> REVISTA RIEMAT JULIO–DICIEMBRE 2022. VOLUMEN 7. NÚMERO 2. ART. 6<



Abstract— Along with technological progress, manufacturing

processes have been constantly innovated, hoping to reduce

manufacturing time, extend the useful life of tools and offer high

quality finishes of the product, however, information on the

product is scarce. Machined in 7075 - T6 aluminum, which, due to

its mechanical properties, is more used for the manufacture of

molds and dies than other materials. In this project, a high-

performance machining is studied, improving cycle times by

comparing trochoidal and conventional milling roughing

strategies, without the use of coolants that can contaminate the

chip allowing the recycling of material, these strategies are found

in a large part of CAM software. The experimentation was carried

out in a Hision CFV 1100 vertical machining center with Fanuc Oi

MF control, supported by the Taguchi L18 methodology for the

milling parameters and roughing strategy. 9 tests were carried out

for each strategy with a 25 mm flat cutting tool with 4 high speed

steel (HSS) lips based on the 3 levels of the milling parameters, in

the range of 800 m / min to 1000 m / min, with a feed per tooth of

0.25 to 0.35 mm / tooth. The results obtained for both time and

temperature have a behavior described by Mr. Salomón for high-

speed machining (HSM), an ANOVA statistical analysis was

carried out that determined that the trochoidal machining strategy

presents a reduction in the 93.27% compared to the conventional

machining strategy and a stable temperature of 25ºC in the cutting

tool.

Index Terms— trochoidal machining, conventional machining,

high speed machining, prodax aluminum

I. INTRODUCTION

LUMINUM (Al) is the most abundant metal in the earth’s

crust, above iron, it is a metal that can be machined without

great difficulty, it has a high thermal conductivity and as

regards the electrical conductivity, it is a good conductor (like

all metals except for titanium), it also has a face-centered cubic

crystalline structure, thus it has a non-ferromagnetic behavior

and resistance to oxidation and corrosion.[1]

The alloying element in Prodax aluminum is zinc, which acts

by giving it greater hardness and resistance. The T6 heat

treatment that the material has, in effect is solubilized and later

aged in order to increase its resistance. Thus, they are delivered

in round bars and plates, heat treated, which are subjected to a

special cold stretching operation for maximum stress relief,

obtaining high strength and good stability. [2]

In 2019, at the University of the Armed Forces -ESPE, a

rough milling comparison was carried out with both

conventional and trochoidal strategies in a range of 400 to 700

m/min [3], for which it seeks to complete the range of 800 to

1000 m/min in which a stabilization of the temperature of the

cutting tool is achieved and the machining time with trochoidal

strategy is significantly reduced.

II. EXPERIMENTAL METHODS

The test machine was a HISION CVF Series vertical

machining center with a Fanuc model Oi MF control unit, the

main specifications are 4 axes, maximum spindle speed of

15000 rpm. The experimentation processes were carried out

with a combination of high-speed machining parameters in

order to reach high-performance machining, that is, to carry out

the tests without coolant that contaminates the chips The cutting

parameters were the following: cutting speeds: 800, 900 and

1000 m / min; feed speeds: 0.25, 0.30 and 0.35 mm / tooth. In

the conventional strategy, the depth constant of 2,185 mm was

used with a cutting width of 64% of the tool diameter. In the

adaptive strategy, a constant depth of cut of 15 mm was used

with a width of cut at 10% of the diameter of the tool. the

configuration of the machining tests is shown in Figure. 1

High- performance manufacturing with

trochoidal milling strategies

Mario Orlando Orellana Jarrín

, Borys Hernán Culqui Culqui

Departamento de Ciencias de la Energía y Mecánica

Universidad de las Fuerzas Armadas ESPE

Figure 1. Machining configuration

> REVISTA RIEMAT JULIO–DICIEMBRE 2022. VOLUMEN 7. NÚMERO 2. ART. 6<

A. Material specification

A 7075- T6 aluminum with a density of 2,810 g/cm3 with a

length of 70 mm, width of 70 mm and height of 20 mm was

used as work piece. The chemical composition is shown in table

TABLE I

AL 7075- T6 CHEMICAL COMPOSITION

Chemical Composition (%)

87-91.4

5.1-6.1

1.2-2

0.18-0.28

0.4

2.1-2.9

0.5

0.2

B. Cutting Tool

The tool used in the test is a 25 mm diameter milling with

four flutes. the specifications for this tool are the following:

 Manufacturer: Somta

 Material: High speed steel (HSS)

 Cutting depth: 1.25 mm

 Cutting feed rate: 4800 mm/min

C. Taguchi methodology

The Taguchi method develops the procedures applying

orthogonal matrices between parameters and levels in the

experiment to obtain the best model with a reduction in the

number of tests and minimizing the time and cost of

experimentation [4].

