Jackson Mark. Machining with Abrasives
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5 Surface Integrity of Materials Induced by Grinding 267
Chapter 6
Traditional and Non-traditional Control
Techniques for Grinding Processes
Jian Liu, Chengying Xu and Mark Jackson
Abstract Owing to the highly demanding geometric accuracy and surface finish
for many modern products, grinding processes have been extensively used in
manufacturing industry. However, it is also well-accepted that grinding is one of
the most complicated machining processes due to the high nonlinearities, intrinsic
uncertainties and time-varying characteristics. Multiple challenging problems exist
in the process that limits its overall quality and production in practice. With the
increasing demands for higher part geometry accuracy, better surface integrity,
more productivity, and other desired product parameters (e.g., minimization of
subsurface micro-damage) with less operator intervention, various control methods
have been studied and implemented to control position, velocity, force, power,
temperature and the Material Removal Rate (MRR) during the grinding process, in
order to achieve the desired system performance within certain cost/time. This
paper reviews different control strategies in order to provide a guideline for
academic researchers and industr ial practitioners to improve the final product
quality with increased possi ble process flexibility.
Keywords Grinding Control systems Mathematical modeling Qua lity
6.1 Introduction
Grinding process is one of typi cal complicated nonlinear systems involving multi-
ple input/output variables, such as position, velocity, force, power, temperature, etc.
C. Xu (*)
Department of Mechanical, Materials and Aerospace Engineering, University of Central Florida,
4000 Central Florida Blvd, Orlando, FL 32816, USA
e-mail: cxu@mail.ucf.edu
M.J. Jackson and J.P. Davim (eds.), Machining with Abrasives,
DOI 10.1007/978-1-4419-7302-3_6,
#
Springer ScienceþBusiness Media, LLC 2011
269
Users usually have multiple goals for the process, such as final parts surface/
subsurface quality, geometry accuracy, cost, cycle time. The process itself is
disturbed in many ways, such as the varying abrasive propert y of the grinding
wheel due to the wear, hardness variation of the workpiece, dimensional deviations
due to elastic deformation of the workpiece-tool-machine system, unbalanced
wheel due to the mounting error. The purpose of this survey paper is to review
existing control methodologies employed in various grinding processes and to
identify potential research directions as a future guideline.
6.2 Conventional Control Techniques
6.2.1 Fixed-Parameter Control Technique
The easiest way to control the grinding process is to design a fixed-parameter
controller based on off-line system identification. To
¨
nshoff et al. [1, 2] applied a
fixed-gain force controller to an internal grinding process to increase the product
quality and shorten the manufacturing cycle time by reducing the times of air
grinding. In this particular application, the Proportional Integral Derivative (PID)
control algorithm embedded in a microcomputer system is used to construct the
digital closed control loop for internal gri nding force control with fixed PID gains,
as shown in Fig. 6.1.
Digital control is applied because the available analogue systems are often not
suited to consider the limited conditions due to noncircular borings; however, the
CNC
Internal Grinding Process
Grinding
Spindle
fr
V
Input power P
Grinding Normal
Force F
Microcomputer
CPU
DAC
S&H
Programmable
low pass filters
Programmable
Oscillator
Feed rate
fr
V
Controlled
variables
Controller
output
Fig. 6.1 Control loop for internal grinding
270 J. Liu et al.
digital data processing allows the implementation of closed-loop controls, which at
the same time increase the process stability, the efficiency and accuracy of machin-
ing and hence the finish surface quality. In Fig. 6.1, it also shows that the controlled
variables, grinding force F
n
and grinding spindle input powe r P, and the necessary
hardware devices. The core part in this control system set up is a microcomputer,
based on the 16bit-micro-processor MC 68010, which is used to execute process
identification and digital control algorithm. PEARL (process and experimental
automation real-ti me language) which was developed in Germany and standardized
in DIN 66253 is used to program the micro processor.
During the development of such a kind of controllers, prerequisites for control
algorithm developing require a process identification for the following two goals:
(1) enforcing the grinding force to reac h the nominal value as soon as possible after
the first cut; (2) Detecting dead times and use power measurement as controlled
variable, namely carry out immediately a dead-beat-controller. Also, controller
parameters tuning process has to be performed to follow the process variations.
Therefore, the behavior of the controlled system could be charact erized to some
extent and the control law could be employed to this corresponding objective plant.
Figure 6.2 illustrates the concept and connections of process identification and
digital closed-loop control.
The process identification tries to exactly capture the real process using the data
acquired and stored during the identification grinding cycle. Therefore, the order
and the dead-time of the transfer function have to be known ahead. A model of a
third order is supposed for the internal grinding cycle, and the Z-transformation of
this process as well as its differential equation can be written as follows:
Microcomputer
Process
parameter
Identification of the
controlled system
Adaptive Grinding
Start End
Random
values
Parameters describing
the process
Dead-beat controller Identification Software
Controlled system Controlled system
Coefficients demanded for
the control algorithm
Feed rate Grinding
force
n
F
Nomina
l
value
Grinding
force
n
F
Feed rate
Fig. 6.2 Diagram of process identification and control
6 Traditional and Non-traditional Control Techniques for Grinding Processes 271
G
ðzÞ
¼
y
ðzÞ
u
ðzÞ
¼
b
0
þ b
1
z
1
þ b
2
z
2
þ b
3
z
3
1 þ a
1
z
1
þ a
2
z
2
þ a
3
z
3
z
d
(6.1)
y
ðkÞ
¼a
1
y
k1ðÞ
a
2
y
k2ðÞ
a
3
y
k3ðÞ
þ b
0
u
kdðÞ
þ b
2
u
k1dðÞ
þ b
2
u
k2dðÞ
þ b
3
u
k3dðÞ
(6.2)
where, k ¼ 0, 1, 2 ...n, and parameters a
i
and b
i
are required to model the real
process. By the random values of feed rate as input and the corresponding sampled
grinding force values as output, both recorded during the identification grinding
cycle, the proce ss parameters a
i
and b
i
can be calculated by the Gaussian algorithm.
