Experimetal Investigation of Surface roughness using Burnished … · 2021. 7. 24. · Experimetal Investigation of Surface roughness using Burnished Sphericalsurface Tool by employing

Experimetal Investigation of Surface

roughness using Burnished Spherical surface

Tool by employing response surface

methodology (RSM)on 24345-Aluminum

Alloy

Dr. Dnyaneshwar M. Mate

Department of Mechanical Engineering

JSPMs, Rajarshi Shahu College of Engineering, Pune, Maharashtra, India

Email- [email protected]

Dr.Nishchal P. Mungle

Department of Mechanical Engineering

Dr. Babasheb Ambedkar College of Engineering, Nagpur, Maharashtra, India

[email protected]

Mr. Prakash S. Patil



Mr. Nagaraj S. Dixit



Abstract- The aim of the proposed research paper is centered on a broad scope of surface roughness processes, including

conventional finish (turning) to ball burnishing, which is relatively new and used to provide modifications to the machined

surface quality. In finish cutting, the effects of edge preparation and tool wear of the cutting tool are considered most critical,

as they directly determine surface finish. Another focus of this research is on the surface enhancement generated by ball

burnishing, which is used machining to improve surface finish and provide a surface layer byf compressive residual stresses.

For a successful ball burnishing process, the selection of process parameters (burnishing pressure, ball diameter, speed, and

feed rate and time for operation, also energy) needs to be optimized. An experimental investigation to study the performance

of a Burnishing process by using ball is reported. It also confirms that burnished surface achieves a surface roughness value

of Ra=0.0456m under defined conditions whereas the initial surface roughness value was about 3.50m.

Keywords – Burnishing, Cutting force, Surface Roughness, Super finishing, response surface methodology

I. Introduction

Finishing processes have always been important in manufacturing of all kinds of parts. A special attention is paid to

surface quality, from the viewpoint of smoothness, physical and mechanical characteristics. Burnishing is a chipless

cold-work process, which consists of plastic deformation the surface layer of the work-piece through the indentation

of a tool accompanied by other simple motions that ensure machining along the desired area. The pressure generated

by the ball as indenter must exceed the yield point of the work-piece‟s material and flattens asperities from previous

machining process. These causes also strain hardening of the surface layer and induce compressive stresses into it.

Finally, the result is a smooth hardened surface with some improved mechanical properties.

Journal of Xi'an University of Architecture & Technology

Volume XII, Issue IV, 2020

ISSN No : 1006-7930

Page No: 5536

Research regarding effective burnishing started in the first half of the 20th

century. In 1950, burnishing became the

object of a systematic study, including theoretical approach. In present days, development of computer techniques

and finite element approach made possible creation of models regarding the intimate phenomena in the surface

layer. Nevertheless, there are not many modeling research in this field. A very good approach belongs to

A.A.Ibrahim [1]

was calculated stress distribution in terms of the applied load. He created a 2D model with his own

codes in FORTRAN, simulating the rolling of a cylinder on a flat surface. Liviu Luca, Sorin Neagu-Ventzel, Ioan

Marinescu [2]

through their illustrious in their research work found out the possibility of burnishing steel components

with high hardness of around 64 HRC. Furthermore the hydrostatic principle of the ball burnishing tool employed

offers a series advantages to the process: pure rolling contact, constant controllable normal force, low coolant

consumption on use of same machine as previous hard turning. It was also observed that when the burnishing feed

increases, the roughness increases.

N.H.LOH and S.C.TAM [3]

also contributed significantly to enhance the process of ball burnishing. The

literature survey and review show that ball burnishing as a process is not only technically correct but also

commercially viable. A required surface finish can be obtained by using proper design parameters. The effect of

surface finish is a combined effort between various parameters. The burnishing force and feed rate are the two most

important factors.

Adel Mahmood Hassan [4]

was a pioneer in taking the progress of ball burnishing a way forward. He

designed a new method of using two balls in opposite direction coming to press the ball.Burnishing results showed

significant effectiveness of the burnishing tool in the process. The surface roughness and roundness error of the

turned test specimens were improved by burnishing from about Ra = 2.5 to about 0.2 µm, and roundness error from

about 7.3 to about 2 µ. For double ball burnishing better surface roughness can be achieved using low values of

forces with low speeds, or using high forces with high speeds. The best results of surface roughness and roundness

error were obtained with double ball burnishing using burnishing force of 170N.

