DESIGN OF EXPERIMENTS (DOE) IN INVESTIGATION OF CUTTING ...

Drégelyi-Kiss Á., Horváth R. Mikó B.: Design of experiments (DOE) in investigation of cutting technologies; in Development in Machining Technology Vol.3. Ed.: W. Zebala, I. Manková; Cracow University of Tehnology 2013. p.20-34. ISBN 978-83-7242-697-0

DESIGN OF EXPERIMENTS (DOE) IN INVESTIGATION OF CUTTING TECHNOLOGIES Drégelyi-Kiss Á, Horváth R, Mikó B. Óbuda University Abstract: This paper contains the short description of design of experiment (DOE) methods, and practical suggestion about the use of them. In the second part the successful application of these methods are demonstrated by four actual projects from the field of cutting technology Keywords: DOE methods, pocket milling, 3D surface milling, die-case aluminium turning Introduction The general purpose of Design of Experiments (DOE) is to maximize the available information obtained by given amount of experiments with the help of well-chosen designs. The manufacturing parameters could not be searched with the test of all possible setting parameters; the output parameter is examined with few, appropriate experiments, and on the basis of the results the right manufacturing setting could be obtained. These experiments must be designed in advance to get the utmost information with the lowest cost and time. In the course of Design of Experiments clear purpose must be chosen. The target values of the setting parameters must be known precisely, have small fluctuation and must carry enough information. It is important to measure exactly and to determine the dependence of parameters what is intended. The good experiments have small size, minimum cost and well-defined area of validity. The experiments must be executed between real circumstances. Before the execution of the experiments there are more to do. First of all the accuracy, precision and resolution of the measurement devices have to be controlled and then let design the experiment as simple as it can be. It is useful to control whether every experiment can be performed. It is important to register all the data arisen during the experiments. There is a misstatement that plenty large enough experiment will answer to our questions. It is better to make a small design first, and then make another one in view of the previous results. From the analysis of the made experiments could be studied continuously, the nature of manufacturing process is recognised, which is more efficient procedure.

Describing the manufacturing process (Figure 1) it can be seen that there are input variables (raw material, incoming parts) which change into final product. The product has various quality characteristics (critical to quality values, CTQ) which depend on the functioning of the process. The manufacturing process and the result of the production are affected by various effects which are the so-called factors. The factors determine the quality of the product.

Figure 1. Process model

The factors could be divided into two types regarding their setting. There are controllable factors which could be set precisely during the manufacturing process, such as feed, cutting speed, depth of the cut. The other part of the factors are the so-called noise factors, which could affect the manufacturing process, but it is not able to set exactly, such as environmental conditions, temperature fluctuation, changes in the incoming material. The factors can be interpreted in two scales; there are quantitative and qualitative factors. The quantitative factors could be characterized by a concrete number (e.g. feed, cutting speed, etc.), the qualitative factors are defined at nominal scale (e.g. type of the material). The setting values of the factors are called as the levels of the factors. The number of the levels of the factors depends on the purpose of the experiments, the size of the experimental plan and on the characteristics of the effect which should be defined. Two levels are appropriate for the examination of linear effect, three levels for square effects. The more often used plan types are the so-called two-level experimental designs. In the course of these experiments the various factors, which are examined, are set up at two levels. For example let analyse a manufacturing process where it is important to achieve the best possible surface. For this reason some experiments are done. One of the factors could be the type of the

Drégelyi-Kiss Á., Horváth R. Mikó B.: Design of experiments (DOE) in investigation of cutting technologies; in Development in Machining Technology Vol.3. Ed.: W. Zebala, I. Manková; Cracow University of Tehnology 2013. p.20-34. ISBN 978-83-7242-697-

manufacturing device (i.e. A or B manufacturing machine), the other factor could be the velocity of feeding on two levels. In this case there are totally 4 experimental set, if all combinations are examined during the study. The factorial experiments, where all combination of the levels of the factors are run, are usually referred referre to as full factorial experiments. In the cases of fractional factorial designs there are carefully chosen subsets of a full experimental design in order to analyse the main effect of the factors with fewer experimental runs. There are more complicated designs designs of experiments where the factors have 3 or more levels. In this case it is possible to fit quadratic equation on the experimental results [1]. [1]

