A Study on the Effect of Depth of Cut, Feed Rate and Tool Overhang on the Induced Vibration and Surface Roughness during Hard Turning of 41Cr4 Alloy Steel using Response Surface Methodology

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International Journal of Emerging Technology and Advanced Engineering

Website: www.ijetae.com (ISSN 2250-2459,ISO 9001:2008 Certified Journal, Volume 6, Issue 3, March 2016)

54

A Study on the Effect of Depth of Cut, Feed Rate and Tool

Overhang on the Induced Vibration and Surface Roughness

during Hard Turning of 41Cr4 Alloy Steel using Response

Surface Methodology

Christopher O. Izelu

1

, Samuel C. Eze

2

, Danladi K. Garba

3

1

Department of Mechanical Engineering, Federal University of Petroleum Resources, Effurun, Nigeria

2,3_{Department of Mechanical Engineering, Nigerian Defence Academy, Kaduna, Nigeria}

Abstract–This paper presents an aspect of a series of

experimental studies in which the effect of the factors, such as depth of cut, feed rate and tool overhang on the response variables, such as machining induced vibration and surface roughness, during hard turning of 41Cr4 alloy structural steel on a conventional lathe with standard cutting tool is of major interest. The response surface methodology, based on central composite design of experiment, was used, and the analysis performed in Design Expert 9 software environment. Quadratic regression models were obtained and evaluated for the response variables as functions of the selected factors. The optimal settings of these factors required to minimize the response variables were also determine. The influence of the factors on the response variables were established through analysis of variance. The optimum setting of 58.2409 mm, for the tool overhang; 0.170594 mm/rev, for the feed rate; and 1.2192 mm, for the depth of cut would minimize the machining induced

vibration of the cutting tool to a value of 0.09 mm/s2, and

the surface roughness of the specimen work-piece to a value of 5.591 µmm if other operating factors were kept constant at their intermediate levels within the experimental design space.

Keywords-- Central Composite Design of Experiment,

Depth of Cut, Design Expert, Feed Rate, Induced

Vibration, Response Surface Methodology Surface

Roughness, Tool Overhang

I. INTRODUCTION

Modern industrial production by metal cutting emphasizes strongly on economically achieving the best product quality and process performance. Clarification on this objective has been and is still being pursued through experimental evaluation, modeling and determination of the optimal settings of both the controllable and uncontrollable cutting conditions, including cutting tool, work-piece and environmental variables.

Metal cutting by turning is of great importance in industrial manufacture of machined components. It is one of the major material removal process mainly used in the industry to generate cylindrical surfaces. This has been achieved when a rotating cylindrical work-piece at given cutting speed encounters a translating cutting tool at given feed rate and depth of cut. It is believed that if the cutting conditions such as the cutting speed, feed rate and depth of cut, as well as the cutting tool and work-piece variables are skillfully set, the best product quality and desired process performance would be achieved.

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The most recent are the works of Khan et al [25], Devkumar et al [26], Devi et al [27], Rajpoot et al [28], Khidhir et al [29], Agrawal et al [30], Ranganath et al [31], Chandra and Prasad [32], Sastry et al [33], Revankar et al [34], Mahajan et al [35], Shihab et al [36], and Gupta and Kohli [37]. For completeness, the works of Kassab and Khoshnaw [38], Han et al [39], Cahuc et al [40], Delijaicov et al [41], Rogov and siamak [42] [43] are equally relevant, but essential to the machining induced vibration of either the cutting tool or work-piece. RSM forms the basis of most of these works, but based on the different design of experiment (DOE), which include central composite (CC) [5] [7] [10] [26] [27] [28] [31] [32] [33] [36] [37], Box-Behnken (BB) [3] [13] [18] [19] [20] [21] [22] [30], Taguchi orthogonal array (AO) [11] [15] [23] [24] [34], factorial (F) [4] [6] [29], and full factorial (FF) [14] design of experiment (DOE). The analysis were executed in software environments, such as the Design Expert [5] [9] [15] [18] [19] [20] [21] [26] [28] [33] [36], Minitab [3] [11] [22] [23] [24] [31], LINGO Solver [12], MATLAB [17] and doe++ [32]. The works also differ due to the work-piece materials considered; the cutting tools, lathe machines, and parameter measurement instruments used; process variables and constants, and performance variables investigated, and the results obtained.