Constantin BUZATU, Adriana BĂLACESCU [5]

was phenomenal in describing the behaviour of materials

in different parameters. They stated that The influence of the cutting fluid on the surface finish through the friction

coefficient is proportional type, according with the experimental tests and the optimization of super finishing

process impose a multicriterion approach of the factors that influence the surface quality, constructive parameters of

the tool, technological parameters, properties and characteristics of the cutting fluid at machining the ball bearing

rings. D. M. Mate [16] in his paper is concerned with the selection of optimum super finishing conditions on

Aluminium alloy HE15. Experimental results are discussed that shows the effect of contact pressure, surface speed

on super finishing performance. These results are used as a basis for selecting super finishing parameters.

JATZ paper format font should be 10 in times new roman with single spacing. In recent years, the accessing of

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license information and to track illegal copies.

II. EXPERIMENTAL APPROACH (QUANTITATIVE)

A theoretical approach can be adopted in this case. If known logic can be applied correlating the various dependent

and independent parameters of the system. Though qualitatively, the relationships between the dependent and

independent parameters are known, based on the available literature, the generalized quantitative relationships are

not known sometimes. Hence formulating the quantitative relationship based on the logic is not possible in the case

of complex phenomenon. Because of no possibility of formulation of theoretical model (logic based), one is left with

the only alternative of formulating experimental data based model. Hence, it is proposed to formulate such a model

in the present investigation.

The approach adopted for formulating generalized experimental model suggested by Hilbert Schenck Jr. [5] .This is

stepwise detailed as below:

1. Identification of independent, dependent and independent extraneous variables



ISSN No : 1006-7930

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2. Reduction of independent variables adopting dimensional analysis

3. Test planning comprising of determination of test envelope, test points, test sequence and

experimentation plan

4. Physical design of an experimental set up

5. Execution of experimentation

6. Purification of experimentation data

7. Formulation of the model

8. Model optimization

9. Reliability of the model

The first six steps mentioned above constitute the design of experimentation. The seventh step constitutes of

model formulation where as eighth and ninth steps are optimization and reliability of model respectively.

IDENTIFICATION OF VARIABLES

The term variables are used in a very general sense to apply any physical quantity that undergoes change. If a physical quantity can be changed independent of the other quantities, then it is an independent variable. If a physical quantity changes in response to the variation of one or more number of variables, then it is termed as dependent or response variable. The variables affecting the effectiveness of the phenomenon under consideration are speed, cutter dimensions, cross section of material to be processed, cutting, angle, feed, power etc. The dependent or the response variables in this case are :-

Table 3.1: Variables, Symbols and Dimensions used in Operations on Aluminum Alloy Material for Experimentations

Sr.

No. Description of Variables Symbol Unit Dimensions Type of Variable

Variable/

Constant

1 Surface Roughness Ra µm [M0L1T 0] Dependent Response

2 Processing Time t sec [M0L0 T 1] Dependent Response

3 Processing Energy E Kw-hr [M1L2 T -2] Dependent Response

4 Ball Material (Hardness) HB N/mm2 [M1L-1 T -2] Independent Variable

5 Workpiece Material (Hardness) Hw N/mm2 [M1L-1 T -2] Independent Variable

6 Circumferential Area of

Material AW mm2 [M0L2 T 0] Independent Constant

7 Burnishing Speed ωB rpm [M0L0T -1] Independent Variable

8 Cutting Feed f mm/min [M0L1 T -1] Independent Variable

9 Burnishing Force FB N [M1L1T -2] Independent Variable

10 Ball Diameter DB mm [M0L1T 0] Independent Constant

11 Cutting Fluid µ N-/mm2 [M1L-1 T -1] Independent Constant

12 Acceleration due to gravity g m/s-2 LT-2 Independent Constant

REDUCTION OF INDEPENDENT VARIABLES / DIMENSIONAL ANALYSIS

Deducing the dimensional equation for a phenomenon reduces the number of independent variables in the experiments. The exact mathematical form of this dimensional equation is the targeted model. This is achieved by applying Buckingham‟s π theorem [1].When we apply this theorem to a system involving n independent variables, (n

minus number of primary dimensions viz. L, M, T, ) i.e. (n-4) numbers of π terms are formed. When n is large, even by applying this theorem number of π terms will not be reduced significantly than number of all independent variables. Thus, much reduction in number of variables is not achieved. It is evident that, if we take the product of the terms it will also be dimensionless number and hence a π term. This property is used to achieve further reduction in number of independent π terms.

