Jackson Mark. Machining with Abrasives

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ðiÞ¼v

i  1ðÞþK

eðiÞþK

eðiÞei 1ðÞ½(6.5)

6.3 Adaptive Force Control Application

Other researchers such as Furukawa and Ohishi [6], Elbestawi et al. [7], Bhatta-

charyya et al. [8] also have applied adaptive control scheme in grinding processes.

For instance, in Elbestawi’s work, the focus is on predictive adaptive force control

during grinding cycle. The conﬁguration for the robotic disk grinding process is

show in Fig. 6.6 and the grinding force model is summarized in the following

equation, which combines a disk wea r model, a metal removal rate model and the

nonlinear stiffness of the robot according to a dynamic force model of Ulrich, B. J.

[9] and Srivastava, A. K. [10].

¼ f



 lF

 F

ðÞ

Bh y

ðÞ

ðF

 F

2pR



ðh  y





(6.6)

where F

is the normal cutting force; L

is the disk wear parameter; F

is the disk

wear threshold force; L

is the length of the workpiece; h and y

are the heights of

the initial and resulting workpiece surfaces from some arbitrary datum. f

 f

are

four coefﬁcients who are functions of ðK

; K

Þ, L

and the distance travelled by the

disk during a pass. The ðK

; K

Þ and ðK

; K

Þ are the horizontal and vertic al

robot stiffness values at the beginning and end points of the grinding pass, respec-

tively. By analyzing the geometry of the grinding process, as show in Fig. 6.7, the

coordinates ðx

; y

Þof the extreme edge could be expressed as:

¼ x



 h  H þ R sin y





tan y

 y

ðÞ (6.7)

sin y

cosðy

 y

H  R sin y



þ h 1 

sin y

cosðy

 y



(6.8)

Fig. 6.6 Conﬁgurations for

robotic disk grinding process

6 Traditional and Non-traditional Control Techniques for Grinding Processes 275

Using force control (regulation) for grinding application can have several advan-

tages: (1) It can be used to maintain speciﬁ ed MRR in order to either achieve the

maximum productivity or save machining time, based on requirements for ﬁnal

product quality. (2) It can help reduce geometric errors in the ﬁnished workpiece

dimensions due to variations in workpiece hardness, wheel wear, external distur-

bances, etc. (3) It can be used to detect and hence prevent workpiece burn since the

monitoring of grinding force has the ability to indicate any severe changes in

grinding temperature. Basically, grinding force control is quite signiﬁcant for

grinding process adaptive control, based on which more effective and efﬁcient

control algorithm.

A basic force control scheme based on PID feedback controller is shown in

Fig. 6.8, which depicts the structure of the PID force controller including the

grinding process and robot dynamics. The digital control signal implemented in

the controller has the form as:

Fig. 6.7 Coordinate system and geometry of grinding disk

Force

Controller

Robot

Servo

Grinding

Process

Force

Sensor

ref

Disturbance

=0.011sec

=0.028sec

Disturbance

Workpiece

Height

Fig. 6.8 Block diagram of the force feedback controller

276 J. Liu et al.

ukTðÞ¼K

e kTðÞþK

x kTðÞ½þK

e kTðÞe k  1ðÞT½



(6.9)

where, ukTðÞis the control signal at the current sample time, e kTðÞis the force error

signal (e kTðÞ¼F

ref

kTðÞF

ðkTÞ) at the current sample time instant, xðkTÞ is the

cumulative sum of e kTðÞat the current sample time, the three leading coefﬁcients

are the gains of proportional, integral, and derivative terms respectively.

Even though the above PID control structural is capable of regulating the

grinding force in the presence of a step disturbance in the workpi ece height, its

performance highly depends on the robot arm location, metal removal and disk

wear parameters. Therefore, adaptive control was found to be necessary to com-

pensate for these variations in system para meters instead of the PID approach. The

structure for this kind of adaptive controller is illustrated in Fig. 6.9.

Similar to the former example for To

nshoff’s [11]work,theplant’s

model should be built ﬁrstly before the actual control works. The modeling parameters

identiﬁcation was proceeded under open-loop conditions, by commanding the robot

end effecter to follow a pseudo-random trajectory signal while simultaneously mea-

suring the normal force during grinding cycle.

Based on the identiﬁed plant model, two adaptive control algorithms, namely,

Generalized Predictive Control (GPC) and Extended Horizon Control (EH C) are

utilized to regulate the grinding force and evaluate the advantages adaptive control

scheme shown above has over non-adaptive PID force controller. The objective of

the GPC strategy is to drive the future plant output as close as possible to the future

set point and the design objective of EHC is to bring the plant output to the set point

within the control horizon with minimum effort.

