Parametric Analytical-experimental Modeling in BLDC Engines … · 2019. 6. 5. · Parametric Analytical-experimental Modeling in BLDC Engines Applied to Propulsion Systems on Chopper

Parametric Analytical-experimental Modeling in

BLDC Engines Applied to Propulsion Systems on

Chopper Motorcycles

Héctor C. Terán, Guido R. Torres, Oscar Arteaga, Jonathan J. Morales, Byron P. León, Daniel A. Morales Universidad de las Fuerzas Armadas ESPE/ Energy and Mechanics, Sangolquí, Ecuador

Email: [email protected], {grtorres, obarteaga, jjmorales7, bpleon, damorales12}@espe.edu.ec

Abstract— The present experimental research proposes to

analyze the behavior and performance of a three-phase

Brushless BLDC electric motor when used as an alternative

propulsion system in Chopper-type motorcycles. To carry

out the study of the BLDC motor, an electric mathematical

model is created and a mathematical model of the

mechanical transmission system , with software the models

are merged creating a universal equation applied to electric

Chopper motorcycles, analytically with the variation of the

electric angle (θe), the operating parameters were calculated:

electromagnetic torque, power and efficiency, which are

used as reference standards and compared with those

obtained with field tests in the laboratory with the

MotorLab Kit MLK-B, performing rpm tests under the

standard IEC 60034-30, efficiency with the standard IEC

60034-31, Rated current with IEC 60038 and power under

IEC 60034-30, with the experimental results is proposed

optimized parameters for idle and load operation and

implement them in the programming of a motor inverter

and achieve the highest performance while meeting the

quality standard for motorcycles set in EN 15194.

Index Terms—BLDC electric motor, mathematical model of

the propulsion system, Chopper motorcycle

I. INTRODUCTION

The most commonly used vehicles in urban mobility to move after cars are two-wheeled vehicles; both motorcycles and bicycles, establishing a model for the implementation of an electric propulsion system [1]. The operation of this type of vehicle is based on a three-phase electric motor coupled to a wheel driven to generate motorcycle movement [2]. A characteristic of electric motors is that approximately 80% of the electrical energy is used by the industrial sector [3].

For the correct operation of a three-phase electric

motor in vehicles and motorcycles requires an electric

regulator, which is a system composed of several

electrical and electronic subsystems called three-phase

inverters [4], which will physically code the voltages,

converting them into optimum push buttons, so that the

motor rotation is efficient [5].

A three-phase electric motor is a rotating electric

machine [6], responsible for converting the supplied

three-phase electric energy into mechanical energy [7]. A

Manuscript received July 26, 2018; revised May 29, 2019.

BLDC brushless motor is ideal for electric motorcycles

because of its high power, good speed torque

characteristics, high efficiency, wide speed ranges and

low maintenance [8], unlike other types of motors, the

power loss at activation is minimal, it also has reduced

space with low noise levels [9].

Most BLDC motors have three-phase stator windings,

while their rotors can have several pairs of magnetic

poles [10]. BLDC motors have a fast dynamic response

due to their low inertia rotor (permanent magnet)

compared to ind3uction motors [11].

BLDC motors use permanent magnets instead of coils

in the armature therefore, do not require any brushless.

This experimental research analyzes the waveforms of the

BLDC motor, with its phase current and electromotive

force [12] by offsetting the rotation each π rad to

determine the mathematical model through differential

equations and its electrical components and fuse them

with the propulsion system of the motorcycle Chopper

[13].

In Fig. 1, the connection configuration of the inverter

with respect to the BLDC motor is shown, points a, b and

c that are the outputs of the inverter installed in the motor

to generate a potential three-phase excitation in the

electric motor in the terminals.

Figure 1. BLDC motor drive system configuration and reference current generation.

600

International Journal of Mechanical Engineering and Robotics Research Vol. 8, No. 4, July 2019

© 2019 Int. J. Mech. Eng. Rob. Resdoi: 10.18178/ijmerr.8.4.600-606

mailto:[email protected]

II. SYSTEM MODELING

For the mathematical modeling of the Chopper electric

motorcycle, it was divided into an electrical subsystem

(batteries, three-phase inverter and electric motor), as

well in a mechanical subsystem (transmission and

pneumatic), as shown in Fig. 2.

Figure 2. Electric motorcycle components.