Figure 2. The types of experimental designs

Choosing the appropriate experimental experimental design it is important to consider what the main purpose of the research is. In the case of manufacturing process, where there is no information about the process itself, it is useful to determine all possible factors which have an effect of the manufacturing manufacturing process with cause and effect techniques, like IshikawaIshikawa (or fishbone-)) diagram. For the first step the factors must be screened, which have significant effect on the result(s) of the examined process. With the using of screening designs the key factors ctors could be chosen with few experimental runs (Figure ( 2). ). To determine the key factors the minimum number of the experimental runs equals to the number of factors plus one. For example in the case of 7 factors the sufficient number for the trials is 8. Increasing the number of experimental runs it could be estimated the effects of some interactions. These fractional factorial designs are used for 4 to 10 factors. In the case of full factorial designs all the main factors and interactions

Drégelyi-Kiss Kiss Á., Horváth R. Mikó B.: Design of experiments (DOE) in investigation of cutting technologies; in Development in Machining Technology Vol.3. Ed.: W. Zebala, I. Manková; Cracow University of Tehnology 2013. p.20-34. ISBN 978-83-7242 7242-697-

could be estimated. Because of the large amount of the experimental runs (e.g. 6 factor means 26=64 experimental runs in a full factorial design) this type of experimental design is used for 1-5 factors. If the parameters affected the manufacturing process is well-known it can be the purpose of the experiment to optimize the output parameter of the process or to determine the response function. These can be terminated by response surface methods which designs are capable of fitting a second-order prediction equation as well. Defining the experimental design consists of the following steps: 1. Defining the problem 2. Determining the factors and their level 3. Determining the output parameter (dependent variable) 4. Choosing the experimental design 5. Doing the experiments 6. Data analysis (perhaps optimization) 7. Conclusion 8. Confirmation with repeated experiments 9. Recommendations During this chapter, several case studies are shown. First of all a pocket milling example is written where the main goal was to estimate the manufacturing time based on geometric parameter of the pocket. In the course of the next study, a 3D surface milling process was analysed where the surface roughness and the manufacturing time as output parameters were estimated with the help of DOE. The third case study is about the Z-level milling where the effects of the milling parameters and the position of the milled surface on the surface roughness were calculated. These three case studies use 2-level factorial designs. The last case study deals with turning aluminium alloys, where equation is calculated on the surface roughness with the help of response surface method of DOE. Pocket milling The manufacturing time estimation is an important phase of the manufacturing process planning. The manufacturing time should be estimated without full process planning, so the time data is estimated based on geometrical parameter. There are lot of methods in the field of estimation [2], the parametric method was used in this current project.


The pocket is an often used geometrical element in machine design. The manufacturing of them is not so complicated, but need more time. Lot of CNC controllers contains rectangular pocket milling cycle. During the pocket milling an H depth rectangular pocket with R radius is manufactured. The tool paths follow the contour of the pocket. Let the J is the number of the cycle in one level, the I is the number of the levels, and the A, B, R and H the geometric parameters of the pocket (Figure 3). If the diameter of the milling cutter is D, than D:=2*R, in order to the shortest tool path length. The length of the tool path and the manufacturing time are calculated based on geometric parameter of the pocket, the tool and process parameter.

Figure 3 Parameters of the pocket and the tool path

Four geometric parameters were selected for the parametric estimation. The type of the milling cutter and the cutting parameters were selected from the Sandvik tool catalogue (R216.34, GC1630), the selected material of the test part was S355 (ISO P). In order to parametric cost estimation several test data are required, and based on these data a mathematical model can be built up. The values of the selected geometric parameters of the pocket were next: A: 40, 50, 60, 80, 100, 150, 200, 250, B: 40, 50, 60, 80, 100, 150, 200, 250, 300, 400 R: 4, 5, 6, 8, 10, 12,5 H: 1, 3, 5, 10, 15, 20 The test was performed in virtual environment, so it was a fast and cheap process, and it allowed generating lot of data. The full factorial experiment plan was used, four parameters in 8, 10, 6 and 6 levels resulted


8x10x6x6=2880 cases. This plane was reduced to 2028 cases by ignore the extreme cases. The calculated data were processed by MiniTab v14 statistical software tool, in order to find connection between the geometric parameters of the pocket and the manufacturing data. After a long iterative analysis the result of the parametric estimation is the next: Regression Analysis: ln t versus A; A2; B; B2; R; H; H2; H3 The regression equation is ln t = 3,33 + 0,0294 A - 0,000066 A2 + 0,0113 B - 0,000013 B2 - 0,299 R + 0,465 H - 0,0254 H2 + 0,000480 H3 Predictor Constant A A2 B B2 R H H2 H3

Coef 3,33362 0,0293667 -0,00006625 0,0112544 -0,00001341 -0,298923 0,465276 -0,0253605 0,00047959

S = 0,217412

SE Coef 0,03017 0,0003926 0,00000142 0,0001965 0,00000042 0,001683 0,005872 0,0005299 0,00001300

R-Sq = 98,4%

T 110,51 74,81 -46,59 57,28 -32,28 -177,66 79,24 -47,86 36,90

P 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000

R-Sq(adj) = 98,4%

The Figure 4 shows the ln values of the original data of the manufacturing time and the results of the estimation. As we can see, the original and the estimated data show appropriate accuracy.