Another example is Bhattach aryya’s work [8]. In this work, the author focused

on improving grinding surface integrity by avoid grinding burn and thermal dam-

age, where phenomena arise from the point when a grinding wheel is in contact with

Robot

Servo

Positioning

Errors

Grinding

Process

Controller

Robot Arm/End

Effector

RLS Parameter

Estimation

Force Sensor &

Filter

Set

point

force

PLANT

Fig. 6.9 Block diagram of the adaptive force control system

6 Traditional and Non-traditional Control Techniques for Grinding Processes 277

the workpiece, and considerable heat is generated and majority of the them enters

the workpiece. This might be responsible for the undesirable surface ﬁnish and

introduces residual stress. Therefore, by evaluating the surface ﬁnish and residual

stress mainly, grinding surface integrity could be enhanced.

However, the surface integrity is only one aspect of optimum grinding condi-

tions, which are deﬁned when achieving the maximum metal removal rate while

maintaining the required surface integrity, mainly in terms of surface ﬁnish and

residual stress, so that the decision of optimum grinding condi tions which has also

been termed as “art of grinding” usually requires expensive and scarce skill and is a

time consuming job. In this case, an adaptive control engine which is able to

optimize automatically will be meaningful. It is important to know the model for

predicting the onset of grinding burn based on which the adaptive control for

grinding process proposed can detect and prevent thermal dam age during machin-

ing and hence improve surface ﬁnish.

According to well-documented literature about the relationship between work-

piece surface ﬁnish and grinding process variables, the surface ﬁnish is primarily

affected by the normal force intensity and the wheel dressing conditions. Also, a

proportional relationship was found between the surface ﬁnish and the metal

removal rate. Surface ﬁnish is also affected by wheel regenerative chatter vibra-

tions. Hah n and Linds ay [12, 13] proposed a correlation between thermal

damage and normal force intensity. As for grinding burn, Cebals propos ed that it

was related to the grinding coefﬁcient, deﬁned as the ratio of the tangential

grinding force to the normal grinding force. A coefﬁcient of less than 0.4 indicates

the production of thermally damaged parts. In general, based on the above investi-

gation, both surface ﬁnish and grinding thermal damage/burn can be controlled

by grinding at a reasonable work speed under controlled force intensities or ratio of

the tangential grinding force to the normal grinding force with wheels, whose

sharpness is maintained above safety level. Its advantages in requiring less grinding

data and less computation load comparing with regression techniques facilitates the

application in grinding adaptive control of workpiece ﬁn ish surface integrity.

However, when comes to the control procedure, more considerations about the

process models should be conducted for thermal damage and surface ﬁnish sepa-

rately.

Firstly, the adaptive control strategy utilizes the monitored grinding force

data to control the feed rate in order to prevent thermal damage. Since the relation-

ship between normal force and feed rate, which to some extent determines

the success of the control law, may vary from different grinding wheel-

workpiece combinations and hard to predict, identiﬁcation of the relationship

is necessary requiring the normal force and feed rates are monitored during

grinding cycle. Once this crucial model is established via process identiﬁcation

in real-time, it could be used to control the feed rate to achieve constant

force grinding and hence prevent thermal damage.

Secondly, surface ﬁnish could be measured in an adaptive control iden tiﬁcation

strategy similar to the strategy adopted for thermal damage, even though it can only

be applied in off-line manner. When the model which connects normal force and

278 J. Liu et al.

vibration levels with workpiece surface ﬁnish is ready, the adaptive control system

could use this model to execute surface ﬁnish control by varying the feed rate of the

grinding wheel.

This control is an extension of the adaptiv e control strategy to achieve constant

force grinding. Also, the identiﬁcation stage could be re-initiated to produce a new

model once the old one is invalidated by an alteration in dressing conditions, wheel,

workpiece proﬁle or material properties etc. The entire control algorithm develop-

ment for thermal damage prevention is summarized as: ﬁrstly, an adaptive control

identiﬁcation strategy is used to compute a pre-burn value of the grinding coefﬁ-

cient from the monitored grinding force data. A control algorithm would then

monitor the grinding forces, compute the current grinding coefﬁcient and compare

it with the pre-burn value. If a signiﬁcant reduction is experienced, workpiece burn

could be detected and the adaptive controller could reduce the wheel feed rate to

produce less aggressive grinding conditions.

6.4 Non-linear Adaptive Control with Self-tuning Ability

By on-line identifying the parameters of the mathematical model, the grinding

conditions could be calculated and adjusted in real time to achieve the optimum

machining efﬁciency. Webster and Zhao [14] developed a time-optimizing adaptive

control strategy for plunge grinding processes. An online identiﬁcation of the

system time constant from size measurements was incorporated in the controller

design to make the method more robust in accelerating the spark-out grinding cycle.