The work piece materials used in these works include AISI 4140 alloy steel [3], EN-31 alloy steel [4] [6] [12], AISI 1040 medium carbon steel [5] [11] [17] [38], aluminum alloy [7] [9] [22] [33], LM25 AL-AL203 metal matric composite [8], resin [9] [33], Inconel 718, a nickel based super alloy [10] [18], AISI 302 austenitic alloy steel [13], AISI 410 alloy steel [14], 6063 aluminum alloy [15] [35], ferrous and non-ferrous materials [16], DSS UNS 31803 (2205) steel [19], EN-24 alloy steel [20] [21], and 11sMn30 alloy steel [23]. Others include SAF 2507, a super duplex stainless steel [24], EN-8 (AISI 1045) mild carbon steel [25] [32] [35] [41] [43], Al 6061 aluminum alloy [26], brass [27] [35], metal matrix composite steel [28], AISI 1020 mild steel [29], hard porcelain material [30], aluminum KS 1275 [31], titanium alloy (Ti-6AI-4V) [34], SS 304 and EN1A alloy [35], AISI 52100 hardened alloy steel [36], AISI 4340 alloy steel [37], chrome molybdenum 42CrMo24 alloy steel [40], and AA 2024 aluminum alloy.

The cutting tools used in these works include carbide rhomboid insert [3], diamond shaped carbide inserts [4] [6] [12], TNMG 160404-FL, WIDIA insert [5], HSS cutting tool [7] [9] [33] [38], SNMG 1204-QM H13A cutting tool [8], Titanium carbide based cermet insert [10] [42] [43], KENNAMETAL-KC5010 insert [11], CNMA 120404 [12], CNMA 120408 [12], CNMA 120412 [12], ceramic inserts [14], THN SNMG 08 Tungsten carbide insert [15], coated carbide insert [18] [22] [36], and coated carbide insert of ISO CNMG 120408 SM grade 1115 [19]. Others include coated tungsten carbide insert of ISO CNMG 120408 [20], WIDIA CNMG120408 coated Tungsten carbide insert [21], WIDIA CNMG 12040-47-TN 2000 cutting tool [23], uncoated cemented carbide cutting tool insert of type CNMG 120408-QM, grade H13A [24], standard carbide tool (ISO6 R2020) [25], Tungsten Carbide Tool [28], cemented carbide insert [29], Al2O3 cutting tool

[30], brass based diamond (VCMW) insert [31], cubic boron nitride (CBN) cutting tool [32], poly crystalline diamond (PCD) insert with ISO of CCMT09T304 [34], PVD and CVD coated inserts [37], and PCBN type VBG160404S01020F insert [41].

The most common amongst the investigated process variables are the cutting conditions, like the cutting speed, depth of cut and the rate of feed. Others include cutting tool variables like tool nose radius [4] [6] [12] [13] [14] [19], tool coatings [37], tool back rake angle [25]; work-piece variables like work-piece overhang [42]; and environmental variables like type of coolant [27] and minimum quantity of lubricant [34]. Phate and Tatwawadi [16] gave a holistic look by investigating a number of factors including the operator data, tool data, work-piece data, cutting conditions, machine data, and the environmental conditions. Mahajan et al [35] also gave a holistic look by investigating various machining field data.

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The results of these works, based on surface roughness data, are much more similar, and essentially, they showed that surface roughness deteriorates with increase in feed rate, depth of cut, and back rake angle, with the feed rate having dominant effect. It improves with increase in cutting speed and tool nose radius, with the effect of nose radius being dominant. It should be noted that the extent of these effects differs due to the different investigated work-piece and cutting tool materials, and also, for the different machining environments (dry, medium or wet) under which the various experiments were performed. In most cases, surface roughness predictions were accurately achieved within limits from the RSM derived second order regression models. As reported in [42] [43] machining vibration was shown to have increase with increase in feed rate, depth of cut, cutting tool overhang, with cutting tool overhang being dominant, but decreased with increase in cutting speed. The established optimum working conditions varied due to the used work-piece and cutting tool materials, and the environment under which the machining processes were performed.

The main focus of this work, therefore, is on the use of response surface methodology (RSM) based on central composite (CC) design of experiment (DOE) to model,

predict and optimize the surface roughness (

R

_a) and machining induced vibration (

V

_i) as functions of depth of cut, feed rate and tool overhang during turning of 41Cr4 alloy structural steel on a conventional lathe using standard work-piece sizes, cutting tool and measurement devices. Also, investigated is the relationship that would exist between surface roughness and machining induced vibration.

II.MATERIALS,EQUIPMENT AND METHODS

A. Work-Piece

[image:3.612.387.493.469.550.2]

The selected work-piece material was first subjected to chemical analysis in conjunction with mechanical tests at Standards Organization of Nigeria (SON), Emene, Enugu, to establish its chemical composition and mechanical properties, respectively. It was found to be 41Cr4 quenched and tempered (QT) alloy special steel, with material number of 1.7035 and equivalent grades of SAE-AISI 5140, BS 530M40, EN 10083-3 or EN18, and VC140, which is different from those previously investigated. Samples of 41Cr4 alloy steel bars are given in Fig. 1, with its chemical composition and mechanical properties given in Tables I and II, respectively. According to a technical report by FUHONG on special steels, 41Cr4 is one of the most widely used alloy steel. It is quite suitable for driving elements like crankshafts, front vehicle axles, axle journals and steering components. After Quenching and Tempering (QT) heat treatment, 41Cr4 alloy steel has good overall mechanical properties, low temperature impact toughness and hardenability. It can get higher fatigue strength after oil cooling. Its machinability is good when subjected to normalizing and QT conditions, but its weldability is not good, and as a result, cannot easily be produce when subjected to welding conditions. Test specimens of this material for the turning experiment are round bars having dimensions of diameter, 25 mm, and length, 150 mm.

