Civil Engineering Reference
In-Depth Information
The determined grinding model appears to be satisfactory over small time spans. However, the use of
a constant coefficient,
K
P
, may to yield inaccurate model results with increasing time. This is expected
due to the known variable nature of the grinding process. If the model grinding parameters can be
frequently updated, the long-term accuracy of the model should be improved.
It should be noted that the threshold force is found to be fairly constant for a given workpiece material
and grinding wheel. Grinding experiments have also indicated that the coefficient,
K
P
, of the selected
grinding model cannot be assumed to be constant for accurate modeling of the grinding process. Thus,
real-time estimation of
K
P
is applied. The first attempt at this is to calculate the coefficient in real-time
and use low-pass filtering to remove the noise due to numerical differentiation. The effectiveness of this
direct approach is limited, depending on the process variation.
Parameter Identification via Force Control
In a second experimental method using the same model, the normal force,
F
N
, is maintained at constant
levels to determine
K
P
and
F
TH
. From Eq. (3.24) it can be seen that maintaining a constant normal
grinding force (along with constant surface speed and contact area) results in a constant MRR. Thus,
an average value of the coefficient,
K
P
, may be experimentally found by achieving a constant normal
grinding force and rewriting Eq. (3.18) to the following form:
x
˙
f
A
-------------------------------
K
P
constant.
(3.24)
(
F
N
F
TH
)
V
A series of experiments using several different force levels can be performed to determine average values
for both
F
TH
and
K
P
.
Multiple Input Estimation Approach
Clearly, correlations exist for sensory data other than normal force, such as wheel speed or input power.
Thus, it is proposed that sensor fusion with multi-input estimation may be employed to extract and
utilize potential additional information from each sensor. Therefore, sensor fusion and multi-variable
estimation using recursive techniques such as Kalman filtering and other recursive methods should
provide an approach for data integration. These techniques should be able to extract this type of
embedded information and improve the estimate of
K
P
.
In noisy processes (such as grinding) where modeling accuracy has limitations, it is often necessary to
use additional sensors to improve the estimate of a model parameter. Indeed, this approach has been
successfully applied in research areas where modeling and direct sensing are difficult or impossible (Jenkins,
1996). In this research several indirect measures of wear have been more successful at grinding model
parameter estimation than any single sensor alone. This indicates that multiple sensor methods can be
more reliable than any single sensor method. (The additional sensors also provide an assurance of esti-
mation accuracy in the presence of a sensor fault.) Multi-sensor approaches (such as Kalman filtering,
recursive least squares methods, neural networks, basis functions, multi-variable regression, etc
.
) have
yielded encouraging results toward improving the on-line estimation of wear. (It should be noted that not
all of these methods may be appropriate for the grinding model parameter estimation problem.) Applied
to grinding, these multi-sensor techniques can integrate normal force, tangential force, velocity, and power
data as input for grinding process model parameter estimation. For example, in the grinding model
presented by Hahn and Lindsay in Eq. (3.11), the unknown parameters, and
F
TH
, are process model
states that are to be estimated. In grinding many correlations exist with sensory data such as wheel speed,
tangential force, or power. Jenkins and Kurfess have shown that additional sensor fusion with multi-input
estimation may be employed to extract and utilize any additional information from each sensor to provide
a more accurate model and robust controller.
To remove noise and random machine vibrations from the model parameter estimation, traditional
low-pass filtering of the sensor data is applied. This can provide adequate filtering for parameter estimation
w