It was considered a BLDC motor that is part of two

systems in both the mechanical and electrical systems, in

charge of transforming the electrical energy supplied into

mechanical energy necessary for the movement of the

motorcycle Chopper according to the capacity of the

batteries

A. Engine Modeling

For the analysis of the BLDC engine the following

equations are established:

[

𝑣𝑎𝑣𝑏𝑣𝑐] = [

𝑟𝑠 0 00 𝑟𝑠 00 0 𝑟𝑠

] [

𝑖𝑎𝑖𝑏𝑖𝑐

] + ⋯

…+ [𝐿 − 𝑀 0 00 𝐿 −𝑀 00 0 𝐿 − 𝑀

]𝑝 [

𝑖𝑎𝑖𝑏𝑖𝑐

] + [

𝑒𝑎𝑒𝑏𝑒𝑐]

𝜏𝑒𝑚 − 𝜏𝑙𝑜𝑎𝑑 − 𝐵𝜔𝑚 = 𝐽𝑑𝜔𝑚

𝑑𝑡, (1)

The electromagnetic torque is defined:

𝜏𝑒𝑚 = (𝑒𝑎𝑖𝑎 + 𝑒𝑏𝑖𝑏 + 𝑒𝑐𝑖𝑐)/𝜔𝑚 , (2)

For the electrical subsystem:

𝑝 is the operator 𝑑

𝑑𝑡

𝑣𝑎, 𝑣𝑏 , 𝑣𝑐: three-phase voltages feeding the BLDC

motor respectively in Volts (𝑉) 𝑟𝑠: electrical resistance at stator windings in ohms (Ω). 𝑖𝑎, 𝑖𝑏 , 𝑖𝑐: three-phase currents flowing through the

stator windings (𝐴). L: inductance of the stator windings in Henrios (𝐻). M: mutual inductance in (𝐻). [𝑒𝑎 𝑒𝑏 𝑒𝑐]𝑇 : vector representing the voltage

generated in the stator windings due to the relative

movement of the rotor with respect to the mechanical

system.

𝜏𝑒𝑚: electromagnetic torque (𝑁.𝑚) 𝜏𝑙𝑜𝑎𝑑 : load torque (𝑁.𝑚)

B: coefficient of viscous friction (𝑁𝑚𝑠

𝑟𝑎𝑑)

J: rotor inertia (𝑘𝑔.𝑚2)

𝜔𝑚: mechanical speed (𝑟𝑎𝑑

𝑠)

The BLDC motor has the magnetic flux winding that

circulates through the iron to the iron, the waveform is

trapezoidal, thus generating a voltage e_(a,b,c) of the

same waveform as the stator windings, these voltages are

a function of the electric angle θe of the motor and is

represented by:

𝑒𝑎 = 𝜆𝜔𝑟𝑓(𝜃𝑒), (3)

𝑒𝑏 = 𝜆𝜔𝑟𝑓 (𝜃𝑒 −2𝜋

3),

𝑒𝑐 = 𝜆𝜔𝑟𝑓 (𝜃𝑒 −4𝜋

3),

Where:

𝜆: flow bond established by the permanent magnet of

the rotor.

𝜔𝑟: rotor speed.

𝑓(𝜃𝑒), 𝑓 (𝜃𝑒 −2𝜋

3) , 𝑓 (𝜃𝑒 −

4𝜋

3) represent the shape of

a trapezoid bounded in the closed range 1,1.

These were generated analytically in MATLAB and

their model is described below:

𝑓(𝜃𝑒) =

{

𝜃𝑒

6

𝜋0 ≤ 𝜃𝑒 <

𝜋

6

1𝜋

6≤ 𝜃𝑒 <

5𝜋

6

(𝜋 − 𝜃𝑒)6

𝜋−1

(𝜃𝑒 − 2𝜋)6

𝜋

5𝜋

6≤ 𝜃𝑒 <

7𝜋

67𝜋

6≤ 𝜃𝑒 <

11𝜋

611𝜋

6≤ 𝜃𝑒 < 2𝜋}

,

𝑓 (𝜃𝑒 −2𝜋

3) =

{

−1 0 ≤ 𝜃𝑒 <

𝜋

2

(𝜃𝑒 −2𝜋

3)6

𝜋

𝜋

2≤ 𝜃𝑒 <

5𝜋

6

1

(5𝜋

3− 𝜃𝑒)

