MODELLING OF SURFACE ROUGHNESS INDEX FOR A ROLLER … · 2015-04-09 · 317 Int. J. Mech. Eng. &...

317

Int. J. Mech. Eng. & Rob. Res. 2012 Neeraj et al., 2012

MODELLING OF SURFACE ROUGHNESS INDEXFOR A ROLLER BURNISHING PROCESS USING

GRAPH THEORY AND MATRIX METHOD

Neeraj1*, Sandeep Kumar1 and Nikhil Dev2

*Corresponding Author: Neeraj,[email protected]

In the present paper, Graph Theoretic Approach is used for the analysis and comparison ofroller burnishing process in terms of surface roughness. The surface roughness is affected bydifferent parameters. In the present work, the important parameters are identified and an indexof surface roughness is proposed with the help of Graph Theoretic Approach which evaluatesthe inhibiting power of these parameters. This index can be used in comparison of differentroller burnishing processes.

Keywords: Roller burnishing process, Parameters, Intensity, Graph theoretic approach

INTRODUCTIONRoller Burnishing (RB) is one of the no-chipfinishing processes for surface engineering.Roller Burnishing is a cold working, surfacetreatment process in which plastic deformationof surface irregularities occurs by exertingpressure through a very hard and smooth rolleron a surface to generate a uniform and work-hardened surface. The burnishing process isan attractive finishing technique which canincrease the work piece surface strength aswell as decreasing its surface roughness(Figure 1).

ISSN 2278 – 0149 www.ijmerr.comVol. 1, No. 3, October 2012

© 2012 IJMERR. All Rights Reserved

Int. J. Mech. Eng. & Rob. Res. 2012

1 University Institute of Engineering and Technology, M.D.University Rohtak, Haryana.2 YMCA University of Science & Technology, Faridabad, Haryana, India

Research Paper

A number of approaches are available inthe literature for the analysis of roller burnishingprocess. The various methods used so far areas following:

• Taguchi method (Philip Selvaraj andChanramohan, 2010; and Ugur Esme, 2010).

• Surface Roughness Methodology (Dabeerand Purohit, 2010).

• Neural network (Stankovic et al., 2012).

• Slip-line field model (Black et al., 1997).

We conclude that Graph Theory has notbeen used for the analysis of Roller Burnishing

318


process. So, we are going to apply Graphtheory and Matrix Approach for the analysis ofRoller burnishing process.

Graph theory is a systematic and logicalapproach. Graph model representation hasproved to be useful for modelling and analysingvarious kinds of systems and problems innumerous fields of science and technology.The matrix approach is useful in analysing thegraph models expeditiously to derive thesystem function and index to meet theobjectives. Moreover, representation of thegraph by a matrix offers ease in computerhandling. In view of these, graph theory andmatrix methods are proposed in this paper forquantification of parameters.

To the best of our knowledge, quantificationof these parameters was not reported in theliterature.In this paper, an attempt is made toanalyse and quantify these parameters usingdigraph and matrix approach. The mainobjectives of this paper are as follows:

• To identify and segregate parameters in tocategories through literature study andmathematical modeling.

• To develop a mathematical model of theseperformance parameters using graphtheoretic approach (GTA).

• To propose a single numerical indexrepresenting the value of the multinomial ofthe model.

IDENTIFICATION OF PERTI-NENT ATTRIBUTES AND THEFACTORS• Feed Direction: Feed direction means the

direction in which the tool approaches theworkpiece. There are two types of feeddirection: 1) along, 2) counter.

1. Along: It implies that the tool is moving inthe direction of workpiece.

2. Counter: It implies that the tool andworkpiece are moving in the oppositedirection.

By the study of literature, it was found thatsurface roughness will improve more incase of counter feed direction.

• Workpiece materials: By the study ofliterature, we found that the RollerBurnishing process has been applied todifferent materials. RB has a positive effecton the surface roughness of O1 alloy steel.The improvement percentage on the surfacequality was 12.5% (Dabeer and Purohit,2010).

