research article surface roughness models and their...

Research ArticleSurface Roughness Models and Their ExperimentalValidation in Micro Milling of 6061-T6 Al Alloy by ResponseSurface Methodology

Jie Yi, Li Jiao, Xibin Wang, Junfeng Xiang, Meixia Yuan, and Shoufeng Gao

Key Laboratory of Fundamental Science for Advanced Machining, Beijing Institute of Technology, Beijing 100081, China

Correspondence should be addressed to Li Jiao; [email protected]

Received 25 May 2015; Accepted 28 July 2015

Academic Editor: John D. Clayton

Copyright © 2015 Jie Yi et al. This is an open access article distributed under the Creative Commons Attribution License, whichpermits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Due to the widespread use of high-accuracy miniature and micro features or components, it is required to predict the machinedsurface performance of the micro milling processes. In this paper, a new predictive model of the surface roughness is established byresponse surface method (RSM) according to the micro milling experiment of 6061-T6 aluminum alloy which is carried out basedon the central composite circumscribed (CCC) design. Then the model is used to analyze the effects of parameters on the surfaceroughness, and it can be concluded that the surface roughness increases with the increasing of the feed rate and the decreasing ofthe spindle speed. At last, based on the model the contour map of the surface roughness and material removal rate is establishedfor optimizing the process parameters to improve the cutting efficiency with good surface roughness. The prediction results fromthe model have good agreement with the experimental results.

1. Introduction

The aluminum and aluminum alloy, with its excellent inher-ent qualities such as small density, high intensity, good con-ductive thermal conductivity, and good corrosion resistance,can easily be processed. Aluminum and its derivatives havebeen widely used in the industries of national economy anddefense, especially in light structure material, light weight,strength, air, sea, and land and all kinds of vehicles, especiallyaircraft, missile, rocket, and the artificial earth satellite, whichneed to use a lot of aluminum. The hardness of 6061-T6 Alalloy has a wider range of application and has gained favorover the years in the industry. Because of the 6061-T6 Al alloyexcellent plasticity it can be molded into any particular shapeof radiator, especially small engines.

Micro manufacturing is defined as a scaling-down ofconventional technologies or process in order tomanufacturemicro products/features [1]. Micro milling is one of micromanufacturing processes that have the ability to producemicro products with complex shape. Surface and size effectbegins to dominate material response and behavior dueto the scaling-down effect [2]. The application of micro

milling technology in complex precision three-dimensionalsmall parts manufacturing has caused major technologicalchange in the field of micro manufacturing. Comparedwith traditional milling method, MEMS and ultra-precisionmachining technology are effective means to manufacturemicro and middle scale small parts with high efficiency andhigh precision. What is more, MEMS and ultra-precisionmachining technology can realize the unique advantages[3, 4] of the three-dimensional curved surface machining,so it received extensive attention of experts and scholarsdomestically and overseas.

Surface finish is an important measure of the technolog-ical quality of a product and a factor that greatly influencesmanufacturing cost. Surface roughness has received seriousattentions for many years. It has formulated an importantdesign feature in many situations such as parts subject tofatigue loads, precision fits, fastener holes, and aestheticrequirements. In addition to tolerance, surface roughnessimposes one of the most critical constraints for selection ofmachines and cutting parameters in process planning [5].For achieving the desired surface finish, it is necessary tounderstand the mechanisms of the material removal and

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015, Article ID 702186, 9 pageshttp://dx.doi.org/10.1155/2015/702186

2 Mathematical Problems in Engineering

the kinetics of machining processes affecting the perfor-mance of the cutting tool [6].

