Surface finish improvement in ball nose end milling by optimizing...

Indian Journal of Engineering & Materials Sciences

Vol. 22, February 2015, pp. 38-50

Surface finish improvement in ball nose end milling by optimizing operating

conditions for different cutting times

Charnnarong Saikaewa* & Paramet Baowan

b

aDepartment of Industrial Engineering, Khon Kaen University, Khon Kaen, 40002, Thailand bDepartment of Industrial Engineering, Rajamangala University of Technology Isan, Khon Kaen Campus, Khon Kaen 40000 Thailand

Received 17 January 2014; accepted 27 August 2014

An important problem of ball nose end milling is degradation of the quality of machined surface for long run machining

due to rapid tool wear. In this work, a practical solution to this problem by employing designed experiments (DOE) and

response surface methodology (RSM) to determine optimal operating conditions with different tool cutting times is

proposed. The significant cutting process factors and corresponding optimal operating conditions are found to depend on the

cutting time. The machined surface finish produced by tools with different cutting times are verified by confirmation

experiments and evaluated by pair comparison method at the optimal and non-optimal operating conditions. The results

show that the optimal operating conditions of the process factors are different when machining with different cutting times.

Surface roughness values are low and insignificantly different over a wider range of cutting time when machining at the

optimal operating conditions. On the other hand, there are significant differences in all pair comparisons under non-optimal

operating conditions. In addition, electron microscopic characterization confirmed that severe notch tool wear would not

occur within short cutting time if the tool is operated at the optimal conditions. Therefore, the surface quality of machined

parts as well as tool life could be effectively improved by the use of optimal operating conditions as a function of cutting

time obtained by DOE and RSM.

Keywords: Surface roughness, Ball nose end milling, Cutting time, Statistical analysis

A main challenge in manufacturing technology

such as milling process is to improve surface finish

quality of products while minimizing machining time

and production cost1-7

. An effective approach to

achieve this goal is to optimize cutting tools and

machining conditions8. The effects of process factors

such as cutting speed, depth of cut and feed per tooth

on the quality of surface finish and tool life have

continuously been widely studied over past decades9.

For instance, a recent study on mould and die

manufacturing showed that surface roughness of

surface finish would be lower with the use of

indexable-insert ball nose end mills (TiCN and

TiAlCrYN coated carbide and uncoated cermet) than

the use of solid tool (TiAlN-TiN coated carbide) but

solid tool had substantially longer life-time than the

insert tools for various cutting speeds10

. In addition, the effects of various milling conditions

on surface roughness had been studied simultaneously. Ding et al.

11 investigated the effects of step over,

cutting speed, feed per tooth, and axial depth of cut on surface roughness in hard milling of AISI H13 steel with coated carbide tools. They found that surface

roughness reduced when the axial depth of cut increased from 1 to 2 mm but became increasing rapidly as the axial depth of cut increased further to 3 mm. Zhang and Guo

12 optimized the step over and feed

rate for end milling of hardened AISI H13 tool steel with TiAlN coated end mill, yielding a very low surface roughness of less than 0.1 µm. Likewise, Gologlu and Sakarya

13 found that step over was one of

the most significant factors on surface roughness of 40CrMnNiMo8-4 DIN 1.2738 mould steel produced by different pocket milling operations. Moreover, Topal

14

reported that step over was a crucial factor affecting average surface roughness of flat end milled surface using predictive models based on artificial neural network methodology with average root mean square error for training and testing. Buj-Corral et al.

15 stated

that surface roughness of ball-end- milled surface decreased more strongly with decreasing step over than decreasing feed rate.

For analysis, control and optimization of these

process factors, various predictive models for surface

roughness as a function of operating factors have been

developed. Erzurumlu and Oktem16

employed the

response surface model (RSM) and an artificial neural

network (ANN) model to predict mould surface —————— *Corresponding author (E-mail: [email protected])

SAIKAEW & BAOWAN: SURFACE FINISH IMPROVEMENT IN BALL NOSE END MILLING

39

roughness in terms of cutting speed, feed rate, depth

of cut and machining tolerance for milling operations.

The results indicated that RSM provided fair accuracy

in predicting surface roughness within a range

of process factors while ANN model gave

better agreement with experimental measurements.