Identifying the factors that affect the machining process is

important, so the factors must vary within the design of the

experiment to assess which factors have the most impact on the

process. For this experiment, the parameters and levels are

shown in Table II.

Table II

PARAMETERS AND LEVELS OF THE EXPERIMENT

Item

Parameter

Units

Level

Strategy

Conventional Machining Strategy

(CMS)

Trochoidal Machining Strategy

TMS

Cutting Speed

m/min

800

900

1000

Feed per tooth

mm/tooth

0.25

0.30

0.35

In the methodology, the minimum number of experiments

must be greater than or equal to DOF [5]

TotalDegreesOfFreedom(DOF) = (ni − 1) ∗ nf (1)

Where:

ni: number of parameters nf:

number of levels

According to the Table II, in this experiment ni=3 and nf=3,

then:

DOF = (3 − 1) ∗ 3 = 6 (2)

Then, the minimum number of experiments is calculated as

follow:

MinimumNumberOfExperiments = DOF + 1 (3)

MinimumNumberOfExperiments = 6 + 1 = 7 (4)

For this project, total combination between parameter and

levels are 18. Therefore, all test was done.

D. Machining strategies and tool path

The tool path in conventional machining strategy (CMS)

was follow periphery, since it is the path with the shortest

execution time [3], and the tool path in the trochoidal

machining strategy was trochoidal through the adaptive

strategy, the machining tool paths that were obtain using

CAD CAM software are show in the Figure 2.

Figure 2. a) Conventional tool path, b) Trochoidal tool path

III. RESULTS

Machining time data were obtained through the HISION

VMC Series. Simulation times were obtained by CAD CAM

software and real times were measured on the experimental test.

similarly, temperatures were measured in tool flutes

immediately after the machining process, data are shown in

Table III.

Table III

EXPERIMENTAL DATA

IV. ANALYSIS OF RESULTS

A. Time analysis

When comparing the data of the conventional machining

strategy and the trochoidal machining strategy with similar

Test

A 1 CMS- 2

TMS

[m/min]

[mm/tooth]

Machining time

[s]

Tool

Temperature

[ºC]

Simulation

Real

A1B1C1

800

0.25

215

217

32.7

A1B1C2

800

0.30

211

213

30.5

A1B1C3

800

0.35

209

212

30.2

A1B2C1

900

0.25

212

213

31.6

A1B2C2

900

0.30

209

210

30.4

A1B2C3

900

0.35

206

208

30.1

A1B3C1

1000

0.25

210

212

29.4

A1B3C2

1000

0.30

207

209

29.2

A1B3C3

1000

0.35

205

208

28.9

A2B1C1

800

0.25

28.0

A2B1C2

800

0.30

27.8

A2B1C3

800

0.35

27.7

A2B2C1

900

0.25

27.5

A2B2C2

900

0.30

27.2

A2B2C3

900

0.35

26.4

A2B3C1

1000

0.25

25.7

A2B3C2

1000

0.30

25.7

A2B3C3

1000

0.35

25.3

> REVISTA RIEMAT JULIO–DICIEMBRE 2022. VOLUMEN 7. NÚMERO 2. ART. 6<

cutting parameters indicated in table IV, the real machining

time of the trochoidal strategy is less than that of the

conventional strategy.

In conventional machining strategy, test A1B1C1 presents a

maximum machining time of 217 [s] and test A1B3C3 shows a

minimum machining time of 208 [s]. Similarly, in the

trochoidal machining strategy, test A2B1C1 presents a

maximum time of 25 [s] and test A2B3C3 shows a minimum

time of 14 s.

At the same cutting speed (B1=800 m/min), the percentage

of machining time reduction increases while the cutting feed

rate increases, it increases from 88.48% to 91.04%. In the same

way (B2=900 m/min), the percentage increases from 89.20%

up to 91.83 %, and soon.

Therefore, tests with the lowest cutting parameters show the

lowest time reduction percentage of 88.48%. On the opposite

side, tests with the highest cutting parameters show the highest

time reduction percentage of 93.27%.

The trend of the graphs is decreasing for both strategies as

can be seen in Figure 3.

Figure 3. Machining time comparison between CMS and TMS

B. Temperature analysis

When comparing the temperature between machining

strategies, in the trochoidal strategy it presents lower

temperature values as can be seen in figure 4, which indicates a

better heat distribution in the cutting tool, thus prolonging its

useful life.

According to the proposed theory and the curves of Dr.

