
the required rapid response to the controller is shown in
Fig. 2. In between-passes monitoring, the sampled tangential
grinding force is analyzed by the time domain average
method (TDA), which is the most effective scheme to derive
the average grinding force of each pass. Then the derived
average grinding force of this pass is compared with that of
the previous pass. The wheel-bite effect is identified once the
average grinding force is found to have increased, with
regard to the fundamentals of grinding, i.e. the up-grinding
force is always larger than the down-grinding one. All of the
signal processing and the decision-making procedure must
be finished before the start of the next pass. Finally, the PC
control signal instead of a manual pulse generator is fed into
the CNC controller to change the grinding depth or to stop
the grinding process.
In within-pass monitoring, the average tangential grinding
force is sampled every 5 mm in grinding length. In other
words, the number of the data in 5 mm is inversely propor-
tional to the workpiece feedrate: higher feedrate gives a
smaller amount of sampled data. The average grinding force
increases with the grinding distance once that wheel-bite has
occurred. The detection by the time-series method for
within-pass monitoring is to identify the coefficient of the
auto-regressive (AR) model. The value of a1 will increase
once wheel-bite has occurred. The control command is given
from the PC to the CNC controller for changing the grinding
conditions.
Since the series of sampled data (forces and AE) is a
stochastic process, it is impossible to distinguish between
the bite and non-bite states directly. The purpose of signal
processing is to transform the measured signal into char-
acteristics related to the bite or non-bite states by methods
such as regression analysis, time-series analysis and spec-
trum analysis. The processing efficiency of regression for
Fig. 1. Experimental set-up.
Fig. 2. The signal processing procedure for within-pass monitoring.
H.H. Tsai, H. Hocheng / Journal of Materials Processing Technology 121 (2002) 189–201 191
on-line monitoring is higher, and thus it is used in the current
study.
Regression analysis is an approach to transforming the
original signal into a generic mathematical model. The
results of the experiments show that the grinding forces
and AE may be described by an regressive model, because it
can be derived effectively from the solution. Even the simple
linear regressive model can be written when the output is
known
yt ¼ a1xt þ a0 þ et (1)
where t ¼ 1 to N and N is the number of data points, and et
the error item. The vector notation for the parameters of
Eq. (1) is defined as
Y ¼
y1
y2
y3
..
.
yN
266666664
377777775; X ¼
1 x1
1 x2
1 x3
..
. ...
1 xN
266666664
377777775;
b ¼a0
a1
� �; e ¼
e1
e2
e3
..
.
eN
8>>>>>>><>>>>>>>:
9>>>>>>>=>>>>>>>;
(2)
using the least-squares method, b is derived as
b ¼ ðX0XÞ�1X0Y (3)
The parameter a1 of b can be used to identify the trend of the
signal. A positive value of a1 shows an increasing trend of
signal, while negative a1 gives a decreasing trend. The
occurrence of over-grinding is predicted by the continuously
derived a1.
4. Monitoring strategy
4.1. Feature selection
As introduced in Section 3, the key problem in process
monitoring is to correlate features of the measured data
series to the states of the process. There is a lot of literature
on this problem, as surveyed by Dooley and Kapoor [28].
The signal processing above is itself a process of character-
istic analysis. The aim of characteristic analysis is to discard
the less important information related to the grinding states
and to retain the useful data as for as possible.
It is advantageous to select some representative charac-
teristics as features to constitute a pattern space for describ-
ing the grinding states. The result of these experiments
suggests that the mean, variance, one-step autocorrelation,
model parameter a1 and residuals e are all suitable to be
selected as characteristic features. The following uses the
mean for between-passes monitoring and the model para-
meter for within-pass monitoring, respectively.
4.2. State identification
There are many methods for pattern recognition [29] that
may be used to identify the grinding states. The qualitative
criterion for state identification in monitoring is the best
criterion in actual application, because the workpiece, wheel
and machine may affect the response of the sensor during
grinding. Taking into account the requirements of the gen-
eral monitoring strategy, one should analyze the reaction
signals of AE, and of the tangential and normal forces when
over-grinding occurs. Attempts can thus be made to interrupt
the grinding and/or to change the grinding parameters after
over-grinding is detected.