Zain et al.17

applied the regression and ANN models

to predict the minimum surface roughness value as a

function of cutting speed, feed rate and radial rake

angle for end milling of Ti-6Al-4V (Ti-64). Both

modeling approaches effectively yielded the

minimum surface roughness value matched with

experimental data while the regression model gave

better results compared with ANN. Raj et al.18

developed a mathematical model for predicting the

surface roughness of end-milled glass fiber reinforced

plastic composites in terms of cutting speed, feed rate,

depth of cut and tool material. The depth of cut and

tool material were found to be the most influential

main factors on surface roughness.

In general, surface finish quality is unavoidably

degraded with increasing cutting time due to tool

wear. The degradation is especially rapid and

significant for mould machining due to relatively high

hardness of mould. Traditionally, cutting tool is

operated continuously under a normal condition until

unacceptable quality of surface finish is observed.

This practice results in considerable loss of tools,

materials and process time. To reduce such losses,

tool should be operated under an optimal operating

condition, which may be adjusted according to tool

condition indicated by tool cutting time. Over

decades, many researchers have investigated and

optimized significant machining factors for optimal

quality characteristics of various machined parts using

design of experiments (DOE), response surface

methodology (RSM) and other evolutionary

techniques16,18-22

. However, they have never explored

the optimal operating conditions of the process factors

at different tool cutting times.

In this work, we proposed a practical solution to

improve tool life and surface finish quality by

operating the cutting tool under optimal operating

conditions that were periodically changed according

to tool cutting time. The significant process factors

and optimal operating conditions for different cutting

times were systematically determined by DOE and

RSM. In addition, the performances of cutting tools

operated at optimal and non-optimal operating

conditions were comparatively evaluated to assess the

effectiveness of the proposed method.

Experimental Procedure

Materials and machine

The work-piece material was AISI P20 steel for

plastic injection mould, which had an average

hardness of 30 HRC and chemical compositions as

shown in Table 1. Firstly, the work-piece was cleaned

by a standard cleaning procedure prior to each

machining experiment. Next, it was machined in

finishing operation to the final shape, which

comprised four regions including a round sector, a

horizontal plane and two inclined planes with 30° and

45° slopes as illustrated in Fig. 1. Ball nose end

Fig. 1—The work-piece designed for the experiments

INDIAN J. ENG. MATER. SCI., FEBRUARY 2015

40

milling experiments were carried out on a CNC

milling machine (MIKRON model VCE 750). The

cutting tools employed for finishing operation

were high speed steel (HSS) ball nose end mills

(OSG model HSS-Co 8%, 10 mm in diameter). The

CNC milling machine and HSS ball nose end mills

are illustrated in Fig. 2.

Procedure

A factorial design with additional four center

points was utilized to investigate the effects of

process factors on surface roughness of ball-nose-end-

milled AISI P20 mould steel. Four process factors

including spindle speed, feed per tooth, depth of cut,

and step over were chosen as factors for experimental

design since they were deemed to be important factors

affecting surface finish quality. The ranges

comprising low and high levels of process factors as

listed in Table 2 were obtained from recommended

values in tool catalog. In this work, the cutting time

was varied from 150 to 750 min with 150 min

increment. In each machining experiment, a cutting

tool was applied for continuous milling along the four

regions of mould (Fig. 1). Surface roughness of

finished work-piece was measured parallel to the feed

direction using a commercial surface analyzer

(Make-Mitutoyo 3D Surf tester) with a cut-off

distance of 0.8 mm. Roughness measurements were

performed in the four regions of mould surfaces with

three replications. The average and standard deviation

of roughness values were then computed from the raw

data and recorded in the experimental design matrix

as shown in Table 3. The surface morphologies of

cutting tools after machining experiments were

examined by scanning electron microscope (SEM)

to evaluate the effect of operating condition on

tool wear.

Statistical analysis

A normal probability analysis was used in order to

identify the significant main and interaction effects on

the quality characteristics (i.e., the average and

standard deviation of surface roughness values). In

this analysis, standardized main and interaction

effects of process factors were calculated and plotted

against cumulative normal probability (in percent).