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TABLE I

CHEMICAL COMPOSITION OF 41CR4 ALLOY SPECIAL STEEL

Quality of material Type of material

Average elements %

Carbon (C)

Silicon (Si)

Manganese (Mn)

Chromium (Cr) Quenched and Tempered Steel 41Cr4 0.40 0.25 0.65 1.00

TABLE II

MECHANICAL PROPERTIES OF 41CR4 ALLOY SPECIAL STEEL

Sample ID Diameter (mm) Area (mm2) BHN Peak load (kN) Uts N/mm2

Solid, Round 10.00 78.55 278.48 70.92 902.83

B. Processing Equipment

A conventional lathe machine (Fig. 2), and a carbide cutting tool of the type F30 (Fig. 3) were used in the turning experiment. The overall dimensions of the tool insert is 25 mm x 25 mm x 12.5 mm. It also has a back rake angle of 10o, side rake angle of 12o, side relief angle of 5o and a side cutting edge angle of 15o.

Figure 2. Conventional Lathe Machine

Figure 3. Cutting Tool with Carbide Insert, F30

C. Input Variables

The selected factors, also known as process or input variables, are the tool overhang (A), feed rate (B) and depth of cut (C). Others were kept constant at intermediate levels of their values for the various runs of the experiment. Tool overhang (A) is the length of that part of the tool that sticks out of the machine tool post [38] [42]. It is measured in mm. Feed rate (B) is the speed of the cutting tool relative to that of the work-piece as the tool takes a cut along the axis of the work-piece [1]. It is measured in mm per revolution. The depth of cut (C) is taken along the radius of the work-piece as the tool cuts into it in a turning operation [1]. It is measured in mm. It is believed that these factors have influence on

the surface roughness (

R

V

_i), the extents of which are being pursued. Within limits, as given in Table III, in three levels, these factors can be set such as to minimize the surface roughness and machining induced vibration, and hence, improve on the quality of the machined part.

TABLE III

LEVELS OF THE INPUT VARIABLES

S/N Parameters Notation Unit

Levels

Low Medium High

1 Tool Overhang A mm 1.0 2.0 3.0 2 Feed rate B mm/rev 0.15 0.20 0.30

3 Depth of cut C mm 50 55 60

D. Output Variables

The selected output variables, also known as the response or process performance variables, are the

surface roughness (

R

V

_i). Surface roughness, or simply, roughness is a measure of the texture of a surface [1].

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Rough surfaces wear faster and have higher friction coefficient than smooth surfaces. Roughness of a surface may form nucleation sites for cracks or corrosion, promote adhesion, and may be very expensive to control in manufacturing. Roughness is measured in microns or micrometers. An inside surface roughness tester, ISR-16 (Fig. 4) was selected for measurement of the surface

roughness. Roughness values (

R

_a) were taken at three different positions located at 120o on surface and about the axis of the work-pieces. The average of these values represents the surface texture of the turned surface. Note

[image:5.612.114.232.327.433.2]

that

R

_a [µm] is the center line average roughness [5]. It is the arithmetic deviation of the surface height from the mean line through the profile while the mean line separates the profile above and below it by equal area.

Figure 4. Surface Roughness Tester, ISR-16

Figure 5. Vibration Meter with Transducer, 908 BE

Vibrations occurring during machining include a sudden clash of a tool against a work-piece; irregular tissues of the work-piece; regular excitation due to asymmetric torque; and bearing defects. Vibration due to a sudden clash of a tool against a work-piece occurs at the cutting zone, and has been treated as self-excited vibration or chatter, if excessive [38] [39] [40]. Chatter may give rise to defective machined surface, and excessive wear and breakage of the cutting tool.

Because self-excited vibration is induced at cutting zone due to interaction of the cutting tool, chips and work-piece during machining, it is being referred to as a machining induced vibration in this work. It influences the surface roughness of machined components [41] [42] [43], but because it cannot be manipulated or controlled as a factor, though can be measured, it is treated here as a response variable, measured as an acceleration amplitude in m/s2. A vibration meter, type 908 BE (Fig. 5), was selected for measurement of the amplitude of displacement and velocity of a point on the cutting tool. The level of tool vibration was measured using a vertical data of a transducer mounted near to the tip and connected to the vibration meter. The data included amplitude of displacement and velocity of the point on the cutting tool for each sample. The acceleration, thereafter, was calculated from the relation between the displacement, velocity and acceleration.