Figure 3.2: Experimental setup of Ball Burnishing on Lathe



ISSN No : 1006-7930

Page No: 5538

Table 5.1: Description of Pi terms

Independent Pi - Terms

Sr. No. Description of Pi Terms Equation of Pi Terms

1 Pi term relating to ratio of Hardness of Workpiece & Ball 1= (HW/ HB )

2 Pi term relating to Area of Workpiece 2= (AW *ωB 4/ g 2)

3 Pi term relating to Burnishing force 3= (f* ωB / g)

4 Pi term relating to Ball Diameter 4= (DB *ωB / g)

6 Pi term relating to effect of Cutting fluid 5= (µ* g 2 / FB 1* ωB 3)

Dependent Pi –Terms

1 Pi term relating to Surface Roughness of material 0Ra= (Ra*ωB2/ g)

2 Pi term relating to Time Required for Process on material 0t= (ωB*t)

3 Pi term relating to Energy Required for Process for burnishing 0E= (E*ωB2/FB* g)

III. EXPERIMENTATION

Experimentation approach starts initializes using Lathe. Based on this approaches it is planned to perform experimentation on workpiece as shown in figure.2 Experimentation is carried for four different speed,feed and , depth of cut. are used for this experimentation. Experiment is carried off for Aluminum Alloy. Experimentation starts set speed and varies as per set condition discussed. and found that energy consumed `E` and time used `t` for different batches `Ra` are found and from that energy consumed and time used per Ra is calculated .Thus one complete process of experimentation is completed in one material .

Figure 2: Configuration of test specimen

IV. MODEL FORMULATION

It is necessary to correlate quantitatively various independent and dependent terms involved as this formulation [7], [8],[9]. This correlation is nothing but a mathematical model as a design tool for such situation. The mathematical model for sliver cutting operations is as given below:

It is necessary to correlate quantitatively various independent and dependent terms involved in this very complex

phenomenon. This correlation is nothing but a mathematical model as a design tool for such situation. The

mathematical models for all processing operations are given below:

Π0Ra1= Mathematical Equation for Processing Surface Roughness (Ra1):

π0Ra 1 = 1.84X10−4. g

ωB2

HW

HB −3.22

A

W .ωB4

g2 1.24

f.ωB

g −0.0031

DB .ωB

2

g −1.18

μ .g2

ωB3 .FB

0.28

… . Equn 5.17

Π0E1 = Mathematical Equation for Energy (E1):

π0E1 = 1.14X1014 FB .g

ωB2

HW

HB

13.93

A

W .ωB4

g2 −5.35

f.ωB

g

0.063

DB .ωB

2

g

10.61

μ .g2

ωB3 .FB

−0.69

…… Equn 5.18

Π0t1= Mathematical Equation for Processing time (t1):

π0t1 = 1.23X108K. ωB.t HW

HB

8.77

A

W .ωB4

g2 −2.63

f.ωB

g

0.0021

DB .ωB

2

g

5.087

μ .g2

ωB3 .FB

−0.45

… . . Equn 5.19

Table 5.3: Sample Calculations of pi terms for operation on Aluminum Alloy



ISSN No : 1006-7930

Page No: 5539

S.N.

𝛑𝟏

= 𝐇𝐖

𝐇𝐁

𝛑𝟐

= 𝐀𝐖.𝛚𝐁

𝟒

𝐠𝟐

𝛑𝟑

= 𝐟.𝛚𝐁

𝐠

𝜋4

= DB .ωB

2

g

𝛑𝟓

= 𝛍.𝐠𝟐

𝛚𝐁𝟑

Surface

Roughnes

s

Z1= 𝑹𝒂.𝝎𝑩

𝟐

𝒈

(0Ra1)

EnergyZ2= 𝑬.𝝎𝑩

𝟐

𝑭𝑩.𝒈 (0E1

)

TimeZ3= 𝝎𝑩. 𝒕 (0t1

)

1 0.2201834

9 25.232027

6.051X10-6

1.87526 8.9X10-8 0.00582 142379.8 1994.662

2 0.22018349

25.232027 6.051X10-6

1.87526 8.9X10-8 0.00569 272894.6 1852.186

3 0.2201834

9 25.232027

6.051X10-6

1.87526 4.5X10-8 0.00569 136447.3 1887.805

4 0.22018349

25.232027 6.051X10-6

1.87526 4.5X10-8 0.00556 59324.92 1852.186

5 0.2201834

9 25.232027

6.051X10-6

1.87526 3X10-8 0.00543 83054.88 1852.186

Solution to Establish Relationship for Ter

A: Operation on Material Aluminum Alloy

Five independent pi terms (1, 2, 3, 4, 5) and three dependent pi terms (0Ra1, 0E1, 0t1) have been identified in the

design of experimentation and are available for the model formulation.