• Spindle Speed: The spindle speed is therotational frequency of the spindle of themachine, measured in revolutions perminute (RPM). The preferred speed isdetermined by working backward from thedesired surface speed (m/min) andincorporating the diameter (of workpiece ortool). Excessive spindle speed will cause

Figure 1: Schematic Illustrationof Burnishing Mechanism

Source: El-Tayeb et al. (2007)

319


premature tool wear, breakages, and cancause tool chatter, all of which can lead topotentially dangerous conditions. Using thecorrect spindle speed for the material andtools will greatly enhance tool life and thequality of the surface finish. In general, anincrease in burnishing speedup to about100 m/min leads to a decrease in meanroughness. With a further increase inburnishing speed mean roughnessgradually increases. The deterioration of thesurface roughness in the burnishingprocess at high burnishing speeds isbelieved to be caused by the chatter thatresults in instability of the burnishing toolacross the workpiece surface. In addition,the low surface roughness can beinterpreted by the low deforming action ofthe roller sat high speeds and also becausethe lubricant loses its effect due to theinsufficient time for it to penetrate betweenthe roller and the workpiece surfaces. It isbetter then to select low speeds becausethe deforming action of the burnishing toolis greater and metal flow is regular at lowspeed (El-Khabeery and El-Axir, 2001).

• Feed Rate: Feed rate is the velocity at whichthe tool is fed, that is, advanced against theworkpiece. It is expressed in units ofdistance per revolution for burnishingprocess. Feed Rate is dependent on the:

• Type of tool.

• Surface finish desired.

• Power available at the spindle.

• Rigidity of the machine and tooling setup.

• Strength of the work piece.

The surface roughness is increased withincreasing the feed rate up to certain point

(0.06 mm/rev) then it begins to decrease, itis also observed that higher reduction insurface roughness happened at very lowburnishing feed rate (Stankovic et al.,2012).

• No of passes: It was found that the numberof burnishing tool passes is an importantparameter for the surface roughness andhardness of burnished components(Hassan, 1997; and Hassan et al., 1998;and Luo et al., 2005). The surfaceroughness can be increased with increasingthe burnishing force or by number of passesto certain limit. The surfaces starts todeteriorate, as the surface of the metal isover work hardened due to the plasticdeformation caused by the burnishing forceor the number of tool passes exceeding thelimits.

• Coolant: A coolant is a fluid which flowsthrough a device to prevent its overheating,transferring the heat produced by the deviceto other devices that use or dissipate it. Anideal coolant has high thermal capacity, lowviscosity, is low-cost, non-toxic, andchemically inert, neither causing norpromoting corrosion of the cooling system.

GRAPH THEORETIC APPROACH(GTA)GTA is a systematic and logical approach thatis applied in various disciplines (Gandhi andAgarwal, 1992; Gandhi and Agarwal, 1996;and Rao and Padmanabhan, 2006). Theconventional representations like blockdiagrams, cause and effect diagrams andflowcharts do not depict interactions amongfactors and are not suitable for further analysisand cannot be processed or expressed in

320


mathematical form. The following featureshighlight the uniqueness of this approach overthe other similar approaches:

• It a single numerical index for all theparameters.

• It is a systematic methodology forconversion of qualitative factors toquantitative values, and mathematicmodelling gives an edge to the proposedtechnique over conventional methods.

• It permits presents modelling ofinterdependence of parameters underconsideration.

• It allows visual analysis and computerprocessing.

• It leads to self-analysis and comparison ofdifferent organisations.

Main Elements of GTA

• The digraph representation.

• The matrix representation.

• The permanent function representation.

