Implementation of Cognitive Chips in Machining Error Attenuation

Maki K. Rashid

Mechanical and Industrial Engineering, Sultan Qaboos University, P.O.Box 33 Al-Khod,

Postal Code No.123, Muscat, Sultanate of Oman

Keywords: Cognitive Chips, Piezoelectric Switching, Vibration Attenuation, Smart Structure, Machining Errors.

Abstract: Machining is a complex process that requires a high degree of precision with tight geometrical tolerance and

surface finish. Those are confronted by the existence of vibration in the turning machine tool. Overcoming a

micro level vibration of a cutting tool using smart materials can save old machines and enhance development

in designing new generations of machine tools. Using smart materials to resolve such problems represent one

of the challenges in this area. As a continuation from previous work for the transient solution for a tool tip

displacement using pulse width modulation (PWM) technique that was implemented for smart material

activation to compensate for radial disturbing cutting forces. A Fuzzy algorithm is developed to control the

actuator voltage level to improve dynamic performance. Such technique together with the finite element

method as dynamic model proved a great successfulness. To implement such results in real life industrial

system we may use chips that mimic human brain as developed recently by IBM which is intelligent to learn

through incidents, find patterns, generate ideas and understand the outcomes to reduce tool vibration error.

1 INTRODUCTION

Demand for higher productivity in automated

manufacturing brought to the attention the control of

machine tool dynamics for a better machining

accuracy. Economical and ecological factors

encouraged the old conventional machines to continue

in service by overcoming the tool vibration problem.

Various factors might affect machining process

(Frankpitt, 1995), some of them are non-measurable

and others might change in real-time. However, the

wider use and the availability of cost effective

microcontrollers encouraged the implementation of

intelligent control schemes to overcome such time

dependent problems. The tiny unfavorable relative

motion between the cutting tool and the working piece

that associated with high excitation forces encouraged

the use of smart material actuators to counteract such

motion errors (Dold, 1996). Rigid fixture is a good

choice for minimizing displacements of cutting tools

from its nominal position during machining.

Unfortunately such a luxury is not available in all

applications. The reconfigurable manufacturing era

prefer fixtures consumes less space with minimum

weight (Gopalakrishnan et al., 2002; Moon and Kota

2002).

Previous dynamic modeling of smart toolpost

(Eshete, 1996) is based on linear piezo-ceramic

actuator. Derived models are either believed as lumped

single rigid mass for tool carrier, tool bit and

piezo-actuator or obtained from the most dominant

mode of system vibration as an effective mass,

stiffness and damping coefficients. Such models then

adopted for designing an adaptive controller using the

measured current and applied voltage as control

signals to the actuator. Based on similar principles

(Zhang et al., 1995) derived a mathematical model for

such smart tool post using the PMN. A control system,

and real time microprocessor implementation was

examined (Dold, 1996) and no details are given for the

design and selection of actuator, tool holder, and tool

bit stiffness, and, actuator switching. In case of future

geometrical changes, the validity of using lumped

masses in system modeling is questionable. Nature and

type of signals controlling smart material and how they

affect toolpost dynamic response is suffering from

information shortage. Recently (Hurtado, 2001)

developed an engineering approach in determining

optimum dimension based on stiffness of machining

fixtures. However, geometrical dynamic design for

smart toolpost requests special attention.

This work presents Fuzzy algorithm using a finite

element model (FEM) (Zienkiewicz and Taylor, 2001)

262

K. Rashid M..

Implementation of Cognitive Chips in Machining Error Attenuation.

DOI: 10.5220/0004106302620267

In Proceedings of the 9th International Conference on Informatics in Control, Automation and Robotics (ICINCO-2012), pages 262-267

ISBN: 978-989-8565-21-1

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

for flexible smart tool post incorporating PZT

actuator, tool holder, holder fixture, and tool bit. The

main dimensional variation in the work-piece that

might be caused by tool radial motion is emphasized.