Certain theories and principles have been proposed bythe researchers who have used conventional macro-machinetools. In the recent years, micro machining became populardue to the development of miniaturized industries. Theexistence of the minimum cutting thickness, the influenceof the scale effect, and the strengthening of the nonfreecutting give rise to a difference between conventional millingand micro milling. Therefore, further study of micro millingcondition influences the process parameters on surfaceroughness and machining before the selection of cuttingparameters, forecast, and control in order to achieve the goalof the surface roughness. Lou et al. examined the multipleregressionmodels for finished surface prediction [7]. Taguchistatistical method was used by Yang and Chen [8] and Ghaniet al. [9] for optimummilling parameters. Recently, Ben Fredjet al. developed surface roughness prediction model usingdesign of experiment method and the neural network [10].Thepsonthi and Ozel [11] studied the chip flow and tool wearof Ti-6Al-4V titaniumalloy inmicro-endmilling. Kopac et al.used signal-to-noise response method to analyze the surfaceroughness with turning [12]; Benardos and Vosniakos intro-duced the prediction method to predict surface roughnessin machining [13]. Kiswanto et al. [14] researched about theeffect of spindle speed, feed rate, and machining time to thesurface roughness and burr formation of aluminum alloy1100 in micro milling operation. Kant and Sangwan [15] usedartificial neural network coupled with Genetic Algorithmfor predictive modelling and optimization of machiningparameters to minimize surface roughness. Campatelli etal. [16] used the response surface method to optimize theprocess parameters for minimizing power consumption inthe milling of carbon steel. However, the research workmentioned above used the conventional machine tool. Theresults could not suit themicromachining. In this paper, newsurface roughness prediction model is developed based onmicro milling process. In the present work, a mathematicalmodel has been developed to predict the surface roughnessof milling 6061-T6 Al alloy using response surface method(RSM). Analysis of variance (ANOVA) is used to checkthe validity of the model and 𝐹-test is used to find thesignificant parameters. The surface roughness and the equiv-alent response of the surface can therefore be established.This model can be effectively used to predict the surfaceroughness of the milled 6061-T6 Al alloy. Some experimentshave been conducted to find the proper important parametersto maximize material removal rate and minimize surfaceroughness.

2. Experimental Scheme and Design

2.1. Central Composite Designs (CCDs). Combination designis generally the test plan which is formed by putting onecombination of regression design point and some specificsites together. Therefore, combination can greatly reducethe number of test designs and can make the secondarydesign on the basis of one design. The design can satisfy theorthogonal concept by adjusting the asterisk arm. The most

Table 1: Similarities and differences of CCC, CCI, and CCF.

CCC CCI CCFDesign domain shape Sphere Sphere CubicDesign level 5 5 3Complexity High High LowFactorial points position ±1 ±0.7 ±1Axial points position 𝛼 = √𝑘 𝛼 = 1.0 𝛼 = 1.0

Recommend the centernumber 3∼5 3∼5 1∼2

Rotatability Rotatable Rotatable Not rotatableUniformity of predictionerror Good Good Bad

Model based parameterestimation Most effective Worst Second

Extrapolation of robustness Second Best SecondWhere 𝑘 is the number of the variables and 𝛼 is the axial distance.

X1

X2

X3

Figure 1: The sketch of CCC design.

well-known and recommended Central Composite Design isa repeat order strategy that is part of the experiment in thedesign of the second order. Central Composite Design hasthree typeswhich are central composite circumscribed design(CCC), central composite inscribed design (CCI), and centralcomposite face-centered design (CCF). Each variable of CCCand CCI requires 5 levels, but CCF only needs 3 levels. Thecomparison [17] of similarities and differences of CCC, CCI,and CCF is shown in Table 1. Compared with the CCF, theprediction error precision of CCC has good consistency andCCC improves the square effect estimates. Furthermore CCCis the most effective method in estimating model parameter.So the design of CCC is adopted in the experiment, and itsdiagram is shown in Figure 1.

2.2. Response Surface Modeling Method. Response surfacemethod is a nonlinear regression which combines prin-ciples of mathematics, statistics, and experimental designtechnique; it also explores the mathematical relationshipbetween influence factors and the response output. A processor system contains the response 𝑦(𝑥), which depends onthe input factors 𝑥1, 𝑥2, . . . , 𝑥𝑝, if there is a linear function

Mathematical Problems in Engineering 3

Uncut chip thickness

Surface roughness

Workpiece

Chip

Tool edge radius

Feed rate Tool

Figure 2: Schematic of tool-workpiece interaction.

relation between response and the independent variables; theapproximate function is the first-order model:

𝑦 (𝑥) = 𝛽0 +

𝑛

∑

𝑖=1

𝛽𝑖𝑥𝑖 + 𝜀, (1)

where 𝛽0 is constant and 𝛽𝑖 is 𝑥𝑖 the linear effect and 𝜀 is theerror.