The Digraph Representation ofRoller Burnishing Parameters

A directed graph (or a digraph) is nothing buta graph with directed edges. A digraph is usedto represent the elements (Roughnessparameters) and their interdependencies interms of nodes and edges (Figures 2 and 3).In an undirected graph, no direction isassigned to the edges in the graph, whereasdirected graphs or digraphs have directionaledges. A Roller Burnishing parameterdiagraph is prepared to represent theparameters of Roller Burnishing in terms ofnodes and edges. It represents parameters(B

i’s) through its nodes and dependence of

parameters (bij’s) through its edges. P

i

indicates the inheritance of parameters andpij indicates the degree of dependence of jth

parameter on ith parameter. In the present worksix parameters such as feed direction (B

1),

workpiece material (B2), speed (B

3), feed (B

4),

number of passes (B5), coolant (B

6) are

identified.

Figure 2: Schematic Arrangementof Roller Burnishing Surface

Roughness Parameters

Feed Direction (FD)

Coolant (CL) Workpiece Material (WM)

Surface Roughness

(SR)

Feed Rate (FR)

No. Of Passes (NP)

Burnishing Speed (BS)

Figure 3: Roller Burnishing SurfaceRoughness Parameter Digraph

FR

FD

BSNP

CL WM

321


The System Structure MatrixRepresentation

A digraph is a visual representation so it helpsin analyse to a limited extent only. To establishthe expression for Roller Burnishing SurfaceRoughness (RBSR) parameters, the digraphis represented in matrix form which is also aconvenient form of computer processing.Consider a digraph of n parameters leadingto nth order symmetric (0, 1) matrix A = [b

ij].

The rows and columns in the matrix representinteractions among parameters, i.e., b

ij

represents the interaction of i-th parameter withthe jth parameter. The matrix (6 6) showing isrepresented as:

FD WM BS FR NP CL Parameters

1 12 13 14 15 15

21 2 23 24 25 26

31 32 3 34 35 36

41 42 43 4 45 46

51 52 53 54 5 56

61 62 63 64 65 6

B b b b b b

b B b b b b

b b B b b bA

b b b B b b

b b b b B b

b b b b b B

FD

WM

BS

FR

NP

CL

...(1)

Generally bij b

ji as RBSR parameters are

directional and bii = 0, as a parameter is not

interacting with itself. This RBSR parametermatrix is square and nonsymmetrical and isanalogous to adjacency matrix in graph theory.On putting the values of interactions like:

bij= 1; if parameter i is connected to

parameter j

= 0 otherwise

The RBSR parameter matrix representingthe graph shown in Figure 3 is written as:

FD WM BS FR NP CL

A =

FD

WM

BS

FR

NP

CL

0 0 1 0 0 0

1 0 1 1 1 1

0 0 0 1 1 1

0 0 0 0 0 1

0 0 0 1 0 1

0 0 1 0 0 0

The interdependency of RBSR parametersis shown by off-diagonal elements with 0 or 1.The diagonal elements are 0 since the effectof roughness parameters is not taken in toaccount. To consider this, another matrix knownas characteristic matrix is defined.

Characteristic Matrix of RBSRParameter (CMRB)

The characteristic matrix is used tocharacterize parameters of RBSR. Consider Ias an identity matrix and b as the variablerepresenting RBSR parameters. The RBSRparameter (CM

RB) characteristic matrix is

written as

C = [BI – A]

FD WM BS FR NP CL

C =

FD

WM

BS

FR

NP

CL

1 13

21 2 23 24 25 26

3 34 35 36

4 45 46

54 5 56

63 6

0 0 0 0

0 0

0 0 0

0 0 0

0 0 0 0

B b

b B b b b b

B b b b

B b b

b B b

b B

...(3)

In the matrix, the value of all diagonalelements is the same, i.e., all surfaceroughness parameters were assigned thesame values depending on variousparameters affecting them. Moreover

322


interdependencies were assigned values of 0and 1 depending on whether it is there or not.To consider this, another matrix, the variablecharacteristic matrix of RB surface parametersis considered.

Variable Characteristic Matrixof RB Parameter (VCMRB)

The variable characteristic matrix of RBsurface roughness parameter (VCM

RB) takes

in to consideration the effect of differentparameters and their interactions. The digraphin figure 3 is considered for defining VCM

RB.