In Fig. 3, the grinding conditions are: pre-set grinding
depth 0.005 mm; grinding velocity 10p m/s, and feedrate
5 m/min. The conventional grinding with transverse strokes
is used in this study. In the figure, the ground profiles of the
workpiece with multi-pass grinding after wheel-bite
occurred is shown. The first pass is from the left side to
the right side. It is easy to find that the grinding depth is
about 0.004–0.005 mm, which indicates that residual depth
is present and that no wheel-bite effect has occurred.
The second pass is from the right to the left. The profile is
clearly concave, and the largest grinding depth is 0.009 mm
at about two-thirds of the total grinding length from the start-
side. Further, the third pass, from the left to the right, is also
concave and the largest grinding depth is 0.010 mm at about
two-thirds of the total grinding length from the start-side.
The heat within the workpiece is conducted from the source
gradually pass by pass. The temperature of the workpiece is
uniform before grinding. At the first pass, the heat is
transferred into the workpiece, the temperature-gradient
inducing a high thermal bending moment (the details are
discussed in Sections 3 and 4). The workpiece is thus
deformed convexly pass by pass due to the high thermal
bending moment, and the largest grinding depth is at about
two-thirds of the total grinding length from the start-side.
However, in the fourth pass, the largest concave-point is at
the middle of the workpiece and the largest grinding depth is
0.015 mm, because the second and the third passes could
leave about equal amounts of heat at both sides.
Fig. 3. The top profiles of cooled workpieces.
192 H.H. Tsai, H. Hocheng / Journal of Materials Processing Technology 121 (2002) 189–201
The corresponding average grinding forces and AE values
of each pass are depicted in Fig. 4(a) and (b). It is found that
the AE increases gradually, the AE of the second pass being
about 1.2 times that of the first pass. Furthermore, the
grinding forces also display similar trends.
With the trends of AE and grinding forces, it is easy to set
the proper monitoring strategy for the wheel-bite effect. The
grinding forces (tangential and normal) of up-grinding are
larger than the down-grinding, and AE should behave the
same as grinding force, since the AE is proportional to the
grinding energy. However, in Fig. 4 it is found that the AE
and grinding forces are increasing pass by pass, which
differs from the basic reactions in surface grinding. The
qualitative criterion gives an effective indication on the
wheel-bite effect, and the grinding forces provide good
identification of the grinding states.
It is noted that the AE increase is not strong as expected,
since the AE transducer is mounted on the side of dynam-
ometer, and the transmission path of AE from the contact
zone to the transducer is disturbed once wheel-bite occurs.Fig. 4. The averaged grinding forces and AE of continuous passes.
Fig. 5. The original normal grinding force and the correlation between NFt and NFt�1 and NFt�2 during wheel-bite.
H.H. Tsai, H. Hocheng / Journal of Materials Processing Technology 121 (2002) 189–201 193
4.3. Dependence of NFt on NFt�1 and NFt�2
Fig. 5(a) shows the normal grinding force during wheel-
bite occurring in the process. It appears that the force signal
is independent of the time (sampling point). The dependency
of the force signal can be further examined by the first-order
model as shown in Fig. 5(b). In this figure, if NFt�1 is small,
NFt tends to be small; whilst NFt�1 is large, NFt tends to be
large.
The averaged normal force of 50 pieces is also analyzed
to check the dependency (Fig. 6). The derived figures show
approximately linear proportional relationships between
NFt and NFt�1, and between NFt and NFt�2. Although a
higher order should describe the signal trend accurately,
the computing time of deriving the model parameters is
longer, which might be unsuitable for on-line within-pass
monitoring. The first-order regressive model is used to
process the collecting signal once the lower-order regres-
sive model can give a clear indication that wheel-bite has
occurred.