Table 1—Chemical composition of the work-piece

material AISI P20 (wt%)

Carbon (C) Manganese (Mn) Chromium (Cr) Molybdenum (Mo)

0.4 1.5 1.9 0.2

Fig. 2—Photograph of CNC milling operation with the diagram of ball nose end mill used in all experiments

Table 2—Milling process factors for experimental design

Factor Low level High level Unit

Spindle speed (A) 2500 3500 rpm

Feed per tooth (B) 0.17 0.36 mm/tooth

Depth of cut (C) 0.1 0.2 mm

Step over (D) 0.1 0.2 mm


41

The effects that fell off from the main straight line

were deemed to be statistically significant while those

that followed along the straight line were considered

to be statistically insignificant23,24

. Main and

interaction effect plots were then constructed in order

to identify the best levels of the process factors, which

gave the minimum surface roughness. In addition,

RSM was applied to obtain the optimal operating

condition of significant process factors25

. The

optimization was conducted using the Design-Expert®

V7 software package26

, which used the optimization

method developed by Derringer and Suich27

and

described by Myer and Montgomery25

.

An analysis of variance (ANOVA) was then used

to identify if the average surface roughness of work-

pieces machined by tools for various cutting times

differed from one another28-30

. If ANOVA indicated a

significant difference, a pair comparison method

would be employed to specifically identify the

differences among results with different tool cutting

times. Differences between pair of average surface

roughness for a pair of two distinct tool cutting times

were evaluated using a test of hypothesis based on

Fisher least significant difference (LSD) method24

. If

any pair of average surface roughness for two

conditions or treatments (e.g., average surface

roughness with 150 min tool cutting time and that

with 300 min tool cutting time) differed in magnitude

by more than the LSD value, the corresponding pair

of surface roughness was considered to be

significantly different.

Results and Discussion

The complete results of average and standard

deviation of surface roughness for all experimental

conditions with different tool cutting times ranging

from 150 to 750 min are listed along with the process

factors of designed experiments in Table 3. In

particular, surface roughness values of all operating

conditions (run#1-20) with 150 min and 750 min tool

cutting times are plotted as shown in Fig. 3. It can be

seen that the average surface roughness values with

150 min cutting time are significantly different and

lower than those with 750 min cutting time for all

runs. In addition, longer tool cutting time tends to

cause large variations of surface roughness values

ranging under various operating conditions. The

results can be explained from the fact that long cutting

Table 3—Experimental design matrix with surface roughness results with various cutting times from 150 to 750 min

Factors

Surface roughness (µm) for various cutting

times (min)

Standard deviation (µm) for various

cutting times (min)

Runs

Spindle

speed (A)

Feed/

tooth (B)

Depth of

cut (C)

Step

over (D)