Consider a matrix D with off diagonal elementsb

ij representing interactions between RBSR

parameters, i.e., instead of 1 (as shown inmatrix A).Consider another matrix E is takenwith diagonal elements B

i, i = 1,2,3,4,5,6 where

the Bi represents the effect of various

parameters, i.e. instead of B only (as shownin matrix C). Considering matrices D and E,VCM

RB is expressed as:

H = [E – D]

FD WM BS FR NP CL

D =

1 13

21 2 23 24 25 26

3 34 35 36

4 45 46

54 5 56

63 6

0 0 0 0

0 0

0 0 0

0 0 0

0 0 0 0

B b

b B b b b b

B b b b

B b b

b B b

b B

FD

WM

BS

FR

NP

CL

This matrix provides a powerful tool throughits determinant, called the variablecharacteristic RBSR parameter multinomial.

The determinant of the matrix H containspositive and negative sign with some of itscoefficients. Hence, complete information inthe RB environment will not be obtained assome will be lost due to addition and

subtraction of numerical values of diagonal andoff-diagonal elements (i.e., B

i’s and b

ij’s). Thus

the determinant of the variable characteristicmatrix, i.e., the matrix H, does not providecomplete information concerning the RBSRsystem. For this, another matrix known asVariable Permanent Matrix of RBSR parameter(VPM

RB) is introduced.

Variable Permanent Matrixof RBSR Parameter (VPMRB)

Since the total quantitative value is notobtained in VCM

RB, VPM

RB is defined for the

organization in general (assuming interactionsamong all parameters) as:

P = [E + D]


1 12 13 14 15 15

21 2 23 24 25 26

31 32 3 34 35 36

41 42 43 4 45 46

51 52 53 54 5 56

61 62 63 64 65 6

B b b b b b

b B b b b b

b b B b b bP

b b b B b b

b b b b B b

b b b b b B

FD

WM

BS

FR

NP

CL

...(5)

where, E and D have the meaning as inmatrix H.

Thus the VPMRB

corresponding to the sixsurface roughness parameters RB digraph(Figure 3) is given by:


H =

1 13

21 2 23 24 25 26

3 34 35 36

4 45 46

54 5 56

63 6

0 0 0 0

0 0

0 0 0

0 0 0

0 0 0 0

B b

b B b b b b

B b b b

B b b

b B b

b B

FD

WM

BS

FR

NP

CL

...(6)

323


The diagonal elements B1, B

2, B

3, B

4, B

5 and

B6 represent the effect of the six critical surface

roughness parameters on Roller Burnishingand off-diagonal elements representinterdependencies of each element in thematrix. The contribution can be expressedquantitatively.

Permanent Representation

Both digraph and matrix representations arenot unique as they are changed by changingthe labelling of nodes. To develop a uniquerepresentation, independent of labelling, apermanent function of the matrix VPM

RB is

proposed. The permanent function is obtainedin a similar manner as its determinant. Thiscomputational process results in a multinomialwhose every term has a physical significance.This multinomial representation includes all theinformation regarding surface roughnessparameters and is called Variable PermanentFunction of RBSR parameters (VPF

RB), also

known as Pm (per Pm) and in general form, itis written as:

6

1 2 3 4 5 61

( )RB i ij ji k l m nVPF perB B b b B B B B

1 2 3 4 5 6

( )ij jk ki ik kj ji l m nb b b b b b B B B

1 2 3 4 5 6

( )( )ij ji kl lk m nb b b b B B

1 2 3 4 5 6

( )ij jk kl li il lk kj ji m nb b b b b b b b B B

1 2 3 4 5 6

( )( )ij jk ki ik kj ji lm ml nb b b b b b b b B

1 2 3 4 5 6

( )( )ij jk kl li il lk kj ji mn nmb b b b b b b b b b

ln1 2 3 4 5 6

( )( )ij jk ki ik kj ji lm mn nl nm mlb b b b b b b b b b b b

1 2 3 4 5 6

( )( )( )ij ji kl lk mn nmb b b b b b

1 2 3 4 5 6

( )ij jk kl lm mn ni in nm ml lk kj jib b b b b b b b b b b b

...(7)

The VPFRB

is a mathematical expressionin symbolic form and it ensures an estimate ofthe RBSR parameters existing in anorganization. It is a complete expression forRBSR parameters as it considers thepresence of all parameters and theirinterdependencies.