Salomon, the value of the temperature decreases when

increasing´ the cutting speed until it becomes constant, it is

observed that for the value of the cutting speed 1000 [m / min]

it is achieved that the temperature stabilizes at 25ºC, its decimal

values being those that vary, in turn the wear on the tool is less

and the cooling medium of the cutting tool is air in a heat

transfer by convection, which does not Contaminates the

aluminum chip making it suitable for recycling.

Figure 4. Machining temperature comparison between CMS and TMS

C. Taguchi analysis

The operating time and temperature of the cutting tool were

analyzed using the Taguchi experimental method to determine

the influence of each parameter (A=strategy, B=Vc, C=fz) in

the machining process as indicated Table V

Respect to machining time, the least values are reached with

the following conditions:

• Strategy trochoidal (A2) with 18.89

• Cutting speed 1000 m/min (B3) with 112.5

• Cutting feed per tooth 0.35 mm/tooth (C3) with 113

Respect to temperature, the least values are reached with the

following conditions:

• Strategy trochoidal (A2) with 26.81

• Cutting speed speed 1000 m/min (B3) with 27.36

• Cutting feed per tooth 0.35 mm/tooth (C3) with 28.1

Table V

RESPONSE FOR THE MEANS OF OPERATION TIME

Level

Control Factors

Machining time [s]

Temperature [ºC]

211.33

118

117.83

30.33

29.48

29.15

18.89

114.83

114.5

26.81

28.86

28.46

112.5

113

27.36

28.1

Delta

192.44

5.5

4.83

3.52

2.12

1.05

Classification

D. ANOVA Method

The ANOVA statistical analysis, known as the analysis of

variance, is used to determine the variability of the data,

obtaining the level of confidence of the experimental data.

Analysis of variance establishes whether the population means

are the same or different and determines the interrelationships

between all the factors using in the test design, in addition to

calculating the degrees of freedom, the sum of squares, F test,

variance [6].

Analysis of the results of ANOVA concerning machining

time is shown in Table VI. It was performed, with a significance

level of 5% and a confidence level of 95%, the control of the

ANOVA methodology was done by comparing the values of F

> REVISTA RIEMAT JULIO–DICIEMBRE 2022. VOLUMEN 7. NÚMERO 2. ART. 6<

and P. According to table VI was defined whether there is a

statistical difference in the results.

Table VI

TIME AND TEMPERATURE VARIANCE ANALYSIS

Time

Temperature

Source

DOF

1666657

14905.96

0.00

54.43

45.40

0.00

477203.33

119346.55

4.00

0.00

14723.14

7361.56

4.00

0.00

238657.11

119328.56

4.00

0.00

14701.51

7350.75

3.99

0.00

Error

179

19.18

Total

166836

73.61

Table VI defines the results of the analysis of variance of

time with a statistical F 95% confidence, the main parameter

that defines this experimentation, that is, FA (0.05: 1: 16) =

14905.96, for the cutting speed that we have FA (0.05: 2: 24) =

- 4 and for the advance per tooth FA (0.05: 2: 24) = - 4, having

a higher value in the strategy rejects the hypothesis that

mentions that the means of the data are equal and accepts the

alternative hypothesis that indicates that the mean of the data

are different, obtaining an error less than the allowed F <0.05.

Table VI shows the summary of the analysis of variance of

the temperature with an F with a 95% reliability for the strategy

we have F (0.05: 1: 16) = 45.40, for the cutting speed and feed

per tooth an F corresponding to 4, as these values are greater

than those tabulated in the Fisher tables, which means that The

null hypothesis that indicates that the data are equal is rejected

and the alternative hypothesis is accepted where the means of

the data are different, therefore the allowed error is less F <0.05,

being reliable values that comply statistically.

E. Regression analysis time and temperature

Regression analysis is used for modeling and analysis that

exists between one or more independent variables concerning

the dependent variable. For this study, the independent

variables are the machining strategy, the cutting speed (Vc) and

the feed per tooth (fz). The prediction equations were obtained

from the linear regression analysis as indicated in equations (5)

and (6). The regression equation of time and temperature will

serve to relate the response parameter, concerning the

experimental model parameters [6].

Time[s] = 443.03 − 192444A − 0.02750B − 48.33C (5)

Temperature[C] = 46.53 − 3.522A − 0.01085B − 10.50C (6)

These mathematical models have an error below 5% which

makes valid models for the design of roughing processes for

both strategies.

We also have the confidence interval (CI) for both time and

temperature that were obtained from the statistical analysis

using software, which can be seen in tables VII and VIII.

Table VII

CONFIDENCE INTERVAL FOR THE TIME

Strategy

No.

Test

Media

standard deviation

C.I.