E. Design and Analysis of Experiment

The turning Experiment is designed so that the number of runs or trials can be reduced; optimum values of parameters can be determined; assessment of experimental error can be made; qualitative estimation of parameters can be made; and inference regarding the effect of parameters on the characteristics of the process can be made [2]. The response surface methodology (RSM), based on central composite (CC) design of experiment (DOE), was selected for modeling, prediction

and optimization of the surface roughness (

R

V

_i), the response or dependent variables, as functions of the tool overhang (A), feed rate (B) and the depth of cut (C), the factors or independent variables, in the turning experiment. RSM requires that, in a functional relationship between the response (

Y

) and k quantitative factors (

k

x

₁

,

₂

,



,

), given as:

Y







x

₁

,

x

₂

,



,

x

_k





e

_r, the function (



) is known as the response surface or

[image:5.612.106.240.456.551.2]

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The higher the degree of the polynomial the better is the correlation, though the higher will be the cost of

experimentation. The second order or quadratic response surface may take the form as:

r k

i

j i ij k

i i ii k

i

ix b x b xx e

b b

Y 













 

 1 1

2

1 1

0

(1)

Or







 







k

i

j i ij k

i i ii k

i i i

k

b

x

b

x

b

x

1 1

2

1 0 2

1

,



,



(2)

Multiple regression equations or models of this form has the linear, square and cross-product terms, and can satisfactorily be used to correlate dependent variables with independent variables. The coefficients of the regression models may be estimated using a number techniques for design of experiment (DOE). For the situation studied the central composite (CC) was selected for design of the turning experiment. Analysis of variance (ANOVA) was used to validate the developed models, and also, to predict the effect of selected factors

A, B and C on the response characteristics,

V

_i and

R

_a. Optimization of the response functions,

V

_i



A

,

B

,

C



and

R

_a



A

,

B

,

C



subject to constraints as determined by the limits of the factors A, B and C was performed as appropriate using standard optimization technique. The RSM was implemented in the Design Expert 9 software version 9.0.6.2 environment.

F. Experimental Procedure

The setup for the turning experiment is given in Fig 6. In the setup, twenty-seven (27) standard specimen 41Cr4 alloy steel bars (Fig 1) were turned on the conventional lathe (Fig. 2) with carbide tool insert (Fig. 3) following a central composite (CC) design of experiment (DOE) in which factor combinations and sequence were appropriate for efficient data collection and analysis. During each experimental run, measurement of the machining induced vibration data were taken three times using a vibration transducer (Fig. 4) placed on the tool post near the cutting zone. The data was transmitted to the vibration meter (Fig. 5), and read out as displacement and velocity. The average cutting tool acceleration was determined from the general relations between displacement, velocity and acceleration. After each experimental run, measurement of the surface roughness also was taken at three (3) different locations, 120o from each other, on the machined surface using a surface roughness tester (Fig. 4). The average values were recorded.

(a)

[image:6.612.111.513.163.470.2]

(b)

Figure 6. Setup for the Turning Experiment

III. RESULTS AND DISCUSSION

The experiment was conducted taking into consideration all factors that could introduce error, which were minimized as appropriate. The data generated from the turning experiment was collected and presented as given in Table IV. Results of its analysis in Design Expert software version 9.0.6.2 environment are presented and discussed as follows:

A. Machining Induced Vibration Data

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The ANOVA for response surface quadratic model of

i

V

, given in Table VI, confirms the significance of the

model as being capable of accurate prediction of

V

_i within the selected limits, and also, that of the model terms A, B, C, A2, B2, C2, AC and BC as predictors of

i

V

with exception of the term AB, which is not signification. For the linear terms, C has dominant

influence on

V

_i followed by B, and then, A. For the square terms, C2 has dominant influence on

V

_i followed by A2, and the B2.

For cross-products terms, BC has dominant influence

on

V

_i when compare to AC. The predicted R-square of 0.9018, given in Table VII, is found to be in reasonable agreement with the adjusted R-square of 0.9392 since the difference of 0.0374 is less than 0.2. The adequacy precision of 24.271, greater than 4, is a desirable signal to noise ratio indicating that there is adequate signal, and that this model can be used to navigate the design space.

The response surface models of the machining

induced vibration

V

_i given in terms of the coded factors (Equation 3), and also, in terms of the actual factors (Equation 4), A, B and C, respectively, are:





BC

AC

AB

C

B

A

C

B

A

C

B

A

V

i

065 .

0

062 .

0 005917

.

0

11 .

0

042 .

0

060 .

0

073 .

0

035 .

0

032 .

0

20 .

0 ,

,

2 2 2

















(3)





BC AC

AB C

B

A C

B A

C B A V_i

86444 . 0 0123 . 0 015778 . 0 11022 . 0 41728 . 7

00239778 .