Equation (6) contains 6! Terms and theseterms are arranged in n + 1 grouping, where nis the number of elements (parameters). Thevalue of n is equal to six in the present case.The physical significance of various groupingsis explained as follows:

• The first grouping contains only one term. Itrepresents a set of N unconnected RBSRparameters, i.e., B

1, B

2, ..., B

6.

• The second grouping is absent as there isno self loop in the digraph (Figure 3).

• The third grouping contains a set of twoRBSR parameter interdependence, i.e., b

ij

bji and measure of remaining (n – 2) RBSR

parameters.

• Each term of fourth grouping represents aset of three RBSR parameterinterdependence, i.e., b

ij b

jk b

ki or its pair b

ik

bkj

bji and measure of remaining (n – 3)

RBSR parameters.

• The terms of fifth grouping are arranged intwo subgroups. The first subgrouping is aset of two RBSR parameter

interdependence i.e., bij b

jk b

kl b

lior its pair

324


bilb

lk b

kj b

ji and measure of remaining (n –

4) RBSR parameters.

• The terms of sixth grouping are alsoarranged in two subgroups. The firstsubgrouping is a set of two RBSRparameter interdependence, i.e., b

ij b

jk b

kl

blm

bmn

bni or its pair b

im b

ml b

lk b

kj b

ji.

Quantification of Bi’s and bij’s

Quantification of RBSR parameters (i.e., Bi)

is carried out on the basis of Equation (5). Toget the complete value of multinomial(Equation 6) the diagonal as well as off-diagonal elements in VPM

RB are to be

assigned some numerical values. As alreadydiscussed, the diagonal elements represent

Table 1: Quantificationof RBSR Parameters

S. Qualitative Measure Assigned Value

No. of Parameter of Parameter

1. Exceptionally low 1

2. Very low 2

3. Low 3

4. Below average 4

5. Average 5

6. Above average 6

7. High 7

8. Very high 8

9. Exceptionally high 9

Table 2: Quantification of RBSRParameter Interdependencies

S. Qualitative Measurep

ijNo. of Parameter

1. Very strong 5

2. Strong 4

3. Medium 3

4. Weak 2

5. Very weak 1

different parameters and the off-diagonalelements represent interdependencies amongsurface roughness parameters. As theinfluence of all parameters may not be equaland the dependence among parametersmeasured directly, hence these values areassigned only after proper interpretationthrough a team of experts. It is suggested touse Tables 1 and 2 for assigning these values.

METHODOLOGYThe Graph theoretic approach evaluates thepermanent qualitative index of Rollerburnishing in terms of single numerical index,which takes into account the individual effectof various surface roughness parameters andtheir interdependencies while analysing andevaluating the RBSR. The various steps of theproposed approach, which would be helpful inevaluation of the RBSR, are enlisted insequential manner as below;

• Identify the various parameters of the RBaffecting the Surface Roughness of theworkpiece.

• Develop a digraph among the RBSRparameters based on interactions amongthem.

• Develop a performance parameter matrixon the basis of digraph developed in step2.

This will be of size M M, with diagonalelements representing surface roughnessparameters and the off-diagonal elementsrepresenting interactions among them.

• Develop a variable permanent matrix(VPM

RB).

• Find the value of permanent function for thesurface roughness parameters of RB.

325


• Compare different roller burnishing processin terms of surface roughness parameterpermanent function obtained in step 5.

• Document the results for future analysis/reference.

Based on the methodology discussedabove, the organization can evaluate the extentof parameters present in roller burnishing.