Independent terms = (1, 2, 3, 4, 5)

Dependent terms = (0Ra, 0E, 0t)

Each dependent term is assumed to be function of the available independent terms,

Ra (0Ra1, First dependent pi term) = f (1, 2, 3, 4, 5)

E (0E1, Second dependent pi term) = f (1, 2, 3, 4, 5)

t (0t1 , Third dependent pi term )= f(1, 2, 3, 4, 5)

5. 4. A.1: Solution to establish relationship for 0Ra1

Model of dependent pi term 0Ra1 for surface roughness required in operation on Material 1 is repeated to compute

the models for 0Ra1 as under-

𝑅𝑎 .𝜔𝐵

2

𝑔 = 𝑘1 .𝜋1

𝑎1.𝜋2𝑏1.𝜋3

𝑐1 .𝜋4𝑑1 .𝜋5

𝑒1

𝜋0𝑅𝑎1 = 𝑘1.𝜋1𝑎1 .𝜋2

𝑏1.𝜋3𝑐1 .𝜋4

𝑑1 .𝜋5𝑒1 …………………………………………… (𝐸𝑞𝑢𝑛 5.1)

Considering Equation 5.1 to simplify

0Ra1 = k1 x (1) a1

x (2)

b1 x

(3)

c1 x

(4)

d1 x

(5)

e1

Taking log of both the sides

Log [D1] = Log [k1 x (1) a1

x (2)

b1 x

(3)

c1 x

(4)

d1 x

(5)

e1]…………….. (Equn 5.2)

Using logarithmic rule,

Log [A x B] = Log A + Log B

Log [D1] = Log [k1] + Log [(1) a1

] + Log [(2)

b1]

+ Log [(3)

c1]

+ Log [(4)

d1]

+ Log

[(5)

e1]

Using logarithmic rule,

Log [AB] = B x Log A

Log π0Ra 1 = log K1 + a1logπ1 + b1 logπ2 + c1logπ3 + d1logπ4 + e1logπ5(Equn 5.2)

Using Following table,

Table 5.2: Various Abbreviations Used For Mathematical Modeling

Z = K + [a1 A] + [b1 B] + [c1 C] + [d1 D] + [e1 E]

In above equation, a1, b1, c1, d1, e1 are unknowns whose value need to be found out, while A,B,C,D,E are set of

values obtained during experimentation.

To solve the above equation, multiply coefficient of a1, b1, c1, d1, e1 individually.

Log (0Ra1) = Z Log (k1) = K Log (1) = A Log (2) = B Log (3) = C Log (4) = D Log (5) = E



ISSN No : 1006-7930

Page No: 5540

Multiplying by A,

AZ = AK + [a1 A2] + [b1 AB] + [c1 AC] + [d1 AD] + [e1 AE]

Multiplying by B,

BZ = BK + [a1 AB] + [b1 B2] + [c1 BC] + [d1 BD] + [e1 BE]

Multiplying by C,

CZ = CK + [a1 AC] + [b1 BC] + [c1 C2] + [d1 CD] + [e1 CE]

Multiplying by D,

DZ = DK + [a1 AD] + [b1 BD] + [c1 CD] + [d1 D2] + [e1 DE]

Multiplying by E,

EZ = EK + [a1 AE] + [b1 BE] + [c1 CE] + [d1 DE] + [e1 E2]

Above Set of equations are valid for the number of reading taken during experimentation, therefore taking

summation of these for n values,

The equations become,

Z1 = nK1 + a1*A + b1*B + c1*C + d1* D + e1*E

Z1*A = K1*A +a1*A*A + b1*B*A + c1*C*A + d1* D*A + e1*E*A

Z1*B = K1*B +a1*A*B + b1*B*B + c1*C*B + d1* D*B + e1*E*B

Z1*C = K1*C +a1*A*C+ b1*B*C + c1*C*C + d1* D*C + e1*E*C

Z1*D = K1*D +a1*A*D + b1*B*D + c1*C*D + d1* D*D + e1*E*D

Z1*E = K1*E +a1*A*E + b1*B*E + c1*C*E + d1* D*E + e1*E*E(Equn 5.3)

X1 = inv (W) x P1 ---------- (Equn 5.4)

The matrix method of solving these equations using „MATLAB‟ is given below.

W = 6 x 6 matrix of the multipliers of K1, a1, b1, c1, d1 and e1

P1 = 6 x 1 matrix of the terms on L H S and

X1 = 6 x 1 matrix of solutions of values of K1, a1, b1, c1, d1 and e1

Then, the matrix obtained is given by,

To solve these equations, reducing it to matrix form

(Z)

=

n (A) B C D E

×

K

(AZ) A (A2) (AB) (AC) (AD) (AE) a1

(BZ) B (AB) (B2) (BC) (BD) (BE) b1

(CZ) C (AC) (BC) (C2) (CD) (CE) c1

(DZ) D (AD) (BD) (CD) (D2) (DE) d1

(EZ) E (AE) (BE) (CE) (DE) (E2) e1

Same method is implemented to get the matrix for Material 1, Material 2, Material 3 and Material 4, respectively.