This endeavor involves a development of a finite

element model to evaluate lumped mass modeling

approach, toolpost stiffness ratios and to work on a

Fuzzy control algorithm for actuator input voltage. A

special attention is given for the model to be a robust

for large variations in design parameters. Such finite

element model offers a methodology for future

development in smart toolpost design for limited

space and weight environments.

2 BUILDING THE FEM MODEL

AND GOVERNING

EQUATIONS

In this work Lead Zirconate Titanate (PZT), is

employed as intelligent material for smart toolpost

actuator. This encouraged by a well-developed

theoretical analysis for this material. Also it is the

most common used piezoelectric materials. Toolpost

model incorporates actuator, tool carrier (holder),

supporting diaphragm and tool bit as a spring buffer

between tool carrier and the net actuating force at tool

tip as shown in Figure 1.

Figure 1: Toolpost Model.

The model incorporated conventional stacked PZT

actuator contain polarized ferroelectric ceramic in the

direction of actuation, adhesive, supporting structure,

and electrodes wired electrically as shown in Figure

Figure 2: PZT Stacked Actuator.

Finite element modeling of the PZT actuator and

toolpost are achieved, through the general

constitutive equations of linear piezoelectricity and

by equations of mechanical and electrical balance the

details are given in (Piefort, 2001 and Abboud et al.,

1998). Structural boundary conditions are assigned in

Figure 1, where zero displacements is applied at the

actuator left end and fixed condition at the outer

diaphragm edge. Specifying the applied voltage at

actuator electrodes using PWM which accompanying

the actuator radial force at tool tip finalizes problem

description.

3 TOOLPOST FORCE

GENERATION VERSUS

DISPLACEMENT

Effectiveness of tool error attenuation depends on

PZT actuator capabilities in resisting tool axial force

within the limited range of motion. To build such

information a force versus displacement curve is

developed for the toolpost under investigation in

Figure 1. Figure 3 shows the force-displacement

characteristics at different values of tool tip (tool bit)

to actuator stiffness ratio (KT/KA, coupling spring in

Figure 1 at force application). The plotted curves in

Figure 3 are emphasizing the importance of

increasing (KT/KA) and (KC/KA) ratios. Also the

worth of reducing structural support stiffness

(diaphragm) in the direction of the PZT activation to

increases the actuation movement toward error

reduction. As a first guessing a suitable actuator can

be selected according to the disturbing force level and

the information offered by the force-displacement

calculations. A special consideration should be given

to the dynamic effects during machining. The smart

material data and, the investigated toolpost

dimensions are given in Table 1 for both static and

dynamic calculations.

Implementation of Cognitive Chips in Machining Error Attenuation

263

Figure 3: Smart toolpost force generation versus

displacement for different tool tip to actuator stiffness

ratios.

Table 1: Toolpost dimension and material.

Item

Value

Units

Cylindrical PZT-8 Stack

PZT Thickness

0.09e-03

Electrode Thickness (Nickel)

0.03e-03

Structural support (Stainless)

0.03e-03

Adhesive Thickness

10.0e-06

Number of layers

500

Effective Radius

5.0e-3

Steel Cylindrical Tool Carrier (holder)

Radius

10.0e-3

Length

55.0e--3

Steel Tool Bit Effective Length

Assumed Effective Length

20.0e-3

Steel Diaphragm

Thickness

0.5e-3

Outside Radius

20.0e-3

4 FUZZY ALGORITHM FOR

VOLTAGE ACTIVATION

Obtained results in (Rashid, 2004) prove significant

deviation of lumped mass modeling from the finite

element solution especially in the range of low

(KD/KA) and high (KC/KA) where the PZT

actuation is maximum as pointed out in Figure 3.

Therefore the finite element method is the reliable

tool of assessing switching methodology and system

damping in smart toolpost during error reduction.

Transient solution for tool displacement in time

domain for system shown in Figure 1 is given in

(Rashid, 2004 and Rashid, 2011). Smart toolpost

configuration and associated data are given in table 1.

