Jackson Mark. Machining with Abrasives

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the controlled process is working within a constrained condition, or the ultimate

objective function has a certain optimum value. The ﬁrst classiﬁcation is

Adaptive Control Constraint (ACC) and the second one is Adaptive Control Opti-

mization (ACO).

A typical Adaptive Control Con straint (ACC) scheme was developed by Hahn

[12, 13] for grinding force control. In this work, a controlled-force grinding

technique is presented to eliminate random size and taper ﬂuctuations resulting

from variable elastic deﬂections. Through this method, the affection coming from

variations of stock, hardness and wheel sharpness could be eliminated from the

sizing problem and allows the comprehensive grinding performance directly related

to grinding force which could simplify practical grinding setups. More over, the

control method is based on an analysis made of the rounding up dynamics of the

controlled-force system and a critical work speed is found which must be exceeded

in order to have a rounding-up action.

Adaptive Control with Optimization (ACO) system has been developed by

multiple researchers, such as Ko

nig and Werner [21], Kelly et al. [22], Xiao and

Malkin [23–25], Li et al. [27], Dong et al. [28, 29], Srivastava et al. [30].

In Li’s [27] work, based on the basic grinding models, the objective function and

constraint functions for the multi-parameter optimum grindin g process have been

built and the non-linear optimum grinding control parameters have been obtained

through computer simulation and the actual grinding process is controlled by these

optimized parameters. According to the multi-parameter optimal theories, the

objective function obtaining the shortest gri nding time f can be formulated with

constraints as:

Minimize :

f ¼ t

þ t

Subject to the constraints :

¼ P  P

b0 (no - burn constraint)

¼ z  qb0 (burning constraint)

¼ R

 R

max

b0 (roughness constraintÞ

¼ RN  RN

max

b0 (roundness constraintÞ

¼ rt

þ t

ðÞDr ¼ 0 (size constraint Þ

¼ u

 u

b0; i ¼ 1; 2 lower infeed constraintðÞ

¼ u

 u

b0; i ¼ 1; 2 upper infeed constraintðÞ

(6.22)

where P is the power of the roughing stage and P

the burning power limit of the

workpiece; z is depth of the burning layer and q the depth of removal in the

subsequent ﬁnishing stage. R

is the actual surface roughness and R

max

its maxi-

mum allowable value; RN is the actual out-of-roundness and RN

max

its

maximum allowable threshold. rt

þ t

ðÞis the total actual infeed for the

whole grinding process and Dr the depth of removal denoting the radial workpiece

allowance. u

is the lower limit of the infeed rate and u

the upper limit, whilst i ¼ 1

denotes the roughing stage and i ¼ 2 denotes the ﬁnishing stage.

6 Traditional and Non-traditional Control Techniques for Grinding Processes 285

The strategies of multi-parameter optimization include three main cases.

The ﬁrst one is for the conventional grinding process under the no-burn state, the

grinding power being much lower than the burning limit in the roughing stage with

the constrained models including g

 g

; the second one, under the critical

burning state, requires that the inequality should be g

¼ 0. The last one is under

the burning state in the roughing stage, its constraint models including g

 g

These optimum strategies were implemented experimentally on an external semi-

automatic grinder and the controlling system is illustrated in Fig. 6.14.

In Dong ’s [28, 29] work, an innovative technology, which allows for continuous

variation of the infeed rate to further reduce the cycle time, is developed for optimal

infeed control of cylindrical plunge grinding cycles. The controller is designed to

identify the state of the cycle at each sampling instant from on-line measurements

of power and size, and to then compute the infeed rate according to the optimal

policy whereby the infeed rate is determined according to the active constraint at

each segment of the cycle.

The objective of the grinding optimization is to ﬁnd the optim al infeed rate uðtÞ

which minimize the cycle time while also satisfying constrains associated with the

machine capability and workpiece quality as well as the parameters assoc iated with

Fig. 6.14 Chart of the grinding controlling system

286 J. Liu et al.

periodically dressing of the wheel. Namely, the magnitude of the grinding infeed

rate which is related to productivity is constrained not only by machine limitations

but also part ﬁnish quality requirements including thermal damage, surface rough-

ness and dimensional tolerance. Consequently, the optimization problem can be

formulated as:

Minimize cycle time :

i¼1

Subject to the constraints :

: zðkÞ

i¼kþ1

vðiÞdtb0

: R

ðNÞR

a;max

: rðNÞr

max

i¼1

vðiÞdt  Q



btol

: u

 uðkÞb0 for all k ¼ 1; :::; K

: uð kÞu

b0 for all k ¼ 1; :::; K

(6.23)

where the inequality g

deﬁnes the depth of thermal damage limit above a critical

temperature referred to as “workpiece burn”; inequality g

deﬁnes the surface

roughness requirement; g

deﬁnes the out-of roundness at the end of the cycle

and r

max

is its maximum allowable value; g

deﬁnes the size requirement and the

last two constraints represent limitations on the machine infeed rate where u

is the

lower bound and u

is the upper bound. A schematic diagram of the corresponding

control system is shown in Fig. 6.15. The core part is the block named “optimiza-

tion” whose task is to identify the state of the cycle using measurement data of

power and size and then compute the desired infeed rate v

. The controller can be

bypassed at ﬁrst and last grinding sections, because the command infeed rate should

