yInternational Journal of Scientific Engineering and TechnologyVolume No.4 Issue N o.3, pp : 207-211

(ISSN : 2277-1581)01 March. 2015

Sc I

Research on Optimization of Plunge Centerless Grinding Process using Genetic Algorithm and Response Surface MethodPhan Bui Khoi1, Do Due Trung2’ , Ngo Cuong2, Nguyen Dinh Man2

'School of Mechanical Engineering, HUS, No. 1, Dai Co Viet, Ha Noi, Viet Nam 2College of Economics and Technology, Thinh Dan ward, Thai Nguyen city, Viet Nam

Corresponding author: dotrung.th@gmail.com

Abstract: This paper presents the research on optimization o f plunge centerless grinding process when grind 20X - carbon infiltration steel (¡'OCT standard - Russia) to achieve minim um o f roundness error value. The input parameters are center height angle o f the workpiece ( j3), longitudinal

grinding wheel dressing feed-rate ( S sd), plunge feed-rate

( S k) and control wheel velocity ( vM ). Using the result o f 29

runs in Central Composite Design matrix to given the second order roundness error model. Genetic algorithm and Response surface method were used to fo cu s on determination o f optimum centerless grinding above parameters fo r minimization o f roundness error fo r each methods.

Keywords: Plunge centerless grinding, optimization, optimization, genetic algorithm, response surface method, roundness error, 20X steel.

1. INTRODUCTIONCenterless grinding is widely used in industry for precision

machining of cylindrical components because of its high production rate, easy automation, and high accuracy. 20X - carbon infiltration steel is a common alloy steel that is usually used in mechanical engineering using centerless grinding process.

To improve the centerless grinding process, it is necessary to optimize roundness errors, the most critical quality constraints for the selection of grinding factors in process planning.

Researches on the optimization o f centerless grinding process were published by many authors: Minimizing the roundness errors of workpiece by selecting the optimization levels o f control wheel speed, feed rate and depth of cut [1], Minimizing the roundness error o f workpiece and carrying out the regression analysis to model an equation to average out roundness error [2], Predicting the set-up conditions to analyze the dynamic and geometrical instabilities, making it possible to study the influence of different machine variables in stability of the process [3]. Minimizing the lobing effect by developing a stability diagram for workpiece and thereby selecting the grinding parameters and having found out that the characteristic root distribution of the lobing loop is periodic[5]. Investigating the workpiece roundness based on process parameters by both simulation and experimental analysis and finding out that a slower worktable feed rate and a faster workpiece rotational speed result in better roundness error [6]. Minimizing the

roundness error of workpiece by selecting the optimization levels o f dressing feed, grinding feed, dwell time and cycle time [7], Minimizing the roundness error o f workpiece by selecting the optimization range of the center height angle [8], Giving a method of how to select the optimal stable geometrical configuration in centerless grinding [9], Giving an algorithm for providing the optimum set-up condition [10]., etc.

This paper presents the research on the optimization of plunge centerless grinding process when grinding the 20X- carbon infiltration steel to achieve the minimum value of roundness errors. The input parameters include center height angle of the workpiece ( ¡3 ), longitudinal dressing feed-rate

( Ssd ), plunge feed-rate ( S k ) and control wheel velocity ( vdd ).The computer-aided single-objective optimization, solved by genetic algorithm and response surface method, is applied.

2. EXPERIMENTAL SYSTEM

2.1. Centerless grinding model

Plunge centerless grinding model is illustrated in figure 1. The value o f center height angle ((3) can be adjusted by the value of A . The relationship between (P) and A in equation 1:

ß = arc si A - R . - H

R,l,„ + J+ arcs il

A - Rc, - HR,UI + Rc< J

(I)

Where, H is the distance from the grinding wheel center, control wheel center to the bottom o f the workrest blade.

F ig l.Plunge centerless grinding model

2.2. ComponentsThe component material was the 20X-carbon infiltration

steel (Fig 2). The chemical composition of experimental

IJSET@2015 Page - 207 -

JET

component is in Table 1, \ workrest blade with a 30° ang

jg ** „ In ternational JournalV olum e N o.4 Issue N

25

11f\: -

30

Fig 2. Experimental component

Table 1: C hem ical com p o sitio n o f ex perim en ta l co m p o nen t

2.3. Experim antal machine tool

The grinding experimen centerless grinder with H = 21 Grinding wheel: the A120 3 Grinding Wheels Joint Cn80.TBiG.V,.500.150.305x35

Control wheel: the standard mm x 150 mm x 127 mm dimesi

3, p p : 207-211

/as supported by specially made

25

C(%) Si(%) Mn(%) P(%) S(%) Cr(%) Ni(%) Cu(%)1,02 0,212 0,51 0,01 8 0,017 0,78 0,017 0,021

's were conducted on a M1080B0 |nm, shown in Fig 3.

rinding wheel o f Hai Duong Dck Company, Viet Nam,

n's.rfibber bonded control wheel of 273 Dr is was employed.