6

𝜋−1

5𝜋

6≤ 𝜃𝑒 <

3𝜋

23𝜋

2≤ 𝜃𝑒 <

11𝜋

611𝜋

6≤ 𝜃𝑒 < 2𝜋}

,

𝑓 (𝜃𝑒 −4𝜋

3) =

{

1 0 ≤ 𝜃𝑒 <

𝜋

6

(𝜋

3− 𝜃𝑒)

6

𝜋

𝜋

6≤ 𝜃𝑒 <

𝜋

2

−1

(𝜃𝑒 −4𝜋

3)6

𝜋−1

𝜋

2≤ 𝜃𝑒 <

7𝜋

67𝜋

6≤ 𝜃𝑒 <

3𝜋

23𝜋

2≤ 𝜃𝑒 < 2𝜋}

,

At all times for the functions to operate correctly it is

necessary to know the angle 𝜃𝑒.

601


© 2019 Int. J. Mech. Eng. Rob. Res

For this mechanical subsystem it is necessary to

determine the electromagnetic torque, so when replacing

(3) in (2) the electromagnetic torque is:

𝜏𝑒𝑚 =𝜆𝜔𝑟𝜔𝑚

(𝑖𝑎𝑓(𝜃𝑒) + 𝑖𝑏𝑓 (𝜃𝑒 −2𝜋

3) + ⋯

…+ 𝑖𝑐𝑓 (𝜃𝑒 −4𝜋

3)) (4)

Equation (4) requires knowledge of the initial velocity

other than zero. However, it is considered that 𝜃𝑒 = 𝑛𝑝𝜃𝑚

and 𝜔𝑟 = 𝑛𝑝𝜔𝑚, to determine the electromagnetic torque

which does not depend directly on the motor speed but on

the number of poles (5).

𝜏𝑒𝑚 = 𝑛𝑝𝜆(𝑖𝑎𝑓(𝜃𝑒) + 𝑖𝑏𝑓 (𝜃𝑒 −2𝜋

3) + ⋯

…+ 𝑖𝑐𝑓 (𝜃𝑒 −4𝜋

3)) (5)

Where:

𝑛𝑝: Number of pole pairs.

Equation (5) allows the theoretical electromagnetic

torque to be calculated from a mathematical model to

compare the laboratory tests to be carried out on the

BLDC vacuum motor.

B. Transmission modeling

An electric motorcycle for propelled with ease must

contain a drive system consisting of an electric motor,

drive pulley, driven pulley, rear pulley, rear tire and a

synchronized belt as shown in Fig. 3:

Figure 3. Schematic of electric motorcycle transmission system

The torque required to drive the motorcycle is set

according to the parameters described (6)

𝜏 =𝑟

𝑛𝑔𝐺𝐹𝑡𝑒, (6)

Where:

r: rim spoke (m).

𝑛𝑔: transmission efficiency.

G: transmission angular velocity reduction ratio.

𝜏: torque generated in the motor shaft (N.m).

𝐹𝑡𝑒: tractive force that drives the electric motorcycle

(N).

The relationship between the angular speed of the

motor 𝜔𝑚 and the linear speed v of the motorcycle is:

𝜔𝑚 = 𝐺𝑣

𝑟 (7)

The forces acting on the electric motorcycle are

determined from the free body diagram, Fig. 4:

Figure 4. Electric motorcycle Free-Body Diagram

The tractive force 𝐹𝑡𝑒 that drives the bike and is

provided by the BLDC engine through the transmission.

The friction force between the tyre and the surface is

given by:

𝐹𝑟𝑟 = 𝜇𝑟𝑟𝑚𝑔 cos𝜑, (8)

Where:

𝜇𝑟𝑟: friction coefficient

m: total mass of the motorcycle (kg).

𝑔 = 9,8 (𝑚 𝑠2⁄ ) gravitational acceleration constant.

𝜑 angle of inclination of the surface on which the

motorcycle is moving.

The frictional force of the wind is given by:

𝐹𝑎𝑑 =1

2𝜌𝐴𝐶𝑑𝑣

2, (9)

Where:

𝜌 = 1,67𝑘𝑔

𝑚3 air density.

A: front area of the bike (𝑚2).

𝐶𝑑: aerodynamic coefficient.

𝑣: linear speed of the motorcycle (𝑚/𝑠),

The component 𝐹ℎ𝑐 generated by the weight of the

bike with an angle of inclination 𝜑, is given by:

𝐹ℎ𝑐 = 𝑚𝑔 sin𝜑, (10)

Applying Newton's second law:

𝐹𝑡𝑒 − 𝐹𝑟𝑟 − 𝐹𝑎𝑑 − 𝐹ℎ𝑐 = 𝑚. 𝑎, (11)

Where:

𝑎: motorcycle acceleration (𝑚

𝑠2).