The studied relationship between response𝑦(𝑥) and input𝑥1, 𝑥2, . . . , 𝑥𝑝 is called response surface research.The second-order response surface model considered the interactioneffect and the second-order effect, which can be expressed as

𝑦 (𝑥) = 𝛽0 +

𝑛

∑

𝑖=1

𝛽𝑖𝑥𝑖 +

𝑛−1

∑

𝑖=1

𝑛

∑

𝑗=𝑖+1

𝛽𝑖𝑗𝑥𝑖𝑥𝑗 +

𝑛

∑

𝑖=1

𝛽𝑖𝑖𝑥2

𝑖+ 𝜀, (2)

where 𝛽𝑖𝑗 is the interaction effect between 𝑥𝑖 and 𝑥𝑗 and 𝛽𝑖𝑖 isthe second-order effect of 𝑥𝑖.

Spindle speed (𝑥1), feed rate (𝑥2), and depth of cut (𝑥3)will affect the value of the surface roughness. In order to accu-rately understand the effects of the processing parameters onsurface roughness, response surface method is adopted toestablish the relationship between the surface roughness andmachining parameters. The model is as follows:

𝑅𝑎 = 𝛽0 + 𝛽1𝑥1 + 𝛽2𝑥2 + 𝛽3𝑥3 + 𝛽12𝑥1𝑥2 + 𝛽13𝑥1𝑥3

+ 𝛽23𝑥2𝑥3 + 𝛽11𝑥2

1+ 𝛽22𝑥

2

2+ 𝛽33𝑥

2

3+ 𝜀,

(3)

where 𝑅𝑎 represents surface roughness.The purpose of the test is to obtain a set of optimum

processing parameters to get the best surface quality.Throughthe response of the surface method analysis, various factorsregarding the response value in the regression model caneventually respond as a predictive value achieving optimiza-tion by determining reasonable level combination.

2.3. Micro Milling Mechanics. As shown in Figure 2, inmicro scale cutting, a great number of critical issues, such astool edge radius, negative rake angle, elastic deformation ofmachined surface,minimumchip thickness, andmicro struc-ture become prominent when uncut chip thickness becomescomparable to the tool edge radius or grain size of workmaterials.These issuesmay be categorized as size effect whichcan influence underlying cutting mechanisms by alteringcutting forces, the chip formation process, burr formation,vibration and process stability, energy consumption, andgeneration of the machined surface.

Workpiece

Feed per tooth

Minimum chip thickness

Ploughing zoneFeed rate

Shearing zone

Figure 3: 2D view of full-immersion of ploughing and shearingmechanisms in micro-end milling.

Because of an intermittent cutting mechanism for micromilling, uncut chip thickness in the radial direction for eachcutting passage varies fromzero to the feed per tooth and thento zero. It is thus inevitable to encounter ploughing or rubbingin theminimum chip thickness effect. In cases where the feedper tooth is larger than minimum chip thickness, ploughingand shearing mechanisms are present in one cutting passage,as shown in Figure 3. The ploughing mechanism becomesdominant when the radial depth of cut is smaller thanminimum chip thickness. However, once radial depth of cutis larger than minimum chip thickness, shearing of workmaterials takes place and chips can be formed. Ploughingdominant zones are located at the entrance and exit of thepassage while the rest of the zone is dominated by shearing.In cases where feed per tooth is smaller than minimumchip thickness, there are probably no chips formed duringseveral consecutive revolutions of cutting on account of theploughing dominantmechanism and elastic recovery of workmaterials.

2.4. Experimental Process and Results. Because of the influ-ence regarding the surface shape error and other factors, theworkpiece zero cross section is not easy to directly determine.In order to eliminate the error, zero planes must be generatedby milling in advance, and then micro groove structureswhose length is 5mm were milled on the datum plane.Diagram of micro milling process is shown in Figure 4. AndFigure 5 shows the machining status of micro milling.

Theworkpiece 6061-T6 Al alloy wasmilled by a cementedcarbide micro milling cutter with diameter being 1mm andthe number of teeth being 2, as shown in Figure 6. Thematerial mechanical and physical properties of 6061-T6 Alalloy are given in Table 2. Test chose high spindle speed,small axial feed, and depth of cut. And three-factor five-levelorthogonal test was designed. The orthogonal experimentfactor level distribution is shown in Table 3. Assume that𝑥1, 𝑥2, and 𝑥3 represent the spindle speed (𝑛), feed rate (𝑓),and depth of cut (𝑎𝑝), respectively. At the same time, the


Table 2: Typical mechanical and physical properties of 6061-T6 Al alloy.