Figure 4. The ln value of the original and the estimated manufacturing time


3D surface milling The manufacturing of free form surfaces is an everyday task in the mould and dies manufacturing industry. The engineers seek the balance between the surface quality and the productivity. In case of 3D finishing milling a ball-end milling cutter creates the final surface, and the coordinate values of the tool path can be changed continuously in X, Y and Z axis. The aim of the research was to determine the effect of the parameters of the 3D finishing milling to the surface quality, which allows to create a mathematical model to predict the surface roughness and manufacturing time [3]. The size of the test part was 175x165x45 mm, which contains two cylindrical surfaces with 100 mm radii. The material of the test part was 42CrMo4 (1.7225). Before the 3D finishing a rough milling and a pre-finishing were applied, the allowance for finishing was 0,2 mm. A ball end milling cutter was selected from the Fraisa catalogue (U5286.501), the diameter (Dc) was 12 mm. The input parameters were the follows: • Cutting speed (vc): 280 m/min, 210 m=min, 140 m/min. • Step over (ae): 0,8 mm, 0,5 mm, 0,2 mm. • Direction of the finishing (A2): 0°, 90º. The fractional factorial design of experiment method was used to generate the parameter setups in order to effective testing. The full factorial plan results 3x3x2=18 cases, but the selected DOE method reduces the number of cases to 6 (Table 1). Table 1 Pattern of the test sets

The Figure 5 shows the CAD model of the test part and the 6 test zones with the specific parameters (2 additional control zones were defined in order to check the results). Instead of the cutting speed the revolutions per minute (n)


was programmed. The feed per tooth (fz) was 0,085 mm, and the feed speed (vf = fz · z · n) were 1265 mm/min, 950 mm/min, 630 mm/min. The required CNC programs were generated based on CAD model by Pro/Engineer WF4 CAM system, and manufacturing was performed in a Mazak Nexus 410A-II manufacturing centre.

Figure 5 Test zones and the simulation of a CNC program

During the test the following parameters were measured or recorded: • machining time (minutes), • cutting force components by KISTLER Type: 9257 A force measurement unit with KISTLER 5019B131 amp and DynoWare software, • surface roughness (Ra, Rz, Rt) in parallel and perpendicular to the milling direction by Mitutoyo Surftest SJ – 301. The cylindrical surfaces ensure to consider the effect of the surface gradient. Five levels were defined in the test part, where the angle to the vertical direction (centre of the tool) of the normal vectors were Ni: 2,9º; 11,5º; 20,4º; 30,0º; 36,9º (i=1...5). The test sets make possible to compare each zones, because 2 zones can be compared based on a selected parameter. For example Zone#1 differs from Zone#3 in ae and n, from Zone#4 in A2 and n, and Zone#3 differs from Zone#4 in A2 and ae. An equal parameter can be found in every cases. In case of centre point Zone#2 differs from Zone#5 only in A2 parameter, so the effect of A2 can be detected. The Figure 6 shows the picture of surface texture. The first two pictures show the Zone#2 in two positions: at the top of the test part (Z2/N1), where the angle of the normal vector was 2,9º, and at


middle (Z2/N3), where the angle of the normal vector was 20,4º. The direction of the milling is parallel with the Y axis (A = 90°). Depends on the normal vector the surface texture is very different, cause of the change of working diameter of the milling cutter. The different strips shows the upmilling and down-milling paths, and the step-over parameter (ae = 0,5 mm) is very clear in the pictures.

Figure 6 Surface texture

The other two pictures show the Zone#5 at same position (Z5/N1, Z5/N3). At the shallow zone (N1) the difference between the up-milling and down-milling strips very characteristic, the step-over (ae = 0,5 mm) is very clear. The effective cutting diameter is very small. When the normal vector is larger (N3), the effective diameter increase, and the difference will be smaller, the texture more homogenous, the step-over parameter is invisible. Z-level milling The other most important finishing strategy in case of finishing milling of free form surface is the z-level milling, when the surface is milled by 2D tool path slice-by-slice. The aim of this research [4] was to study the effect of the milling parameters and the position of the milled surface.