Process Model

Parameter

Estimation

Optimization

Process

PI Controller

Filter

Power, Size

or 0

Surface Roughnes

Fig. 6.15 Schematic diagram of the on-line control strategy

6 Traditional and Non-traditional Control Techniques for Grinding Processes 287

be at its maximum allowable limit for the ﬁrst section of the cycle and at zero for the

last. The actual infeed rate v is obtained on-line from size measurements, and

parametric values of the time constant t and the effective wear ﬂat area A

eff

can

be estimated in the block “parameter Estimation” from measurements of power and

size. Moreover, the control system uses feedback from power and size to compen-

sate for modeling uncertainty caused by parameter variations and external distur-

bances.

This kind of control system seeks to adjust operating condition according to

a predeﬁned performance index in order to optimize the grinding process during

real-time operation. The identiﬁed process models allow to predict workpiece

burn and estimate the compliance of the workpiece-tool-machine system. The

drawback of such control strategy is that some para meters cannot easily be

measured online, e.g., surface roughness is often measured off-line, and hence is

not controllable with such a scheme. In addition, the optimization calculation load

is usually heavy for multiple process goals with multiple input/output constraints

during online operation and the optimal solutions largel y depend on a carefully

selected initial condition, which needs to be determined by experienced operators.

Based on optimal control theory, Malkin and Koren [31] derived an accelerated

spark-out method by reducing the time required to recover the accumulated elastic

deﬂection in the system and therefore the cycle time was successfully minimized in

cylindrical plunge grinding processes. And this optimal control policy is particu-

larly advantageous for grinding systems having a long characteristic time constant.

It has been proposed by Malkin [5] that this accelerated spark-out method can be

beneﬁcial to incorporate into the Adaptive Control Optimization (ACO) system in

optimizing the grinding and dressing parameters for maximum Material Removal

Rate (MRR) within constraints on workpiece burn and surface ﬁnish. Grinding

processes are complex in nature with multiple cutting points, which are deﬁned by a

large number of grits possessing irregular shapes, sizes and spacing. Inevitable

variations of the tool position, velocity and force ﬂuctuation heavily affect the ﬁnal

part’s geometry accuracy, surface ﬁnish, and the overall process Material Removal

Rate (MRR). Moreover, various uncertainties and disturbances inherently exist in

the process. It is therefore necessary to control the grinding process under various

system variations. Jenkins et al. [17] presented a robust controller for a grinding

system where the normal grinding force was decoupled from the tangential feed

velocity of the system. Two separate control loops were designed as a standard feed

velocity loop and a force loop, so that the two variables could be controlled

simultaneously. A variet y of other system performance speciﬁcations were success-

fully achieved, such as reduced overshoot value and transient settling time. The

objective of the compensator design is to control the force and velocity to

meet speciﬁ c target while simultaneously decoupling the feed velocity from the

normal grinding force.

The grinding system used in this work consists of a three-axis prismatic servo

stage, which is controlled by a programmable multi-axis controller (PMAC). The

controlled grinding system has two input trajectories, desired force and velocity,

and two outputs, act ual force and velocity. A least squares parameter estimation

288 J. Liu et al.

technique (ARX, autoregressive external input, Ljung, L. [32]) is used to determine

the transfer function between the input commands and the outputs, and analyze step

commands in force and velocity. The block diag ram of the closed-loop system with

the appropriate transfer functions is shown in Fig. 6.16.

For the compensator design, a PID-type controller form is selected for imple-

mentation in both the velocity and force loops. In this case, by increasing the

forward loop gain, cross coupling between force and velocity is easily decoupled.

In general, many parameters needed for designing a new compensa tor in similar

application circumstances can be gained by using the control design tools and

procedures in this work.

6.6 Intelligent Control Techniques

Although various adaptive and robus t control techniques have been studied to

maintain the desired closed loop performance in the pres ence of parameter varia-

tions and process uncertainties, they often encounter difﬁculties in actual design

when the system dynamics are not well known. In addition, in the control process,

all the necessary coefﬁcients of the controller need to be calculated and updated on-

line, which makes the computation burden quite heavy. In contrast, intelligent

controllers based on neural networks and fuzzy logic are attractive alternatives

output 2

output 1

Vd1

SUM4

SUM3

SUM1

SUM

-1.84

s+0.0058

+32.34s+1149.4

1.625

s+0.007

0.8252

+15.33s+249.2

156

Gcv Subsystem1

In1

Out1

Gcv Subsystem

In1 Out1

Fig. 6.16 System block diagram

6 Traditional and Non-traditional Control Techniques for Grinding Processes 289

since they do not require precise mathemat ical models. The information from

human experts and experimental data could be extracted and formulated in the

control law design, which make these intelligent control techniques most suitable

for precision grinding and other abrasive processes, since the current industrial

practices heavily rely on experienced human operators in order to achieve the

desired results. By incorporating operators’ skills and knowledge, the following

grinding activities can be possibly performed by intelligent systems, such as:

Controlling the ﬁnal part’s surface roughness

Preventing burning on the ﬁnal part’s surface

Compensating for grinding machine and process variations

Reducing grinding vibration and chatter

Determining an appropriate dressing interval for grinding wheel

Rowe et al. [33, 34] provided an extensive review on different intelligent control

techniques in grinding processes. This review describes the object-oriented devel-

opment method of the generic intelligent control system for grinding based on the

proposed modular conceptual framework (as Fig. 6.17), also reviews previous work

towards intelligent grinding control and summarizes the previously used strategies

and introduces the structure and operation of the generic intelligent control system.

The most common practical operations are for external and internal cylindrical

grinding due to the lack of accurate analytical models or incomplete information

about the processes, where the intelligent control technologies emerged to be

promising when the conventional methods often fail. The trend of increasing

usage of machine intelli gence in grinding systems and operations is clearer and

more researchers are working in this area nowadays. A most signiﬁcant reas on is

that the human specialist knowledge and lessons grained from previous operations

can be incorporate in the controller design to ensure a better system performance for

the future operations. A conceptual framework for a typical intelligent grinding

machine is illustrated in Fig. 6.17, where all essential elements have been tested and

integrated into practical gri nding systems.

Above conceptual framework provides a general guide to the design of the

intelligent control system. Of all the components, the executor plays the central

role, which is basi cally a software drive, capable of selecting relevant software

modules and integrating them to form an intelligent control system for a speciﬁc

grinding process following predetermined rules. Besides, it consists of several other

components, including I/O routines, process models and rules, a database, an

intelligent parameter selection system, typical grinding cycles, safety strategies,

adaptive strategies and learning strategies.

Nakajima et al. [35] presented a neuro & fuzz y in-process control technique for

plunge grinding processes, where a back-propagation neural network was built up

to predict the surface roughness during the process. The infeed rate to the speed

ratio was controlled and the grinding efﬁciency was optimized with the desired ﬁnal

surface roughness, independent of the wheel surface condition. Xiao and Malkin

[25] proposed an intelligent grinding system, where the system used power and the

part size information (which was measured online) as the feedback signal to

290 J. Liu et al.

estimate and optimize the grinding performance for the next workpiece part.

Additionally, the intelligent controller took the surface roughness and roundness

measured during post-process to adjust the dressing feedrate and also identiﬁed the

process to minimize the cycle time. The com bined online system identiﬁcation and

the meta control ensured the resultant system intelligence. The integrated intelligent

grinding system is illustrated in Fig. 6. 18 .

The fuzzy technique has been recognized and utilized to control complex

grinding processes since early 1980s. The basic idea of a fuzzy inference system

is to incorporate human’s knowledge into a set of fuzzy IF-THEN rules, which

involve operations on linguistic variables. The general fuzzy infere nce system can

be shown in Fig. 6.19, which consists of four components as: a fuzziﬁer, a fuzzy

rule base, a fuzzy inference engine and a defuzziﬁer.

Zhu et al. [26] did the ﬁrst implementation of a fuzzy controller to obtain

the desired surface ﬁnish by controlling the workpiece feedrate without any mathe-

matical model. Zhao and Webster [14] applied fuzzy pattern recognition to the

Executor

Input/

output

routines

Grinding

machine

DATA BASE

Part programs

Wheel data

Material data

Workpiece data

Coolant data

Learned values

Default values

Selection

strategy

Safety

strategy

DATA LOGGER

Production

Information

Process

Information

PROCESS

MODELS & RULES

Kinematics

Thermal

Surface texture

Compliance

Chatter

Roundness

Wheel wear

dressing

Adaptive

strategy

Database

learning

strategy

CYCLES

Set feedrate

Multiple feedrate

Pecking cycle

Adaptive feedrate

Overshoot

Adaptive power

Adaptive offset

dressing

Axis

control

Sensors

Power

Size

vibration

Fig. 6.17 Conceptual framework for a typical intelligent grinding machine

6 Traditional and Non-traditional Control Techniques for Grinding Processes 291

automatic control of roller grinding processes. This adaptive control strategy

could eliminate the highly skilled, time consuming and tedious task of manually

adjustment of supporting steadies. The method is based on microcomputer con-

trolled in-process size measurement techniques and enables faster and more

accurate grinding, replacing the experienced operators by an expert system.

The experimental results showed that this approach yielded a more reliable and

more accurate result than an experienced operator could.

The hardware layout of the system is shown in Fig. 6.20, in which ﬁve studies are

adopted, each of which is shown in Fig. 6.21, has a horizontal and a vertical pad

driven by separate stepper motors.