Tensile strength 𝜎𝑢(MPa) Yield strength 𝜎

𝑠(MPa) Hardness (HB) Density (g/cm3) Young’s modulus 𝐸 (GPa) Poisson ratio

310 276 95 2.7 70 0.33

Table 3: Important factors and their levels.

Parameter Notation Unit Levels−2 −1 0 1 2

Spindle speed 𝑛 𝑥1 r/min 10000 12000 14000 16000 18000Feed rate 𝑓 𝑥2 𝜇m/r 0.4 0.8 1.2 1.6 2.0Depth of cut 𝑎𝑝 𝑥3 𝜇m 10 20 30 40 50

Table 4: The test design matrix and results.

S.number

Design 𝑅𝑎, average surfaceroughness (𝜇m)𝑥1 𝑥2 𝑥3 𝑥

2

1𝑥2

2𝑥2

3𝑥1𝑥2 𝑥1𝑥3 𝑥2𝑥3

1 −1 −1 −1 1 1 1 1 1 1 1.3152 1 −1 −1 1 1 1 −1 −1 1 1.0163 −1 1 −1 1 1 1 −1 1 −1 1.4364 1 1 −1 1 1 1 1 −1 −1 1.0015 −1 −1 1 1 1 1 1 −1 −1 1.5036 1 −1 1 1 1 1 −1 1 −1 1.1177 −1 1 1 1 1 1 −1 −1 1 1.4028 1 1 1 1 1 1 1 1 1 1.3019 −2 0 0 4 0 0 0 0 0 1.51110 2 0 0 4 0 0 0 0 0 1.11311 0 −2 0 0 4 0 0 0 0 1.00812 0 2 0 0 4 0 0 0 0 1.34913 0 0 −2 0 0 4 0 0 0 1.16514 0 0 2 0 0 4 0 0 0 1.30415 0 0 0 0 0 0 0 0 0 1.27116 0 0 0 0 0 0 0 0 0 1.26917 0 0 0 0 0 0 0 0 0 1.23818 0 0 0 0 0 0 0 0 0 1.25619 0 0 0 0 0 0 0 0 0 1.247

processing parameters ranges are determined: the range ofparameter 𝑛 is 10000∼18000 r/min, 𝑓 is 4∼36mm/min, and𝑎𝑝 is 0.01∼0.05mm.The milling test numbers are 19. Accord-ing to statistical inference, the average surface roughnessvalue can be measured and obtained by taking the averagefive groups of experimental data. In Figure 7, it shows themethod to obtain the average surface roughness whose valueis 1.271 𝜇m with the cutting parameters 𝑛 = 14000 r/min, 𝑓= 1.2 𝜇m/z, and 𝑎𝑝 = 30 𝜇m, and test results are shown inTable 4 and Figure 8.

3. Experimental Results Discussion

From Figure 8, the range of the average surface roughness isdifferent. Comparing the red I-shaped line (𝑅𝑎 = 1.511 𝜇m)with the green I-shaped line (𝑅𝑎 = 1.001 𝜇m), the range of the

Referenceplane

Milling cutter

Workpiece

n

ap

�f

Figure 4: Diagram of micro milling 6061-T6 Al alloy process.

Figure 5: Machining status of micro milling.

red one is obviously larger than the green one.This is becausethe cutting parameters in the green one are better than thered one.

From Table 3, the experimental factors of free vari-ables and surface roughness are converted into matrix formthrough the test parameter transformation; then (3) coeffi-cient can be found by using the least squares regression, so themultivariate regression empirical formula between surfaceroughness and cutting parameters is established. The finalmodel was developed in coded values and is given as follows:

𝑅𝑎 = 1.26 − 0.128𝑥1 + 0.0568𝑥2 + 0.0544𝑥3

+ 0.0233𝑥1𝑥2 + 0.0356𝑥1𝑥3 − 0.0189𝑥2𝑥3

+ 0.0149𝑥2

1− 0.0185𝑥

2

2− 0.0045𝑥

2

3.

(4)

The adequacy of the model is checked by using the analy-sis of variance (ANOVA) technique. As this technique, if thecalculated value of the 𝐹 ratio of the developed model doesexceed the standard tabulated value of 𝐹 ratio for a desiredlevel of confidence (say 99%), then the model is consideredto be adequate within the desired limit. ANOVA and 𝐹-testresults are presented in Table 5. The value of 𝐹0.01 (9, 9)equals 5.35 which is less than the fitting 𝐹-value that equals7.06 in the present research, and hence the developed modelmay be accepted. The regression equation was analyzed


Table 5: Analysis of variance for surface roughness.