150 300 450 600 750 150 300 450 600 750

1 2500 0.24 0.1 0.1 1.03 1.15 1.38 1.74 1.81 0.39 0.41 0.42 0.53 0.39

2 3500 0.17 0.1 0.1 0.99 1.33 1.46 1.74 2.04 0.16 0.35 0.40 0.52 0.57

3 2500 0.36 0.1 0.1 1.23 1.69 1.70 2.09 2.49 0.60 0.62 0.58 0.37 0.56

4 3500 0.26 0.1 0.1 1.41 1.70 1.85 2.07 2.45 0.55 0.57 0.40 0.40 0.44

5 2500 0.24 0.2 0.1 0.97 1.12 2.20 2.60 3.27 0.17 0.17 0.31 0.38 0.42

6 3500 0.17 0.2 0.1 0.94 1.18 2.22 2.58 3.24 0.19 0.13 0.21 0.39 0.48

7 2500 0.36 0.2 0.1 1.40 1.77 2.49 3.16 3.59 0.67 0.57 0.28 0.50 0.60

8 3500 0.26 0.2 0.1 1.39 1.85 2.69 3.25 3.61 0.67 0.50 0.34 0.53 0.62

9 2500 0.24 0.1 0.2 1.81 1.92 2.07 2.18 2.40 0.94 0.65 0.59 0.56 0.56

10 3500 0.17 0.1 0.2 1.62 1.67 2.06 2.21 2.42 0.58 0.80 0.75 0.72 0.61

11 2500 0.36 0.1 0.2 2.20 2.32 2.39 2.58 3.17 1.28 0.99 0.96 0.91 0.74

12 3500 0.26 0.1 0.2 1.99 2.36 2.48 2.77 3.20 1.00 0.73 0.88 0.81 0.72

13 2500 0.24 0.2 0.2 1.92 2.30 2.82 2.94 3.77 0.76 0.52 0.71 0.72 0.75

14 3500 0.17 0.2 0.2 1.62 2.15 2.93 3.10 3.77 0.76 0.58 0.70 0.72 0.64

15 2500 0.36 0.2 0.2 1.84 2.35 3.54 3.80 4.11 1.04 0.66 0.64 0.66 0.70

16 3500 0.26 0.2 0.2 2.42 2.55 3.50 3.87 4.19 1.36 0.76 0.67 0.64 0.70

17 3000 0.25 0.15 0.15 1.72 1.80 2.34 2.54 3.03 0.67 0.65 0.43 0.50 0.59

18 3000 0.25 0.15 0.15 1.67 1.74 2.36 2.67 3.13 0.74 0.63 0.54 0.55 0.62

19 3000 0.25 0.15 0.15 1.68 1.80 2.41 2.72 3.10 0.61 0.63 0.63 0.50 0.56

20 3000 0.25 0.15 0.15 1.63 1.85 2.44 2.62 3.10 0.58 0.56 0.52 0.54 0.59


42

time naturally leads to tool wear, which will result in

poor cutting characteristics with large irregular chip

formation and high surface irregularity.

Figure 4 shows the normal probability plot of

effects of process factors on surface roughness for

finishing operations in ball nose end milling with

750 min cutting time. It can be seen that three main

process factors including feed per tooth, depth of cut,

and step over have significant influence on surface

roughness since their normal probability drop below

the main straight line. Similarly, one interaction effect

between feed per tooth and depth of cut is statistically

significant at 95% level of confidence. Plots of the

residuals for the full factorial design with additional

four center points as shown in Fig. 5 are used for

checking model adequacy. Figure 5a, a normal

probability plot of the residuals, suggests that there is

neither severe indication of non-normality nor any

evidence pointing to possible outliers. In addition,

Fig. 5b, plots of the residuals versus the predicted

values, reveals no correlation between the size of the

residuals and the predicted values. This means that the

variance of the surface roughness values is constant as

the magnitude of surface roughness values increases

and the surface roughness values should follow a

normal distribution. Figure 5c, plots of the residuals

in time order of surface roughness data collection,

indicates no correlation between the residuals and

confirms the assumption of error independency.

In running the factorial experiments, adding the

replicate runs at the design center provides protection

Fig. 3—Surface roughness results with 150 and 750 min cutting times

Fig. 4—Normal probability plot of effects of process factors on

surface roughness for finishing operation in ball nose end milling

using 750 min cutting time


43

Fig. 5—Model adequacy checking for ball nose end milling using

750 min cutting time (a) a normal probability plot of the residuals,

(b) plots of the residuals versus the predicted values and (c) plots

of the residuals in time order of surface roughness data collection

against curvature from second-order effects and

allows an independent estimate of error to be

obtained24,25

. According to the results in Table 3, the

average of the points in the factorial portion of the

design (Runs#1-16) is 3.0956 and the average of the

center points (Runs#17-20) is 3.09 for 750 min

cutting time. Very small difference between the

averages of factorial and center points indicates the

absence of curvature from second-order effects. The

sum of squares of pure quadratic curvature from

ANOVA in Table 4 can be directly computed

according to Eq. (1):

( )2

Curvature

2(16)(4)(3.0956 3.09)0.0001

16 4

F C F C

F C

n n y ySS

n n

−=

+−

= =+

… (1)

where F

y represents the average of the points in the

factorial portion with nF runs and C

y represents the

average of the center points with nC runs. The

ANOVA result confirms that there is no second-order

curvature in the response over the explored region

with a high p-value of 0.8879. The ANOVA result

in Table 4 also shows insignificant lack-of-fit.

The lack-of-fit factor is used to determine the

variation of the data around the fitted model.

Generally, a good model must be statistically

significant and the lack-of-fit must be insignificant.

The additional center points in the factorial design

allow an estimate of pure experimental error24

, which

can be decomposed from the residual sum of squares

SSE according to Eq. (2):

0.069 0.0054 0.0636E PE LOF

SS SS SS= += +

… (2)

Table 4—ANOVA table for finishing operation in ball nose end

milling with 750 min cutting time

Source of

variation

Sum of

squares

df Mean

square

F value p-value

Model 8.14 4 2.04 414.32 < 0.0001

B-Feed per

tooth

1.05 1 1.05 212.85 < 0.0001

C-Depth of cut 5.72 1 5.72 1165.31 < 0.0001

D-Step over 1.28 1 1.28 261.1 < 0.0001

BC 0.089 1 0.089 18.02 0.0008

Curvature 0.0001 1 0.0001 0.021 0.8879

Residual 0.0690 14 0.0049

Lack of fit 0.0636 11 0.0058 3.2 0.1839

Pure error 0.0054 3 0.0018

Total 8.21 19


44

where SSPE is the sum of squares due to pure error and

SSLOF is the sum of squares due to lack-of-fit. The

statistical test for lack-of-fit can be determined from

Eq. (3):