By putting the values for various parameters in the matrices shown above the following matrices are obtained.

-136.976 70 -46.0051 140.4957 -336.959 40.29384 -543.032 K

90.02264 -46.0051 30.23523 -92.3359 221.4543 -26.4817 356.8889 a1

-262.692 140.4957 -92.3359 309.6502 -669.124 94.70497 -1110.92 b1

662.5535 -336.959 221.4543 -669.124 1626.573 -190.372 2608.637 c1

-72.7322 40.29384 -26.4817 94.70497 -190.372 30.11017 -323.089 d1

1053.347 -707.04 464.6773 -1384.77 3412.479 -389.832 4231.279 e1

[P1] = [W1] [X1]

Using Mat lab, X1= W1\ P1 , after solving X1 matrix with K1 and indices a1, b1, c1, d1, e1 are as follows

K -3.7323

a1 -3.2251

b1 1.2472

c1 -0.0031

d1 -1.1813

e1 0.2813

But K1 is log value so converted into normal value by taking antilog of K1



ISSN No : 1006-7930

Page No: 5541

Antilog (-3.7323) = 1.85E-04

Hence the model for dependent term 0Ra1

𝑅𝑎 .𝜔𝐵

2

𝑔 = 𝑘1 .𝜋1

𝑎1.𝜋2𝑏1 .𝜋3

𝑐1.𝜋4𝑑1 .𝜋5

𝑒1

𝜋0𝑅𝑎1 = 𝑘1.𝜋1𝑎1 .𝜋2

𝑏1.𝜋3𝑐1 .𝜋4

𝑑1.𝜋5𝑒1

𝜋0𝑅𝑎1 = 1.85𝑋10−4.𝜋1−3.225 .𝜋2

1.247 .𝜋3−0.0031 .𝜋4

−1.1813 .𝜋50.2831

Ra = 1.84X10−4. HW

HB −3.22

AW .ωB

4

g2 1.24

f.ωB

g −0.0031

DB .ωB

2

g −1.18

μ .g2

ωB3 .FB

0.28

…… . . . Equn 5.5

1. 5. 4. A.2: Solution to establish relationship for 0E1

Model of dependent pi term 0E1 for processing Energy required in operation on Material 1 has been repeated to

compute the models for 0E1 as under-

𝐸.𝜔𝐵

2

𝐹𝐵 .𝑔 = 𝑘2.𝜋1

𝑎2.𝜋2𝑏2 .𝜋3

𝑐2 .𝜋4𝑑2 .𝜋5

𝑒2

𝜋0𝐸1 = 𝑘2.𝜋1𝑎2 .𝜋2

𝑏2.𝜋3𝑐2 .𝜋4

𝑑2.𝜋5𝑒2

For determination of values K2, a2, b2, c2, d2 and e2, similar procedure has been adopted and the matrix obtained is

given by,

372.7039 70 -46.005 140.495 -336.959 40.293 -543.032 K2

-244.947 -46.0051 30.235 -92.335 221.4543 -26.481 356.88 a2

761.6155 140.4957 -92.335 309.650 -669.124 94.704 -1110.92 b2

-1790.46 -336.959 221.454 -669.12 1626.573 -190.37 2608.63 c2

221.3224 40.29384 -26.481 94.7049 -190.372 30.110 -323.08 d2

-2898.76 -707.04 464.677 -1384.7 3412.479 -389.83 4231.27 e2

[P2] = [W2] [X2]


K2 14.0585

a2 13.9306

b2 -5.3542

c2 0.0628

d2 10.6063

e2 -0.6915


Antilog (14.0585) = 1.144x1014

Hence the model for dependent term 0E1

𝜋0𝐸1 = 𝑘2.𝜋1𝑎2 .𝜋2

𝑏2.𝜋3𝑐2 .𝜋4

𝑑2.𝜋5𝑒2

𝐸.𝜔𝐵

2

𝐹𝐵 .𝑔 = 𝑘2.𝜋1

13.93.𝜋2−5.35 .𝜋3

0.0628 .𝜋410.60 .𝜋5

−0.69

𝜋0𝐸1 = 1.14𝑋1014 .𝜋113.93.𝜋2

−5.35 .𝜋30.0628 .𝜋4

10.60 .𝜋5−0.69

E = 1.14X1014 FB . g

ωB2

HW

HB

13.93

AW.ωB

4

g2

−5.35

f.ωB

g

0.063

DB .ωB

2

g

10.61

μ. g2

ωB3 . FB

−0.69

Equn5.6

2. 5. 4. A.3: Solution to establish relationship for 0t1

Model of dependent pi term 0t1 for processing time required in Operation in Material 1 is repeated to compute the