By replacing the corresponding expressions of the

forces acting on the motorcycle (11), the tractive force is

obtained by 𝐹𝑡𝑒:

𝐹𝑡𝑒 = 𝑚𝑎 + 𝜇𝑟𝑟𝑚𝑔cos𝜑 +1


2 +𝑚𝑔 sin 𝜑, (12)

602



The equation does not include parameters related to the

engine and transmission, therefore, based on the

mechanical system expressed in (1), the electromagnetic

torque is obtained 𝜏𝑚 engine:

𝜏𝑒𝑚 = 𝐽𝑑𝜔𝑚

𝑑𝑡+ 𝜏𝑙𝑜𝑎𝑑 + 𝐵𝜔𝑚, (13)

The total inertia in the engine's mechanical system is

the sum of the BLDC motor's rotor inertia and the

motorcycle's inertia:

𝐽 = 𝐽𝑀𝐵 + 𝐽𝑀𝐸, (14)

The inertia of the electric motorcycle EM is 𝐽𝑀𝐸 =1

2𝑚

𝑟2

𝐺2. Substituting (6) and (14) in (13) gives:


𝑑𝑡+ 𝐵𝜔𝑚 +

𝑟𝐹𝑡𝑒

𝑛𝑔𝐺, (15)

With equation (12) in (15),


𝑑𝑡+ 𝐵𝜔𝑚 +

𝑟

𝑛𝑔𝐺(𝑚𝑎 + 𝜇𝑟𝑟𝑚𝑔 cos𝜑 +⋯

…+1


2 +𝑚𝑔 sin𝜑),

(16)

The resulting electromagnetic torque contains both the

angular velocity of the rotor 𝜔𝑚 as the linear speed v of

the EM electric motorcycle.

The model of the mechanical system is determined

from terms of 𝜔𝑚. This is achieved with the equation (7).

Therefore, the expression of the mechanical system is:

𝑑𝜔𝑚

𝑑𝑡=

1

𝐽[𝜏𝑒𝑚 − 𝐵𝜔𝑚 −

𝑟

𝑛𝑔𝐺(

𝜇𝑟𝑟𝑚𝑔 cos𝜑 + ⋯

…+1

2𝜌𝐴𝐶𝑑 (

𝑟

𝐺)2

𝜔𝑚2 +𝑚𝑔 sin𝜑

)]. (17)

Equation (17) represents the mechanical system of the

electric motorcycle EM shown in Fig. 2, this including

the BLDC engine with the mechanical transmission

system, the tests are performed from this mathematical

modeling with load to perform its experimental analysis.

III. EXPERIMENTAL TESTING

To test a BLDC motor, the MLK-B MotorLab

equipment is used, see Fig. 5, which provides data on

motor performance with no-load speed as a function of

time, where results were obtained: torque, speed, current,

voltage, input power, output power, power factor and

efficiency with methods and standards established in the

Table I.

Figure 5. BLDC engine test equipment.

With regard to the dynamic tests, they will be carried

out once the electrical and mechanical systems have been

assembled and installed on the motorcycle Chopper.

TABLE I. STANDARD BLDC ENGINE TESTING

Tests Evaluation Standard and

Method

Equipment

and Materials

N rpm Engine working speed IEC 60034-30

MotorLab

Kit

Efficienc

y

Relationship between

the Pout (mechanical) and the Pin (electrical)

IEC 60034-31

Current Electrical charge flow through the motor

IEC 60038

Power

output

Speed of mechanical

work IEC 60034-30

In Table II, measured values of the BLDC motor are

established, which were carried out under no load

conditions.

TABLE II. BLDC ENGINE TEST PARAMETERS

U [V] I [A] Pin [W] PF [%] N [rpm] Pout [W]

100 200 20000 1 5000 20000

99,53 180,65 18062,32 0,9 4887 18009,28

99,05 161,30 16124,64 0,8 4774 16018,57

98,58 141,95 14186,95 0,7 4660 14027,85

98,11 122,60 12249,27 0,6 4547 12037,14

97,63 103,25 10311,59 0,5 4434 10046,42

97,16 83,90 8373,91 0,4 4321 8055,70

96,69 64,55 6436,23 0,3 4208 6064,99

96,22 45,20 4498,54 0,2 4094 4074,27

95,74 25,85 2560,86 0,1 3981 2083,56

95,27 6,49 623,18 0 3868 92,84

To perform the BLDC motor tests from the

mathematical models represented by equations (5) and

(17), the electromagnetic torque is determined as a

function of the electrical angle. 𝜃𝑒 considering the

parameters of factory, see Table III.