0 84967 . 0 27519 . 0 23627 . 0 37021 . 5 , ,

2 2

2

 



 

 

 

[image:7.612.110.507.403.717.2]

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TABLE IV

DATA GENERATED FROM TURNING EXPERIMENT

Standard Run

A B C Vi Ra

Tool Overhang Feed Rate Depth of Cut Acceleration Surface Roughness

mm mm per rev mm mm per min square micro mm

1 6 50 0.15 1 0.18 9.080

2 22 55 0.15 1 0.17 5.870

3 4 60 0.15 1 0.04 6.878

4 1 50 0.225 1 0.29 7.381

5 2 55 0.225 1 0.20 4.226

6 15 60 0.225 1 0.09 7.680

7 10 50 0.3 1 0.42 8.700

8 27 55 0.3 1 0.40 6.795

9 3 60 0.3 1 0.19 10.910

10 7 50 0.15 2 0.20 8.730

11 24 55 0.15 2 0.20 5.620

12 26 60 0.15 2 0.10 6.292

13 23 50 0.225 2 0.15 6.895

14 5 55 0.225 2 0.19 5.700

15 19 60 0.225 2 0.14 7.149

16 8 50 0.3 2 0.25 8.319

17 9 55 0.3 2 0.24 6.342

18 16 60 0.3 2 0.18 11.510

19 12 50 0.15 3 0.34 7.250

20 18 55 0.15 3 0.48 4.850

21 25 60 0.15 3 0.41 5.790

22 17 50 0.225 3 0.27 5.570

23 14 55 0.225 3 0.42 4.447

24 11 60 0.225 3 0.31 7.436

25 20 50 0.3 3 0.32 7.290

26 13 55 0.3 3 0.37 5.845

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Equation (4), was used to generate the predicted

values of

V

_i, a plot of which against the actual values (Table IV), given in Fig. 7, illustrates how well the

predicted

V

_i data fits the actual data. As shown in Fig. 8, the machining induced vibration

V

_i has nonlinear relationship with factors A, B and C, and that effect of

these factors on

V

_i became more significant at the higher levels of these factors, when compared to that at lower levels.

At higher levels of these factors, V_i decreased with

increase in A, but increased with increase in B and C from the reference point. At lower levels of the factors,

i

V

increased with increase in A, but decreased with increase in B and C toward the reference point. The

implication of the behavior is that

V

_i is minimized when the factors, except A, are set at lower level of their values. These behaviors can also be seen in the contour and response surface plots given in Figs 9 to 14. It can be attributed to the observed multiple interaction between factors.

TABLE V

MODEL SUMMARY STATISTICS

Source

Standard

Deviation R-Squared

Adjusted R-Squared

Predicted

R-Squared PRESS

Linear 0.097 0.3892 0.3096 0.1435 0.30

2FI 0.077 0.6625 0.5612 0.4448 0.20

Quadratic 0.029 0.9603 0.9392 0.9018 0.035 Suggested

[image:8.612.111.502.415.570.2]

Cubic 0.033 0.9688 0.9189 0.7174 0.100 Aliased

TABLE VI

ANOVA FOR RESPONSE SURFACE QUADRATIC MODEL OF THE ACCELERATION AMPLITUDE (VI)

Source

Sum of Squares

Degree

of Freedom Mean Square

F Value

p-value Prob > F

Model 0.34 9 0.038 45.66 < 0.0001 Significant

A-Tool Overhang 0.019 1 0.019 22.62 0.0002

B-Feed Rate 0.022 1 0.022 26.70 < 0.0001

C-Depth of Cut 0.097 1 0.097 117.23 < 0.0001

AB 4.201E-004 1 4.201E-004 0.51 0.4847

AC 0.045 1 0.045 55.13 < 0.0001

BC 0.050 1 0.050 61.27 < 0.0001

A^2 0.022 1 0.022 26.19 < 0.0001

B^2 0.010 1 0.010 12.69 0.0024

C^2 0.073 1 0.073 88.55 < 0.0001

Residual 0.014 17 8.232E-004

Cor Total 0.35 26

TABLE VII

QUADRATIC MODEL STATISTICS

Standard Deviation 0.029 R-Squared 0.9603

Mean 0.26 Adjusted R-Squared 0.9392

C.V. % 11.18 Predicted R-Squared 0.9018

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Figure 7. A Plot of the Predicted

V

_i against the Actual values

Figure 8. A Plot of

V

_i against the deviation from reference point (Coded Unit) or perturbation

Figure 9. A Contour plot of

V

_i against A and B with C set at 2 mm

Figure 10. A Response surface plot of

V

_i against A and B with C set at 2 mm

Figure 11. (a) A Contour plot of

V

_i against A and C with B set at 0.225 mm/rev

V

_i against A and C with B set at 0.225 mm

Figure 13. A Contour plot of

V

_i against B and C with A set at 55 mm

V

_i against B and C with A set at 55 mm

Design-Expert® Software Acceleration Amplitude Color points by value of Acceleration Amplitude: 0.48 0.04 Actual P r e d ic te d