Guo et al. [15, 16] presented a nonlinear indirect adaptive control scheme based on

the model following scheme and applied to the grinding force control of a form

grinding process. During the process, a nonlinea r adaptive observer was used

to estimate the model parameter and therefore increase the robustness of the control

system against parame ter uncertainties. The stability of the whole closed-loop

system is thus guaranteed with satisfactory system performance.

The mathematical force model of a grinding process belongs to the class of

nonlinear systems with the form as below:

x ¼

f xðÞþ

i¼1



’

xðÞ#

þ g xðÞþ

j¼1

’

xðÞ#

u (6.10)

y ¼ h

xðÞþ

k¼1

’

xðÞ#

(6.11)

where

xðtÞ, uðtÞand yðtÞ denote the state vector, the input and the output of

the system at time instant t respectively. This model represents the uniform of

6 Traditional and Non-traditional Control Techniques for Grinding Processes 279

nonlinear system with uncertain parameters and the purpose of the control work is

to regulate yðtÞ to be a desired value y

, namely,

ðtÞyðtÞ

<e for a given e or lim

t!1

½y

ðtÞyðtÞ ¼ 0 (6.12)

Adaptive controller becomes a suitable candidate for this kind of nonlinear

control problem because it can dynamically compensate the variations of the uncer-

tain system parameters in a real-time manner. Based on a reduced nonlinear system

model, after deriving a nonlinear controller by extending the well known global

linearization theory to the case where system parameters may be uncertain, a nonlin-

ear adaptive observer was designed as below:

State estimation:

^zðtÞ¼R^zðtÞþOðtÞ

yðtÞþ

gðtÞþkðy 

yÞþ



y ¼ 10... 0½

(6.13)

Parameter adaptation:

yðtÞ¼

GfðtÞ y 

yðÞ (6.14)

Auxiliary ﬁlter:

V tðÞ¼



V tðÞþOðtÞ; f

ðtÞ¼V

ðtÞ (6.15)

where

^z the estimated state variable;

y the estimated parameter vector;

y the

estimated output;

k constant vector that has to be chosen to guarantee the stability;



constant matrix that has to be chosen to guarantee the stability; After the

parameter determination and stability analysis, in the real grinding control applica-

tion, a reduced model for the grinding force control can be written as:

¼ a

þ b

wdesired

;

¼ n

(6.16)

¼ K

ðy



½a

½Dðy

Þ

(6.17)

where y

rotating angle of workpiece; F

normal grinding force per width of cut;

Dðy

Þ equivalent wheel diameter; a depth of cut; n

workpiece speed; l

ðy

lever of the tangent force; v

wheel circumference speed; e

; e

exponential

coefﬁcients; K

Proportional factor (Fig. 6.10).

280 J. Liu et al.

By comparing the simulation results using this adaptive controller with PI-

controller, it can be seen that the PI-controller has difﬁculties during shaping the

unsymmetrical part of the features, which indicates that the uncertainty and time

varying properties of a nonlinear system /process such as grinding requires a more

adaptive control algorithm to regulate or optimize in order to improve the perfor-

mance of the system/process.

Jenkins and Kurfess [17, 18] developed a self-tuning adaptive controller for the

plunge grinding and traverse grinding processes. A pole-zero cancellation tech-

nique was devel oped and implemented to remove the process variations based on

real-time model parameter estimation.

As shown in Fig. 6.11, the entire control system model consists of several

functional blocks: G

ðsÞ – force controller; G

ðsÞ – the programmable multi-

axis controller (PMAC) position control loop; G

TWP

ðsÞ – the tool-workpiece and

grinding process interaction, as well as estimation and adaptation functions.

The gains of the adaptive force controller are updated in real-time style from the

host computer that estimates the grinding process parameters and determines the

force cont roller gains accordingly. The force controller is implemented on a PC-

hosted PMAC using a high sampling rate, running continuously. Since force is

being controlled via position, two control loops must be designed, a position loop

and a force loop. The servo controller for the position loop is implemented

using the PID servo algorithm in the PMAC. The gains are determined using

Ziegler-Nichols PID tuning techniques. The resulting closed-loop PMAC

position transfer function G

ðsÞ is represented by block between the commanded

Fig. 6.10 Comparison for simulation results of (a) the adaptive control scheme with (b) PI-control

scheme

6 Traditional and Non-traditional Control Techniques for Grinding Processes 281

position and the actual position of the X-axis. Due to the high speed of servo

loop a ﬁrst-order linear model of position response is estimated using an autore-

gressive, least squares parameter estimation technique.