WORKING EXAMPLEFor the demonstration of proposed metho-dology, an organization is taken as anexample. It is proposed to find the value of RBpermanent function of surface roughnessparameters. For this purpose, some numericalvalues of all surface roughness parametersand their interdependencies are required. Themethodology discussed in the previous sectionis used to evaluate the permanent function ofparameters of RBSR in this example.

The various parameters affecting theSurface roughness are identified andpresented and explained in the previous section.The dependencies of performance parametersare visualized in digraph in Figure 3.

The variable permanent matrix for digraphis written as


H =

1 13

21 2 23 24 25 26

3 34 35 36

4 45 46

54 5 56

63 6

0 0 0 0

0 0

0 0 0

0 0 0

0 0 0 0

B b

b B b b b b

B b b b

B b b

b B b

b B

FD

WM

BS

FR

NP

CL

...(8)By taking the numerical values of six

Surface roughness parameters from Table 1as: B

1 = 5, B

2 = 5, B

3 = 8, B

4 = 6, B

5 = 4, B

6 = 7.

For interdependencies, the values takenfrom Table 2 are: b

13 = 4, b

21 = 2, b

23 = 3, b

24 =

4, b25

= 1, b26

= 2, b34

= 5, b35

= 3, b36

= 4, b46.

=3, b

54 = 2, b

56 = 2, b

63 = 1.

Substituting these values in above matrix:


VPMRB

=

5 0 4 0 0 0

2 5 3 4 1 2

0 0 8 5 3 4

0 0 0 6 0 3

0 0 0 2 4 2

0 0 1 0 0 7

FD

WM

BS

FR

NP

CL

...(9)

The value of permanent function ascalculated by c++ Software is

Variable Permanent Function, VPF = 38850

FD WM BS FR NP CL

Max VPMRB

=

FD

WM

BS

FR

NP

CL

9 0 4 0 0 0

2 9 3 4 1 2

0 0 9 5 3 4

0 0 0 9 0 3

0 0 0 2 9 2

0 0 1 0 0 9

...(10)

The maximum value of variable permanentfunction is

Max VPFRB

= 574452

FD WM BS FR NP CL

Min VPMRB

=

FD

WM

BS

FR

NP

CL

1 0 4 0 0 0

2 1 3 4 1 2

0 0 1 5 3 4

0 0 0 1 0 3

0 0 0 2 1 2

0 0 1 0 0 1

...(11)

326


The minimum value of variable permanentfunction is, Min VPF

RB = 44

With the above method, the effect of eachindividual surface roughness parameter canbe seen by putting the maximum (9) andminimum (1) values of each individualparameter.

For Feed Direction, the maximum andminimum values of permanent function arecalculated as;

FD WM BS FR NP CL

VPMRB

=

FD

WM

BS

FR

NP

CL

9 0 4 0 0 0

2 5 3 4 1 2

0 0 8 5 3 4

0 0 0 6 0 3

0 0 0 2 4 2

0 0 1 0 0 7

...(12)

The value of maximum permanent functionfor FD is, Max VPF

1 = 69930

FD WM BS FR NP CL

VPMRB

=

FD

WM

BS

FR

NP

CL

1 0 4 0 0 0

2 5 3 4 1 2

0 0 8 5 3 4

0 0 0 6 0 3

0 0 0 2 4 2

0 0 1 0 0 7

...(13)

The value of minimum permanent functionfor FD is, Min VPF

1 = 7770

For WM, the maximum and minimum valuesof permanent function are calculated as;

FD WM BS FR NP CL

VPMRB

=

FD

WM

BS

FR

NP

CL

5 0 4 0 0 0

2 9 3 4 1 2

0 0 8 5 3 4

0 0 0 6 0 3

0 0 0 2 4 2

0 0 1 0 0 7

...(14)

The value of maximum permanent functionfor WM is, Max VPF

2 = 69930

FD WM BS FR NP CL

VPMRB

=

FD

WM

BS

FR

NP

CL

5 0 4 0 0 0

2 5 3 4 1 2

0 0 9 5 3 4

0 0 0 6 0 3

0 0 0 2 4 2

0 0 1 0 0 7

...(16)