Predicted vs. Actual

0.00 0.10 0.20 0.30 0.40 0.50

Design-Expert® Software Factor Coding: Actual Acceleration Amplitude (mm per min square) Actual Factors A: Tool Overhang = 55 B: Feed Rate = 0.225 C: Depth of Cut = 2

-1.000 -0.500 0.000 0.500 1.000

0.00 0.10 0.20 0.30 0.40 0.50 A A B B C C Perturbation

Deviation from Reference Point (Coded Units)

A c c e le r a ti o n A m p li tu d e ( m m p e r m in s q u a r e ) Design-Expert® Software Factor Coding: Actual Acceleration Amplitude (mm per min square)

Design Points

0.48

0.042

X1 = A: Tool Overhang X2 = B: Feed Rate Actual Factor C: Depth of Cut = 2

50 52 54 56 58 60

0.15 0.18 0.21 0.24 0.27

0.3 Acceleration Amplitude (mm per min square)

A: Tool Overhang (mm)

B : F e e d R a te ( m m p e r r e v ) 0.15 0.2 0.2 0.25 Design-Expert® Software Factor Coding: Actual Acceleration Amplitude (mm per min square)

Design points above predicted value

Design points below predicted value

0.48

0.042

0.15 0.18 0.21 0.24 0.27 0.3 50 52 54 56 58 60 0 0.1 0.2 0.3 0.4 0.5 A c c e le ra ti o n A m p li tu d e ( m m p e r m in s q u a r e )

A: Tool Overhang (mm) B: Feed Rate (mm per rev)

Design-Expert® Software Factor Coding: Actual Acceleration Amplitude (mm per min square)

Design Points

0.48

0.042

X1 = A: Tool Overhang X2 = C: Depth of Cut Actual Factor B: Feed Rate = 0.225

50 52 54 56 58 60

1 1.5 2 2.5

3 Acceleration Amplitude (mm per min square)

C : D e p th o f C u t ( m m ) 0.1 0.2 0.2 0.3 Design-Expert® Software Factor Coding: Actual Acceleration Amplitude (mm per min square)

0.48

0.042

1 1.5 2 2.5 3 50 52 54 56 58 60 0 0.1 0.2 0.3 0.4 0.5 A c c e le ra ti o n A m p li tu d e ( m m p e r m in s q u a r e )

A: Tool Overhang (mm) C: Depth of Cut (mm)

Design-Expert® Software Factor Coding: Actual Acceleration Amplitude (mm per min square)

Design Points

0.48

0.042

X1 = B: Feed Rate X2 = C: Depth of Cut Actual Factor A: Tool Overhang = 55

0.15 0.18 0.21 0.24 0.27 0.3

1 1.5 2 2.5

3 Acceleration Amplitude (mm per min square)

B: Feed Rate (mm per rev)

C : D e p th o f C u t ( m m ) 0.2 0.3 0.3 0.4 Design-Expert® Software Factor Coding: Actual Acceleration Amplitude (mm per min square)

0.48

0.042

1 1.5 2 2.5 3 0.15 0.18 0.21 0.24 0.27 0.3 0 0.1 0.2 0.3 0.4 0.5 A c c e le r a ti o n A m p li tu d e ( m m p e r m in s q u a r e )

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International Journal of Emerging Technology and Advanced Engineering

63

B. Surface Roughness Data

The model summary statistics, given in Table VIII, shows that a quadratic regression model is suggested as being adequate for accurate fitting of the surface roughness data, with a standard deviation of 0.51, R-square value of 0.9523, adjusted R-R-square value of 0.9270, predicted R-square value of 0.8903. Analysis of variance (ANOVA), given in Table IX, shows that the model is significant for accurate prediction of the surface

roughness

R

_a within the design limits of the factors A, B and C. It also shows that the influence of model terms,

A, B, C, A2, B2, AB, and AC on

R

_a is significant, except the terms C2 and BC. Amongst the linear terms, B

has dominant influence on

R

_a followed by C, and then, A.

Whereas, for the square terms, A2 has dominant

influence on

R

_a when compare to B2, the least being C2. For the cross-product terms, AB has dominant

influence on

R

_a followed by AC, with the least being BC. The quadratic model statistics, given in Table X, shows that the predicted R-square value of 0.8903 is in reasonable agreement with the adjusted R-square value of 0.9270, since the difference of 0.0367 is less than 0.2. The adequacy precision of 22.671, greater than 4, is a desirable signal to noise ratio. This indicates that there is adequate signal, and that this model can also be used to navigate the design space.

The response surface models of the surface roughness

(

R

_a), given in terms of the coded factors (Equation 5) and actual factors (Equation 6), are given as follows:





2 2

2

33 .

0

35 .

1

48 .

2

15 .

0

33 .

0

28 .

1

44 .

0

91 .

0

31 .

0

85 .

4 ,

,

C

B

A

BC

AC

AB

C

B

A

C

B

A

R

a











(5)





2 2

2

3335

.

0 17037

.