The test part was made of non-alloyed structural steel S355 (Fe 510). The part contains two different test surfaces with different gradients. Three different gradients were defined: A1 = 65° / 75° / 85°. Every test surface contains two surfaces: the first one ensures parallel milling with the x axes (A2 = 0°), and the second one is angled with x axes (A2 = 45°) (Figure 7). The CAD model and the NC programs was generated by Pro/Engineer WildFire 4 integrated CAD/CAM software, and the machining was performed by Mazak Nexus 410-A II machining centre. The surface roughness was measured by Mitutoyo SJ-301. The surface roughness is determined by average of 3 measured values.

Figure 7 Test part

Two milling cutter was used for the tests: Fraisa U5250.445 and U5250.450, the cutting diameter is 10 mm, in both cases, and the corner radii are 0,5 and 1 mm. The number of teeth is 6, the cutting speed (vc) 200 m/min, the revolution (n) 6.400 1/min. The feed per teeth (fz) and the depth of cut (ap) were varied based on tool catalogue, feed per teeth were: 0.08/0.12/0.16 mm (feed speed: vf = 3000/4500/6000 mm/min) and the depth of cut: 0.15/0.20/0.25 mm. The profile milling strategy was selected in the CAM system, and conventional milling was used.


Table 2 Pattern of the test sets

The Table 2 shows the 10 test sets, which was determined by design of experiment (DOE) method. The DOE method ensures less number of tests with same effectiveness. Four parameters was selected, one in 2 levels and 3 in 3 levels. In case of full factional plan 2x3x3x3=54 cases, but based on fractional factorial plan 10 test sets ensure small machining demand but enough data for analysis. The tests sets make possible several analyses; here only one interesting result is highlighted. The Figure 8 shows the measured Ra surface roughness values. The first curve (continuous blue curve) shows the surface roughness in case of x axes parallel milling, and the second curve (interrupted red curve) shows the 45° milling. Based on the test in case of parallel milling the surface roughness is larger in nine cases, the maximum difference is up to 35% in case of 6th test surface. The cause of it is the less vibration, because the parallel motion of the x and y axes don’t permit to develop the harmful vibration.

Figure 8 Surface roughness in function of milling direction


Die-cast aluminium part turning The machining of aluminium parts has been made more important in recent years and decades. The aluminium alloys are used by the automotive, aero and war industries increasingly because of their numerous good advantageous mechanical and chemical properties. The most often used cut types are the soso called AlMgSi alloys, of which the most widespread are the reinforced silicon alloys. One of the main goals when planning technology is to reach required surface roughness values (e.g. Ra, Rz). The knowledge of surface surface roughness is essential depending on the cutting parameters. The aim of this research was to find an approximate function between surface roughness parameters and cutting parameters with the help of DOE [5]. In this case a turning process was made where where the examined material was AS 17 (pressure die-cast cast aluminium alloy with 17% silicon) and the tool was PCD with ISO geometry (Figure Figure 9). 9 During the examination response surface method was used because of the possible second-order second prediction equation. The examined part is a cylinder with diameter of 110 mm. The experimental runs were made by every 10 mm.

Al = 74.35 % Si = 20.03 % Cu = 4.57 % Fe = 1.06 %

front surface

flank surface b) examined material and its content Figure 9. The picture of the used part and tool

a) the pictures of the examined tool (CVD-D, (CVD ISO)

The set of experimental design can be seen in Table 3. There were three controllable factors like cutting speed (vc), feed rate (f) and depth of cut (a). Each factor has 5 different levels. In case of a full factorial design the number of the experimental runs would be 125 instead of this case where the number of the trials was 16. This type of response surface method is called central composite design (CCD). (CCD)

Drégelyi-Kiss Kiss Á., Horváth R. Mikó B.: Design of experiments (DOE) in investigation of cutting technologies; in Development in Machining Technology Vol.3. Ed.: W. Zebala, I. Manková; Cracow University of Tehnology 2013. p.20-34. ISBN 978-83-7242 7242-697-

Table 3 Response surface design (CCD) parameters for turning and the measured results Runs 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 (C) 16 (C)

vc, m/min 667 667 667 667 1833 1833 1833 1833 500 2000 1250 1250 1250 1250 1250 1250

f, mm 0.058 0.058 0.112 0.112 0.058 0.058 0.112 0.112 0.085 0.085 0.05 0.12 0.085 0.085 0.085 0.085

a, mm 0.267 0.733 0.267 0.733 0.267 0.733 0.267 0.733 0.5 0.5 0.5 0.5 0.2 0.8 0.5 0.5