The adaptive approach taken in this work, namely the self-tuni ng regulator (STR)

is an indirect method, also is a design procedure used to determine controller’s

parameters. In other words, the STR uses model parameter estimation to determine

current states for use in the real-time design calculations to adjust the controller

parameters. Different form the work done by To

nshoff who appl ied a ﬁxed-gain

controller to regulate the grinding force, the STR approach here perform s real-time

estimation of the grinding process and uses a pole-zero cancellation approach which

will be shown brieﬂy below to remove the process variation.

Based on the block diagram and grinding force model as below:

 F

(6.18)

The derivation of the adaptive force controller was achieved via an important step

which cancel the process dynamics pole by the zero of a PI-type controller, G

ðsÞ,

and the complete open-loop discrete transfer function is deﬁned as:

TWP

ðzÞ¼

PROP

1 þ a

ðÞ

z  C



(6.19)

The implementation of this controller uses a windowed data handling scheme for

recursive parameter estimation and the best window size was determined

via experiments and simulations. This approach to grinding force control has

demonstrated the potential for increasing productivity with the reduc tion of tarry

time by use of the stable force control in plunge grinding, with higher ﬁdelity in

force regulation.

Brinksmeier and Popp [19] presented an adaptive control system to reduce the

grinding time and ensure a good workpiece quality with a self-tuning force

Desired

force

Process Model

Parameter

Estimator

Adaptation

Control

Force

Error

Commanded

Position

Force

Control

(s) G

twp

(s)

Position

Loop

Encoder

Position

Tool-work-process

Impedance

Other Sensed

Parameters

Estimated Process

Parameters

Controller

Gains

Fig. 6.11 Plant and controller scheme for PMAC-based force controller.

282 J. Liu et al.

controller for external grinding processe s. A system identiﬁcation procedure was

used to adapt the control parameters online in order to compensate for the time-

varying grinding process behavior. The iden tiﬁcation result was also used to

monitor the wheel wear and compensate for the unknown system variations, such

as the elastic deformation of the workpiece-tool-machine system.

The model for the grinding process taken in this work can be described with the

p-transfer function as:

ðpÞ¼

p þ 1



p þ 1

(6.20)

where p – complex variable; o

; D

– parameters of the feed drive behavior; N –

compliance; C – abrasive property; F

– grinding normal force; The disturbances

mainly come from disturbances added to the measured plant output and those

changing the system parameters.

Also, since digital control algorithm could effectively improve the controller

accuracy, the above differential equation has to be transformed into a difference

equation, represented by Z-transformation, similar to (6.1)

ðzÞ¼

1

þ b

2

þ b

3

1 þ a

1

þ a

2

þ a

3

 z

d

(6.21)

For the unknown parameters, as the process behavior can vary during the grinding

cycles, the on-line process identiﬁcation is needed, which is shown in Fig. 6.12.In

general, a process variable which sufﬁciently represents the process state is very

important. The normal grinding force is preferred here because it is convenient to

monitor and allows additional utilization to reveal process mechanisms, namely

Controller Grinding Process

Controller

Modification

Parameter

Estimation

Conventional

controller

w: desired value

u: controller output

Selftuning

controller

Controller Grinding Process

Fig. 6.12 The structure of a self tuning controller

6 Traditional and Non-traditional Control Techniques for Grinding Processes 283

more relative to most of the anomalies. The signal processing of the adaptive

control system is illustrated in Fig. 6.13.

The hardware is based on an external VME-bus-based computer system,

which contains a MC68020 CPU-board with coprocessor. The prototy pe of

the adaptive control system consists of a studer S50-42 grinding machine with a

bruetsch-CNC. The dead centers of the grinding machine contain piezoelectric

force sensors measuring the grinding force in normal, tangential and axial direc-

tions, power meter detecting electrical power of the spindle motor etc.

For the adaptive strategy, two stages are applied. The task of the ﬁrst stage is

to detect the ﬁrst cut while the second stage is the removal of workpiece eccentri-

cities. After that, the actual selftuning adaptive controller is used. The controller

is predetermined with an assumed set of model parameters for the grinding

process. Information acquired during the second stage can be partially utilized

for the parameter estimation. In short, during the grinding process the

system computes the correct model parameters within a few workpiece revolutions.

Then the controller is tuned continuously and the identiﬁed set of parameters can

be saved and used in the future grinding.

6.5 Adaptive Control Constraint and Adaptive Control

Optimization

Wada and Kodama [20] proposed the concept that the general adaptive control

in grinding process can be classiﬁed into two categories depending on whether

Fig. 6.13 Signal processing of the adaptive control system

284 J. Liu et al.