models for 0t1 as under-

𝜔𝐵 . 𝑡 = 𝑘3.𝜋1𝑎3 .𝜋2

𝑏3 .𝜋3𝑐3.𝜋4

𝑑3 .𝜋5𝑒3

𝜋0𝑡1 = 𝑘3.𝜋1𝑎3 .𝜋2

𝑏3.𝜋3𝑐3 .𝜋4

𝑑3.𝜋5𝑒3

For determination of values K3, a3, b3, c3, d3 and e3, similar procedure has been adopted and the matrix obtained is

given by,

239.628 70 -46.00507 140.4957 -336.959 40.29384 -543.032 K



ISSN No : 1006-7930

Page No: 5542

-157.487 -46.0051 30.235233 -92.3359 221.4543 -26.4817 356.8889 a3

487.931 140.4957 -92.33592 309.6502 -669.124 94.70497 -1110.92 b3

-1151.72 -336.959 221.45432 -669.124 1626.573 -190.372 2608.637 c3

141.4252 40.29384 -26.48173 94.70497 -190.372 30.11017 -323.089 d3

-1864.23 -707.04 464.6773 -1384.77 3412.479 -389.832 4231.279 e3

[P3] = [W3] [X3]


K3 8.0911

a3 8.7733

b3 -2.6305

c3 0.0021

d3 5.0868

e3 -0.446


Antilog (8.0911) = 1.23x109

Hence the model for dependent term 23

𝜋0𝑡1 = 𝑘3.𝜋1𝑎3 .𝜋2

𝑏3.𝜋3𝑐3 .𝜋4

𝑑3.𝜋5𝑒3

𝜋0𝑡1 = 1.23𝑋108 .𝜋18.77 .𝜋2

−2.63 .𝜋30.0021 .𝜋4

5.0868 .𝜋5−0.446

t = 1.23X108. ωB.t HW

HB

8.77

AW .ωB

4

g2 −2.63

f.ωB

g

0.0021

DB .ωB

2

g

5.087

μ .g2

ωB3 .FB

−0.45

… . . Equn 5.7

V. SENSITIVITY ANALYSIS

The influence of the various independent π terms has been studied by analyzing the indices of the various π terms in the models [9]. Through the technique of sensitivity analysis, the change in the value of a dependent π term caused due to an introduced change in the value of individual π term is evaluated. In this case, of change of ± 10 % is introduced in the individual independent π term independently (one at a time).Thus, total range of the introduced change is ± 20 %. The effect of this introduced change on the change in the value of the dependent π term is evaluated .The average values of the change in the dependent π term due to the introduced change of ± 10 % in each independent π term. This defines sensitivity. The total % change in output for ±10% change in input is shown in Table III.

VI. ESTIMATION OF LIMITING VALUES OF RESPONSE VARIABLES

In this section attempt has been made to find out the limiting value of three response variables viz. quantity of processing mass at outlet, processing time and processing energy of processing operations each. To achieve this,

limiting values of independent pi terms viz. 1, 2, 3, 4 and 5 are put in the respective models. In the process of maximization, maximum value of independent pi term is put in the model if the index of the term is positive and minimum value if the index of the term is negative. In the process of minimization, minimum value of independent pi term is put in the model if the index of the term is positive and maximum value is put if the index of the term is negative. The limiting values of three response variables are computed as given below for roughness operation. Table IV shows limiting values of response variables.

VII. EMPLOYING RESPONSE SURFACE METHODOLOGY (RSM).

Three mathematical models have been developed for the phenomenon. The ultimate objective of this work is not merely developing the models but to find out best set of independent variables, which will result in maximization / minimization of the objective functions[10][11]. In this case there are three different models corresponding to the Processing mass (Q), Processing Time required (T), Processing Energy required (E) for Agglomerator operation. There are thus three objective functions corresponding to these models. The objective functions for processing mass, time and energy required for processing of Agglomerator need to be minimized. The models have non linear form; hence it is to be converted into a linear form for the optimization purpose. This can be achieved by taking the log of both the sides of the model, we get



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The 70 experiments were conducted, with the process parameter levels set as given in experimental table to study the effect of process parameters over the output parameters.

The experiments were designed and conducted by employing response surface methodology (RSM). The selection of appropriate model and the development of response surface models have been carried out by using statistical software, “MATLAB R2009a”. The best fit regression equations for the selected model were obtained for the response characteristics, viz., Surface Roughness, Processing Energy and Processing time. The response surface equations were developed using the experimental data and were plotted (Fig.7, Fig. 9 and Fig.11) to investigate the effect of process variables on various response characteristics (Fig.8, Fig. 10 and Fig.12).