0.00583.2

0.0018

LOF

LOF

PE

MSF

MS=

= =

… (3)

where MSLOF is the mean square due to lack-of-fit and

MSPE is the mean square due to pure error. The FLOF

value gives the corresponding p-value of 0.1839,

which indicates insignificant lack-of-fit. Hence, the

factorial design with additional four center point

model allows good fit of the outer points in the

factorial portion (insignificant lack of fit) as well as

the inner center points (insignificant curvature),

indicating sufficient information to adequately model

the true surface. Thus, it is not necessary to take more

sequential experimentation via additional

experimental runs at new levels of the significant

factors.

In order to interpret interaction effect more

effectively, an interaction plot between feed per tooth

and depth of cut is constructed as shown in Fig. 6.

The non-parallel lines of the two process factors

indicate significant interaction between them because

the effect of feed per tooth on the surface roughness is

different at low and high levels of depth of cut. This

result agrees with some previous reports, which

demonstrated that increasing feed per tooth and depth

of cut resulted in higher cutting forces and higher

surface roughness values31-35

. Figure 7 illustrates main

effect plots of the three significant process factors

(feed per tooth, depth of cut, and step over) and non-

significant process factor (spindle speed) on the

surface roughness for 750 min cutting time. It is

evident that depth of cut is the most active factor

compared with the other two. The result is deviated

from the basic machining theory and many studies, in

which feed rate or feed per tooth is the most

influential factor on surface roughness. Yang et al.36

and Kivak37

reported that feed rate was the most

significant factor affecting surface roughness in dry

milling with different carbide inserts of high-purity

graphite and Hadfield steel (austenitic manganese

steel), respectively. Durakbasa et al.35

confirmed that

feed rate was the most effective factor on surface

roughness based on the linear model for the flat and

spherical surfaces of steel and aluminium. Sonawane

and Joshi31

reported that feed per tooth was a more

significant factor than depth of cut in a single-pass of

ball-end milling on Inconel 718. Theoretically, the

surface roughness on feed direction increased with the

square of feed per tooth since chip size would

significantly increase with feed rate due to enhanced

shear deformation36

.

In contrast, several other reports demonstrated that depth of cut was the most dominant factor on surface roughness of end-milled work pieces. Ding et al.

11

stated that depth of cut contributed the most to surface roughness whereas the interactions among other process factors provided secondary contribution to surface roughness in hard milling of AISI H13 steel with coated carbide tools. Raj et al.

18 found that

cutting speed and depth of cut and interactions among other process factors were the most influential main factors on surface roughness of glass fiber reinforced plastic composites after end milling operation. Ghani et al.

38 reported that depth of cut, cutting speed, and

feed rate are important main factors for end milling of hardened steel AISI H13 with TiN coated carbide insert tool. Yong et al.

34 demonstrated that depth of

cut, feed rate, the interaction of feed rate and depth of cut, and the quadratic term of depth of cut were the significant factors affecting surface roughness in end milling of nano-crystalline hydroxyapatite bioceramic using polycrystalline diamond insert. The deviations could be due to the fact that the theory does not take into account for factors of tool and work-piece materials as well as nonlinearity over different ranges

Fig. 6—Interaction plot between feed/tooth and depth of cut for

ball nose end milling using 750 min cutting time


45

of experimental conditions. Practically, large depth of cut substantially increased the cutting force and caused tool wear along with large discontinuous chip formation, leading to high surface irregularity

33.

According to statistical analysis for standard

deviation of surface roughness, the results from

normal probability analysis of effects together with

main and interaction effect plots indicates the conflict

between the average and standard deviation of the

surface roughness (i.e., one decreases as the other

increases). This conflicting response problem can be

solved by RSM with desirability function25,27

. A

numerical analysis using RSM was carried out in

order to obtain the optimal operating condition of the

significant process factors influencing surface

roughness for finishing operations. From the

regression analysis, an empirical relationship between

the surface roughness and the significant process

factors is given by Eq. (4):

3.1 0.26 0.6 0.28 0.074Ra B C D BC= + + + −)

… (4)

where Ra)

, B, C, and D are the predicted surface

roughness, feed per tooth, depth of cut, and step over,

respectively. The residual analysis of the model was

performed to verify the normality, independence and

constant variance requirements. The analysis result

confirmed that the model was well conformed to these

prerequisites. The coefficient of determination (R2)

and adjusted R2 were estimated to be as high as

0.99 and 0.98, respectively. Thus, the model can

explain 99% of the variability in the surface

roughness data 24,25

.