Source 𝐷𝐹𝑎 Sum of squares Mean square 𝐹-value 𝐹-tab

Regression 9 0.376 0.041 7.06 5.35Residual error 9 0.0532 0.006Total 18 0.675 7.06 > 5.35

100.000 𝜇m

Figure 6: Micro milling cutter.

180.0

160.0

140.0

120.0

100.0

80.0

60.0

40.0

20.0

0.0

1000.0

500.0

0.0

(𝜇m

)

(𝜇m

)

(𝜇m)

(𝜇m)

(𝜇m)

(𝜇m)

(𝜇m

)(𝜇

m)

(𝜇m

)

(𝜇m

)(𝜇

m)

(𝜇m

)

(𝜇m)

(𝜇m)

1418.1

184.3

0.0

133.840130.000

124.210

133.134130.000

123.112

134.348130.000

124.464

132.872130.000

124.189

133.394130.000

124.945

0.000 100.000 200.802

0.000 100.000 200.109

0.000 100.000 200.109

0.000 100.000 200.802

0.000 100.000 200.802

500.0 1000.0

0.0

Ra1 = 1.265𝜇m

Ra2 = 1.261𝜇m

Ra3 = 1.271𝜇m

Ra4 = 1.273 𝜇m

Ra5 = 1.285 𝜇m

Figure 7: Schematic diagram of obtaining average surface roughness.

19181716151413121110987654321

1.6

1.5

1.4

1.3

1.2

1.1

1.0

0.9

1.247

1.256

1.2381.2691.271

1.304

1.165

1.349

1.008

1.113

1.511

1.031

1.402

1.117

1.503

1.001

1.436

1.016

1.315

Experimental number

Aver

age s

urfa

ce ro

ughn

ess (𝜇

m)

Figure 8: Plot of average surface roughness.


2

1

0

−1

−2

−0.15 −0.10 −0.05 0.00 0.05 0.10

Residual error

Valu

e of e

xpec

tatio

n

Figure 9: Rankit plot of the regression model.

11020

3040

50

0.81

1.6

1.61.8

1.4

1.4

1.2

1.2Depth of cut (𝜇m)

Surfa

ce ro

ughn

ess (𝜇

m)

×104

Spindle speed (r/min)

Figure 10: The influence of surface roughness by spindle speed anddepth of cut (f = 1.2 𝜇m/r).

by variance and 𝐹-tests that indicate the prediction modelhas significant state, fitting well with the actual situation.Micro milling predicted the surface roughness of hard 6061aluminum alloy which has higher credibility.

Further, as shown in Figure 9 which is the modelof residual analysis Rankit, residual error and the value ofexpectations have a near linear relationship. As a result, theregression equationmodel is suitable, the analysis of varianceis credible, and the regression model is effective.

According to (4), the figures of the surface roughnessmodel can be drawn, so the influence law of parameters onsurface roughness is obtained, as shown in Figures 10∼12:

(a) Figure 10 shows that the surface roughness valuedecreases obviously with increasing of spindle speedunder the condition with 𝑎𝑝 = 10∼50 𝜇m and 𝑓 =1.2 𝜇m/r. And the surface roughness (𝑅𝑎) is closeto 0.8 𝜇m when spindle speed is nearly 18000 r/minand depth of cut’s value is the minimum. Thereforeimproving spindle speed has significant effect onreducing the surface roughness.

(b) In Figure 11, the change of surface roughness’s valuewas not large with increasing of feed rate under thelow spindle speed and depth of cut. But increasingfeed rate has significant effect on surface roughnesswhen the spindle speed reaches 16000 r/min, and

0.81

1.61.41.2

1

1.61.8

1.41.200.5

11.5

2Surfa

ce ro

ughn

ess (𝜇

m)

×104

Spindle speed (r/min)Feed rate (𝜇m/r)

Figure 11: The influence of surface roughness by spindle speed andfeeding rate (𝑎𝑝 = 30 𝜇m).