239 099073

.

0 97889

.

1 065367

.

0 40533

.

3 14692

.

3 68222

.

286 73341

.

11 28939

.

360 ,

,

C

B

A

BC

AC

AB

C

B

A

C

B

A

R

a







[image:10.612.135.475.455.520.2]

(6)

TABLE VIII

MODEL SUMMARY STATISTICS

Source

Standard.

Deviation R-Squared

Adjusted R-Squared

Predicted

R-Squared PRESS

Linear 1.79 0.2150 0.1127 -0.0922 102.89

2FI 1.63 0.4392 0.2709 -0.0465 98.58

Quadratic 0.51 0.9523 0.9270 0.8903 10.34 Suggested

Cubic 0.42 0.9814 0.9516 0.9015 9.28 Aliased

TABLE IX

ANOVA FOR RESPONSE SURFACE QUADRATIC MODEL FOR SURFACE ROUGHNESS

Source

Sum of Squares

Degree of freedom

Mean Square

F Value

p-value Prob > F

Model 89.71 9 9.97 37.68 < 0.0001 significant

A-Tool Overhang 1.71 1 1.71 6.45 0.0211

B-Feed Rate 15.06 1 15.06 56.93 < 0.0001

C-Depth of Cut 3.49 1 3.49 13.20 0.0021

AB 19.57 1 19.57 73.98 < 0.0001

AC 1.28 1 1.28 4.85 0.0418

BC 0.26 1 0.26 1.00 0.3315

A^2 36.81 1 36.81 139.16 < 0.0001

B^2 10.86 1 10.86 41.06 < 0.0001

C^2 0.67 1 0.67 2.52 0.1306

Residual 4.50 17 0.26

[image:10.612.139.475.558.704.2]

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International Journal of Emerging Technology and Advanced Engineering

64

TABLE X

QUADRATIC MODEL STATISTICS``

Std. Dev. 0.51 R-Squared 0.9523

Mean 7.17 Adjusted R-Squared 0.9270

C.V. % 7.17 Predicted R-Squared 0.8903

PRESS 10.34 Adequacy Precision 22.671

The predicted values of the surface roughness

R

_a are generated from Equation (6), and a plot of

R

_a against the actual values (Table IV), given in Fig 15, illustrates how well the predicted R_a data fits the actual data. As

shown in Fig. 16, R_a has nonlinear relationship with

factors A, B and C, and that the influence of these factors

on

R

_a is equally significant at lower and higher levels. At higher levels of these factors, R_a increased with

increase in A and B, but decreased with increase in C from the reference point. At lower levels of the factors,

a

R

decreased with increase in A and B, but increased with increase in C toward the reference point. The implication of the behavior is that

a

[image:11.612.56.557.112.735.2]

R is minimized when the factors A and B are set at the neighbourhood of the intermediate level of their values, and the factor C set either at the extreme low or high level of its value. These behaviors can also be seen in the contour and response surface plots given in Figs 17 to 22. It can be attributed to the observed multiple interactions of factors.

Figure 15. A Plot of the Predicted R_a against the Actual values

Figure 16. A Plot of

R

_a against the deviation from reference point (Coded Unit) or perturbation

a

R against A and B with C set at 2 mm

[image:11.612.106.235.482.574.2]

Figure 18. A Response surface plot of R_a against A and B with C set at 2 mm

R

_a against A and C with B set at 0.225 mm/rev

Figure 20. A Response surface plot of a

R against A and C with B set at 0.225 mm

Design-Expert® Software Surface Roughness Color points by value of Surface Roughness: 11.510 4.226 Actual P r e d ic te d

Predicted vs. Actual

4.000 6.000 8.000 10.000 12.000

Design-Expert® Software Factor Coding: Actual Surface Roughness (micro mm) Actual Factors A: Tool Overhang = 55 B: Feed Rate = 0.225 C: Depth of Cut = 2

-1.000 -0.500 0.000 0.500 1.000

4.000 6.000 8.000 10.000 12.000 A A B B C C Perturbation

Deviation from Reference Point (Coded Units)

S u r fa c e R o u g h n e s s ( m ic r o m m ) Design-Expert® Software Factor Coding: Actual Surface Roughness (micro mm)

Design Points

11.51

4.226

50 52 54 56 58 60

0.15 0.18 0.21 0.24 0.27

0.3 Surface Roughness (micro mm)

B : F e e d R a te ( m m p e r r e v ) 6 8 8 10 Design-Expert® Software Factor Coding: Actual Surface Roughness (micro mm)

11.51

4.226

0.15 0.18 0.21 0.24 0.27 0.3 50 52 54 56 58 60 2 4 6 8 10 12 S u r fa c e R o u g h n e s s ( m ic r o m m )

A: Tool Overhang (mm) B: Feed Rate (mm per rev)

Design-Expert® Software Factor Coding: Actual Surface Roughness (micro mm)