603



TABLE III. DATASHEET OF BLDC ENGINE AND TRANSMISSION

SYSTEM

Parameter Magnitude Parameter Magnitude

𝜆 0,262 𝑉𝑠/𝑟𝑎𝑑 𝜌 1,67 𝑘𝑔/𝑚3

𝐵 1𝑥10−5 𝑁𝑚𝑠/𝑟𝑎𝑑 𝐴 0,6 𝑚2

𝑛𝑝 4 𝐶𝑑 0,5

𝐿 −𝑀 0.0012 H 𝐺 2,4

𝐽 0,022 𝑘𝑔𝑚2 𝑢𝑟𝑟 0,015

𝑟𝑠 0,121 Ohms 𝑛𝑔 0,95

𝐵𝑢𝑠 𝑑𝑒 𝑐𝑑 100V 𝑚 175 𝑘𝑔

𝑟 0,3778 𝑚 𝑔 9,8 𝑚/𝑠2

In Table IV, values calculated using mathematical

vacuum models and implemented the transmission

system on the electric motorcycle.

TABLE IV. RESULT OF THE MATHEMATICAL MODEL UNDER LOAD

AND UNDER LOAD

𝜃𝑒 (rad) No-load torque (N.m) Loaded torque (N.m)

0 0 -15251,823

0,9076 190,227 -6605,144

1,815 380,454 2041,534

2,723 570,681 10688,212

3,630 760,908 19334,891

4,538 951,135 27981,569

4,573 958,451 28314,134

4,608 965,767 28646,698

4,643 973,084 28979,263

4,678 980,4 29311,828

4,712 0 0

IV. ANALYSIS OF RESULTS

The parameters obtained are used to determine the

characteristic curves of efficiency, power, speed current

as a function of torque with intervals of: efficiency 80%,

power 19907.16 W, current 193.51 A, with a speed

variation between 3868 and 5000 rpm, see Fig. 6.

Figure 6. BLDC motor no-load work curves.

Figure 7. Theoretical electromagnetic torque of BLDC motor.

With the results of the vacuum test calculated from the

mathematical models Table IV, the electrical angle θe

varies proportionally with respect to torque reaching

maximum values of 4.67 rad at 980.4 Nm, see Fig. 7.

From the results of Table IV using mathematical

models of the propulsion system of the Chopper

motorcycle, the minimum electric angle θe to overcome

the load is 1,815 rad, see Fig. 8.

Figure 8. Electromagnetic torque with transmission system.

The values obtained in the no-load tests when

implementing the BLDC motor in the MotorLab Kit

MLK-B equipment, are compared with the mathematical

models, analyzing the amount of mechanical energy

delivered by the BLDC motor with respect to the

electrical energy consumed to establish the appropriate

operating performance. The analysis of the amount of

energy lost is also carried out to obtain the efficiency of

an electric motor Chopper, see Table V.

TABLE V. BLDC ENGINE TEST VALUES ON AN ELECTRIC CHOPPER

MOTORCYCLE

Description Charging

point

Increased efficiency

Maxi

mum power

Maximum torque

Maximum point

Nominal rotation

Voltage (V)

95,97

95,53

95,41

95,41

95,41

95,41

Current (A)

6,494

77,446

161,14

2

161,142

161,173

161,142

Pin (W)

623,18

7391,74

15376,

06

15376,06

15377,01

15376,06

Torque

(mN.m)

707,5

15347,3

32641,

1

32641,1

32646,7

32641,1

Revolutions

(RPM)

4762

4245

3868

3868

3868

3868

Pout (W)

352,79

6754,33

13220,

94

13220,94

13222,75

13220,94

Eff (%)

56,6

91,4

86

86

86

86

With the operating curves of the parameters set out in

Table V: voltage, current, input power, efficiency and

load point as a function of torque, the load point curve is

determined which sets minimum parameters for operation,

see Fig. 9.