RSM with desirability function was then used to

determine an optimal operation condition of the

Fig. 7—Main effect plots of the four process factors on the surface roughness for ball nose end milling using 750 min cutting time


46

significant process factors that simultaneously

minimized the average and standard deviation of

surface roughness values. The average and standard

deviation of surface roughness were transformed into

two minimization desirability functions, which had

decreasing value from 0 to 1 as each process factor

increased from low to high values. Next, an overall

desirability function was calculated using the

normalized product formulation24

(the square root of

the product of the two desirability functions). The

optimization of the overall desirability function gave a

minimum surface roughness of 1.89 µm at spindle

speed of 2500 rpm, feed per tooth of 0.24 mm/tooth,

depth of cut of 0.1 mm and step over of 0.1 mm for

finishing operation with 750 min cutting time.

The confirmation experiments were conducted to

verify whether the predicted surface roughness

response based on the regression model and the

expected optimal surface roughness at the optimal

operating condition lied within the confidence

interval. If predicted responses of surface roughness

fell within the 95% confidence interval, the predicted

model would be considered valid and sound. In

confirmation experiments, ten mould steel samples

were machined with the optimal operating condition.

From statistical estimation, the 95% confidence

interval for the predicted mean response at the

optimal operating condition was determined to be

(1.78, 1.93) and the average surface roughness from

the ten confirmation runs was equal to 1.86. Thus, the

expected optimal surface roughness value lied within

the 95% confidence interval, confirming the validity

of the model.

For other cutting tools with different cutting times,

the same procedure including normal probability

analysis of effects, main and interaction effect plots,

RSM with desirability function and confirmation

experiments were carried out to investigate the effects

of the process factors on the surface roughness and

obtain the optimal operating conditions for finishing

operation. The normal probability plots for effects of

process factors and regression analysis of surface

roughness with different tool cutting times give the

significant process factors and regression equations as

given in Table 5. The significant process factors are

ordered from the most to the least important ones

based on percentage contribution values of the factors

denoted in parentheses in Table 5. It is seen that step

over with percentage contribution of 71.97 and feed

per tooth with percentage contribution of 17.40 are

the only significant factors for short cutting times of

150 and 300 min and depth of cut becomes significant

when the cutting time increases to 450 min. As the

cutting time increases further to 600 and 750 min,

interaction factor of feed per tooth and depth of cut

becomes important while spindle speed remains

insignificant for all cases.

The dependence of significant factors on cutting

time may be ascribed to the change of tool

performances due to tool wear. For short cutting time,

the tool is fresh with full strength and chips are

formed based on normal shear cutting mechanisms

that are mainly controlled by feed per tooth and step

over. For longer cutting time, tool wear becomes

significant and chip formation will be considerably

affected by depth of cut since the weak tool will be

worn out more quickly due to larger force with

increasing depth of cut. The increasing wear of tool

leads to irregular chip formation and larger surface

roughness of surface finish. With very long cutting

time, weaker tool may be more sensitive to the

coupling between shear and normal cutting forces,

which are directly related to feed per tooth and

depth of cut.

RSM with desirability function and confirmation

experiments for different cutting tools give various

optimal operating conditions for finishing operations

and confirmation data as listed in Tables 6 and 7,

Table 5—Significant process factors with percentage contribution for tools operated with different cutting times

(starting with the most significant factors)

Cutting time (min) Significant process factors with percentage contribution values Regression equation

150 Step over (D, 71.97%), feed per tooth (B, 17.40%) 1.55 + 0.19B + 0.38D

300 Step over (D, 63.29%), feed per tooth (B, 26.46%) 1.84 + 0.24B + 0.36D

450 Depth of cut (C, 50.51%), step over (D, 34.67%), feed per tooth

(B, 12.63%)

2.36 + 0.22B + 0.44C + 0.36D

600 Depth of cut (C, 60.49%), feed per tooth (B, 19.53%), step over

(D, 17.17%), BC interaction (1.44%)

2.67 + 0.28B + 0.50C + 0.26D + 0.075BC

750 Depth of cut (C, 69.72%), step over (D, 15.62%), feed per tooth

(B, 12.74%), BC interaction (1.08%)

3.10 + 0.26B + 0.60C + 0.28D – 0.074BC


47

respectively. From Table 6, the optimal surface

roughness considerably increases from 0.98 to

1.82 µm as the cutting time increases from 150 to

450 min and the optimal surface roughness became

almost constant as the cutting time increased further.