Design Points

11.51

4.226

50 52 54 56 58 60

1 1.5 2 2.5

3 Surface Roughness (micro mm)

C : D e p th o f C u t ( m m ) 5 5 6 6 7 7 Design-Expert® Software Factor Coding: Actual Surface Roughness (micro mm)

11.51

4.226

1 1.5 2 2.5 3 50 52 54 56 58 60 2 4 6 8 10 12 S u r fa c e R o u g h n e s s ( m ic r o m m )

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International Journal of Emerging Technology and Advanced Engineering

[image:12.612.60.520.106.562.2]

65 R

_a against B and C with A set at 55 mm

Figure 22. 55 mm; (b) A Response surface plot of

R

_a against B and C with A set at 55 mm

C. Parameter Optimization

The machining induced vibration (

V

_i) of the cutting tool, and the surface roughness (

R

_a) of the specimen work-piece are undesirable process characteristics that are required to be minimized to improve on product quality. Both are uncontrollable, and therefore, were measured with standard instruments in the turning experiment. Within the selected design space, the optimum setting of the considered factors A at 58.2409 mm, B at 0.170594 mm/rev, and C at 1.2192 mm, would

minimize

V

_i to a value of 0.09 mm/s2 and

R

_a to a value of 5.591 µmm as given in the ramps of Fig 13, with desirability of 0.850. As shown in Fig. 23 and

confirmed by the contour and surface plots of

V

_i and

a

R

are both minimized at lower values of B and C, and higher value A.

Figure 23. Ramps of the Optimum Setting of Factors, which Minimized the Surface Roughness and Machining Induced Vibration

D. Surface Roughness vs Machining Induced Vibration

Normally, the machining induced vibration (

V

_i) is expected to have influence on surface roughness (

R

_a) as it impacts negatively on the cutting zone in turning operations.

However, as shown in the plot of

R

_a versus

V

_i

given in Fig 24, there is nonlinear relationship, but no significant correlation between these process characteristics within the experimental design limits as can be seen from the R-square value of the trend line of 0.0561, but there may be correlation outside these limits.

Design Points

11.51

4.226

0.15 0.18 0.21 0.24 0.27 0.3

1 1.5 2 2.5

3 Surface Roughness (micro mm)

B: Feed Rate (mm per rev)

C

:

D

e

p

th

o

f

C

u

t

(

m

)

4

5

5 6

7

11.51

4.226

1 1.5 2 2.5 3

0.15 0.18

0.21 0.24

0.27 0.3 2

4 6 8 10 12

S

u

r

fa

c

e

R

o

u

g

h

n

e

s

(

m

ic

r

o

m

)

B: Feed Rate (mm per rev) C: Depth of Cut (mm)

A:Tool Overhang = 58.2409

50 60

B:Feed Rate = 0.170594

0.15 0.3

C:Depth of Cut = 1.2192

1 3

Acceleration Amplitude = 0.09

0.04 0.48

Surface Roughness = 5.591

4.226 11.510

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International Journal of Emerging Technology and Advanced Engineering

[image:13.612.139.472.135.305.2]

66

Figure 24. A plot of

R

_a against

V

_i

IV. CONCLUSION

A turning experiment was conducted on 41Cr4 alloy special steel with standard cutting tool and measuring instruments. The response surface methodology, based on the central composite design of experiment was used to model, predict and optimize the machining induced vibration and surface roughness as functions of the tool overhang, feed rate and depth of cut. Analyses and optimization of the response characteristics data was performed in the Design Expert version 9.0.6.2 software environment. It was found that:

a. The developed quadratic regression models can be used for accurate prediction of the selected process characteristics within limits of the selected factors. b. The machining induced vibration of the cutting tool

has nonlinear relationships with the tool overhang, feed rate and the depth of cut. The effect of these factors on the machining induced vibration is more significant at the higher levels of their values, when compared to the same effect at lower levels of their values. Also, the machining induced vibration would be minimized when the factors are set at values within the lower levels of the factors. An exception is the tool overhang whose value must be set a higher level. c. The surface roughness of the work-piece also has

nonlinear relationship with the tool overhang, feed rate and the depth of cut. The effect of tool the overhang and feed rate on the surface roughness are quite significant both at lower and higher levels of their values. There is no significant effect of the depth of cut on this parameter. The surface roughness is minimized at neighbourhood of the intermediate levels of the factors.

An exception is the depth of cut whose value set at the high level would lead to minimization of the surface roughness

d.Within the selected design space, the optimum setting of the considered factors A at 58.2409 mm, B at 0.170594 mm/rev, and C at 1.2192 mm, would

minimize

V

_i to a value of 0.09 mm/s2 and

R

_a to a value of 5.591 µmm, with desirability of 0.850. e. Also within the selected design space, there is

nonlinear relationship, but there is no significant correlation between the surface roughness and the machining induced vibration, as can be seen from the R-square value of 0.0561. However, there may be correlation outside this limits.

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