St

Fig3 .Experima,

1.4. Measuring equipment

The roundness error was jrecision of 5/10.000. Each desigjn three ground components), ¡ummaiized in Table 3, are the a neasurements.

i. EXPERIMENT MATRIX

JSET@2015

ital machine tool

measured by a dial gage with a points was measured three times

Ihe roundness error response, /erage reading of three consecutive

i y

The experin conditions to ke> grinding depth (0. spark-out time ( 1

In this work.input paremeters (

in Table 2. This include 16 single­points located and

Table 2. Input par

(ISS

ent matrix was conducted p the grinding wheel sp 05 mm), the depth of dress ) and the coolant flow cons

u^ing the central composit

ß > S s d ’ S k ’ Vdd )> t h e i r l

experimental matrix with replicated orthogonal facto 5 centre points, shown in J

ameters and theirs levels

N31

un;edmgtan

e ceve

29'iaiabl

2277-1581) vfarch. 2015

ier chatter free (34 m/s), the

(0,01 mm), the

esign with fourIs are presented

sets; these sets points, 8 axial

2 3.

Inpu t parairictei S Sym bolPar Î111C er levels

-2 -1 0 l 2

Center height angl T ß 4,8 6,0 ' ,2 8,4 9,6

D ressing feed-ra (m m /m in)

teS * 100 200 3 DO 400 500

In-feed speec (jin /s) Sk 2 6 0 14 18

C ontrol w heel velo (m /m in)

cityv dd 18,9 >4,25 2! ,6 34,95 40,3

Table 3. Experime tal natrix

Set ß<r Sk v dd a ;f j n 0 A* (/im)

1 1 1 -1 1 2 .67 2.84

2 0 0 -2 0 2 ,33 2.11

3 -2 0 0 0 2 ,50 2.28

4 -1 1 -1 -1 3 ,33 3.46

5 -1 1 -1 1 2 ,67 2.81

6 0 ) 0 0 ,00 1.23

7 -1 1 1 -1 2 ,50 2.58

8 1 1 1 1 :t ,00 3.05

9 -1 1 -1 -1 ,17 2.29

10 1 1 1 ,00 1.15

11 0 ) 0 -2 ::,33 3.14

12 -1 1 1 83 2.00

13 -1 1 -1 i 67 2.76

14 1 I -1 17 1.30

15 0 0 0 33 1.23

16 0 0 0 1 00 1.23

17 0 0 0 1 33 1.23

18 0 0 2 3 33 3.08

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\ In ternational Journal o f S cien tific E ng ineering and T echnologyf ' V olum e N o.4 Issue N o .3, pp : 207-211

(IS S N : 2277-1581)01 M arch. 2015

J S E T

19 1 -1 -1 -1 1,50 1.58

20 1 -1 1 -1 2,33 2.45

21 1 1 -1 1 1,83 1.94

22 -1 -1 -1 1 2,33 2.38

23 -1 1 1 1 1,33 1.44

24 2 0 0 0 1,50 1.28

25 0 2 0 0 2,00 1.75

26 0 -2 0 0 2,67 2.48

27 1 1 -1 -1 1,33 1.42

28 0 0 2 0 1,83 1.61

29 0 0 0 0 1,50 1.23

The statistical analysis software Minitab 16 was used to determine the regression coefficients. The roundness error models was developed in the form of non-reduced final equation in terms of coded parameters.

(2)

A = 1,232 - 0,25p - 0 ,18083^ - 0,1255,

- 0,014167v(W + 0,13658p 1 + 0,220335^

+ 0,156585' + 0,46908v^ - 0,33375p.Ssd

+ 0,14625p.Sk + 0,2925p.vM - 0,24875S tl/Sk- 0,18 7 5 5 > rf(/- 0,1675Skvdtl

The upper model can be used to predict surface roughness at particular design points. The numerical values o f predicted responses A * are also summarized in Table 3. The differences between the measured and predicted responses is shown in Figs 4.

4.ÛU

3*00

2,00 -

Î X'O

—♦- ^ A*

A / A .

0,00 4 i '1—i i i i—i i i i—i i i i—r—i—i—n —i—m —r~ n —m —i1 3 5 1 9 11 13 15 17 19 21 23 25 27 29

Experimental run

Fig 4. Measured and predicted roundness error

4. OPTIMIZATION

4.1. Using Genetic Algorithm

GAs form a class of adaptive heuristics based on principles derived from the dynamics o f natural population genetics. The searching process simulates the natural evolution o f biological creatures and turns out to be an intelligent exploitation of a random search. A candidate solution (chromosomes) is represented by an appropriate sequence o f numbers. In many applications the chromosome is simply a binary string of 0 and 1.

Fig 5. Structure of a general GA

The quality o f its fitness is the function which evaluates a chrom osom e with respect to the objective function o f the optim ization problem. A selected population o f the solution (chrom osom e) initially evolves by employing m echanism s m odelled after those currently believed to apply in genetics. Generally, the GA mechanism consists o f three fundam ental operations: reproduction, crossover, and m utation. R eproduction is the random selection o f copies o f solutions from the population, according to their fitness value, to create one or more offspring. Crossover defines how the selected chromosomes (parents) are recom bined to create new structures (offspring) for possible inclusion in the population. M utation is a random m odification o f a random ly selected chromosome. Its function is to guarantee the possibility to explore the space o f solutions for any initial population and to perm it the freeing from a zone o f local minimum. Generally, the decision about the possible inclusion o f crossover/m utation offspring is governed by an appropriate filtering system. Both crossover and m utation occur at every cycle, according to an assigned probabilty.The aim o f the three operations is to produce a sequence o f populations that, on the average, tends to improve.