4.4. State identification
Fig. 7(a) shows the grinding forces of a non-bite grinding
process. The workpiece is 100Cr6 steel of width 10 mm,
thickness 20 mm and length 150 mm. The average value of
each batch of data is derived, where a batch includes 50
pieces of data. The series of data are shown in Fig. 7(b). The
grinding forces depict a quasi-stable state. The value of a1 is
shown in Fig. 7(c), the value of a1 being based on the zero
line. In regression analysis, a positive value of a1 means that
the trend of the signal is to increase gradually. Therefore,
when the trend of the signal rises, the value of a1 is indicated
as positive. The value of a1 fluctuates in Fig. 7(c) when
wheel-bite does not occur.
Fig. 8(a) shows the top profile of the workpiece, where the
preset grinding depth is 0.01 mm. It can be seen that the
wheel-bite occurs where the grinding starts at the left side.
The corresponding original normal grinding force is shown
in Fig. 8(b). The trend of the normal force is to gradually
increase with respect to the depth of over-grinding. The
Fig. 6. The averaged normal grinding force and the correlation between NFt and NFt�1 and NFt�2 during wheel-bite.
194 H.H. Tsai, H. Hocheng / Journal of Materials Processing Technology 121 (2002) 189–201
original normal grinding force is averaged per batch of data,
as shown in Fig. 8(c). Using the regression model, the
averaged normal grinding force is processed and the value
of a1 is derived (Fig. 8(d)). The value of a1 in the regression
model is positive until the 14th sampling point, which means
that the depth of over-grinding increases gradually.
The original tangential grinding force is shown in
Fig. 9(a), whilst the corresponding averaged tangential force
Fig. 7. The normal grinding forces and the value of a1 without wheel-bite.
Fig. 8. The top profile, the original and average normal grinding force and the value of a1 in wheel-bite.
Fig. 9. The original and average tangential grinding force and the value of
a1 in wheel-bite.
H.H. Tsai, H. Hocheng / Journal of Materials Processing Technology 121 (2002) 189–201 195
and the value of a1 are shown in Fig. 9(b) and (c). The value
of a1 is positive until the 14th sampling point, although the
10th data has a slight negative value. The corresponding AE
signal processing is shown in Fig. 10. It can be seen that an
AE signal is not evident at the occurrence of the wheel-bite,
the reason was described in the previous section. A strong
AE signal is produced when the grinding depth increases,
but the bottom of the workpiece is separated due to the
convex deformation of the workpiece during wheel-bite.
Therefore, an AE transducer mounted on the side of
Fig. 10. The original and average AE and the value of a1 in wheel-bite.
Fig. 11. The top profile, original and average normal grinding force and the value of a1 in wheel-bite.
Fig. 12. The original and average tangential grinding force and the value
of a1 in wheel-bite.
196 H.H. Tsai, H. Hocheng / Journal of Materials Processing Technology 121 (2002) 189–201
magnetic chuck is unsuitable for receiving the AE, unless
wheel-bite does not occur.
Fig. 11(a) shows the lowest point of the workpiece top
profile exceeding the preset grinding depth. From Fig. 11(b)
and (c), it is found that the normal grinding force has a
significant trend to increase, so that the corresponding values
of a1 are positive until the 16th sampling point. Using this
signal processing, the wheel-bite effect can be detected
easily. Similar results can be found in Fig. 12, where the
Fig. 13. The original and average AE and the value of a1 in wheel-bite.
Fig. 14. The top profile, original and average normal grinding force and the value of a1 in wheel-bite.
Fig. 15. The original and average tangential grinding force and the value
of a1 in wheel-bite.
H.H. Tsai, H. Hocheng / Journal of Materials Processing Technology 121 (2002) 189–201 197
Fig. 16. The original and average AE and the value of a1 in wheel-bite.
Fig. 17. (a) The concave profile of the ground surface; (b) the average tangential forces per 5 mm of workpiece of the whole pass; (c) the value of a1.
198 H.H. Tsai, H. Hocheng / Journal of Materials Processing Technology 121 (2002) 189–201
tangential grinding force also gives a good indication of
wheel-bite. The AE values cannot provide a good trend with
respect to the actual grinding depth, as shown in Fig. 13.