Conventional

211.33

2.915

208.971 -

213.696

Trochoidal

18.89

3.72

16.53 - 21.25

Table VIII

CONFIDENCE INTERVAL FOR THE TEMPERATURE

Strategy

No. Test

Media

standard deviation

C.I.

Conventional

30.333

1.200

29.560 - 31.107

Trochoidal

26.856

0.979

26.082 - 27.629

V. CONCLUSIONS

It was determined that the trajectory with the shortest time is

follow the periphery, being a parameter that influences the

machining time, in which an operating time of the trochoidal

machining strategy of 14 seconds is established with the

A2B3C3 parameters, it presents an optimization of the time

versus machining time of the conventional strategy that

presents 208 seconds with A1B3C3 parameters, for a cutting

speed of 1000 [m / min] and a time feed of 0.35 [mm / tooth], a

reduction of 93.27% of the time, for a cutting speed of 700 [m

/ min] and a feed per tooth of 0.25 [mm / tooth] a reduction of

88.48% in time.

With the design of parameters using the Taguchi method-

ology, it is observed that for temperature the parameter with the

greatest influence on cutting speed, determining a minimum

temperature for conventional machining of 28.9ºC and a

minimum temperature for trochoidal machining of 25.3ºC, this

being a reduction of 12.46% between strategies.

In the process of the tests using the trochoidal and

conventional machining strategy without the use of coolants

that contaminate the chip, they present a good finish, without

blunting the cutting tool in both cases, without leaving burrs in

any of the test tubes of the experiment, there was a correct chip

evacuation, stabilizing the temperature of the cutting tool at

25ºC

Optimization of the machining parameters of the Somta

brand four lips 25 mm HSS cutting tool obtained in the

Ecuadorian market was obtained, the manufacturer

recommends a radial depth of 1.25 mm and an advance of 4800

mm / min. , using in this study a radial depth of 2.5 mm which

is an increase of 50%, in addition to using a feed rate of 17825.4

[mm / min] which gives us an increase of 13025 [mm / min]

being an increase of the 271.36%, there were no pitting or burns

in the cutting tool during the tests, which prolongs the useful

life of the tool.

With the statistical analysis of the data obtained in table 18

of temperature and machining time, with the Anova statistical

analysis presented in table VI, values of F <0.05 are established,

which shows that it is unlikely that the data is due to randomly,

resulting in a reliable study, that is, it is likely to obtain the same

or similar values when performing the experiment under the

same study parameters.

By means of the regression equation 5 corresponding to the

combination of parameters A2B2C2 for time, an error was

> REVISTA RIEMAT JULIO–DICIEMBRE 2022. VOLUMEN 7. NÚMERO 2. ART. 6<

obtained 4.94 % and with the corresponding regression

equation 6 for the temperature a 3.38 %, being the two

equations are a good mathematical approximation of machining

design for both time and temperature.

Through experimentation with the Taguchi methodology, the

optimal machining parameters were obtained, reducing the

machining time and reaching a temperature stability of 25ºC in

the cutting tool with the combination of the A2B3C3

parameters: trochoidal machining strategy with cutting speed of

1000 m / min, with an advance by tooth of 0.35 mm / tooth.

With this machining configuration, the behavior of time and

temperature is decreasing as shown in figures 3, as the curves

of Dr. Salomón describes, that at a higher cutting speed the

temperature drops until it stabilizes.

REFERENCES

Basic format for books:

[1] . W. W. Askeland, d., Ciencia e ingeniería de materiales. Cengage

Learning Editores S.A., 2016.

[2] Uddeholm, Ficha tecnica Prodax´ . Uddeholm, 2020.

[3] I. F, Experimentación de las estrategias de mecanizado adaptativas en el´

fresado de alta velocidad en aluminio Prodax. Repositorio Universidad de

las Fuerzas Armadas ESPE, 2019.

[4] R. J. roy, “A primer on the method taguchi,” 2010.

[5] M. H. R. N. H. Dharam, V., “Experimental investigation of surface´

roughness on al alloy by hsm using taguchi method,” 2016.

[6] S. Sunilkumar, “Optimization of process parameters in milling operation

by taguchi’s technique using regression analysis,” 2016.

Mario Orlando Orellana Jarrín, nacio en

Quito en 1991, Ingeniero Mecánico

graduado en la Universidad de las Fuerzas

Armadas ESPE, sede Sangolquí,

desarrollador de proyectos de ingeniería

tanta para diseño y construcción de

maquinarias y estructuras, actualmente

reside en Murcia, España por trabajo y

estudios de post grado.

moorellana@espe.edu.ec

Borys Hernán Culqui Culqui, docente a

tiempo completo en el Departamento de

Ciencias de la Energía y Mecánica de la

Universidad de las Fuerzas Armadas

ESPE.

bhculqui@espe.edu.ec