4.1 PWM Modeling

Tool tip position error is reduced by appropriate

voltage activation to the smart material. An

economical way for smart material activation in

vibration attenuation is by using Pulse Width

Modulation (PWM). It is a common technique

available on microcontroller units (MCU) to govern

the time average of power input to actuators. The

time dependent motion accompanying the tool

vibration attenuation using the PWM for the smart

material activation is the next step.

The smart material voltage activation is either

triggered by a piezo stack with force sensing layer or

by using a suitable type of displacement sensor. In

both methods sensing location should reflect cutting

tool position error correctly. Switching circuits (Luan

and Lee, 1998) are not investigated in this work. But

the level of the required activation voltage for the

piezo stack is carefully discussed.

Representation of switching voltage as a series of

PWM cycles is based on the peak cutting force level

at the measured frequency ( ), where, the initial

peak voltage is estimated accordingly from Fig. 3. A

complete period of force cycle ( ) is then divided

into number of duty cycles (

). At any of these

divisions, the time duration of the PWM high

DC-voltage is calculated according to the obtained

voltage factor from the fuzzy algorithm discussed

next. A time delay in voltage activation can be

incorporated as a function of force period. Two

switching are associated with each PWM cycle

segment, therefore switching rate is

fPWM



Effects of switching voltage input, forcing frequency

, and, damping level upon toolpost time response

are parameters to be discussed in smart toolpost

transient solution. A harmonic force waveform is

assumed for all presented results.

4.2 The Fuzzy Algorithm

For such a nonlinear problem a fuzzy modeling

algorithm (Passino, 1998) is launched to extract rules

that relate actuator voltage factor (a multiplication

factor to the estimated voltage from Figure 3) to the

toolpost position error and the time rate of change of

error as shown in Figure 4. Five linguistic values are

used, namely L=‘‘Low’’, M/L=‘‘Medium to low’’,

M=‘‘Medium’’, M/H=‘‘Medium to High’’ and

H=‘‘High’’.

The algorithm considers each input and output

variables to be equally divided by symmetric

membership functions of triangular type, and the

algorithm uses the t-norm max to select the degree to

which two fuzzy sets match. The output of each fuzzy



PWM



ICINCO 2012 - 9th International Conference on Informatics in Control, Automation and Robotics

264

inference system is derived using the standard

Zadeh–Mamdani’s min–max gravity reasoning

method. The rules in the fuzzy model have the

following form:

(1)

Where,

)(i

is the ith rule,

are the antecedent

variables, and

is the consequent variable. For the

toolpost,

will be the error and, the rate of change

of error as obtained from the FEM model, and z will

be the actuator voltage factor. Symbols

)(i

represent the fuzzy sets, and,

)(i

are the rules

conclusion of the fuzzy system. The inference

operation and the defuzzification formula of the

fuzzy algorithm are described in various literatures

(Passino, 1998). A number of calculations and

fine-tuning are pursued to obtain the final

membership functions and the rule-base for the

voltage factor of the controller as given in table 2.

Table 2: The controller rule base.

Figure 4 shows the control surface of the fuzzy

controller, offering a correlation between the voltage

factor VF as a function of the normalized error



and the normalized rate of change in error





. By

considering the negative error is the tool tip

displacement away from the work piece axis then



is the negative of the normalized tool tip error with

respect to the maximum static displacement of the

peak radial cutting force? The universe of discourse

of the input variable



is defined to be within the

range [0, 1] where the voltage is only applied when

the tool has an inward motion away from the work

piece axis. While





is the time rate of change of

error



calculated every one tenth of the force period

and given a universe of discourse [-0.2, 0.2]. Finally

VF is a multiplication factor for the estimated voltage

from the static tool force-displacement chart in Fig. 4

and given a universe of discourse [0, 1].

Figure 4: Fuzzy control surface for voltage factor.