Fig. 14(a) shows a very poor top profile of the work-
piece. The corresponding normal grinding force has an
overt trend. After processing the average normal grinding
force, a continuous positive value of a1 is derived (shown
in Fig. 14(c) and (d)). The tangential grinding force also
gives a clear indication of the wheel-bite effect in Fig. 15,
whilst the AE cannot give a good prediction of wheel-bite
in Fig. 16. By within-pass monitoring, the force signal can
detect the thermally-induced problem (wheel-bite), but the
AE sensing technique is insensitive for monitoring the
over-grinding effect due to the separation between the
workpiece bottom and the top surface of the chuck that
disturbs and weakens the transmission of AE to the AE
transducer.
5. Monitoring the experiments
Identification problems may be classified in qualitative
and quantitative terms. Quantitative identification is amen-
able to wheel-bite and deals with the estimation of the real
grinding depth once wheel-bite occurs. Qualitative identifi-
cation aims at discriminating between the occurrence and
non-occurrence of wheel-bite by its characteristics.
Qualitative identification is well used in this study for
detecting the wheel-bite between passes regardless of
the variation of the cutting parameters. The time-series
approach is crucial for within-pass, on-line identification
and in the previous section, it has been shown how it can be
employed for within-pass wheel-bite during the process.
However, the feasibility of a stochastic criterion must be
identified. In this section, the derived schemes for on-line
identification of the between-passes and within-pass
Fig. 18. (a) The concave profile of the ground surface; (b) the average tangential forces per 5 mm of workpiece of the whole pass; (c) the value of a1.
H.H. Tsai, H. Hocheng / Journal of Materials Processing Technology 121 (2002) 189–201 199
wheel-bite effect during the grinding process are, therefore,
required to be verified by a series of experiments.
The verification of within-pass monitoring is conducted
under the following conditions: workpiece HRC 58, SKD11;
wheel WA80K8V 187 mm � 10 mm � 25 mm; preset grind-
ing depth 0.010 mm; tangential velocity of the wheel
35.25 m/s; feedrate 3.28 m/min (up-grinding).
The tangential grinding force of the whole one-pass is
shown in Fig. 17(b). The variation of the value of a1 from
the time-series regressive model is depicted in Fig. 17(c).
The results indicate that the value of a1 is positive until
X ¼ 65 mm, then it changes transits to negative. It is thus
known that the grinding depth is gradually increased with
respect to the dimension X before X ¼ 65 mm (Fig. 17(a)).
The monitoring scheme thus can identify that over-grinding
has occurred.
The second verification of within-pass monitoring is
conducted under the following conditions: workpiece
HRC 58, SKS3; wheel: WA80K8V 187 mm � 10 mm�25 mm; preset grinding depth 0.020 mm; tangential velocity
of the wheel 35.25 m/s; feedrate 3.04 m/min (down-grind-
ing).
The concave profile of the ground surface is shown in
Fig. 18(a). The actual grinding depth is larger than the preset
grinding depth, and the lowest point of the profile is at about
X ¼ 95 mm. The tangential grinding force of the whole one-
pass is shown in Fig. 18(b). The variations of the value of a1
are depicted in Fig. 18(c). The results indicate that the value
of a1 is positive until X ¼ 85 mm, then changes to negative.
It is thus known that the grinding depth is gradually
increased with respect to the dimension X before
X ¼ 85 mm (Fig. 18(a)). In fact, the monitoring scheme
can identify that over-grinding has occurred before
X ¼ 45 mm, since the value of a1 is consistently positive
and the scheme judges the over-grinding by five values of
positive a1 coefficient.
6. Conclusions
Using the time-series modeling technique of grinding
forces, by the monitoring scheme can be identified over-
grinding induced by thermal convex deformation within one
pass effectively. While the AE signal fails to reflect the
corresponding grinding force due to the separation between
the workpiece bottom and the top surface of the chuck
resulting from the convex deformation of the workpiece,
a regressive model of order 1 gives a good indication on the
occurrence of within-pass wheel-bite. In monitoring verifi-
cation, it is shown that the earlier the over-grinding is
detected the better are the opportunities to avoid over-
grinding, therefore, prediction is an important requirement
of the monitoring strategy. In practice, it is found that the
identification algorithms of the within-pass work well. One
of the major benefits of using stochastic identification
resides in the improved efficiency to process the sampled
data. Experiments are well verified with the monitoring
strategy.
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