The results may be explained based on consideration

of tool wear under different optimal operating

conditions. The initial increase of optimal surface

roughness with cutting time can be ascribed to natural

tool flank wear due to shear deformation. For long

tool cutting time, the surface roughness may become

independent from the cutting time because further tool

wear could be minimized by the use of new optimal

operating conditions that result in much less severe

shear deformation. According to the data in Table 7,

the measured average surface roughness at the

optimal operating conditions for all cutting times lie

within the 95% confidence intervals, confirming the

validity and reproducibility of the optimal operating

conditions for finishing operations in ball nose end

milling of the mould steel. Figure 8 also illustrates

surface roughness values obtained from milling

operation at the optimal operating conditions

compared after confirmation experiments for cutting

tools operated with different cutting times. These

results confirm that there are no significant

differences of surface roughness values obtained from

the milling operation with the confirmation

experiments and the predictions by model are highly

accurate.

The surface finish and wear characteristic tools

with various cutting times at the optimal operating

conditions and non-optimal operating conditions were

further evaluated and compared. ANOVA of the

confirmation results with different cutting times

indicated that at least one average surface roughness

result of a case (e.g., 150 min cutting time) differed

from another case for different cutting times.

However, ANOVA could not specifically identify the

differences. Thus, a pair comparison with LSD

method was employed to determine the exact

differences among tools with different cutting times.

Tables 8 and 9 show the results of differences

between each pair of average surface roughness with

various cutting times at the optimal and non-optimal

operating conditions, respectively. It is seen that the

Table 6—Optimal operating conditions for tools with

different cutting times

Cutting

time (min)

Spindle

speed

(rpm)

Feed per

tooth

(mm/tooth)

Depth

of cut

(mm)

Step

over

(mm)

Surface

roughness

(µm)

150 3500 0.171 0.10 0.1 0.98

300 3460 0.173 0.20 0.1 1.24

450 3500 0.171 0.15 0.1 1.82

600 2500 0.300 0.10 0.1 1.96

750 2500 0.240 0.10 0.1 1.89

Table 7—Results of confirmation experiments

Cutting time

(min)

Average Surface

roughness (µm)

Lower of 95%

C.I. (µm)

Upper of 95%

C.I. (µm)

150 0.99 0.91 1.05

300 1.19 1.11 1.28

450 1.86 1.78 1.94

600 2.01 1.88 2.13

750 1.86 1.78 1.93

Table 8—Pair comparisons at optimal operating conditions

Treatment

pair

Mean

difference

df Standard

error

t for H0

Coeff = 0

Prob > |t|

150 vs 300 -0.2025 1 0.1346 -1.5049 *0.1531

150 vs 450 -0.8675 1 0.1346 -6.4467 < 0.0001

150 vs 600 -1.0100 1 0.1346 -7.5057 < 0.0001

150 vs 750 -0.8575 1 0.1346 -6.3724 < 0.0001

300 vs 450 -0.6650 1 0.1346 -4.9419 0.0002

300 vs 600 -0.8075 1 0.1346 -6.0009 < 0.0001

300 vs 750 -0.6550 1 0.1346 -4.8676 0.0002

450 vs 600 -0.1425 1 0.1346 -1.0590 *0.3064

450 vs 750 0.0100 1 0.1346 0.0743 *0.9417

600 vs 750 0.1525 1 0.1346 1.1333 *0.2749

*indicates not significant difference at the level of

significance 0.05

Fig. 8—Surface roughness values obtained from milling operation

at the optimal operating conditions compared after confirmation

experiments with different tool cutting times


48

average surface roughness are not significantly

different if the steel moulds are machined with the

optimal operating conditions using tools with cutting

times in the same range. The range of cutting time can

be divided into low range from 150 to 300 min and

high range from 450 to 750 min because the result of

150 min cutting time is not significantly dissimilar

from that of 300 min cutting time and the result of

450 min cutting time is not significantly different

from those of 600 min and 750 min cutting times.