For Response variable Surface Roughness, response surface equation is

Ra .ωB

2

g = fx

HW

HB

AW .ωB

4

g2

f.ωB

g

DB .ωB2

g

μ. g2

ωB3 . FB

……… . . Equn

Ra01 = K. g

ωB2

HW

HB

AW .ωB

4

g2

f.ωB

g

DB .ωB2

g

μ. g2

ωB3 . FB

……… Equn

Ecg

E3

6

= -0.06868 + 0.4022 *x + 1.054 *y -1.97 *x2 -1.122*x*y + 0.06694*y

2 + 2.983*x

3 -2.369*x

2*y +

1.165*x*y2

Goodness of fit:

SSE: 0.02774, R-square: 0.9941, Adjusted R-square: 0.9932, RMSE: 0.02267

Fig.7: Actual x Computed values using response surface methodology for Surface Roughness

a b

Fig. 8 : a) RSM model b) Contour plot for Surface Roughness

For Response variable Energy, response surface equation is

E .ωB

2

FB . g = f x

HW

HB

AW .ωB

4

g2

f.ωB

g

DB .ωB2

g

μ. g2

ωB3 . FB

………… . Equn

E01 = K. FB . g

ωB

HW

HB

AW .ωB

4

g2

f.ωB

g

DB .ωB2

g

μ. g2

ωB3 . FB

……… . Equn

0 10 20 30 40 50 60 700

0.2

0.4

0.6

0.8

1

No. of Experiments

Obs

erve

d ou

tput

(E

nerg

y)

Sliver cutting Energy Comparison of Experimental and RSM Model



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Ecg

E3

6

= -0.06868 + 0.4022 *x + 1.054 *y -1.97 *x2 -1.122*x*y + 0.06694*y

2 + 2.983*x

3 -2.369*x

2*y +

1.165*x*y2

Goodness of fit:

SSE: 0.8702, R-square: 0.7629, Adjusted R-square: 0.7277, RMSE: 0.1269

Fig. 9: Actual x Computed values using response surface methodology for Energy

a b

Fig. 10. a) RSM model ;b) Contour plot for Energy

For Response variable time response surface equation is

ωB . t = f . HW

HB

AW .ωB

4

g2

f.ωB

g

DB .ωB2

g

μ. g2

ωB3 . FB

………… . . Equn

t01 = K. ωB . t HW

HB

AW .ωB

4

g2

f.ωB

g

DB .ωB2

g

μ. g2

ωB3 . FB

……… . . Equn

Ecg

E3

6

= -0.06868 + 0.4022 *x + 1.054 *y -1.97 *x2 -1.122*x*y + 0.06694*y

2 + 2.983*x

3 -2.369*x

2*y +

1.165*x*y2

Goodness of fit: SSE: 1.059, R-square: 0.3007, Adjusted R-square: 0.1971, RMSE: 0.14

0 10 20 30 40 50 60 700

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Sliver cutting Torque Comparison of Experimental and RSM Model

No. of Experiments

Obse

rved o

utput

(Torqu

e)

0 10 20 30 40 50 60 700.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Sliver cutting time Comparison of Experimental and RSM Model

No. of Experiments

Obser

ved ou

tput (t

ime)



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Fig.11: Actual x Computed values using response surface methodology for Time

a b

Fig. 12. a) RSM model; b) Contour plot for Time

VIII. Optimization of RSM Models

Optimized values of RSM models are found form RSM graph as per the objective function of the response parameter. If the objective function is maximization then select the highest part of the graph and choose the values for optimization. . If the objective function is minimization then select the lowest part of the graph and choose the values for optimization. Fig. 8, 10, and 12 shows scaled minimum values for surface roughness, energy and time. Fig. 8, 10, and 12 , it is found that the minimum surface roughness required is 00000 mm, minimum energy is required 0.005KW-hr and minimum time required is 0.26 Seconds for material 1(HE15) operation.

IX. CONCLUSION

In this model there are five independent pi terms and three dependent pi terms. It is very difficult to plot a 3D graph.

To obtain the exact 3D graph dependent pi terms are taken on Z-axis where as from five independent pi-terms, three

are combined and a product is obtained which is presented on X-axis. Whereas remaining two independent pi terms

are combined by taking product and represented on Y-axis. Figure 7.1.A to Figure 7.1.C shows 3D and 2D graphs

for three dependent terms i.e. processing Surface Roughness, processing Energy, and processing time. Table 7.7

shows sample calculations for 3D Graphs for all Processing operations.