0.8

1

1.6

1.4

1.2

00.5

11.5

2

10 2030

4050

Depth of cut (𝜇m)

Surfa

ce ro

ughn

ess (𝜇

m)

Feed rate (𝜇m/r)

Figure 12: The influence of surface roughness by depth of cut andfeeding rate (𝑛 = 14000 r/min).

the result is that surface roughness’s value is increas-ing. When the spindle speed is between 15000 and17000 r/min, it has a little influence on the surfaceroughness value. At this area, the relatively stablemachining surface quality can be obtained (𝑅𝑎 =0.7 𝜇m).

(c) Figure 12 shows that the value of surface roughnessbecomes large with increasing of feed rate and depthof cut with 𝑛 = 14000 r/min. And the feed rate hasgreater influence on the surface roughness than depthof cut.The value of surface roughness is theminimumwhen depth of cut and feed rate are the minimumvalue.

The profile of machined surface mainly depends on thefeed rate.The distance between two adjacent profiles becomeslarger when the feed rate is increased as shown in Figure 13.And from Figure 13, there is another conclusion where theheight of burr becomes smaller with increasing of the feedrate. Maybe this is because of size effect where the cuttingedge radius is less than the grain size of 6061-T6 Al alloy.Another reason is the chips stick together for Al alloy’scohesive property. Hence the burr is high because the chipis difficult to remove.

In regression analysis, the significance of regression equa-tion does not mean that the influence of each independentvariable on the dependent variable is important. Test ofregression coefficients is needed where the purpose is to


Table 6: Significance test analysis of regression coefficient.

𝛽1

𝛽2

𝛽3

𝛽11

𝛽22

𝛽33

𝛽12

𝛽13

𝛽23

𝑃 value 0.000 0.018 0.022 0.372 0.272 0.782 0.431 0.240 0.562Significant degree (1) (2) (3) (6) (5) (9) (7) (4) (8)

70.0

60.0

50.0

40.0

30.0

20.0

10.0

0.0

1000.0

1000.0

500.0

500.0

0.0

0.0

(𝜇m

)

(𝜇m

) (𝜇m

)

1418.1

71.7

(𝜇m)

100.000 𝜇m

(a) Feed rate is 1.2𝜇m/r

60.0

50.0

40.0

30.0

20.0

10.0

0.0

1000.0

500.0

0.01000.0500.00.0

(𝜇m

)

(𝜇m)

(𝜇m

)

(𝜇m

)

1418.1

64.8

100.000 𝜇m

(b) Feed rate is 1.6𝜇m/r

50.0

40.0

30.0

20.0

10.0

0.0

1000.0

500.0

0.0

1000.0500.00.0

(𝜇m

)

(𝜇m

) (𝜇m

)

1418.1

56.8

(𝜇m)

100.000 𝜇m

(c) Feed rate is 2.0𝜇m/r

Figure 13: The profile of machined surface by micro milling process with 1mmmilling cutter (𝑛 = 14000 r/min, 𝑎𝑝 = 10𝜇m).

examine significant degree of each independent variable onthe dependent variable and thereby test results can be betterforecasted and controlled. Table 6 is the significance testanalysis of regression coefficients.

From Table 6, the difference of influence on surfaceroughness prediction model by the spindle speed, depth of

cut, and feed rate can be seen. Spindle speed and feed ratehave significant influence on surface roughness. Improvingthe spindle speed and reducing feed rate and depth of cutcan effectively reduce the micro milling surface roughnessvalues under this experimental condition. The comparisonof surface roughness between the predicted values which


Table 7: Results of verification tests.

Number 𝑛 [r/min] 𝑓 [𝜇m/r] 𝑎𝑝 [𝜇m] Surface roughness 𝑅𝑎[𝜇m]

Predicted value Experimental value1 10000 2.0 50 1.395 1.3592 12000 1.2 40 1.417 1.4003 14000 1.6 10 1.209 1.2484 16000 2.0 30 1.233 1.1955 18000 1.6 30 1.149 1.186

Experimental number54321

1.45

1.40

1.35

1.30

1.25

1.20

1.15

1.10

1.186

1.195

1.248

1.40

1.233

1.209

1.395

1.359

1.149

1.417

Experimental valuePredicted value

Experimental valuePredicted value

Surfa

ce ro

ughn

ess (𝜇

m)

Figure 14: Comparison predicted with experimental value ofsurface roughness.

obtained by (4) through the quadratic response surface andexperimental values is shown in Table 7 and Figure 14,and from Table 7, the error between predicted value andexperimental value is less than 3.13%, so the error is allowableand the accuracy of the prediction model is proved.