This result agrees with the above observation in

Table 6 and may also be explained based on the

variation of tool wear under different optimal

operating conditions discussed earlier for Table 6.

However, there are some differences of results with

cutting times across the low and high ranges but the

differences are not large. On the other hand, there are

significant differences of average surface roughness

in all pair comparisons (i.e., 150 vs 300, 450 vs

600, etc.) when the mould steel was machined with

non-optimal operating conditions (Table 9).

Moreover, the average surface roughness substantially

increases as the cutting time increases when tools are

operated at non-optimal conditions. The results

indicate that non-optimal condition leads to severe

tool wear that is progressively increased with tool

cutting time. Therefore, the tool wear resistance and

surface quality of the mould can be greatly improved

if the cutting tool is operated at the optimal operating

conditions that are varied as function of cutting time.

The effect of optimal and non-optimal operating

conditions on tool wear was further examined by

SEM. Figures 9 (a) and (b) show typical SEM

micrographs of surface of tools for 450 min cutting

Table 9—Pair comparisons at non-optimal operating conditions

Treatment

pair

Mean

difference

df Standard

error

t for H0

Coeff = 0

Prob > |t|

150 vs 300 -0.1246 1 0.0363 -3.4349 0.0037

150 vs 450 -0.7165 1 0.0363 -19.7535 < 0.0001

150 vs 600 -0.9604 1 0.0363 -26.4797 < 0.0001

150 vs 750 -1.4179 1 0.0363 -39.0935 < 0.0001

300 vs 450 -0.5919 1 0.0363 -16.3186 < 0.0001

300 vs 600 -0.8358 1 0.0363 -23.0448 < 0.0001

300 vs 750 -1.2933 1 0.0363 -35.6586 < 0.0001

450 vs 600 -0.2440 1 0.0363 -6.7262 < 0.0001

450 vs 750 -0.7015 1 0.0363 -19.3400 < 0.0001

600 vs 750 -0.4575 1 0.0363 -12.6138 < 0.0001

Fig. 9—Typical SEM micrographs of surface of tools operated with 450 min cutting time (a) under optimal operating operation and

(b) non-optimal operating operation.


49

time operated under the optimal and non-optimal

operating conditions, respectively. It is seen that tool

operated under non-optimal operating condition

(Fig. 9b) exhibits a severe notch wear on the cutting

edge of the ball nose end mill while that operated

under optimal operating condition shows much

weaker flank wear on the flank face (Fig. 9a). The

occurrence of notch wear signified severe tool

damage that occurred within a short cutting time

when tools operated under a non-optimal operating

condition while much less tool damage would take

place if optimal operating conditions were used.

Nevertheless, the weak flank wear occurred under

optimal operating condition after 450 min also

signifies considerable degradation of tool

performances. This observation supported the above

significant factor analysis that tool wear occurred

after cutting time of ≥ 450 min could cause depth of

cut to become significant factor affecting surface

finish. The much less severe tool wear with optimal

operating conditions may be attributed to appropriate

cutting force produced at moderate feed per tooth,

depth of cut and step over. These results demonstrate

that the tool wear and tool life can be significantly

improved by the use of optimal operating conditions

as a function of cutting time determined from DOE

and RSM approaches.

Conclusions

The rapid degradation of mould’s surface finish

quality problem for increasing cutting time has been

effectively solved by employing DOE and RSM. The

significant process factors and corresponding optimal

operating conditions of tools with different cutting

times were determined by normal probability analysis

and RSM with desirability function. The optimal

operating conditions of the process factors were

different when machining at different cutting times.

The reproducibility and performance of tools with

different cutting times operated at optimal operating

conditions were successfully verified by confirmation

experiments and pair comparison with LSD method.

The quality of surface finish of AISI P20 steel for

plastic injection mould produced by high speed steel

ball nose end mills with different cutting times was

found to be high and insignificantly different over a

wider range of cutting time if optimal operating

conditions were used and adjusted according to tool

cutting time. Moreover, the improvements of tool

wear resistance and surface finish were qualitatively

confirmed by SEM characterization. Consequently,

machining at optimal operating conditions with

different cutting times would increase tool life and

reduce machining time and cost while maintaining

satisfactory product quality.

Acknowledgements The authors would like to thank Khon Kaen

University for financial support for this study.

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