It would be seen that there are different trends of variation of each dependent pi terms corresponding to the variation

of the various independent pi terms (i.e.𝜋1,,𝜋2, 𝜋3,𝜋4,𝜋5). It has been observed that the phenomenon is complex

because variation in the dependent pi terms is in a fluctuating form mainly due to continuous variation in the

parameters for the operations. This variation in the angular speed and feed of lathe is exponentially changing. This

in turn is due to nonlinearly varying depth of cut and feed on the workpiece due to the process resistance and inertia

resistances which are likely to be instantaneous speed depending upon the variation in supply voltage, speed of lathe

and quality of material in 3 to 4 seconds. From Figure 7.1.A, it is observed that there are 9 peaks in graph of Z i.e.

processing surface roughness vs. X. There must be in all 18 mechanisms which are responsible for giving these 9

peaks. Whereas in graph of Z i.e. processing surface roughness vs. Y, there are 8 peaks. Hence there must be in all

16 mechanisms which are responsible for giving these 8 peaks. From Figure 7.1.B, it has been observed that there

are 7 peaks in graph of Z i.e. processing Energy vs. X. There must be in all 14 mechanisms which are responsible

for giving these 7 peaks. Whereas in graph of Z i.e. processing Energy vs. Y, there are 7 peaks. Hence there must be

in all 14 mechanisms which are responsible for giving these 7 peaks. Similarly from Figure 7.1.C, it has been

observed that there are 8 peaks in graph of Z i.e. processing time vs. X There must be in all 16 mechanisms are

responsible for giving these 8 peaks. Whereas in graph of Z i.e. processing time vs. Y, there are 5 peaks. Hence there

must be in all 10 mechanisms which are responsible for giving these 5 peaks.

REFERENCES

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faculty of Enggering, Benha University, Egypt

[2] Liviu Luca, Sorin Neagu-Ventzel, Ioan Marinescu, “Burnishing Of Hardened Steel Components – An Alternative Method of Finishing”, the University of Toledo

[3] N. H. Loh and S. C. Tam, “Effects of ball burnishing parameters on surface finish - A literature survey and discussion”, Precision Engineering, (1988), 14-23

[4] Adel Mahmood Hassan,“The effects of ball- and roller-burnishing on the surface roughness and hardness of some non-ferrous metals”, Journal of Materials Processing Technology (72) (1997), 385–391



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[5] Constantin BUZATU,Adriana BĂLĂCESCU, “Surface Roughness Modeling At Ball Bearing rings Superfinishing On The Cutting Fluid And Process Parameters Influence”, International Conference on Economic Engineering and Manufacturing Systems Brasov, October (2007),25 -26.

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[10] Pande S.S. and Patel, S.M. “Investigations on vibratory burnishing process”, Int Journal. Mach Tool Design, Research, (24) (1984), 195-206

[11] G.K. Awari Master‟s Thesis, NITTTR, Chandigarh, and Thapar Institute of Engineering and Technology, October (1995), Patiala (Deemed University)

[12] G. K. Awari, Dr. M. Adithan, “Parametric Study of Superfinishing process” Proceedings of National Conference on precision Engineering, IIT, Madras, Narosa Publishing, New Delhi, (2000), 195-203.

[13] Puthanangady and Malkin, “Experimental investigation of the superfinishing process” Wear Journal (185) (1995), 173-182.

[14] J.P.Modak, “Design of Experimentation for Comparison of Various Bicycle Drive Mechanisms Modeling”, Simulation and Control, B, AMSE Press, France (9) (1987), 33-66

[15] D. M. Mate, Dr. G. K. Awari, J. P. Modak “Modification of surface integrity by burnished spherical surface tool on cylindrical workpiece”, International Journal of Advances in Machining and Forming Operations, Vol.:4, Issue: 1 pp 55-62, 2012.

[16] D. M. Mate, “An Approach to Design of Child Saver Machine for Child Trapped in Borehole”, International Journal of Research in Mechanical Engineering Volume 1, Issue 2, pp 26-38, December 2013.

[17] D. M. Mate, Dr. G. K. Awari, “Formulation of Experimental Data Based Model for Aluminum Alloy HE15 Operation with Burnishing Tool on Lathe Machine Using Dimensional Analysis”, International Journal of Research in Mechanical Engineering Volume 1, Issue 2, pp-80-90, October-December, 2013.

[18] D. M. Mate, Prof. P.S Choudhari, “Formulation of Experimental Data Based Mathematical Model for Al2014 with Spherical Surface Burnishing Tool”, International Journal of Research in Mechanical Engineering, Volume-2, Issue-3, pp 1-6, May-June, 2014.

[19] H. Sqenck .Jr, ``Theory of engineering experimentation`` Mc-GrawHill, inc., Newyork, 1961



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