604



Figure 9. Input power, output and torque curves

The Current and Voltage curves are based on Table 5,

the nominal current reached is 77.44 A with a maximum

efficiency of 91.4%; keeping the constant voltage of

95.7V in function of efficiency, s

ee Fig. 10.

Figure 10. Voltage and Current curves

The speed curve as a function of the efficiency

generated in Table V determines that the maximum

efficiency is 91.4% at 4245 rpm, see Fig. 11.

Figure 11. Revolutions and efficiency curve

V. CONCLUSIONS

Modeling of the drive system of the BLDC engine

including transmission and satisfies the operating

parameters required by EN 15194 for electrically assisted

vehicles.

The minimum electric angle θe of 1,815 rad is the one

necessary to overcome the inertia resistance of the

chopper motorcycle to start the start.

Considering the parameters determined for the load

point, the critical point related to the efficiency is

determined as 91.4 %, stabilizing the input and output

power at 86% efficiency.

The maximum torques reached by a mathematical

model with load are 29311.828 Nm and the real torque

needed to move the motorcycle is 32646.7 Nm, this

difference in torques is due to the friction between the

parts of the transmission system.

The optimum parameters found were entered into the

programming of the inverter controller, obtaining the

highest real efficiency for electric motorcycle

applications of the Chopper type.

In future research, it is planned to analyze the

mathematical model of the batteries to establish their

autonomy according to the circuit and driving modes.

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Transactions on Magnetics, vol. 43, no. 6, pp. 2573–2575, 2007. [10] H. Moghbeli, A. H. Niasar, and M. B. Shahrbabak, "Direct power

control of brushless DC motor drive," in Proc. 2014 IEEE 23rd

International Symposium on Industrial Electronics (ISIE), pp. 789–794, 2014.

[11] A. Tashakori, M. Hassanudeen, and M. Ektesabi, "FPGA based controller drive of BLDC motor using digital PWM technique," in

Proc. 2015 IEEE 11th International Conference on Power

Electronics and Drive Systems (PEDS), pp. 658–662, 2015. [12] M. R. Feyzi, M. Ebadpour, K. M. Niapour, A. Feizi, and R. M.

Aghdam, "A new single current strategy for high-performance

brushless DC motor drives," in Proc. 2011 24th Canadian

55

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95

0 20 40 60 80 100 120 140 160

Efi

cien

cy (

%)

Current (A) Voltage (V) Current (A)

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75

80

85

90

95

3700 3900 4100 4300 4500 4700

Efi

cien

cy (

%)

Revolutions (rpm)

Revolution (rpm)

605



Conference on Electrical and Computer Engineering (CCECE), pp. 419-424, 2011.

[13] A. D. Bautista, G. V. G. Ramírez, C. D. G. Beltrán, M. A. Medina,

and F. d. J. T. d. Carmen, "Control of a three-phase direct current brushless motor with application to electric vehicles," Cenidet, pp.

515-520, 2015.

Hector C. Terán, born in New York, USA in

1982, obtained his MSc. in Energy Management from the Technical University of

Cotopaxi in 2014, and his engineering degree

in Electromechanics from the Polytechnic School of the Army in 2008.

He works as a tenured research professor at the

University of the Armed Forces ESPE, in the Department of Energy and Mechanical

Sciences in the area of Manufacturing and

Energy, has written some books being the latest works "The Metallurgy for welding" and the paper "Mobile robotic table with artificial

intelligence applied to the separate and classified positioning of objects

for computer-integrated manufacturing" His research areas are manufacturing, materials, automation and mechatronics.

Msc. Terán is a member of the Research Group on Robotic Automation

and Intelligent Systems ARSI of the National Research and Education

Network of Ecuador.

Guido R. Torres, born in Alausi Ecuador

1960, obtained MSc. in Energy Management

from the Technical University of Cotopaxi in 2014, MSc. in Higher Education from the

Indo-American Technological University in

2002 and his engineering degree in Mechanics from the Polytechnic Superior School of

Chimborazo in 1990.

He is working as a research professor at the University of the Armed Forces ESPE, in the

Department of Energy and Mechanical Sciences, for the area of Design

and Computational Mechanics, has written the book of the “Fundamentals of fluid mechanics” and paper “Redesign of the rear

suspension of the prototype vehicle for competition in the SAE formula”

and others, his research area is based on the design of conventional and alternative vehicles.

Msc. Torres Muñoz is a member of the Mechanical Engineers

Association of Ecuador.

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