Structure o f a general GA is illustrated in figure 5.To get the optimization o f (5 , Ssd > S k , vdd value for

minimum the value o f roundness error ( A ) , objective function

A can be written:

IJSET@2015 Page 209

>C_ I

A = f [ ß , S sdk , v M )

A > 0

- 2 < ß , S sd, S L v dd <Table 4. Genetic

\ International Journal- * V olum e N o.4 Issue N

) f S c ien tif ic E ng ineering and T echnologyo 3, p p : 207-211

ß

S sd

S„

vdd

Population

C rossover probab ility

M utation probability

A

0.8

07 -

0.6

0 u.u -if)c U.4 -LL

0.3-

0.2 -

0.1 -

0 -20 40 60

GfeiFig. 6. Genetic

atiThis is performed with

developed in Excel [11]; populi chosen between the lower and uppi evolution in a simulated coir mechanism consists of toumamer t uniform mutation. Both bit-exclm occur at every cycle, according tc has been achieved by determinati genetic algorithm; the size of the for crossover and mutation, quoti ranges relate to the region of inte evaluated (Fig. 6).

4.2. Using Response Surface

In the process of optimiz .̂1

roundness error ( A) . Minitab this objective. The optimizatio shown in Figure 7 and Table 5

[JSET @ 2015

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Jorithm optimization

on

:ed

M

(3)

1,9999

1,9996

1,0889

-0,0056

150

0,25

0,05

0,2893

80 100 120 iterations algorithm graph

140 160

an adopted optimization program, on of appointed size is randomly

ier values and undergoes a process of petitive environment. The latter selection, linear crossover and non- ge crossover and bit-flip mutation

Assigned probabilities. Optimization of three control parameters of the

lipulation and the probability values in Table 4. The considered factor

st. The fitness of each individual is

ethod

.tion, the goal is to minimize the software is used to optimize

graph and numerical values are e spectively.

Optimal u . .D HÆ h

0.91221 fo lv

CompositeDesirability

0.S4221

Minimum \ | y = 0.2839 \d = 0.94221 \

Table 5. RSM opt

ß

s sd

S,,

v did

A

5. COPARISON

odtiIn put the done by G A (Tab 4) of roundness error Optimization value

GA and RSM. Ho' RSM

Table 6. Com

ß

6. CONCLUSION*

- For optimizatic accuracy o f GA is

- For the work achieve the mini infiltration steel, t 9,5999(degree); 29,570 (m/min) re

(I SS

Ssd2.0

12.01-2.0'

Sk 2.0

[ .030: -2.0

Fig 7. RSM graph

mization

2,0

2,0

0,

FOR GA AND RSM

imization values of (3 , and RSM (Tab 5) in to eq’

( A * ) , the result is 5 of f i , Ssd , Sk , vdd vever, in detail, accuracy

paris on for optimization ot

S'.sd

1, 0303 - 0,0202

A

0, 28! »

n o f plunge centerless better than RSM

material 20X-carbon iniiltr :num roundness error o" th le num erical values o f ß, Ssd 499,960(m m /m in); 14,3 55 i

spectively.

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|\V1'h id

Gof

'GA

grir

vdd2.0-0.0202-2.0

/

\ ! , /

Sl\, Vdd that n 2, to get value

in Table 6. are similar for

\ is better than

and RSM

A ;

ding process,

cjtion steel, to : 20X-carbon Sk and vdd are

(|im/s) and

Page 210

I S E T

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ii. Dhavlikar MN, Kulkarni MS, Mariappan V (2003) Combined Taguchi and dual response method fo r optimization o f a centerless grinding operation. Int J Mater Process Technol

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v. Zhou SS, Gartner JR, Howes TD (1996) On therelationship between setup parameters and lobing behavior in centerless grinding. Ann CIRP 45(l):34l-346.

' \ International Journal o f S cien tific E ng ineering and T echnologyV olum e N o.4 Tssue N o .3, pp : 207-211

(IS S N : 2277-1581)01 M arch. 2015

Vi. Xu W, Wu Y, Sato T, Lin W (2010) Effects o f process parameters on workpiece roundness in tangential-feed centerless grinding using a surface grinder. Int J Mater Process Technol 210:759-766.

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viii. Subramanya Udupa NG, Shunmagam MS and Radhakrishman V (1987) Optimizing workpiece position in centerless grinding by roundness profile analysis. Butter & Co

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x. Hashimoto F, Kanai A and Miyshita M (2004)Optimisation o f Set-Up Conditions o f the Centerless Grinding Process. Ann. CIRP 53 (!) 271-274 '

xi. Turk/am N, Floating Point Genetic Algorithm - Genetik V2.02, htto://www.umoncton.œ/turk/logic.htin. (2001)

IJS E T @ 2015 Page 211