5 RESULTS OF FUZZY

CONTROLLED RESPONSE

FOR INTEGRATED TOOLPOST

Requirements to reduce tool holder size and weight

encourage developing new tactics of using smart

actuators to attain high precision by compensating

unfavorable motion errors.

Estimation of cutting tool radial force might

involve several variables. In general the static force

relation (Frankpitt, 1995) which expressed in terms of

depth of cut ( , mm), cutting speed ( , mm/s), feed

( , mm/rev), and, coefficients describing the

nonlinear relationships (



,,, and

) can be used

as a first guess in error attenuation:

rrr

KtfVdKF )(





a general constant (2)



and,



are to be calibrated for each

tool-workpiece, tool-work material combinations,

process types, tool-wear condition, workpiece

hardness, tool geometry and speed. For presented

results both Eq. (2) and Figure 3 deliver the first

estimate of the force and applied voltage to the

actuator. Following force values are obtained

according to the Fuzzy control surface in response to

error and rate of error. Data for the produced results

are given in Table 1. Using a few PWM cycles per

force period can cause unfavorable switching

dynamic excitation by actuator to tool post as shown

in Figure 5 for ten PWM cycles. Twenty PWM cycles

per force period produce more favorable results but

more than twenty have little effect. For comparison,

the outcome of increasing



by ten folds from

selected datum of 1% damping ratio for first mode

)1(BiszTHENAisxand

...AisxandAisxIF:R

)i()i(

)i(





M/H

M/L

M/H

M/L

Implementation of Cognitive Chips in Machining Error Attenuation

265

and 5% for second mode produce significant

reduction in tool tip normalized error. Both damping

and voltage activation are contributed to reduction in

normalized error as shown in Figure 5. Using a high

damping only does not solve error attenuation

problem as indicated in Figure 6.

Figure 5: Normalized tool tip error versus time for KT/KA

= 10, KC/KA = 10 and KD/KA = 0,01 for high damping

(HD), low damping (LD) and N

PWM

of 20 or 10.

Figure 6: Normalized tool tip error versus time for

KT/KA=10, KC/KA=10, KD/KA=0,01, high damping

(HD), delay of 0,1, delay of 0,2 and N

PWM

of 20 or 10.

Negative normalized error in Figures 5-6 indicates

outward tool tip retraction away from the workpiece

axis. Tool bit to actuator stiffness ratio (KT/KA) has

importance in terms of force availability for tool tip

error elimination and accurate displacement sensing

as shown in Figure 3. For a stiffness ratio greater than

ten identical displacements produced between tool tip

and tool carrier main body. Taking into consideration

the geometrical factors, deviation starts to be

noticeable when stiffness ratio (KT/KA) drops below

one. Importance of such parameter depends on

required final error limits and type of application.

Time delay in voltage activation has a significant

effect if the delay is exceed 10% of the force

frequency period as shown in Figure 6.

6 CONTROLLER

CONFIGURATION USING

COGNITIVE CHIP

It is difficult to acquire a controller that ensures

continuous error tracking under stabilized condition

for smart toolpost under continuous exposal to an

erratic real time force inputs. The idea of using an

intelligent controller is generated by the random

nature of system excitations which largely depends

on unpredictable parameters such as structural

properties, friction, and other variable dynamic forces

(Rashid, 2011). A neural network can model the

response of such system by means of a nonlinear

regression in the discrete time domain. The result is a

network, with adjustable weights, that might

approximate the system dynamics. Though it is a

problem since the knowledge is stored in an opaque

fashion and the learning results in a large set of

parameter values which almost impossible to be

interpreted in words. Conversely using a fuzzy rule

based controller that consists of readable if-then

statements which is almost a natural language, cannot

learn new rules alone.

The structure of using intelligent controller is

shown in Figure 7 (Rashid, 2011) where MF is the

membership function. The idea of implementing the

cognitive chip is described in Figure 8.

Figure 7: Intelligent controller architecture (Rashid, 2011).

Figure 8: Flow chart for cognitive chip implementation.