The maximum value of variable permanentfunction for BS is, Max VPF

3 = 43050

FD WM BS FR NP CL

VPMRB

=

FD

WM

BS

FR

NP

CL

5 0 4 0 0 0

2 5 3 4 1 2

0 0 1 5 3 4

0 0 0 6 0 3

0 0 0 2 4 2

0 0 1 0 0 7

...(17)

The minimum value of variable permanentfunction for BS is, Min VPF

3 = 9450

For FR, the maximum and minimum valuesof permanent function are calculated as;

FD WM BS FR NP CL

VPMRB

=

FD

WM

BS

FR

NP

CL

5 0 4 0 0 0

2 5 3 4 1 2

0 0 8 5 3 4

0 0 0 9 0 3

0 0 0 2 4 2

0 0 1 0 0 7

...(18)

The maximum value of variable permanentfunction for FR is, Max VPF

4 = 57300

327


FD WM BS FR NP CL

VPMRB

=

FD

WM

BS

FR

NP

CL

5 0 4 0 0 0

2 5 3 4 1 2

0 0 8 5 3 4

0 0 0 1 0 3

0 0 0 2 4 2

0 0 1 0 0 7

...(19)

The minimum value of variable permanentfunction for FR is, Min VPF

4 = 8100

For NP, the maximum and minimum valuesof permanent function are calculated as;

FD WM BS FR NP CL

VPMRB

=

FD

WM

BS

FR

NP

CL

5 0 4 0 0 0

2 5 3 4 1 2

0 0 8 5 3 4

0 0 0 6 0 3

0 0 0 2 9 2

0 0 1 0 0 7

...(20)

The maximum value of variable permanentfunction for NP is, Max VPF

5 = 85725

FD WM BS FR NP CL

VPMRB

=

FD

WM

BS

FR

NP

CL

5 0 4 0 0 0

2 5 3 4 1 2

0 0 8 5 3 4

0 0 0 6 0 3

0 0 0 2 1 2

0 0 1 0 0 7

...(21)

The minimum value of variable permanentfunction for NP is, Min VPF

5 = 10725

For CL, the maximum and minimum valuesof permanent function are calculated as;

FD WM BS FR NP CL

VPMRB

=

FD

WM

BS

FR

NP

CL

5 0 4 0 0 0

2 5 3 4 1 2

0 0 8 5 3 4

0 0 0 6 0 3

0 0 0 2 1 2

0 0 1 0 0 9

...(22)

The maximum value of variable permanent

function for CL is, Max VPF6 = 38850

Table 3: Variable Permanent Function (Max and Min)of Surface Roughness Parameter

S. No. Parameter Max. VPF Min. VPF

1. FD 69930 7770

2. WM 69930 7770

3. BS 43050 9450

4. FR 57300 8100

5. NP 85725 10725

6. CL 38850 10050

328


FD WM BS FR NP CL

VPMRB

=

FD

WM

BS

FR

NP

CL

5 0 4 0 0 0

2 5 3 4 1 2

0 0 8 5 3 4

0 0 0 6 0 3

0 0 0 0 4 2

0 0 0 0 0 1

...(23)

The minimum value of variable permanentfunction for CL is, Min VPF

6 = 10050

RESULTS AND DISCUSSION• Graph Theory and Matrix Method is a multi-

attribute decision making method (MADM)which is successfully applied on the rollerburnishing process.

• By the application of Graph Theory andMatrix Method, we have identified thecritical parameter affecting the surfaceroughness of roller burnishing process. Inthe present work, number of passes is themost critical parameter having value ofmaximum variable permanent function =85725.

• Graph Theory and Matrix Method is used inthe selection of an improved process amongvarious roller burnishing processes by thecomparison of variable permanentfunctions of the different processes.