Thereby, the six parameters will be used to calculate the coefficients of the
controller. These coefficients are valid as long as the machining conditions are
unchanged. When grinding condition has to be modified due to dif ferent feature
requirements, the parameters should be identified again for the new grinding cycle.
In summary, the implementation of this kind of controller is usually simple.
However, the fixed-gain controller does not have the adaptation ability and there-
fore cannot compensate for various process uncertainties and parameter variations.
Hence, the overall system performance cannot be guaranteed in practical industry
applications.
6.2.2 Adaptive Control Technique
In comparison with fixed-parameter cont rol approach, adaptive controllers are
able to adjust the control parameters on-line and are useful to maintain the
system stability and improve the control performance over the entire operating
time. Kaliszer et al. [3] develop ed an adaptive control system for a cylindrical
grinding process. The overall cycle time was minimized based on feedback signals
on the workpiece size and surface roughness.
Amitay et al. [4] designed a computerized adaptive control system to
optimize both the grinding and dressing conditions for the maximum Metal/Mate-
rial Removal Rate (MRR), subjected to two process constraints on the wor kpiece
burn and surface finish. Both the grinding and dressing parameters are controlled
based upon the data from on-line sensing of the grinding power and off-line
measurement of surface roughness. On-line convergence to the optimal conditions
proceeds along a predetermined optimization position trajectory derived
from grinding theory, where the optimization strategy has been used for off-line
grinding and dressing optimization as well. This Adaptive Control Optimization
(ACO) is advantageous to optimize grinding cycle due to easy implementation,
requiring a set up of a micro-computer, power sensor, and interface s to the basic
grinding machine.
272 J. Liu et al.
The performance index of the grinding process is the volumetric material
removal rate, which can be expressed in the below equation for external cylindrical
grinding:
Z ¼ pd
w
n
f
b (6.3)
Since the workpiece diameter d
w
is almost constant and the grinding width b is
fixed for any particular optimization, the performance index can be simplified as the
radial infeed velocity v
f
, the optimization problem therefore can be formulated as:
Maximize v
f
:
Subject to: P
bP
b
R
a
bR
ax
(6.4)
where Pis the total grinding power, which can be sensed on-line during control
process; P
b
is the threshold grinding power; R
a
is surface finish, which can be
measured off-line, after several individual grinding cycle; R
ax
is the desired surface
finish limit.
The overall scheme for such a control system is shown in Fig. 6.3, which
includes a grinding machine, a computer, and the operator interconnected. Control
algorithm is executed by the compute r in order to control the grinding process,
based on some partially human-interfered expertise imported by the operator.
Measurements of the grinding power Pare fed from the grinding machine to the
computer and the computer in turn controls the grinding parameters v
f
and n
w
to
operate along the optimal locus (as seen in Fig. 6.4) and converge towards the
optimal operating point. Moreover, the required surface finish limit R
ax
and inter-
mediate surface finish measurements R
a
are inputs by the operator to the computer
while off-line, and the computer suggests new dressing conditions to the operator
which he sets on the grinding machine.
A pilot ACO system which constitutes a cylindrical grinder interfaced to an
industrial compute r was developed to demonstrate this control concept, as shown in
Fig. 6.5. The pivot of the on-line control system here is an algorithm incorporating
the optimal locus optimization skill, as illustrated in Fig. 6.4, with an ID-type
COMPUTER
GRINDING
MACHINE
OPERATOR
Dressing
Dressing
n
w
v
f
R
a
R
ax
R
a
P
Fig. 6.3 Optimal adaptive
control concept
6 Traditional and Non-traditional Control Techniques for Grinding Processes 273
control law for v
f
as shown in (6.5). The grinding operation could start at an
arbitrary point in the v
f
n
w
plan, but is immediately transferred by the computer
to a point on the optimal locus by changing n
w
. Thereafter, the trajectory of
convergence towards the optimal operating point is along the optimal locus. For
the rate of convergence, instead of providing an external reference, the reference to
the control loop P
b
is calculated according to Malkin’s [5] model in the block G
b
to
which the control variables v
f
and n
w
are fed. Consequently, the convergence rate
depends on the error e ¼ P
b
P, which converges to zero when proceeding along
the optimal locus adaptively. The infeed velocity is determined by the controller in
Fig. 6.5 based on:
Fig. 6.4 Illustration of optimal locus together with machine tool limitations in v
f
n
w
plane
Fig. 6.5 On-line adaptive control system: 1 –stepping motor infeed drive; 2 – infeed control hand
wheel; 3 – grinding wheel motor; 4 – power sensor; 5 – workpiece spindle DC motor; 6 – tacho-
generator; 7 – voltage-to-frequency converter
274 J. Liu et al.