ICINCO 2012 - 9th International Conference on Informatics in Control, Automation and Robotics

266

7 CONCLUSIONS

Reducing machining error in old turning machines

using smart material can reduce industrial waste, save

money and, improve design flexibility for new

cutting tools. The outcome of this work show

stiffness ratios in toolpost structural design have a

major rule in actuator selection and design. Support

stiffness in the direction of actuation should be

minimal. Tool bit to actuator stiffness should be

higher than one and to the extents that make tool error

is acceptable. Tool bit to actuator stiffness and tool

carrier (holder) to actuator stiffness both are preferred

to be high. The developed fuzzy algorithm for voltage

activation factor based on normalized error and its

rate proved a significant effectiveness in error

attenuation. Implementation if intelligent scheme

proved effectiveness during FEM simulation. Using

cognitive chips in real application as in Figure 8 is the

idea of future development.

REFERENCES

Abboud, N. N., Wojcik, G. L., Vaughan, D. K., Mould, J.,

Powell, D. J., and, Nikodym, L., (1998), Finite Element

Modeling for Ultrasonic Transonic Transducers,

Proceedings SPIE Int. Symposium on Medical Imaging,

San Diego, Feb 21-27, 1-24.

Dold, G., (1996), Design of a Microprocessor-Based

Adaptive Control System for Active Vibration

Compensation Using PMN Actuators, MS Thesis,

University of Maryland at College Park.

Eshete, Z., (1996), In Process Machine Tool Vibration

Cancellation Using Electrostrictive Actuators, Ph.D.

Thesis, University of Maryland at College Park.

Frankpitt, B. A., (1995), A Model of the Dynamics of a

Lathe Toolpost that Incorporates Active Vibration

Suppression, Institute for System Research, University

of Maryland at College Park.

Gopalakrishnan, V., Fedewa, D., Mehrabi, M. G., Kota, S.

and Orlandea, N., (2002), Design of Reconfigurable

Machine Tools, ASME J. Manuf. Sci. Eng., Technical

Briefs, 124, 483-485.

Hurtado, J. F., and Melkote, S. N., (2001), Improved

Algorithm for Tolerance-Based Stiffness Optimization

of Machining Fixtures, ASME J. Manuf. Sci. Eng., 123,

720-730.

Luan, J., and, Lee, F. C., (1998), Design of a High

Frequency Switching Amplifier for Smart Material

Actuators with Improved Current Mode Control, PESC

98, Vol. 1, Fukuoka, 59-64.

Moon, Y., and, Kota, S., (2002), Design of Reconfigurable

Machine Tools, ASME J. Manuf. Sci. Eng., Technical

Briefs, 124, 480-483.

Passino, K. M., and Yurkovich, S., (1998), Fuzzy Control,

Addison Wesley Longman, Inc.

Piefort, V., (2001), Finite Element Modeling of

Piezoelectric Active Structures, Ph.D. Thesis, ULB,

Active Structures Laboratory- Department of

Mechanical Engineering and Robotics.

Rashid, M. K. (2011). Neurofuzzy Implementation in

Smart Toolpost To Improve Performances. Global

Journal of Researches in Engineering (A), Volume XI,

Issue VII, Version 1.0 December, 1-10.

Rashid, M. K., (2004), Smart Actuator Stiffness and

Switching Frequency in Vibration Suppression of a

Cutting Tool, Smart Materials and Structures, Vol.13:

1-9.

Zhang, G., Ko, W., Luu, H., and Wang, X. W., (1995),

Design of a smart Tool Post for Precision Machining,

Proceedings of the 27

CIRP International Seminar on

Manufacturing Systems, Ann Arbor, MI, 157-164.

Zienkiewicz, O. C., and, Taylor, R. L., (2001), The Finite

Element Method, Fifth edition Vol.1: The Basis,

Butterworth-Heinemann.

Implementation of Cognitive Chips in Machining Error Attenuation

267