• The Graph Theory and Matrix Method isused in the arrangement of the parametersaccording to their relative importance in theprocess. The sequence of parameters inour work is number of passes, feeddirection, workpiece material, feed rate,coolant, burnishing speed.

• If some improvement is done in theparameters affecting the surface roughnessof the process, then we can compare theimproved process with the previousprocess.

REFERENCES1. Black A J, Kopalinky E M and Oxley P L B

(1997), “Analysis and ExperimentalInvestigation of a Simplified BurnishingProcess”, Int. J. Mech. Sci., Vol. 39,No. 6, pp. 629-641.

2. Dabeer P S and Purohit G K (2010),“Effect of Ball Burnishing Parameters onSurface Roughness Using SurfaceRoughness Methodology”, Avances inProduction Engineering & Management,Vol. 5, No. 2, pp. 111-116.

3. El-Khabeery M M and El-Axir M H (2001),“Experimental Techniques for Studying theEffects of Milling Roller-BurnishingParameters on Surface Integrity”,International Journal of Machine Tools& Manufacture, Vol. 41, pp. 1705-1719.

4. El-Tayeb N S M, Low K O and Brevern PV (2007), “Influence of Roller BurnishingContact Width and Burnishing Orientationon Surface Quality and TribologicalBehaviour of Aluminium 6061”, Journal ofMaterials Processing Technology ,Vol. 186, Nos. 1-3, pp. 272-278.

5. Gandhi O P and Agarwal V P (1992),“FMEA-0A Digraph and MatrixApproach”, Reliability Engineering andSystem Safety, Vol. 35, pp.147-158.

6. Gandhi O P and Agarwal V P (1996),“Failure Cause Analysis: A StructuralApproach”, Transactions of ASME,pp. 434-439.

329


7. Hassan A M (1997), “Effects of Ball andRoller Burnishing on the SurfaceRoughness and Hardness of Some Non-Ferrous Metals”, J. Mater. Process.Technol., Vol. 72, No. 3, pp. 385-391.

8. Hassan A M, Al-Jalil H F and Ebied A A(1998), “Burnishing Force, Number of BallPasses for the Optimum Surface Finishof Brass Components”, J. Mater.Process.Technol., Vol. 83, Nos. 1-3,pp. 176-179.

9. Luo H Y, Liu J Y, Wang L J and Zhong Q P(2005), “Investigation of the BurnishingProcess with PCD Tool on Non-FerrousMetals”, Int. J. Adv. Manuf. Technol.,Vol. 25, Nos. 5-6, pp. 454-459.

10. Philip Selvaraj D and Chanramohan P(2010), “Optimizaton of SurfaceRoughness of AISI 304 AusteniticStainless Steel in Dry Turning Opertion

Using Taguchi Design Method”, Journalof Engineering Science and Technology,Vol. 5, No. 3, pp. 293-301.

11. Rao R V and Padmanabhan K K (2006),“Selection, Identification and Comparisonof Industrial Robots Using Digraph andMatrix Methods”, Robotics and ComputerIntegrated Manufacturing, Vol. 22, No. 4,pp. 373-383.

12. Stankovic I, Perinic M, Jurkovic Z, MandicV and Maricic S (2012), “Usage of NeuralNetwork for the Prediction of SurfaveRoughness After the Roller Burnishing”,Metabk, Vol. 51, No. 2, pp. 207-210.

13. Ugur Esme (2010), “Use of Grey BasedTaguchi Method in Ball BurnishingProcess for the Optimization of SurfaceRoughness and Microhardness of AA7075 Aluminium Alloy”, Prejemrokopisa –Received: 2009-11-09; Sprejemzaobjavo –Accepted for Publication: 2010-03-20.

MODELLING OF SURFACE ROUGHNESS INDEX FOR A ROLLER … · 2015-04-09 · 317 Int. J. Mech. Eng. &...

Documents

Transcript of MODELLING OF SURFACE ROUGHNESS INDEX FOR A ROLLER … · 2015-04-09 · 317 Int. J. Mech. Eng. &...