Rz1

Rz2

Rz3

2.440 3.770 5.490 8.190 2.710 3.860 4.640 6.620 5.890 5.300 3.370 7.900 5.170 5.250 4.960 4.210

3.190 3.260 4.840 7.940 2.890 3.430 5.320 6.590 5.630 5.290 2.970 7.860 4.170 4.370 4.480 5.470

2.580 3.010 5.070 8.190 3.550 3.940 5.220 6.790 6.180 5.900 3.390 8.380 4.510 4.490 4.600 4.710

Rzaverage Rzpredicted 2.737 3.347 5.133 8.107 3.050 3.743 5.060 6.667 5.900 5.497 3.243 8.047 4.617 4.703 4.680 4.797

2.913 3.153 5.873 7.751 3.232 3.472 5.077 6.956 5.468 5.161 3.226 7.402 3.785 5.149 5.314 5.314

The 15(C) and 16(C) experimental runs are control points in the centre of the parameter range. After completing experiments, the surface roughness was determined by the average of 3 measured values in each experimental run. The measured Rz values and the mean of these values can be found in Table 3 as well. Regression analysis was made with Minitab14 statistical software. The examined model was the next expression: R z = b0 + b1 ⋅ vc + b2 ⋅ f + b3 ⋅ a + b11 ⋅ vc2 + b22 ⋅ f 2 + b33 ⋅ a 2 + b12 ⋅ vc ⋅ f + b13 ⋅ vc ⋅ a + b23 ⋅ f ⋅ a + ε

where the bj values are coefficients. ε is the measurement error. The results of the regression analysis as it follow: Term Constant Vc [m/perc] f [mm] a [mm] a [mm]*a [mm] Vc [m/perc]*f [mm] f [mm]*a [mm]

S = 0.582464 R-Sq = 88.66%

Coef -2.1049 0.0013 49.2298 6.1536 -9.4139 -0.0177 65.1062

SE Coef 1.3415 0.0007 13.8597 3.1223 2.6427 0.0076 18.8992

PRESS = 18.5043 R-Sq(pred) = 84.92%

T -1.569 1.957 3.552 1.971 -3.562 -2.337 3.445

P 0.124 0.057 0.001 0.056 0.001 0.024 0.001

R-Sq(adj) = 87.00%


It can be seen that the following factors have significant effect (at 95% level) on the results (i.e. p is greater than 0.05). The calculated equation is: Rz = −2.1049 + 0.0013⋅ vc + 49.2298⋅ f + 6.1536⋅ a − 9.4139⋅ a 2 − 0.0177⋅ vc ⋅ f + 65.1062⋅ f ⋅ a

This equation can be shown in the Figure 10. As can be seen there is quite small dependence of the Rz from the cutting speed. but the feed rate has a great impact on the results. With this method a simple connection can be found between the surface roughness and the cutting parameter within the examined parameters’ range because it is important in planning of the turning technology processes.

Figure 10. Dependence of the Rz on the cutting speed and the feed rate

Acknowledgement The project was realised through the assistance of the European Union with the co-financing of the European Social Fund namely: TÁMOP-4.2.1.B11/2/KMR-2011-0001 Researches on Critical Infrastructure Protection. References [1.] [2.]

[3.]

MONTGOMERY. D.C.: Statistical Quality Control; John Wiley and Sons. Asia. 2009. MIKÓ B: Manufacturing time estimation of rough pocket milling by statistical analysis; 7th Int. Tool Conf. ITC2009. Zlin (Cz) 2009. CD proceeding MIKÓ. B.. BEŇO. J.. IZOL. P.. MAŇKOVÁ. I.: Surface quality of sculpture surface in case of 3D milling; 8th Int. Tool Conf. ITC2011. Zlin (Cz) 2011. CD proceeding; ISBN:978-80.7454-026-4


[4.]

[5.]

MIKÓ B.: Study of z-level finishing milling strategy; International Scientific Seminar “Development in Machining” DiM’2012; Krakow (Pl) 2012. HORVÁTH R.. MÁTYÁSI GY.: Alumínium alkatrészek forgácsolhatóságának vizsgálata kísérletterv alkalmazásával (in Hungarian. The examination of cutting ability with design of experiments in case of aluminium parts). FMTÜ. 2013. 03.21-22.. ClujNapoca. Romania. pp. 121-125.


DESIGN OF EXPERIMENTS (DOE) IN INVESTIGATION OF CUTTING ...

DESIGN OF EXPERIMENTS (DOE) IN INVESTIGATION OF CUTTING ...

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