In the optimization of cutting parameters, the valuerange of factors which have great effect must be determinedto ensure the 𝑅𝑎 value of the mechanical parts. And forthe choice of small effect factors, improving the machiningefficiency in relation to the parts should be considered. Thematerial removal rate [18] can be defined as

𝑄 =

𝜋𝐷𝑛𝑓𝑎𝑝

1000. (5)

From Table 3 and (4), it can be concluded that

𝑅𝑎 = 3.4123 − 2.5665 × 10−4𝑛 + 0.1535𝑓 − 0.01111𝑎𝑝

+ 3.725 × 10−9𝑛2− 0.115625𝑓

2− 4.5 × 10

−5𝑎2

𝑝

+ 2.9125 × 10−5𝑛𝑓 + 1.78 × 10

−6𝑛𝑎𝑝 − 4.725

× 10−3𝑓𝑎𝑝.

(6)

1832.5957

1832.5957

1832.59571832.5957

3577.2268

3577.2268

3577.2268

5321.858

5321.858

7066.4891

8811.1202

1.0003

1.0003

1.1099

1.1099

1.1099

1.1099

1.2195

1.2195

1.2195

1.2195

1.2195

1.3291

1.329

11.3291

1.3291

1 2 310

20

30

40

50

60

70

80

0.5 1.5 2.5

AB

C

D

E

Dep

th o

f cut

(𝜇m

)

QRa

Feed rate (𝜇m/r)

Figure 15: Contours of surface roughness and metal removal rate at𝑛 = 14000 r/min.

In the process of micro milling, the purpose of optimiz-ing the cutting parameters is to improve cutting efficiencyunder the premise without increasing the surface roughness.Combining the above analysis, the determination of the scopeof 𝑛 can ensure the value of 𝑅𝑎. Then appropriate 𝑓 and𝑎𝑝 are chosen to improve the value of 𝑄. Assume that 𝑛 =14000 r/min and combine (5) and (6); the contour between𝑅𝑎 and 𝑄 can be drawn as shown in Figure 15.

From Figure 15, the contours of 𝑅𝑎 = 1.3291 𝜇m and 𝑄 =1832.5957, 3577.2268, 5321.858mm3/min intersect at points A,B, and C which show that these three groups of processingparameters have the same 𝑅𝑎 value. However, at point C themachining efficiency is much higher than A and B; therefore,the metal removal rate of C is larger than that of A and B.In addition, under the same processing efficiency, the bestsurface quality can also be acquired by selecting reasonableparameters. From the contour lines of𝑄= 5321.858mm3/minit can be seen that point E processing parameters of 𝑅𝑎value are smaller than C and D. Therefore, in the actualprocessing, the optimal processing parameters ultimately canbe determined by a combination of the specific productionconditions.The optimalmethodmay be not precisely to showthe better parameters which will make the minimum surfaceroughness and the maximummetal removal rate. However, itcan give the manufacturing engineer the approximate valueof surface roughness and metal removal rate which caneffectively help them to choose the proper cutting parameterswhen machining the similar material. Because of the timeand the length of the paper, in the long future, a lot of new


optimization techniques such as artificial neural network andGenetic Algorithm should be considered andmade better useof to improve the surface finish.

4. Conclusion

A new mathematical model has been developed to predictthe surface roughness of micro milling of 6061-T6 aluminumalloy.The experimental plan is based on the central compositecircumscribed (CCC) design. The validity of the model ischecked by ANOVA and 𝐹-test. The following conclusionscan be drawn as follows:

(a) A new surface roughness model is built using theRSMmethod formicromilling process, in which feedrate, spindle speed, and depth of cut are considered.Upon examination, the model has high confidenceand practicality in the test conditions. The modelcan be used to select proper cutting parameters inorder to predict and control surface roughness beforemachining.

(b) The surface roughness increases with the increasingof feed rate and the decreasing of the spindle speed.

(c) With the increasing feed rate, the distance betweentwo adjacent profiles becomes larger, and the heightof burr becomes smaller.

(d) After determining the scope of the main factors,the contour map between the surface roughness andmaterial removal rate can be obtained to optimizethe process parameters under the specific productionconditions.

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper.

Acknowledgment

The authors wish to acknowledge the financial support forthis research from the National Natural Science Foundationof China (Item no. 51105035).

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